WO2018230476A1 - Device for estimating shape of figure pattern - Google Patents

Abstract

According to the present invention, the shape of a real figure pattern formed on a real substrate is estimated by simulating a lithography process. An evaluation point (E) is set on a contour of an original figure pattern (10) included in an original image (Q1). A filtering process (convolution) and a contraction process (pulling) for contracting an image are alternately performed on the original image (Q1), and an image pyramid (PP) is created which is formed from n sets of layered images (P1~Pn) having different image sizes. For each of the layered images (P1 to Pn), feature amounts (x1 to xn) are extracted on the basis of pixel values of pixels around the evaluation point (E), and the extracted feature amounts are provided to an estimation calculation unit (132). A neural network in the estimation calculation unit (132) performs calculations for an intermediate layer by using the feature amounts (x1 to xn) as values of an input layer, and outputs, as values of an output layer, an estimation value (y) of a process bias that indicates a deviation amount between a location of the evaluation point (E) on the original figure pattern (10) and that on the real figure pattern.

Description

Shape estimation device for figure pattern

The present invention relates to a figure pattern shape estimation apparatus, and more particularly to an apparatus for estimating the shape of an actual figure pattern formed on a substrate through a lithography process.

In fields that require fine patterning of specific material layers, such as semiconductor device manufacturing processes, a fine pattern is formed on a physical substrate through a lithography process that involves drawing using light or an electron beam. The technique to form is taken. Usually, a fine mask pattern is designed using a computer, and the resist layer formed on the substrate is exposed based on the obtained mask pattern data. After developing this, the remaining resist layer is masked. Etching is performed to form a fine pattern on the substrate.

However, there is a slight discrepancy between the actual figure pattern actually obtained on the substrate through such a lithography process and the original figure pattern designed on the computer. This is because the lithography process includes steps of exposure, development, and etching, so that the actual graphic pattern finally formed on the substrate does not exactly match the original graphic pattern used in the exposure process. Because. In particular, in the exposure process, the resist layer is drawn with light or an electron beam. At that time, the exposure area actually drawn on the resist layer by the proximity effect (PE: Proximity Effect) It is known that the area is slightly wider than the pattern.

Also, in the etching process, an etching loading phenomenon occurs, so that the shape after development and the pattern after etching differ. It is known that the effect of the etching loading phenomenon varies depending on the area exposed from the resist layer on the surface of the actual substrate. The proximity effect in the drawing process and the loading phenomenon in the etching process are all phenomena that cause a difference between the shape of the original graphic pattern and the shape of the actual graphic pattern. The range (scale size) is different for each phenomenon.

Under these circumstances, in a semiconductor device manufacturing process including a lithography process, a desired original figure pattern is designed on a computer, and then the lithography process using the original figure pattern is simulated on a computer, and an actual substrate is obtained. A procedure is performed to estimate the shape of the actual graphic pattern that will be formed above. Based on the shape (dimension) of the actual figure pattern obtained as a result of the simulation, the shape (dimension) of the original figure pattern is corrected if necessary, and the actual figure pattern is obtained using the corrected figure pattern obtained by this correction. The actual lithography process is performed to manufacture an actual semiconductor device.

Therefore, in order to manufacture a final product having a precise pattern as designed, it is necessary to accurately perform the above simulation and accurately estimate the shape of the actual figure pattern. Therefore, for example, in Patent Document 1 below, a feature factor that characterizes the layout of the original graphic pattern and a control factor that affects the size of the resist pattern formed on the substrate by the lithography process are used as an input layer. A method of performing a highly accurate simulation using a neural network is disclosed. Patent Document 2 discloses a method for improving the accuracy of simulation using two sets of neural networks, and Patent Document 3 discloses an appropriate method for extracting feature values from a photomask pattern. A method for improving the accuracy of simulation by setting various extraction parameters is disclosed.

JP 2008-122929 A JP 2010-044101 A JP 2010-156866 A

In order to accurately estimate the shape of the actual figure pattern formed on the substrate through the lithography process, it is necessary to improve the accuracy of the simulation executed on the computer. For that purpose, it is indispensable to extract an accurate feature amount from the original figure pattern. However, in the above-described prior art, a sufficient simulation cannot be performed because accurate feature amount extraction is not necessarily performed.

For example, in the method disclosed in Patent Document 1, the dimensions of each part of the original figure pattern, the pattern occupation ratio, the number of patterns, the process conditions (exposure amount, illumination conditions, numerical aperture of the optical system, lens aberration, resist type, etc.) ) Is extracted as a feature value, but a method using such a feature value cannot always perform an accurate simulation, and in particular, it is difficult to perform an accurate simulation considering the influence of the proximity effect. It is.

Accordingly, the present invention provides a graphic pattern shape estimation apparatus capable of accurately estimating the shape of an actual graphic pattern formed on an actual substrate by extracting an accurate feature amount from the original graphic pattern and performing an accurate simulation. The purpose is to provide.

(1) A first aspect of the present invention is a graphic pattern shape estimation apparatus that estimates the shape of an actual graphic pattern formed on an actual substrate by simulating a lithography process using the original graphic pattern.
An evaluation point setting unit for setting evaluation points on the original figure pattern;
A feature quantity extraction unit that extracts a feature quantity indicating features around the evaluation point for the original graphic pattern;
A bias estimation unit that estimates a process bias indicating the amount of deviation between the position of the evaluation point on the original graphic pattern and the position on the actual graphic pattern based on the feature amount;
Provided,
The evaluation point setting unit sets an evaluation point at a predetermined position on the contour line based on the original graphic pattern including information on the contour line indicating the boundary between the inside and the outside of the figure,
The feature extraction unit
Based on the original graphic pattern, an original image creating unit that creates an original image composed of a collection of pixels each having a predetermined pixel value;
An image pyramid creation unit that performs image pyramid creation processing including reduction processing to create a reduced image by reducing the original image, and creates an image pyramid composed of a plurality of hierarchical images each having a different size;
For each hierarchical image constituting the image pyramid, a feature amount calculation unit that calculates a feature amount based on the pixel value of the pixel according to the position of the evaluation point;
And have
The bias estimation unit is
A feature amount input unit for inputting the feature amount calculated for the evaluation point;
An estimation calculation unit that obtains an estimated value according to a feature amount based on learning information obtained by a learning stage performed in advance, and outputs the obtained estimated value as an estimated value of a process bias for an evaluation point;
It is made to have.

(2) According to a second aspect of the present invention, in the graphic pattern shape estimation apparatus according to the first aspect described above,
The original image creation unit superimposes the original figure pattern on a mesh composed of a two-dimensional array of pixels, and based on the relationship between the position of each pixel and the position of the outline of the figure constituting the original figure pattern, The pixel value of the pixel is determined.

(3) A third aspect of the present invention is the figure pattern shape estimation apparatus according to the second aspect described above,
The original image creation unit recognizes the internal area and external area of each graphic based on the original graphic pattern, and creates an area density map with the occupancy of the internal area in each pixel as the pixel value of the pixel as the original image It is what you do.

(4) According to a fourth aspect of the present invention, in the shape estimation apparatus for graphic patterns according to the second aspect described above,
The original image creation unit recognizes the outline of each figure based on the original figure pattern, and creates an edge length density map having the length of the outline existing in each pixel as the pixel value of the pixel as the original image. It is what I did.

(5) According to a fifth aspect of the present invention, in the shape estimation apparatus for graphic patterns according to the second aspect described above,
Based on the original figure pattern that includes the outline information indicating the boundary between the inside and outside of the figure and the information about the dose amount for each figure in the lithography process, the original image creation unit Recognize the area, further recognize the dose amount for each figure, find the "product of the occupancy of the internal area and the dose amount of the figure" for each figure present in each pixel, and calculate the sum of the products A dose density map as a pixel value of the pixel is created as an original image.

(6) According to a sixth aspect of the present invention, in the shape estimation apparatus for graphic patterns according to the first to fifth aspects described above,
The image pyramid creation unit has a function of performing a filtering process using a predetermined image processing filter on the original image or the reduced image, and by executing the filtering process and the reducing process alternately, a plurality of layers An image pyramid made up of images is created.

(7) According to a seventh aspect of the present invention, in the shape estimation apparatus for graphic patterns according to the sixth aspect described above,
The image pyramid creation unit uses the original image created by the original image creation unit as the first preparation image Q1, and the image obtained by the filter processing for the kth preparation image Qk (where k is a natural number) As an image Pk, an image obtained by the reduction process for the kth hierarchical image Pk is set as the (k + 1) th preparation image Q (k + 1), and the filter process and the reduction process are alternately performed until the nth hierarchical image Pn is obtained. By executing this, an image pyramid composed of a plurality of n hierarchical images including the first hierarchical image P1 to the nth hierarchical image Pn is created.

(8) An eighth aspect of the present invention is the figure pattern shape estimation apparatus according to the sixth aspect described above,
The image pyramid creation unit uses the original image created by the original image creation unit as the first preparation image Q1, and the filtered image Pk obtained by the filter processing for the kth preparation image Qk (where k is a natural number) The difference image Dk from the k preparation image Qk is obtained, the difference image Dk is set as the k-th layer image Dk, and the image obtained by the reduction process on the k-th filtered image Pk is the (k + 1) -th preparation image Q ( k + 1), by alternately executing the filtering process and the reduction process until the n-th hierarchical image Dn is obtained, from a plurality of n hierarchical images including the first hierarchical image D1 to the n-th hierarchical image Dn. An image pyramid is created.

(9) A ninth aspect of the present invention is the figure pattern shape estimation apparatus according to the sixth aspect described above,
The image pyramid creation part
The original image created by the original image creation unit is defined as the first preparation image Q1, the image obtained by filtering the kth preparation image Qk (where k is a natural number) is the kth main hierarchy image Pk, The image obtained by the reduction process for the k main hierarchy image Pk is defined as the (k + 1) th preparation image Q (k + 1), and the filter process and the reduction process are alternately executed until the nth main hierarchy image Pn is obtained. To create a main image pyramid composed of a plurality of n hierarchical images including the first main hierarchical image P1 to the n-th main hierarchical image Pn,
Further, a difference image Dk between the k-th main layer image Pk and the k-th preparation image Qk is obtained, and the difference image Dk is set as the k-th sub-layer image Dk. creating a sub-image pyramid composed of a plurality of n-layer images including n sub-layer images Dn;
The feature amount calculation unit calculates a feature amount for each hierarchical image constituting the main image pyramid and the sub image pyramid based on the pixel value of the pixel corresponding to the position of the evaluation point.

(10) According to a tenth aspect of the present invention, in the shape estimation apparatus for graphic patterns according to the sixth to ninth aspects described above,
The image pyramid creation unit creates the image pyramid by executing filter processing by a convolution operation using a Gaussian filter or a Laplacian filter as an image processing filter.

(11) An eleventh aspect of the present invention is the figure pattern shape estimation apparatus according to the first to tenth aspects described above,
The image pyramid creation unit executes, as a reduction process, an average pooling process that replaces a plurality of m adjacent pixels with a single pixel having an average value of pixel values of the plurality of m adjacent pixels as a pixel value. Thus, a reduced image is created.

(12) A twelfth aspect of the present invention is the figure pattern shape estimation apparatus according to the first to tenth aspects described above,
The image pyramid creation unit executes, as a reduction process, a max pooling process in which a plurality of m adjacent pixels are replaced with a single pixel having a maximum pixel value of the plurality of m adjacent pixels as a pixel value. Thus, a reduced image is created.

(13) According to a thirteenth aspect of the present invention, in the shape estimation apparatus for graphic patterns according to the first to twelfth aspects described above,
The original image creation unit performs an original image creation process based on a plurality of different algorithms, creates a plurality of original images,
The image pyramid creation unit performs image pyramid creation processing based on multiple original images to create multiple image pyramids,
The feature amount calculation unit calculates a feature amount for each hierarchical image constituting each of the plurality of image pyramids based on the pixel value of the pixel corresponding to the position of the evaluation point.

(14) According to a fourteenth aspect of the present invention, in the shape estimation apparatus for graphic patterns according to the first to thirteenth aspects described above,
The image pyramid creation unit performs image pyramid creation processing based on a plurality of different algorithms for one original image, creates a plurality of image pyramids,
The feature amount calculation unit calculates a feature amount for each hierarchical image constituting each of the plurality of image pyramids based on the pixel value of the pixel corresponding to the position of the evaluation point.

(15) According to a fifteenth aspect of the present invention, in the graphic pattern shape estimation apparatus according to the first to fourteenth aspects described above,
When the feature quantity calculation unit calculates a feature quantity for a specific evaluation point on a specific hierarchical image, it pays attention to a total of j pixels in order from the pixel constituting the specific hierarchical image to the specific evaluation point. A pixel is extracted as a pixel, and an operation for obtaining a weighted average considering the weight according to the distance between a specific evaluation point and each target pixel is performed on the pixel values of the extracted j target pixels.

(16) According to a sixteenth aspect of the present invention, in the shape estimation apparatus for graphic patterns according to the first to fifteenth aspects described above,
The estimation calculation unit includes a neural network in which the feature quantity input by the feature quantity input unit is used as an input layer and the process bias estimation value is used as an output layer.

(17) According to a seventeenth aspect of the present invention, in the shape estimation apparatus for graphic patterns according to the sixteenth aspect described above,
The neural network included in the estimation calculation unit is obtained from the dimension value obtained by measuring the actual dimension of the actual figure pattern formed on the actual substrate by the lithography process using a large number of test pattern figures and each test pattern figure. The parameter obtained by the learning stage using the feature amount is used as learning information to perform process bias estimation processing.

(18) An eighteenth aspect of the present invention is the figure pattern shape estimation apparatus according to the sixteenth or seventeenth aspect described above,
The estimation calculation unit obtains an estimated value of the deviation amount of the evaluation point in the normal direction of the contour line as the estimated value of the process bias for the evaluation point located on the contour line of the predetermined figure.

(19) According to a nineteenth aspect of the present invention, there is provided a figure pattern shape correcting apparatus for correcting the shape of the original figure pattern using the figure pattern shape estimating apparatus according to the first to eighteenth aspects described above. for,
In addition to the evaluation point setting unit, the feature amount extraction unit, and the bias estimation unit that constitute the shape estimation device of the graphic pattern
A pattern correction unit for correcting the original figure pattern based on the estimated value of the process bias output from the bias estimation unit is further provided.
The correction figure pattern obtained by the correction by the pattern correction unit is given as a new original figure pattern to the figure pattern shape estimation apparatus, so that the correction for the figure pattern is repeatedly executed.

(20) According to a twentieth aspect of the present invention, a graphic pattern shape estimation apparatus according to the first to eighteenth aspects described above or a graphic pattern shape correction apparatus according to the nineteenth aspect described above is stored in a computer. This is realized by incorporating a program.

(21) According to a twenty-first aspect of the present invention, there is provided a graphic pattern shape estimation method for estimating a shape of an actual graphic pattern formed on an actual substrate by simulating a lithography process using the original graphic pattern.
An original graphic pattern input stage in which a computer inputs an original graphic pattern including contour information indicating the boundary between the inside and the outside of the graphic;
An evaluation point setting stage in which the computer sets an evaluation point at a predetermined position on the contour line;
A feature amount extraction stage in which the computer extracts a feature amount indicating features around the evaluation point for the original graphic pattern;
A process bias estimation stage in which a computer estimates a process bias indicating a deviation amount between the position of the evaluation point on the original graphic pattern and the position on the actual graphic pattern based on the feature amount;
And do
In the feature extraction stage,
An original image creating stage for creating an original image composed of a collection of pixels each having a predetermined pixel value based on the original graphic pattern;
An image pyramid creation stage that performs an image pyramid creation process including a reduction process for creating a reduced image by reducing the original image, and creating an image pyramid composed of a plurality of hierarchical images each having a different size,
A feature amount calculation stage for calculating a feature amount based on the pixel value of the pixel corresponding to the position of the evaluation point for each hierarchical image constituting the image pyramid;
And do
In the process bias estimation stage, an estimation value corresponding to the feature amount is obtained based on the learning information obtained in the learning stage performed in advance, and the obtained estimation value is output as the process bias estimation value for the evaluation point. An operation stage is performed.

(22) According to a twenty-second aspect of the present invention, in the shape estimation method for a graphic pattern according to the twenty-first aspect described above,
In the image pyramid creation stage, a filter process stage that performs a filter process using a predetermined image processing filter on the original image or the reduced image, and a reduction process stage that performs a reduction process on the image after the filter process By executing them alternately, an image pyramid composed of a plurality of hierarchical images is created.

(23) According to a twenty-third aspect of the present invention, in the shape estimation method for a graphic pattern according to the twenty-second aspect described above,
In the image pyramid creation stage, an image pyramid is created in which the image after filtering, or the difference image between the image after filtering and the image before filtering, is used as a hierarchical image.

(24) According to a twenty-fourth aspect of the present invention, in a shape estimation apparatus for a graphic pattern that estimates the shape of a real graphic pattern formed on a real substrate by simulating a lithography process using the original graphic pattern,
An evaluation point setting unit for setting evaluation points on the original figure pattern;
A feature quantity extraction unit that extracts a feature quantity indicating features around the evaluation point for the original graphic pattern;
A bias estimation unit that estimates a process bias indicating the amount of deviation between the position of the evaluation point on the original graphic pattern and the position on the actual graphic pattern based on the feature amount;
Provided,
The evaluation point setting unit sets an evaluation point at a predetermined position on the contour line based on the original graphic pattern including information on the contour line indicating the boundary between the inside and the outside of the figure,
The feature extraction unit
A rectangular aggregate replacement unit that replaces a graphic included in the original graphic pattern with a rectangular aggregate;
For one evaluation point, a calculation function providing unit that provides a calculation function for calculating a feature amount based on a positional relationship with respect to a rectangle positioned around the evaluation point;
A feature amount calculation unit that calculates a feature amount for each evaluation point set by the evaluation point setting unit using a calculation function provided from the calculation function providing unit;
Have
The bias estimation unit is
A feature amount input unit for inputting the feature amount calculated for the evaluation point;
An estimation calculation unit that obtains an estimated value according to a feature amount based on learning information obtained by a learning stage performed in advance, and outputs the obtained estimated value as an estimated value of a process bias for an evaluation point;
It is made to have.

(25) A twenty-fifth aspect of the present invention is the graphic pattern shape estimation apparatus according to the twenty-fourth aspect described above,
The calculation function providing unit obtains a plurality of n types of feature amounts in which the consideration range is changed from a feature amount considering a narrow range near the evaluation point to a feature amount considering a wide range including far from the evaluation point. In order to calculate, a plurality of n calculation functions are provided,
The feature amount calculation unit calculates a plurality of n types of feature amounts for each evaluation point using the plurality of n types of calculation functions.

(26) According to a twenty-sixth aspect of the present invention, in the shape estimation apparatus for graphic patterns according to the twenty-fifth aspect described above,
The calculation function providing unit provides a calculation function for calculating a feature amount based on a positional relationship with respect to four sides of a rectangle positioned around one evaluation point.

(27) According to a twenty-seventh aspect of the present invention, in the shape estimation apparatus for a graphic pattern according to the twenty-sixth aspect described above,
In the XY two-dimensional orthogonal coordinate system in which the rectangular aggregate replacement unit takes the X-axis positive direction to the right and the Y-axis positive direction to the upper direction, the upper and lower sides parallel to the X-axis And a rectangular assembly having a left side and a right side parallel to the Y axis,
The calculation function providing unit has, on the XY two-dimensional orthogonal coordinate system, a left side position deviation indicating a distance from the left side in the X axis direction of the evaluation point, a right side position deviation indicating a distance from the right side, and a Y axis direction of the evaluation point. The calculation function for calculating the feature amount is provided based on the upper side position deviation indicating the distance from the upper side and the lower side position deviation indicating the distance from the lower side.

(28) According to a twenty-eighth aspect of the present invention, in the figure pattern shape estimation apparatus according to the twenty-seventh aspect described above,
The calculation function provider
For one particular rectangle of interest,
The function value increases monotonously as the variable value increases, and the function value decreases monotonously as the variable value increases, as well as the X-axis monotonically increasing function when the X coordinate value of the left side of the target rectangle is given as a variable. A horizontal function that is the sum of an X-axis monotonically decreasing function that gives a function value of 0 when the X coordinate value of the right side of the target rectangle is given as a variable,
The function value increases monotonously as the variable value increases, and the function value decreases monotonously as the variable value increases. A vertical function that is the sum of a Y-axis monotonically decreasing function that has a function value of 0 when the Y coordinate value of the upper side of the target rectangle is given as a variable,
, And a function value of a horizontal function having the X coordinate value of the target evaluation point as a variable and a Y coordinate value of the target evaluation point Calculate based on the product of the function value of the vertical function as a variable,
A calculation function is provided in which the sum of the amounts indicating the positional relationship with respect to each rectangle located around the target evaluation point is used as a feature amount for the target evaluation point.

(29) A twenty-ninth aspect of the present invention is the figure pattern shape estimation apparatus according to the twenty-eighth aspect described above,
The calculation function providing unit provides a plurality of n types of calculation functions using functions having different degrees of monotonic increase or monotonous decrease as calculation functions for calculating a plurality of n types of feature amounts with different consideration ranges. It is a thing.

(30) According to a thirtieth aspect of the present invention, in the shape estimation apparatus for graphic patterns according to the twenty-ninth aspect described above,
The calculation function provider prepares a calculation function including a monotonically increasing function or a monotonically decreasing function with the value obtained by dividing the left side position deviation, right side position deviation, upper side position deviation, and lower side position deviation by the spreading coefficient σ, and the spreading coefficient. By changing the value of σ to a plurality of n types, a plurality of n types of calculation functions are provided.

(31) According to a thirty-first aspect of the present invention, in the shape estimation apparatus for graphic patterns according to the thirtieth aspect described above,
The calculation function providing unit sets σk = 2 ^(k−1) when the k-th expansion coefficient is expressed as σk using the parameter k in the range of 1 ≦ k ≦ n. It is.

(32) In a thirty-second aspect of the present invention, in the shape estimation apparatus for graphic patterns according to the twenty-fourth to thirty-first aspects described above,
Based on the original graphic pattern including the information on the outline indicating the boundary between the inside and the outside of the graphic and the information on the dose amount for each graphic in the lithography process, the rectangular aggregate replacement unit Recognize the external area, further recognize the dose amount for each figure, set the dose amount for each rectangle corresponding to each figure,
The calculation function providing unit provides a calculation function including a dose amount set for each rectangle as a variable.

(33) According to a thirty-third aspect of the present invention, in the graphic pattern shape estimating apparatus according to the twenty-fourth to thirty-first aspects described above,
The rectangle assembly replacement unit recognizes the unit line segments that form the contour lines of each figure based on the original figure pattern, and sets the minute width for each unit line segment, so that the figure included in the original figure pattern is It is replaced with a rectangular aggregate with a very small width.

(34) According to a thirty-fourth aspect of the present invention, in the figure pattern shape estimation apparatus according to the twenty-fourth to thirty-third aspects described above,
When the feature quantity calculation unit calculates the feature quantity for the evaluation point, it defines a reference circle having a predetermined radius with the evaluation point as the center, and the position of the rectangle belonging to the predetermined neighborhood range according to the reference circle The calculation is performed considering only the relationship.

(35) According to a thirty-fifth aspect of the present invention, in the graphic pattern shape estimation apparatus according to the twenty-fourth to thirty-fourth aspects described above,
The estimation calculation unit includes a neural network in which the feature quantity input by the feature quantity input unit is used as an input layer and the process bias estimation value is used as an output layer.

(36) A thirty-sixth aspect of the present invention is the figure pattern shape estimation apparatus according to the thirty-fifth aspect described above,
The neural network included in the estimation calculation unit is obtained from the dimension value obtained by measuring the actual dimension of the actual figure pattern formed on the actual substrate by the lithography process using a large number of test pattern figures and each test pattern figure. The parameter obtained by the learning stage using the feature amount is used as learning information to perform process bias estimation processing.

(37) A thirty-seventh aspect of the present invention is the figure pattern shape estimation apparatus according to the thirty-fifth or thirty-sixth aspect described above,
The estimation calculation unit obtains an estimated value of the deviation amount of the evaluation point in the normal direction of the contour line as the estimated value of the process bias for the evaluation point located on the contour line of the predetermined figure.

(38) According to a thirty-eighth aspect of the present invention, a graphic pattern shape correcting apparatus for correcting the shape of an original graphic pattern is configured using the graphic pattern shape estimating apparatus according to the twenty-fourth to thirty-seventh aspects described above. for,
In addition to the evaluation point setting unit, the feature amount extraction unit, and the bias estimation unit that constitute the shape estimation device of the graphic pattern
A pattern correction unit for correcting the original figure pattern based on the estimated value of the process bias output from the bias estimation unit is further provided.
The correction figure pattern obtained by the correction by the pattern correction unit is given as a new original figure pattern to the figure pattern shape estimation apparatus, so that the correction for the figure pattern is repeatedly executed.

(39) A thirty-ninth aspect of the present invention provides a computer with the graphic pattern shape estimating apparatus according to the twenty-fourth to thirty-seventh aspects described above or the graphic pattern shape correcting apparatus according to the thirty-eighth aspect described above. This is realized by incorporating a program.

(40) According to a 40th aspect of the present invention, there is provided a graphic pattern shape estimation method for estimating a shape of an actual graphic pattern formed on an actual substrate by simulating a lithography process using the original graphic pattern.
An original graphic pattern input stage in which a computer inputs an original graphic pattern including contour information indicating the boundary between the inside and the outside of the graphic;
An evaluation point setting stage in which the computer sets an evaluation point at a predetermined position on the contour line;
A feature amount extraction stage in which the computer extracts a feature amount indicating features around the evaluation point for the original graphic pattern;
A process bias estimation stage in which a computer estimates a process bias indicating a deviation amount between the position of the evaluation point on the original graphic pattern and the position on the actual graphic pattern based on the feature amount;
And do
In the feature extraction stage,
A rectangular assembly replacement stage for replacing a graphic included in the original graphic pattern with a rectangular assembly;
For each evaluation point, a feature amount calculation stage for calculating a feature amount based on a positional relationship with respect to a rectangle positioned around the evaluation point;
And
In the process bias estimation stage, an estimation value corresponding to the feature amount is obtained based on the learning information obtained in the learning stage performed in advance, and the obtained estimation value is output as the process bias estimation value for the evaluation point. An operation stage is performed.

According to the shape estimation apparatus and shape estimation method for a graphic pattern according to the present invention, an evaluation point is set on the original graphic pattern, and a process bias indicating a deviation amount with respect to the evaluation point is estimated. Moreover, in the basic embodiment, a reduction process for reducing the original image corresponding to the original graphic pattern is performed, an image pyramid composed of a plurality of hierarchical images having different sizes is created, and the evaluation point position is determined for each hierarchical image. Features are extracted as feature values. Further, in the additional embodiment, the graphic included in the original graphic pattern is replaced with a rectangular aggregate, and the feature amount is extracted based on the positional relationship with respect to the rectangle for each evaluation point. For this reason, it becomes possible to perform accurate simulation by extracting accurate feature values from the original graphic pattern, and it is possible to accurately estimate the shape of the actual graphic pattern formed on the actual substrate.

More specifically, in the basic embodiment of the present invention, since feature amounts are extracted from an image pyramid composed of a plurality of hierarchical images having different sizes, various features ranging from the vicinity of each evaluation point to a distant location are used. It is possible to obtain an individual feature amount indicating a unique feature. Therefore, it is possible to perform an accurate simulation in consideration of the influence of various phenomena having different scales such as the proximity effect and the etching loading phenomenon. The same applies to the case where a plurality of calculation functions are used to calculate the feature amount in the additional embodiment of the present invention.

In addition, if the figure pattern shape estimation apparatus according to the present invention is used, the original figure pattern can be corrected based on the estimation result, so that the figure pattern that can accurately correct the shape of the original figure pattern can be obtained. It is also possible to provide a shape correction apparatus.

It is a block diagram which shows the structure of the shape correction apparatus 100 of the figure pattern which concerns on fundamental embodiment of this invention. It is a top view which shows an example in which the difference in shape produced between the original figure pattern and the real figure pattern. In the example shown in FIG. 2, it is a top view which shows the example of a setting of each evaluation point, and the process bias which arises in each evaluation point. It is a flowchart which shows the design / manufacturing process of a product using the shape correction apparatus 100 of the graphic pattern shown in FIG. It is a top view which shows the concept which grasps | ascertains the surrounding characteristic about the evaluation point defined on the outline of a figure pattern. It is a figure which shows the outline | summary of the process performed in the feature-value extraction unit 120 and the bias estimation unit 130 shown in FIG. It is a flowchart which shows the process sequence performed in the feature-value extraction unit 120 shown in FIG. It is a top view which shows the specific example of the original figure pattern 10 given to the shape correction apparatus 100 of the figure pattern shown in FIG. It is a top view which shows the state in which the process which superimposes the original figure pattern 10 on the mesh which consists of a two-dimensional arrangement | sequence of a pixel was performed in the original image creation part 121 shown in FIG. It is a figure which shows the area density map M1 produced based on the original figure pattern 10 shown in FIG. It is a figure which shows the edge length density map M2 produced based on the original figure pattern 10 shown in FIG. It is a top view which shows the original figure pattern 10 containing the information of dose amount. It is a figure which shows the dose density map M3 produced based on the original figure pattern 10 with a dose amount shown in FIG. It is a top view which shows the procedure which produces the kth hierarchy image Pk by performing the filter process which used the Gaussian filter GF33 to the kth preparation image Qk. It is a top view which shows the kth hierarchy image Pk obtained by the filter process shown in FIG. It is a top view which shows the example of the image processing filter utilized for the filter process shown in FIG. It is a top view which shows another example of the image processing filter utilized for the filter process shown in FIG. It is a top view which shows the procedure which produces the (k + 1) th preparation image Q (k + 1) by performing an average pooling process with respect to the kth hierarchy image Pk. It is a top view which shows the procedure which produces the (k + 1) th preparation image Q (k + 1) by performing a max pooling process with respect to the kth hierarchy image Pk. FIG. 7 is a plan view showing a procedure for creating an image pyramid PP composed of n hierarchical images P1 to Pn in the image pyramid creation unit 122 shown in FIG. 1; FIG. 6 is a plan view showing a procedure for calculating a feature value for an evaluation point E from each hierarchical image in the feature value calculation unit 123 shown in FIG. It is a figure which shows the specific calculating method used with the feature-value calculation procedure shown in FIG. FIG. 7 is a plan view showing a procedure for creating an image pyramid PD composed of n types of difference images D1 to Dn in the image pyramid creation unit 122 shown in FIG. 1; It is a block diagram which shows the Example using a neural network as the estimation calculating part 132 shown in FIG. FIG. 25 is a diagram showing a specific calculation process executed by the neural network shown in FIG. 24. FIG. FIG. 26 is a diagram illustrating an arithmetic expression for obtaining each value of the first hidden layer in the diagram illustrated in FIG. 25. It is a figure which shows the specific example of the activation function f (ξ) shown in FIG. FIG. 26 is a diagram illustrating an arithmetic expression for obtaining each value of a second hidden layer to an Nth hidden layer in the diagram illustrated in FIG. 25. FIG. 26 is a diagram illustrating an arithmetic expression for obtaining a value y of an output layer in the diagram illustrated in FIG. 25. It is a flowchart which shows the procedure of the learning step for obtaining the learning information L which the neural network shown in FIG. 24 uses. It is a flowchart which shows the detailed procedure of the estimation calculating part learning of step S84 in the flowchart shown in FIG. It is a block diagram which shows the structure of the shape correction apparatus 200 of the figure pattern which concerns on additional embodiment of this invention. FIG. 33 is a plan view illustrating an example of a process of replacing the original graphic pattern 10 with a rectangular aggregate 50 by the rectangular aggregate replacing unit 221 illustrated in FIG. 32. FIG. 33 is a plan view illustrating another example of a process of replacing the original graphic pattern 10 with the rectangular aggregate 50 by the rectangular aggregate replacing unit 221 illustrated in FIG. 32. FIG. 33 is a diagram illustrating an example of a feature amount calculation principle by a feature amount calculation unit 222 and a calculation function provided by a calculation function providing unit 223 illustrated in FIG. 32; It is a figure which shows an example of the specific calculation function provided by the calculation function provision part 223 shown in FIG. It is a figure explaining the error function erf (ξ) used for the calculation function shown in FIG. FIG. 37 is a diagram showing a positional relationship between an X-axis monotonically increasing function + erf [(X−Li / σk)] used in the calculation function shown in FIG. 36 and a rectangle Fi. FIG. 37 is a diagram showing a positional relationship between an X-axis monotone decreasing function −erf [(X−Ri / σk)] used in the calculation function shown in FIG. 36 and a rectangle Fi. It is a figure which shows the positional relationship of the horizontal direction function fhi ((sigma) k) used for the calculation function shown in FIG. 36, and the rectangle Fi. FIG. 37 is a diagram showing a positional relationship between a horizontal direction function fhi (σk) and a vertical direction function fvi (σk) used in the calculation function shown in FIG. 36 and a rectangle Fi. It is a figure which shows the role of the expansion coefficient (sigma) k used for the calculation function shown in FIG. It is a figure which shows an example of the calculation function in consideration of the dose amount. It is a top view which shows the process substituted by the rectangular aggregate | assembly by dividing | segmenting a figure by the rectangular aggregate replacement part 221 shown in FIG. FIG. 33 is a plan view showing a process of replacing a rectangular aggregate by setting a minute width to a unit line segment constituting a contour line of a graphic by the rectangular aggregate replacing unit 221 shown in FIG. 32. It is a figure which shows an example of the calculation function applied about the rectangular aggregate shown in FIG. FIG. 33 is a plan view illustrating a method for improving the efficiency of calculation of feature amounts by the feature amount calculation unit 222 illustrated in FIG. 32. It is a figure which shows the 1st example (example of Line & space pattern) which compares the processing time of feature-value extraction about basic embodiment and additional embodiment of this invention. It is a figure which shows the 2nd example (Example of Array | Hole | pattern) which compares the processing time of feature-value extraction about basic embodiment and additional embodiment of this invention. It is a figure which shows the 3rd example (example of an ISO-Space pattern) which compares the processing time of the feature-value extraction about basic embodiment and additional embodiment of this invention.

Hereinafter, the present invention will be described based on the illustrated embodiment.

<<< §1. Basic configuration of figure pattern shape correction device >>>
Here, the configuration of the figure pattern shape correcting apparatus 100 according to the basic embodiment of the present invention will be described with reference to the block diagram of FIG. As shown in the figure, the figure pattern shape correction apparatus 100 includes an evaluation point setting unit 110, a feature amount extraction unit 120, a bias estimation unit 130, and a pattern correction unit 140. Here, the figure pattern shape estimation apparatus 100 ′ according to the present invention is configured by the three units of the evaluation point setting unit 110, the feature amount extraction unit 120, and the bias estimation unit 130, and the figure pattern shape correction apparatus 100. Is configured by adding a pattern correction unit 140 as a fourth unit to the figure pattern shape estimation apparatus 100 ′.

<1.1 Shape Estimation Device for Graphic Pattern>
First, the configuration and function of the figure pattern shape estimation apparatus 100 ′ will be described. The figure pattern shape estimation apparatus 100 ′ serves to estimate the shape of the actual figure pattern 20 formed on the actual substrate S by simulating a lithography process using the original figure pattern 10. In the upper part of FIG. 1, an alternate long and short dash line arrow from the original graphic pattern 10 is shown, and an actual substrate S having a real graphic pattern 20 is drawn at the tip of the arrow. This dashed-dotted arrow indicates a physical lithography process.

The original graphic pattern 10 shown in the figure is graphic pattern data created by design work using a computer, and the alternate long and short dash line arrow indicates a lithography process such as physical exposure, development, and etching based on this data. It is shown that the actual substrate S is manufactured by carrying out. On the actual substrate S, an actual graphic pattern 20 corresponding to the original graphic pattern 10 is formed. However, when such a lithography process is performed, there is a slight discrepancy between the original graphic pattern 10 and the actual graphic pattern 20. This is because, as described above, it is difficult to form an accurate figure on the actual substrate S according to the various conditions of the steps of exposure, development, and etching included in the lithography process.

FIG. 2 is a plan view showing a specific example in which a difference in shape occurs between the original graphic pattern 10 and the actual graphic pattern 20. In a semiconductor device or the like, it is actually necessary to form a very fine and complicated figure pattern on the surface of an actual substrate S such as silicon. Here, for convenience of explanation, a simple pattern as shown in FIG. A case where a simple figure is given as the original figure pattern 10 will be described. The illustrated original figure pattern 10 is a pattern composed of one rectangle, for example, original figure data indicating that a material layer corresponding to the hatched rectangular inner region is formed on the actual substrate S. Become.

In an actual lithography process, a resist layer is formed on the upper surface of the material layer on the actual substrate S, and exposure to light or an electron beam is performed to perform drawing on the resist layer. For example, if the resist layer is exposed to the inner region (hatched portion) of the original graphic pattern 10 shown in FIG. 2 (a), the resist layer is developed to remove the non-exposed portion. The exposed portion remains as a remaining resist layer (hatched portion). Furthermore, if the remaining resist layer is used as a mask and the material layer is etched, theoretically, the inner region (hatched portion) of the original figure pattern 10 can be left also for the material layer. On the actual substrate S, the same actual figure pattern as the original figure pattern 10 shown in FIG.

However, actually, the actual graphic pattern 20 obtained on the actual substrate S does not exactly match the original graphic pattern 10. This is because the conditions of the steps of exposure, development, and etching included in the lithography process affect the shape of the actual figure pattern 20 finally obtained. For example, in the exposure process, the resist layer is drawn with light or an electron beam. At that time, the exposure area actually drawn on the resist layer by the proximity effect (PE: Proximity Effect) It is known that the area is slightly wider than the pattern 10. Under the influence of such a proximity effect, the actual graphic pattern 20 obtained on the actual substrate S is an area wider than the original graphic pattern 10 (indicated by a broken line) as shown in FIG. become.

In addition, conditions such as the characteristics of the developer used in the developing process, the characteristics of the etching solution and plasma used in the etching process, the time of the developing process and the etching process, and the like also affect the shape of the actual figure pattern 20. Therefore, when actually manufacturing a semiconductor device or the like, after designing a desired original figure pattern 10 on a computer, a lithography process using the original figure pattern 10 is simulated on the computer, and the actual substrate S is formed. The procedure for estimating the shape of the actual graphic pattern 20 that will be formed in the next step is executed. The figure pattern shape estimation apparatus 100 'shown in FIG. 1 is an apparatus having a function of performing such estimation, and does not actually perform a lithography process (exposure, development, etching process) for creating an actual substrate S. In addition, it has a function of estimating the shape of the actual figure pattern 20 that will be formed on the actual substrate S by simulation.

In the figure pattern shape estimation apparatus 100 ′ shown in FIG. 1, an evaluation point E is set on the original figure pattern 10 by the evaluation point setting unit 110. Specifically, the shape estimation apparatus 100 ′ is provided with graphic data including contour information indicating the boundary between the inside and the outside of the figure as the original figure pattern 10, and the evaluation point setting unit 110 performs such processing. Based on the original graphic pattern 10, a process for setting an evaluation point at a predetermined position on the contour line is performed.

FIG. 3 is a plan view showing an example in which several evaluation points are set for the original graphic pattern 10 shown in FIG. 2 (a) and the process bias (dimensional error) occurring at each evaluation point. First, FIG. 3A is a plan view showing an example in which evaluation points E11, E12, and E13 are set on the outline of the original graphic pattern 10 (rectangular figure) shown in FIG. 2A. FIG. 3 shows a simple example in which three evaluation points E11, E12, and E13 are set for convenience of explanation, but actually, a larger number of evaluation points are set on each side of the rectangle. The For example, if it is determined that the evaluation points are set continuously at a predetermined pitch along the contour line, a large number of evaluation points can be automatically set.

Here, let us consider a case where an actual graphic pattern 20 as shown in FIG. 2B is obtained based on the original graphic pattern 10 shown in FIG. FIG. 3B is a plan view showing the contour (solid line) of the real graphic pattern 20 shown in FIG. 2B compared with the contour (broken line) of the original graphic pattern 10 shown in FIG. There is shown a state in which the contour line of the real graphic pattern 20 indicated by a solid line extends outward by a dimension y as compared to the contour line of the original graphic pattern 10 indicated by a broken line. For this reason, the horizontal width a of the original graphic pattern 10 extends to the horizontal width b in the actual graphic pattern 20. Similarly, the vertical width slightly expands.

3B, the evaluation points E21, E22, E23 on the actual graphic pattern 20 are evaluation points determined as points corresponding to the evaluation points E11, E12, E13 on the original graphic pattern 10. Here, the evaluation point E21 is defined as a point shifted from the evaluation point E11 by a predetermined dimension y11 toward the outer side in the normal direction of the contour line indicated by a broken line. Similarly, the evaluation point E22 is defined as a point shifted from the evaluation point E12 by a predetermined dimension y12 toward the outside in the normal direction of the contour line indicated by a broken line, and the evaluation point E23 is a contour line indicating the evaluation point E13 by a broken line. Is defined as a point shifted by a predetermined dimension y13 toward the outside in the normal direction.

As in the example shown in FIG. 3, here, in order to quantitatively indicate the shape change of the actual graphic pattern 20 with respect to the original graphic pattern 10, the deviation amount y in the normal direction of the contour line generated for each evaluation point E is set. I will use it. Further, this deviation amount y is referred to as “process bias y” because it is a bias amount caused by the lithography process. The process bias y is a value having a positive / negative sign, and in the embodiment described below, the direction in which the figure exposure part (drawing part) is fattened is defined as a positive value, and the direction in which the figure is thinned is defined as a negative value. In the example shown in the figure, the inside of the figure surrounded by the contour line is the exposure part (drawing part), so if it is shifted in the outer direction of the contour line, it is a positive value, and it shifts in the inner direction of the contour line. Is negative. In the case of the example shown in FIG. 3, since each evaluation point E is shifted in the outward direction, the process bias y11, y12, y13 takes a positive value.

In FIG. 3, only three evaluation points E11, E12, and E13 are shown for convenience of explanation, but actually, more evaluation points E are defined on the contour line of the original graphic pattern 10. The Therefore, if the process bias y can be estimated for each evaluation point E, the position of each evaluation point E after the lithography process is shifted by shifting each evaluation point E by the process bias y in the normal direction of the contour line. The contour position of the actual graphic pattern 20 can be estimated.

However, the value of the process bias y of each evaluation point E differs for each evaluation point. For example, in the example shown in FIG. 3B, the values of the process biases y11, y12, and y13 are individual values. This is because the relative positions of the evaluation points E11, E12, and E13 with respect to the original graphic pattern 10 are different, so that the influence of the lithography process is also different, and the amount of deviation that occurs is also different. Therefore, in order to improve the estimation accuracy when the shape of the actual graphic pattern 20 is estimated by simulation based on the original graphic pattern 10, the influence of the lithography process is appropriately predicted for each evaluation point, and an appropriate process bias is determined. It is important to obtain y.

Therefore, in the figure pattern shape estimation apparatus 100 ′ shown in FIG. 1, first, an evaluation point is set on the original figure pattern 10 by the evaluation point setting unit 110. Specifically, each evaluation point E may be set at a predetermined position on the contour line based on the contour line information indicating the boundary between the inside and the outside of the figure included in the original figure pattern 10. For example, evaluation points can be set continuously at predetermined intervals along the contour line.

Subsequently, the feature amount extraction unit 120 extracts feature amounts indicating features around each evaluation point E for the original graphic pattern 10. The feature amount x for one evaluation point E is a value indicating the features around the evaluation point E. In order to perform the process of extracting the feature quantity x, the feature quantity extraction unit 120 includes an original image creation unit 121, an image pyramid creation unit 122, and a feature quantity calculation unit 123, as shown in FIG.

The original image creation unit 121 creates an original image composed of a collection of pixels each having a predetermined pixel value based on the given original graphic pattern 10. For example, when an original figure pattern 10 as shown in FIG. 2A is given, a pixel value 1 for a pixel inside a rectangle (a hatched pixel in the figure) and a pixel value 0 for a pixel outside the rectangle. Is added, an original image composed of binary images is created.

The image pyramid creation unit 122 performs an image pyramid creation process including a reduction process for creating a reduced image by reducing the original image, and creates an image pyramid including a plurality of n layer images. Each of the n layer images constituting each layer of the image pyramid is an image obtained by performing predetermined image processing on the original image created by the original image creation unit 121, and has different sizes. Yes. Such a set of hierarchical images is called an “image pyramid” because each layered image is stacked in order from the largest to the smallest to form a hierarchical structure, as if a pyramid is formed. This is because it can be seen.

The feature amount calculation unit 123 calculates a feature amount based on the pixel values of the pixels in the vicinity of the evaluation point E for each of the n layer images constituting the layer of the image pyramid. Specifically, the feature amount x1 is calculated based on the pixel value of the pixel near the evaluation point E in the first hierarchical image, and the pixel value of the pixel near the evaluation point E in the second hierarchical image is calculated. On the basis of the feature amount x2, similarly, the feature amount xn is calculated based on the pixel value of the pixel in the vicinity of the evaluation point E in the nth hierarchical image. n feature amounts x1 to xn are extracted. For example, in the example shown in FIG. 3A, n feature values x1 (E11) to xn (E11) are extracted for the evaluation point E11, and n feature values x1 (E12) for the evaluation point E12. To xn (E12) are extracted, and n feature quantities x1 (E13) to xn (E13) are extracted for the evaluation point E13.

On the other hand, the bias estimation unit 130 is a process that indicates the amount of deviation between the position of the evaluation point E on the original graphic pattern 10 and the position on the actual graphic pattern 20 based on the feature value x extracted by the feature value extraction unit 120. A process for estimating the bias y is performed. In order to perform such estimation processing, the bias estimation unit 130 includes a feature amount input unit 131 and an estimation calculation unit 132. The feature amount input unit 131 is a component that inputs the feature amounts x1 to xn calculated for the evaluation point E by the feature amount calculation unit 123, and the estimation calculation unit 132 performs the learning obtained by the learning stage performed in advance. Based on the information L, an estimated value corresponding to the feature amounts x1 to xn is obtained, and the obtained estimated value is output as the estimated value y of the process bias for the evaluation point E.

More specifically, the estimation calculating unit 132 estimates the process bias for each evaluation point E located on the contour line of the graphic constituting the original graphic pattern 10 as a deviation amount in the normal direction of the contour line. y is output. For example, with respect to the original figure pattern 10 shown in FIG. 3A, as shown in FIG. 3B, the process bias y11 for the evaluation point E11, the process bias y12 for the evaluation point E12, and the process bias y13 for the evaluation point E13. , Respectively, are output from the estimation calculation unit 132 as estimated values. Thus, if the estimated value y of the process bias for each evaluation point E is obtained, a new position of each evaluation point E (a position shifted by the process bias y in the normal direction of the contour line) can be determined. Therefore, as shown in FIG. 3B, the shape of the actual graphic pattern 20 can be estimated.

The above is the basic configuration and basic operation of the figure pattern shape estimation apparatus 100 ′. The specific operation of the feature quantity extraction unit 120 will be described in detail in §2, and the specific operation of the bias estimation unit 130 will be described in detail in §3.

<1.2 Shape Pattern Correction Device>
Next, the configuration and function of the figure pattern shape correction apparatus 100 will be described. The figure pattern shape correction apparatus 100 is an apparatus that corrects the shape of the original figure pattern 10 using the figure pattern shape estimation apparatus 100 'described above. As shown in FIG. 1, the figure pattern shape estimation apparatus 100' is used. In addition to the evaluation point setting unit 110, the feature amount extraction unit 120, and the bias estimation unit 130 which are constituent elements of the above, a pattern correction unit 140 is further provided. The pattern correction unit 140 is a component that corrects the original graphic pattern 10 based on the estimated value y of the process bias output from the bias estimation unit 130, and the corrected graphic pattern obtained by the correction by the pattern correction unit 140 15 is the final output of the shape correction apparatus 100 for this graphic pattern.

The correction by the pattern correction unit 140 is performed by moving each evaluation point E on the original graphic pattern 10 in a direction to cancel the process bias y, and correcting the boundary line of each graphic to the position of each evaluation point E after the movement. It can be carried out. For example, let us consider a case where an actual graphic pattern 20 as shown in FIG. 3B is estimated for the original graphic pattern 10 shown in FIG. In this case, the horizontal width “a” of the rectangle included in the original graphic pattern 10 is increased to the horizontal width “b” on the actual graphic pattern 20, and if (ba) / 2 = y, the positions of the left and right sides of the rectangle If both are moved inward by y, a rectangle having the same horizontal width a as that of the original graphic pattern 10 is obtained. Therefore, basically, if correction is performed to reduce the width a of the original graphic pattern 10 by 2y, and a lithography process is executed based on the corrected graphic pattern, the actual graphic pattern 20 is formed on the actual substrate S. A rectangle having a width a as originally designed can be obtained.

In the case of the original graphic pattern 10 shown in FIG. 3A, the evaluation point E11 is moved to the left (inside the rectangle) by the process bias y11, and the evaluation point E12 is moved to the left (inside the rectangle) by the process bias y12. Then, the correction may be performed by moving the evaluation point E13 upward (inside the rectangle) by the process bias y13. Of course, since more evaluation points are actually defined, correction is performed to move all the evaluation points to the inside of the rectangle by a dimension corresponding to the process bias, and new evaluation points are connected. If a simple contour line is defined, a corrected graphic pattern 15 including a graphic defined by the contour line is obtained. Since such correction processing itself is a known technique, detailed description thereof is omitted here.

However, actually, even if a lithography process is executed using the corrected graphic pattern 15 obtained in this way and a real graphic pattern 25 (not shown) is formed on the real substrate S, the actual graphic pattern 25 obtained is It does not exactly match the original figure pattern 10 at the beginning of the design (for example, the lateral width of the rectangle formed on the actual substrate S is not exactly a). This is because the graphic included in the original graphic pattern 10 and the graphic included in the corrected graphic pattern 15 are different in size and shape, so that there is a difference in the influence such as the proximity effect when the lithography process is executed.

In other words, even if it is found that a process bias y occurs as a result of simulation for a specific evaluation point E, simply moving the position of the evaluation point E in the reverse direction by the process bias y Accurate correction cannot be performed.

Of course, compared to the actual figure pattern 20 obtained as a result of executing the lithography process using the original figure pattern 10, the actual figure pattern 25 obtained as a result of executing the lithography process using the corrected figure pattern 15 is Since the pattern becomes closer to the original figure pattern 10, the actual lithography process is performed using the corrected figure pattern 15 obtained by the correction by the pattern correction unit 140, rather than executing the actual lithography process using the original figure pattern 10 as it is. The more accurate figure pattern can be obtained on the actual substrate S by executing the above. That is, if correction is performed by the pattern correction unit 140, it is certain that the error is reduced.

Therefore, practically, as shown in FIG. 1, the process of giving the corrected figure pattern 15 output from the pattern correction unit 140 to the figure pattern shape correcting apparatus 100 is repeated. That is, the corrected figure pattern 15 is given as a new original figure pattern to the figure pattern shape estimation apparatus 100 ', and this new original figure pattern (corrected figure pattern 15) is described in §1.1. Processing is executed. Specifically, each evaluation point E is set on the corrected graphic pattern 15 by the evaluation point setting unit 110, the feature amount for each evaluation point E is extracted by the feature amount extraction unit 120, and the bias estimation unit 130 performs the setting. An estimated process bias value y for each evaluation point E is calculated. Then, the correction process is performed again in the pattern correction unit 140 using the calculated process bias estimated value y.

The graphic pattern shape correction apparatus 100 shown in FIG. 1 has a function of repeatedly executing correction on a graphic pattern in this way. In other words, a first corrected graphic pattern 15 is obtained based on the original graphic pattern 10, a second corrected graphic pattern is obtained based on the first corrected graphic pattern 15, and based on the second corrected graphic pattern. Thus, a third corrected graphic pattern is obtained, and the correction process of... Is repeated. Each time correction processing is performed, the shape error between the original graphic pattern and the graphic pattern obtained by the simulation is reduced.

Therefore, for example, when the shape error between the original figure pattern and the figure pattern obtained by simulation converges within a predetermined tolerance, the correction is completed, and the actual lithography process is executed using the last obtained figure pattern Then, a real graphic pattern close to the original graphic pattern 10 at the initial design can be formed on the real substrate S. Thus, by using the figure pattern shape correcting apparatus 100 according to the present invention, the shape of the original figure pattern can be accurately corrected.

Note that each of the evaluation point setting unit 110, the feature amount extraction unit 120, the bias estimation unit 130, and the pattern correction unit 140 shown in FIG. 1 is configured by incorporating a predetermined program into a computer. Therefore, the figure pattern shape estimation apparatus 100 ′ and the figure pattern shape correction apparatus 100 according to the present invention are actually realized by incorporating a dedicated program into a general-purpose computer.

FIG. 4 is a flowchart showing a product design / manufacturing process using the figure pattern shape correcting apparatus 100 shown in FIG. First, in step S1, a product design stage is performed. This product design stage is a process of creating a graphic pattern for configuring a semiconductor device or the like, and the original graphic pattern 10 shown in FIG. 1 is created at this product design stage. An apparatus for designing a product such as a semiconductor device and creating a graphic pattern is already a known apparatus, and therefore detailed description thereof is omitted here.

The evaluation point setting stage in the next step S2 is a stage executed in the evaluation point setting unit 110 shown in FIG. For example, when the original figure pattern 10 as shown in FIG. 2A is given, evaluation points E11, E12, E13, etc. as shown in FIG. 3A are set. The subsequent feature quantity extraction stage of step S3 is a stage executed in the feature quantity extraction unit 120 shown in FIG. 1. As described above, n kinds of feature quantities x1 to xn are extracted for one evaluation point E. (The detailed extraction procedure is described in §2). Then, the process bias estimation stage of step S4 is a stage executed in the bias estimation unit 130 shown in FIG. 1, and as described above, a process using n feature quantities x1 to xn is performed for one evaluation point E. The estimated bias value y is obtained (the detailed calculation procedure is described in §3).

Then, the pattern shape correction stage in step S5 is a stage executed in the pattern correction unit 140 shown in FIG. 1, and as described above, using the process bias estimated value y obtained for each evaluation point E, the original figure A corrected graphic pattern 15 is obtained by correcting the pattern 10. Since such correction is not sufficient once, the process of returning to step S2 is repeated until it is determined that “correction is completed” in step S6. That is, by treating the corrected graphic pattern 15 obtained in step S5 as a new original graphic pattern 10, the processes in steps S2 to S5 are repeatedly executed.

If it is determined in step S6 that “correction is complete” as a result of such repeated processing, the process proceeds to step S7, and the lithography process is executed. The determination of “correction completion” is, for example, “the error between the position on the original graphic pattern and the position on the graphic pattern obtained by the simulation is equal to or less than a predetermined reference value for a certain percentage of evaluation points E”. This can be done by satisfying certain specific conditions. In the lithography process in step S7, actual processes such as exposure, development, and etching are performed based on the finally obtained corrected graphic pattern, and the actual substrate S is manufactured.

In the flowchart shown in FIG. 4, steps S1 to S6 are processes executed on a computer (computer), and step S7 is a process executed on an actual substrate S.

<1.3 Basic Concept of Feature Extraction in the Present Invention>
So far, the basic configuration and basic operation of the figure pattern shape estimation apparatus 100 ′ and the figure pattern shape correction apparatus 100 shown in FIG. 1 have been described. In each of these apparatuses, the most characteristic component of the present invention is a feature quantity extraction unit 120. The present invention produces an effect of extracting an accurate feature amount from the original graphic pattern 10 and performing an accurate simulation to accurately estimate the shape of the actual graphic pattern 20 formed on the actual substrate S. However, the component that plays the most important role in obtaining such an effect is the feature quantity extraction unit 120. In other words, an important feature of the present invention is that feature amounts are extracted from the original graphic pattern 10 by a very unique method. Therefore, here, the basic concept of feature quantity extraction in the present invention will be described.

FIG. 5 is a plan view showing the concept of grasping the surrounding features of each evaluation point E11, E12, E13 defined on the outline of the graphic pattern 10 made of a rectangle. FIG. 5A shows a state in which features inside the reference circle C1 and the inside of the reference circle C2 are extracted for the evaluation point E11 set at the center of the right side of the rectangle. The reference circles C1 and C2 are both circles centered on the evaluation point E11, but the reference circle C2 is larger than the reference circle C1. Similarly, FIG. 5 (b) shows two reference circles C1, for the evaluation point E12 set below the right side of the rectangle, and FIG. 5 (c) shows the evaluation point E13 set for the center of the lower side of the rectangle. The state where the internal features of C2 are extracted is shown.

Here, when the internal features of the reference circle C1 are compared for each evaluation point, for the evaluation points E11 and E12, the left half is inside the figure (hatching area) and the right half is outside the figure (blank area). There is no difference in the internal features of the reference circle C1. On the other hand, the internal features of the reference circle C1 for the evaluation point E13 are such that the upper half is inside the figure (hatched area) and the lower half is outside the figure (blank area), and the inside of the reference circle C1 of the evaluation points E11 and E12 However, there is no difference in the occupation ratio of the hatched area. On the other hand, comparing the internal features of the reference circle C2 with respect to the respective evaluation points E11, E12, E13, it can be seen that the distributions of the hatched regions are different and have different features.

As described above, for each evaluation point E11, E12, E13 on the graphic pattern 10, even if the features of the neighborhood are grasped, the feature of the narrow neighborhood region such as the reference circle C1 is extracted or the reference circle C2 Thus, the extracted features differ depending on whether or not features in a slightly wide neighboring region are extracted. Therefore, when a feature of a neighboring region is quantitatively extracted as some feature amount x with respect to a certain evaluation point E, the feature amount can be extracted by various methods by changing the range of the neighboring region stepwise. You can see that

Further, as described above, when the lithography process is executed based on the original graphic pattern 10, the actual graphic pattern 20 obtained on the substrate has a dimensional error (process bias) with respect to the original graphic pattern 10 due to the proximity effect in the exposure process. ) Will occur. In particular, the proximity effect in electron beam exposure includes various effects such as an effect caused by forward scattering having a narrow influence range and an effect caused by back scattering having a wide influence range. For example, forward scattering is explained as a phenomenon in which, when an electron beam is irradiated onto a molding layer composed of a resist layer or the like, electrons having a small mass spread while being scattered by molecules in the resist, It is described as a phenomenon in which electrons scattered and bounced near the surface of a metal substrate or the like under the resist layer are diffused in the resist layer. In addition, a process bias is also generated by the etching process, and the magnitude of the process bias varies depending on a loading phenomenon during etching. Similar to the proximity effect in the exposure process described above, this loading phenomenon is also caused by combining various components such as a component having a narrow influence range and a component having a wide influence range.

After all, the value of the process bias y for a certain evaluation point E becomes a value determined by the fusion of phenomena having various scale feelings. Therefore, extracting various feature values from feature values related to a narrow range to feature values related to a wide range is different from the various phenomena in each process that affect the process bias that have different influence ranges. This is important for accurate simulation. Therefore, in the present invention, for one evaluation point E, feature quantities for various regions around it are extracted from the vicinity to the distance. As described above, in order to extract a plurality of feature amounts for one evaluation point E, the present invention employs a method of creating an “image pyramid” composed of a plurality of hierarchical images each having a different size. This image pyramid includes information obtained by multiplexing various phenomena having different influence ranges.

FIG. 6 is a diagram showing an outline of processing executed in the feature amount extraction unit 120 and the bias estimation unit 130 shown in FIG. An original image Q1 shown in the upper part of the figure is an image created by the original image creating unit 121 shown in FIG. 1 and is an image corresponding to the given original figure pattern 10. As described above, the original graphic pattern 10 is data created by a semiconductor device design apparatus or the like, and is data indicating a graphic as shown in FIG. 2 (a), but usually indicates a contour line of the graphic. It is given as vector data (data indicating the coordinate value of each vertex and the connection relationship between each vertex).

The original image creation unit 121 executes a process of creating an original image Q1 composed of an aggregate of pixels each having a predetermined pixel value based on the data of the given original graphic pattern 10. For example, if a pixel having a pixel value of 1 is arranged inside a graphic constituting the original graphic pattern 10 and a pixel having a pixel value of 0 is arranged outside, the original image Q1 composed of an aggregate of a large number of pixels U Can be created. An original image Q1 shown in FIG. 6 is an image composed of such an assembly of pixels U, and has a rectangular figure included in the original figure pattern 10 as image information, as indicated by a broken line. The evaluation point E is set on the contour line of the figure by the evaluation point setting unit 110. In FIG. 6, only one evaluation point E is drawn for convenience, but actually, a large number of evaluation points are set along the contour line of the figure.

The image pyramid creation unit 122 shown in FIG. 1 creates an image pyramid PP based on the original image Q1. The image pyramid PP is composed of a plurality of hierarchical images having different sizes. The figure shows an image pyramid PP composed of a plurality of n (n ≧ 2) hierarchical images P1 to Pn. The specific procedure for creating the hierarchical images P1 to Pn from the original image Q1 will be described in Section 2. Basically, the hierarchical images P1 to Pn are created by a reduction process for reducing the number of pixels. For example, in the illustrated example, the hierarchical image P1 is an image having the same size as the original image Q1 (an image having the same number of vertical and horizontal pixels), whereas the hierarchical image P2 is reduced to a small size image. The hierarchical image P3 is an image having a smaller size obtained by further reducing the hierarchical image P2.

As described above, in the present invention, hierarchical images P1 to Pn whose image size is gradually reduced are created based on the original image Q1. In this way, the state in which a plurality of hierarchical images having different sizes are arranged one above the other is in the form of a pyramid as shown in the figure. Therefore, in the present application, an aggregate of the plurality of hierarchical images P1 to Pn is referred to as an image pyramid PP. It is out. Since each of the hierarchical images P1 to Pn is created based on the original image Q1, it has information of the original graphic pattern 10, and the position of the evaluation point E can be defined for each of the hierarchical images P1 to Pn. In the figure, a rectangular figure is drawn on each of the hierarchical images P1 to Pn, and an evaluation point E is arranged on the contour line.

1 performs a process of calculating a feature value for each hierarchical image constituting the image pyramid based on pixel values of pixels in the vicinity of the evaluation point. FIG. 6 shows a state in which feature amounts x1 to xn of the evaluation points E are extracted from n layer images P1 to Pn constituting the image pyramid PP, respectively. The illustrated feature amounts x1 to xn are values indicating features around the same evaluation point E, but the feature amount x1 is a pixel value of a pixel near the evaluation point E on the first hierarchical image P1. The feature amount x2 is a value calculated based on the pixel values of the neighboring pixels of the evaluation point E on the second hierarchical image P2, and the feature amount x3 is the third value. This is a value calculated based on the pixel values of the neighboring pixels of the evaluation point E on the hierarchical image P3. A specific calculation procedure for each of the feature amounts x1 to xn will be described in Section 2.

FIG. 6 shows only one evaluation point E for convenience, but in actuality, n feature values x1 to xn are calculated for each of a large number of evaluation points. Each of the feature amounts x1 to xn is a predetermined scalar value, but n feature amounts x1 to xn are obtained for each evaluation point E, respectively. Therefore, if the n feature quantities x1 to xn are grasped as n-dimensional vectors, the feature quantity extraction unit 120 performs a process of extracting feature quantities composed of n-dimensional vectors for one evaluation point E. .

The feature amount (n-dimensional vector) for each evaluation point extracted in this way is input by the feature amount input unit 131 in the bias estimation unit 130 and given to the estimation calculation unit 132. In the case of the embodiment shown here, the estimation calculation unit 132 is configured by a neural network, and based on the learning information L obtained in advance by the learning stage, the estimation calculation unit 132 applies the feature amounts x1 to xn given as n-dimensional vectors. Accordingly, an operation for calculating an estimated value y (scalar value) of the process bias for the evaluation point E is performed. A specific calculation procedure will be described in §3.

As described above, according to the present invention, an accurate feature amount can be extracted for every original figure pattern 10 even if a physical / experimental simulation model is not constructed for an actual lithography process. Can do. In addition, since it is not necessary to construct a physical / experimental simulation model in the first place, it is not necessary to consider various set values of material properties and process conditions in the learning stage of the neural network described later in §3.2.

As described above, the example of using the figure pattern shape estimation apparatus 100 ′ and the shape correction apparatus 100 according to the present invention in the lithography process for manufacturing a semiconductor device has been described. The present invention is not limited to use, and can be used for manufacturing processes of various products including lithography processes. For example, the present invention can be used in manufacturing processes of various products including lithography processes such as NIL (Nano Imprint Lithography) and EUV (Extreme UltraViolet Lithography). In particular, in the NIL, the original graphic pattern may be corrected so that the actual graphic pattern on the master template produced from the original graphic pattern through exposure lithography matches the original graphic pattern. Or you may correct | amend an original figure pattern so that the real figure pattern on the replica template produced through the imprint from the master template may correspond with the original figure pattern.

In addition, the present invention can be applied to all product fields including lithography processes such as MEMS (Micro Electro Mechanical Systems), LSPM (Large-size Photomask), lead frames, metal masks, metal mesh sensors, color filters, etc. is there.

<<< §2. Details of feature extraction unit >>
Next, a detailed processing operation of the feature amount extraction unit 120 will be described. As shown in FIG. 1, the feature amount extraction unit 120 includes an original image creation unit 121, an image pyramid creation unit 122, and a feature amount calculation unit 123, and performs the feature amount extraction process in step S3 in the flowchart of FIG. Has the function to execute. This feature amount extraction processing is actually executed by each procedure shown in FIG. Here, steps S31 and S32 are procedures executed by the original image creation unit 121, steps S33 to S36 are procedures executed by the image pyramid creation unit 122, and step S37 is a feature amount calculation unit 123. The procedure executed by Hereinafter, a procedure executed by each unit will be described in detail with a specific example.

<2.1 Processing Procedure by Original Image Creation Unit 121>
The original image creation unit 121 performs a function of creating an original image composed of a collection of pixels each having a predetermined pixel value based on the given original graphic pattern 10, and performs steps S31 and S32 in the flowchart of FIG. Execute. First, in step S31, the process of inputting the original graphic pattern 10 is performed, and in the subsequent step S32, the original image creation process is performed.

In §1, for convenience of explanation, as an example of the original figure pattern 10 input in step S31, a simple pattern including only one rectangular figure as shown in FIG. Here, in order to give a more detailed explanation, consider the case where an original figure pattern 10 including five figures F1 to F5 (rectangles) as shown in FIG. 8 is given. As described above, the original figure pattern 10 given to the figure pattern shape correction apparatus 100 is usually vector data indicating the outline of the figure. Therefore, in FIG. 8, the inside of each of the figures F1 to F5 is indicated by hatching. However, in reality, the original figure pattern 10 includes the coordinate values of the vertices of the five rectangles F1 to F5 and the vertices thereof. Is given as vector data indicating the connection relationship.

The original image creation process of step S32 is a process of creating data (raster data) of the original image Q1 composed of a collection of pixels based on the original graphic pattern 10 given as such vector data. Specifically, the original image creation unit 121 defines a mesh composed of a two-dimensional array of pixels U, overlays the original graphic pattern 10 on this mesh, and configures the position of each pixel U and the original graphic pattern 10. The pixel value of each pixel U is determined based on the relationship with the positions of the contour lines of the graphics F1 to F5.

FIG. 9 is a plan view showing a state where the original image creation unit 121 has performed processing for superimposing the original figure pattern 10 on a mesh composed of a two-dimensional array of pixels U. FIG. In this example, a mesh is defined in which pixels U having pixel dimensions u both vertically and horizontally are two-dimensionally arranged, and a large number of pixels U are arranged at a pitch u both vertically and horizontally. The pixel size u is set to an appropriate value that can represent the shapes of the figures F1 to F5 with sufficient resolution. The smaller the pixel size u is set, the higher the resolution of shape expression, but the later processing load becomes heavier. In general, since the original figure pattern 10 used for manufacturing a semiconductor device is a very fine pattern, it is preferable to set, for example, a value of about u = 5 to 20 nm as the pixel dimension u.

Thus, when the two-dimensional array of pixels U is defined, pixel values are defined for the individual pixels U based on the relationship with the positions of the contour lines of the graphics F1 to F5. There are several methods for defining pixel values.

The most basic definition method is to recognize the internal area and external area of each graphic F1 to F5 based on the original graphic pattern 10, and use the occupancy of the internal area in each pixel U as the pixel value of the pixel. Is the method. In FIG. 8, the hatched area is the internal area of each of the figures F1 to F5, and the white area is the external area. Therefore, when this method is adopted, the pixel value of each pixel is defined as the occupancy rate (0 to 1) of the internal area (hatched area) in the pixel in the state of being overlapped as shown in FIG. An image in which pixel values are defined by such a method is generally called an “area density map”.

FIG. 10 is a diagram showing an area density map M1 created based on the “original graphic pattern 10 + two-dimensional array of pixels” shown in FIG. Here, each cell is each pixel defined in FIG. 9, and the numbers in the cell are pixel values defined for each pixel. A blank cell is a pixel having a pixel value of 0 (illustration of the pixel value of 0 is omitted). In this area density map M1, for example, a pixel having a pixel value of 1.0 is a pixel whose occupancy ratio of the hatching area in FIG. 9 is 100%, and a pixel having a pixel value of 0.5 is the hatching area in FIG. This is a pixel with an occupation ratio of 50%. This area density map M1 is basically a binary image in which the inside of the figure is represented by a pixel value of 1 and the outside of the figure is represented by a pixel value of 0. However, for the pixel where the outline of the figure is located, Since the value indicating the ratio is given as the pixel value, the whole image is a monochrome gradation image.

As another definition method of the pixel value, a method of recognizing the contour lines of the graphics F1 to F5 based on the original graphic pattern 10 and setting the length of the contour line existing in each pixel U as the pixel value of the pixel. Can also be taken. When this method is adopted, the pixel value of each pixel is defined as the total sum of the lengths of the contour lines existing in the pixel in the superimposed state as shown in FIG. An image in which pixel values are defined by such a method is generally called an “edge length density map”. As a unit of the length of the contour line, for example, a unit in which the pixel dimension u is 1 may be used.

FIG. 11 is a diagram showing an edge length density map M2 created based on the “original graphic pattern 10 + two-dimensional array of pixels” shown in FIG. Again, each cell is each pixel defined in FIG. 9, and the numbers in the cell are defined as the sum of the lengths of the contour lines existing in each pixel (the length when the pixel dimension u is 1). Pixel value. A blank cell is a pixel having a pixel value of 0 (illustration of the pixel value of 0 is omitted). In the edge length density map M2, for example, a pixel having a pixel value of 1.0 is a pixel having a length u of the contour line existing in the pixel in FIG. Since the edge length density map M2 is basically a monochrome gradation image showing the density distribution of the contour line, the image is considerably different from the area density map M1 described above. However, as in the present invention, it is a very useful image in extracting the feature amount for the evaluation point E defined on the contour line.

As described above, the method for defining the pixel value of each pixel based on the original graphic pattern 10 shown in FIG. 8 has been described. However, the original graphic pattern 10 used in the lithography process shows the boundary between the inside and the outside of the graphic. In addition to the geometric information of the contour line, information on a dose amount for each figure may be further added. FIG. 12 is a plan view showing the original graphic pattern 10 including information on such a dose amount. The original figure pattern 10 with dose shown in FIG. 12 includes the outline information of the figures F1 to F5, as in the original figure pattern 10 shown in FIG. For each of F5, information defining the dose amount is included.

Specifically, in the illustrated example, a dose amount of 100% is defined for the figures F1 to F3, a dose amount of 50% is defined for the figure F4, and a dose amount of 10% is defined for the figure F5. . These dose amounts indicate the intensity of light or electron beam to be irradiated (including the case where the total energy amount is controlled by the number of exposures) in the exposure process of the lithography process. In the case of the illustrated example, light and electron beams are irradiated with 100% intensity when exposing the internal area of the figures F1 to F3, but 50% of the figure F5 is exposed when the internal area of the figure F4 is exposed. When the internal region is exposed, light or an electron beam is irradiated with an intensity of 10%. As described above, when the dose is controlled for each figure during the exposure process, the dimensions of the actual figure pattern 20 formed on the actual substrate S can be further finely adjusted.

In the case where such dose control is performed in the exposure process of the lithography process, it is necessary to consider the dose even in the simulation. In such a case, when determining the pixel value of the original image, it is necessary to adopt a method that takes the dose amount into consideration. That is, when an original graphic pattern 10 including information on a contour line indicating the boundary between the inside and the outside of the graphic and information on a dose amount for each graphic in the lithography process is given, Based on this, the internal area and external area of each figure are recognized, the dose amount for each figure is recognized, and for each figure existing in each pixel, the occupancy rate of the internal area and the dose amount of the figure are determined. What is necessary is just to take the method which calculates | requires "product" and makes the total of the said product the pixel value of the said pixel.

When this method is adopted, the pixel values of each pixel in the state of being overlapped as shown in FIG. 9 are the occupancy ratio (0 to 1) of the internal area (hatched area) of the specific graphic in the pixel and the specific value. It is defined as the sum of products of doses related to figures. An image in which pixel values are defined by such a method is generally called a “dose density map”. This dose density map also becomes a monochrome gradation image as a whole.

FIG. 13 is a diagram showing a dose density map M3 created based on the original figure pattern 10 with a dose amount shown in FIG. Here, each cell is each pixel defined in FIG. 9, and the numbers in the cell are pixel values defined for each pixel. A blank cell is a pixel having a pixel value of 0 (illustration of the pixel value of 0 is omitted). When this dose density map M3 is compared with the area density map M1 shown in FIG. 10, the pixel value for the pixels where the figures F1 to F3 to which the dose amount 100% is given is not changed, but the dose amount 50%. It can be seen that the pixel value of the pixel in which the figure F4 to which the figure is given and the figure F5 to which the dose amount is 10% is arranged is reduced by an amount corresponding to the dose quantity. This shows a phenomenon in which light or an electron beam with reduced intensity is irradiated to the inside of the figures F4 and F5 in the actual exposure process.

As described above, an example in which three images (an aggregate of pixels U having a predetermined pixel value), that is, the area density map M1, the edge length density map M2, and the dose density map M3 are created based on the original figure pattern 10 has been shown. . In the original image creation process in step S32 in the flowchart of FIG. 7, any of these three images may be created and used as the original image. FIG. 7 shows an example in which the area density map M1 is the original image Q1. Of course, it is also possible to create the original image Q1 by a method other than the three methods described above.

Note that the original image Q1 created in step S32 is used as the first preparation image Q1 in the filtering process of step S33. As will be described later, the filtering process in step S33 is a process of creating a kth hierarchical image Pk by applying an image processing filter to the kth preparation image Qk. Therefore, it can be said that the procedure of step S32 is a process of creating the first preparation image Q1 by setting the parameter k (k = 1, 2, 3,...) To the initial value k = 1. . The first preparation image Q1 is an original image that is first created based on the original graphic pattern 10, and is a reference image that is first used in an image pyramid creation process described later.

<2.2 Processing Procedure by Image Pyramid Creation Unit 122>
Subsequently, a procedure of image pyramid creation processing by the image pyramid creation unit 122 will be described. The image pyramid creation unit 122 has a function of performing a reduction process for reducing the number of pixels based on the original image Q1 created in step S32 of FIG. 7 (for example, the area density map M1 shown in FIG. 10). An image pyramid creation process is performed to create an image pyramid composed of a plurality of hierarchical images having different sizes. In the case of the embodiment described here, this image pyramid creation process is executed by the procedure shown in steps S33 to S36 in the flowchart of FIG.

Here, in step S31, an original graphic pattern 10 as shown in FIG. 8 is input, and in step S32, a specific image is taken as an example where the area density map M1 shown in FIG. 10 is created as the original image Q1. The procedure of the pyramid creation process will be described.

First, in step S33, a filter process for creating the kth hierarchical image Pk by applying an image processing filter to the kth preparation image Qk is executed. Specifically, this filter processing is executed, for example, as a convolution operation using a Gaussian filter as an image processing filter. FIG. 14 is a plan view showing a procedure for creating the k-th hierarchical image Pk by performing the filtering process using the Gaussian filter GF33 on the preparation image Qk. The kth preparation image Qk shown in FIG. 14 is actually the same as the area density map M1 shown in FIG.

That is, the area density map M1 shown in FIG. 10 is shown as an 8 × 8 pixel array for convenience, and the description of the pixel value 0 is omitted, whereas the preparation image Qk shown in FIG. Although shown as a pixel array of 10 and a pixel value of 0 is also shown, they are substantially the same image. In short, in FIG. 14, for the convenience of executing the filtering process, pixels having a pixel value of 0 are arranged around the area density map M1 including the 8 × 8 pixel array shown in FIG. It is only doing. At this stage, the parameter k has an initial value of 1, and the preparation image Qk shown in FIG. 14 is the first preparation image Q1. As described above, the first preparation image Q1 is nothing but the original image created by the original image creation process in step S32.

In the filter processing shown in FIG. 14, a convolution operation using the Gaussian filter GF33 is executed. The Gaussian filter GF33 has a 3 × 3 pixel array as shown in the figure. The Gaussian filter GF33 is superposed on a predetermined position of the k-th preparation image Qk to perform a product-sum operation process, thereby performing the k-th operation. Layer image Pk (filtered image) is obtained. FIG. 15 is a plan view showing the k-th hierarchical image Pk obtained by the filtering process shown in FIG. This k-th hierarchical image Pk has a 10 × 10 pixel array as in the k-th preparation image Qk, and the pixel value of each pixel is obtained by a product-sum operation using the Gaussian filter GF33. Value.

For example, in the k-th hierarchical image Pk shown in FIG. 15, when attention is paid to a pixel surrounded by a thick frame (pixel in the fourth row and third column), a pixel value of 0.375 is given to the target pixel. . The pixel value is obtained by superimposing the illustrated Gaussian filter GF33 on the 3 × 3 pixel array (9 pixels centered on the pixel in the fourth row and the third column) surrounded by a thick frame in FIG. , The product of the pixel values of pixels superposed at the same position is obtained, and the product is obtained as the sum of nine products. Specifically, the pixel value 0.375 of the target pixel is “(1/16 × 0) + (2/16 × 0.25) + (1/16 × 0.5) + (2/16 × 0). ) + (4/16 × 0.5) + (2/16 × 1.0) + (1/16 × 0) + (2/16 × 0.25) + (1/16 × 0.5) ” Is obtained as a product-sum operation value. Such filter processing by product-sum operation is generally known as convolution operation processing for an image, and thus detailed description thereof is omitted here.

In the filter processing shown in FIG. 14, a convolution operation is performed using a Gaussian filter GF33 having a 3 × 3 pixel array as shown in FIG. 16A as the image processing filter. b) A convolution operation using a Laplacian filter LF33 having a 3 × 3 pixel array as shown in may be performed. In general, it is known that filter processing using a Gaussian filter gives an effect of blurring the contour of an image, and filter processing using a Laplacian filter gives an effect of enhancing the contour of an image. Regardless of which filter processing is employed, the k-th hierarchical image Pk having slightly different characteristics from the k-th prepared image Qk can be obtained, and thus includes a plurality of hierarchical images each having different characteristics. It is effective in creating an image pyramid.

Of course, the image processing filter used for the filter processing in step S33 is not limited to the Gaussian filter GF33 shown in FIG. 16 (a) and the Laplacian filter LF33 shown in FIG. 16 (b). Processing filters can be used. Further, the size of the image processing filter to be used is not limited to the 3 × 3 pixel array, and an image processing filter of an arbitrary size can be used. For example, a Gaussian filter GF55 having a 5 × 5 pixel array as shown in FIG. 17A or a Laplacian filter LF55 having a 5 × 5 pixel array as shown in FIG. 17B may be used. .

Thus, when the filtering process in step S33 in the procedure of FIG. 7 is completed, it is determined in step S34 whether or not the parameter k has reached a predetermined set value n. If k <n, the reduction in step S35 is performed. Processing is executed. This reduction processing is processing for creating an image having a smaller number of pixels than the target image based on the predetermined target image. In the case of the example shown here, the (k + 1) th preparation image Q (k + 1) is created by executing the reduction process on the kth hierarchical image Pk created by the filtering process of step S33. Processing is executed. Therefore, the preparation image Q (k + 1) is an image having a smaller size than the hierarchical image Pk (an image having a small number of vertical and horizontal pixels in the pixel array).

Such a reduction process for an image is also referred to as a “pooling process”, and as the reduction process performed in step S35, for example, an “average pooling process” can be employed. FIG. 18 is a plan view showing a procedure for creating an (k + 1) th preparation image Q (k + 1) as a reduced image by performing an average pooling process on the kth hierarchical image Pk. . Specifically, an average pooling process (reduction process) is performed on the hierarchical image Pk having the 4 × 4 pixel array shown in FIG. 18 (a) to obtain a 2 × 2 image as shown in FIG. 18 (b). A preparation image Q (k + 1) having a pixel array is created as a reduced image.

The average pooling process shown in FIG. 18 is a process of converting (reducing) four pixels having a 2 × 2 pixel array into one pixel, and an average value of pixel values of the original four pixels is expressed as follows: By using the pixel value of one pixel after conversion, a reduced image is created. For example, four pixels (pixels within a thick frame) having a 2 × 2 pixel arrangement arranged at the upper left of the hierarchical image Pk shown in FIG. 18A are shown in FIG. On (k + 1), it is converted (reduced) to one pixel indicated by a thick frame. The pixel value 0.5 of the thick frame pixel after this conversion (reduction) is an average value of the pixel values of the original four pixels.

On the other hand, FIG. 19 is a plan view showing a procedure for creating a (k + 1) th preparation image Q (k + 1) as a reduced image by performing a max pooling process on the kth hierarchical image Pk. It is. Specifically, by applying a max pooling process (reduction process) to the hierarchical image Pk having the 4 × 4 pixel array shown in FIG. 19A, the 2 × 2 as shown in FIG. A preparation image Q (k + 1) having a pixel array is created as a reduced image.

The maximum pooling process shown in FIG. 19 is a process for converting (reducing) four pixels having a 2 × 2 pixel array into one pixel, similar to the average pooling process shown in FIG. By using the maximum value of the pixel values of the four pixels as the pixel value of one pixel after conversion, a reduced image is created. For example, four pixels (pixels within a thick frame) having a 2 × 2 pixel array arranged at the upper left of the hierarchical image Pk shown in FIG. 19A are shown in FIG. On (k + 1), it is converted (reduced) to one pixel indicated by a thick frame. The pixel value 1.0 of the thick frame pixel after this conversion (reduction) is the maximum value of the pixel values of the original four pixels.

Each of the pooling processes shown in FIGS. 18 and 19 is a reduction process for converting four pixels having a 2 × 2 pixel array into a single pixel, but of course, having a 3 × 3 pixel array. It is also possible to perform a reduction process for converting nine pixels into a single pixel, and it is also possible to perform a reduction process for converting six pixels having a 3 × 2 pixel array into a single pixel. It is.

After all, the image pyramid creation unit 122 replaces the plurality of m adjacent pixels with a single pixel having an average value of the pixel values of the plurality of m adjacent pixels as a pixel value as the reduction processing in step S35. It is also possible to create a reduced image by executing the pooling process, and to replace a plurality of m adjacent pixels with a single pixel having the maximum pixel value of the plurality of m adjacent pixels as a pixel value. -It is also possible to create a reduced image by executing a pooling process. Of course, other reduction processing can be performed as the reduction processing in step S35. In short, a process that can create a small-sized preparation image Q (k + 1) by performing conversion that reduces the number of pixels on the hierarchical image Pk, in other words, “the number of pixels has decreased. As long as it is a process for creating a “reduced image”, any reduction process may be executed in step S35.

Thus, when the reduction process of step S35 is completed, the parameter k is increased by 1 in step S36, and the filter process of step S33 is executed again. Eventually, as described above, k = 1 and the first preparation image Q1 (original image) is filtered in step S33 to create the first hierarchical image P1, and then step S35. Thus, the second preparatory image Q2 is created by performing the reduction process on the hierarchical image P1, and is updated to k = 2 in step S36. In step S33, the filter for the second preparatory image Q2 is again performed. By performing the process, the second hierarchical image P2 is created.

Such an iterative procedure is repeatedly executed until it is determined in step S34 that k = n. Here, as the value of n, an appropriate value may be set in advance as the number of layers of the image pyramid (that is, the total number of layer images constituting the image pyramid). As the value of n is set larger, the number n of feature quantities extracted for one evaluation point E increases, so that more accurate simulation becomes possible, but the calculation burden increases. Further, as the reduction process in step S35 is repeated, the size of the image becomes smaller. Therefore, if the value of n is set too large, the reduction process in step S35 cannot be performed. Therefore, in practice, the value of n may be set appropriately in consideration of the size of the original image Q1 and the calculation burden.

Thus, when it is determined in step S34 that k = n, the processing by the image pyramid creation unit 122 is completed. At this time, as shown in FIG. 6, an image pyramid PP composed of a plurality of n hierarchical images P1 to Pn is created. Therefore, the process proceeds from step S34 to step S37, and a feature amount calculation process is executed.

FIG. 20 is a plan view showing a procedure (steps S33 to S36 in FIG. 7) for creating an image pyramid PP composed of n hierarchical images P1 to Pn in the image pyramid creation unit 122. The first preparation image Q1 shown in the upper left of the figure is an original image created with k = 1 in the original image creation processing in step S32. The area density map M1 shown in FIG. The pixel value is defined as follows. As described above, in step S33, the filter process is performed on the first preparation image Q1. Specifically, for example, a first hierarchical image P1 as shown in the upper right of FIG. 20 is created by a convolution operation using a Gaussian filter GF33 having a 3 × 3 pixel array. The size of the first hierarchical image P1 is the same as the size of the first preparation image Q1.

Subsequently, in the reduction process of step S35, a reduction process (for example, average pooling process) is performed on the first hierarchical image P1, and a second preparation image Q2 shown in the middle left of FIG. 20 is created. The size of the second preparation image Q2 is smaller than the size of the first hierarchical image P1. Subsequently, in step S36, the value of the parameter k is updated to 2, and the filtering process of step S33 is executed again. That is, the second hierarchical image P2 as shown in the middle right of FIG. 20 is created by the convolution operation using the Gaussian filter GF33 having a 3 × 3 pixel array. The size of the second hierarchical image P2 is the same as the size of the second preparation image Q2.

Then, the reduction process in step S35 is executed again. That is, reduction processing (for example, average pooling processing) is performed on the second hierarchical image P2, and a third preparation image Q3 shown on the lower left of FIG. 20 is created. The size of the third preparation image Q3 is smaller than the size of the second hierarchical image P2. Subsequently, in step S36, the value of the parameter k is updated to 3, and the filtering process of step S33 is executed again. That is, a third layer image P3 as shown in the lower right of FIG. 20 is created by a convolution operation using a Gaussian filter GF33 having a 3 × 3 pixel array. The size of the third layer image P3 is the same as the size of the third preparation image Q3.

Such processing is repeatedly executed until the parameter k = n, and finally, the n-th preparation image Qn and the n-th layer image are obtained. In this way, the image pyramid PP is constituted by n hierarchical images having different sizes from the first hierarchical image P1 to the nth hierarchical image Pn.

After all, in the case of the embodiment shown in the procedure of FIG. 7, the image pyramid creation unit 122 has a function of performing filter processing using a predetermined image processing filter on the original image Q1 or the reduced image Q (k + 1). By alternately executing the filter process and the reduction process, an image pyramid PP composed of a plurality of hierarchical images P1 to Pn is created.

More specifically, the image pyramid creation unit 122 uses the original image created by the original image creation unit 121 as the first preparation image Q1, and performs a filtering process on the kth preparation image Qk (where k is a natural number). The obtained image is the k-th hierarchical image Pk, and the image obtained by the reduction process for the k-th hierarchical image Pk is the (k + 1) -th prepared image Q (k + 1), and is filtered until the n-th hierarchical image Pn is obtained. By alternately executing the processing and the reduction processing, an image pyramid PP composed of a plurality of n hierarchical images including the first hierarchical image P1 to the nth hierarchical image Pn is created.

Since the image pyramid PP according to the present invention only needs to be composed of a plurality of hierarchical images having different sizes, the reduction process of step S35 is an essential process in the procedure shown in the flowchart of FIG. The filtering process in step S33 is not necessarily a necessary process. However, when the filter process is performed, the influence of the pixel values of the surrounding pixels can be applied to the pixel values of the individual pixels. For this reason, by adding filter processing, it is possible to create a plurality of hierarchical images rich in variations, and it is possible to extract feature quantities including more diverse information, resulting in more accurate results. Simulation becomes possible. Therefore, in practice, it is preferable to alternately perform the reduction process and the filter process as in the procedure shown in the flowchart of FIG.

<2.3 Processing Procedure by Feature Quantity Calculation Unit 123>
Next, a procedure of feature amount calculation processing by the feature amount calculation unit 123 will be described. As shown in step S37 of FIG. 7, the feature amount calculation unit 123 performs a process of calculating the feature amounts x1 to xn for each evaluation point E based on the hierarchical images P1 to Pn constituting the image pyramid PP. Here, the procedure for calculating the feature amounts x1 to xn will be specifically described.

FIG. 21 is a plan view showing a procedure for calculating feature amounts x1 to xn for a specific evaluation point E from the hierarchical images P1 to Pn in the feature amount calculation unit 123. FIG. Specifically, on the left side of FIGS. 21A to 21C, the original graphic pattern 10 is arranged in each pixel arrangement of the first hierarchical image P1, the second hierarchical image P2, and the third hierarchical image P3, respectively. A rectangle (indicated by a thick frame) is formed on the right side of FIGS. 21 (a) to 21 (c), and specific evaluation points are shown on the right side based on the hierarchical images P1, P2, and P3. The principle of calculating feature amounts x1, x2, and x3 for E is shown.

21 is a part of an image constituting each layer of the image pyramid PP. Actually, n hierarchical images from P1 to Pn are prepared and n sets of feature values x1 to xn are extracted. In FIG. 21, for convenience of explanation, three hierarchical images P1, A state in which three sets of feature values x1, x2, and x3 are extracted from P2 and P3 is shown.

Here, the first hierarchical image P1 is an image obtained by performing a filtering process on the original image Q1 (first preparation image). In the illustrated example, the first hierarchical image P1 has a 16 × 16 pixel array. is doing. In contrast, the second hierarchical image P2 is an image obtained by performing reduction processing and filtering processing on the first hierarchical image P1, and in the illustrated example, an 8 × 8 pixel array is formed. Have. The third hierarchical image P3 is an image obtained by performing reduction processing and filtering processing on the second hierarchical image P2, and has a 4 × 4 pixel array in the illustrated example. Yes.

In FIG. 21, since each of the hierarchical images P1, P2, and P3 is drawn so that the outline thereof becomes a square having the same size, the images are all the same size, but the pixel arrangement is 16 The image size is gradually reduced to x16, 8x8, and 4x4, and the image size is gradually reduced. However, in FIG. 21, the outer frame of each hierarchical image P1, P2, P3 is drawn as a square of the same size, so the size of the pixels gradually increases. In other words, the resolution of the image decreases in the order of the hierarchical images P1, P2, and P3, and gradually becomes a coarse image.

As described above, in the figure, the rectangle constituting the original figure pattern 10 is drawn with a thick frame. Since each of the hierarchical images P1, P2, and P3 is a raster image made up of a collection of pixels, the rectangular outline drawn with a thick frame in the figure is actually included as information on the outline itself. However, it is included as information on pixel values of individual pixels. However, in FIG. 21, for the convenience of explanation, the positions of the rectangles on the hierarchical images P1, P2, and P3 are indicated by bold lines. Here, a process of extracting feature amounts x1 to xn for a specific evaluation point E defined on the rectangular outline will be described.

As can be seen from FIGS. 21A to 21C, for each of the hierarchical images P1, P2, and P3, the rectangles indicated by the thick frames are arranged at the same relative position, and the specific evaluation point E is also at the same relative position. Placed in position. In the case of the embodiment shown here, the feature amount for one evaluation point E is calculated based on the pixel values of the neighboring pixels.

First, as shown in FIG. 21 (a), a feature quantity x1 for the evaluation point E is extracted based on the first hierarchical image P1. Specifically, the feature quantity calculation unit 123, as shown on the right side of FIG. 21A, four pixels (in the figure) located in the vicinity of the evaluation point E from the pixels constituting the first hierarchical image P1. Are extracted as the target pixel, and the feature amount x1 is calculated by the calculation using the pixel values of these four target pixels. Similarly, as shown on the right side of FIG. 21 (b), attention is paid to four pixels (hatched pixels in the figure) located in the vicinity of the evaluation point E from the pixels constituting the second hierarchical image P2. Extracted as pixels, the feature amount x2 is calculated by calculation using the pixel values of these four target pixels. Further, as shown on the right side of FIG. 21 (c), four pixels (pixels hatched in the figure) located in the vicinity of the evaluation point E from the pixels constituting the third hierarchical image P3 are focused pixels. And the feature amount x3 is calculated by calculation using the pixel values of these four target pixels.

If such processing is also performed for the fourth hierarchical image P4 to the nth hierarchical image Pn, n sets of feature quantities x1 to xn can be extracted for a specific evaluation point E. These n sets of feature amounts x1 to xn are parameters indicating the surrounding features of the same evaluation point E on the original graphic pattern 10, but the ranges affected by the original graphic pattern 10 are different from each other. . For example, the feature quantity x1 extracted from the first hierarchical image P1 becomes a value indicating the feature in the narrow area hatched in the diagram on the right side of FIG. 21 (a), but the second hierarchical image P2 The feature amount x2 extracted from FIG. 21B is a value indicating the feature in the wider area hatched in FIG. 21B, and the feature amount x3 extracted from the third hierarchical image P3 is The value on the right side of FIG. 21 (c) is a value indicating a characteristic in a wider area where hatching is performed.

As described above, the value of the process bias y for a certain evaluation point E is a value determined by merging phenomena having various scale feelings such as forward scattering and back scattering. Therefore, if various feature amounts x1 to xn are extracted from the feature amount x1 related to a very narrow range to the feature amount xn related to a wider range as the feature amount for the same evaluation point E, the influence range is extracted. It is possible to perform an accurate simulation in consideration of various phenomena different from each other. FIG. 21 shows a process of extracting n sets of feature amounts x1 to xn for one evaluation point E. Actually, each of a large number of evaluation points defined on the original graphic pattern 10 is shown. N sets of feature quantities x1 to xn are extracted by the same procedure.

As a method for calculating the feature amount x based on the pixel value of the pixel of interest near the evaluation point E, a simple method can be adopted in which the simple average of the pixel values of the pixel of interest is the feature amount x. For example, as shown in FIG. 21A, in order to extract the feature value x1 for the evaluation point E from the first hierarchical image P1, the pixel of interest (in the vicinity of the evaluation point E) indicated by hatching in the drawing is used. A simple average of the pixel values of (four pixels) may be the feature amount x1. However, in order to calculate a more accurate feature quantity, it is preferable to obtain a weighted average that takes into account the weight according to the distance between the evaluation point E and each pixel of interest, and to use the weighted average value as the feature quantity x1. .

FIG. 22 is a diagram showing a specific calculation method (calculation method using a weighted average value as a feature amount) used in the feature amount calculation procedure shown in FIG. Here, an example is shown in which four pixels A, B, C, and D are selected as the pixel of interest located in the vicinity of a specific evaluation point E. Specifically, the target pixels A, B, C, and D can be determined by performing a process of selecting a total of four pixels in order from the evaluation point E on the hierarchical image P to be processed. Therefore, for the pixel values of the four target pixels A, B, C, and D, a calculation may be performed using a weighted average considering the weight according to the distance between the evaluation point E and each pixel as the feature amount x.

In FIG. 22A, a mark x is displayed at the center point of each pixel of interest A, B, C, D, and a broken line connecting these marks x is drawn. The pixel size of each pixel of interest A, B, C, and D is u both vertically and horizontally, and the broken line is a dividing line that divides the pixel having the pixel size u in half. In the embodiment shown here, the distance between the evaluation point E and each pixel of interest A, B, C, D is the lateral distance between the evaluation point E and the center point of each pixel of interest A, B, C, D, and The vertical distance is adopted. Specifically, in the example shown in FIG. 22A, the target pixel A has a horizontal distance a and a vertical distance c, and the target pixel B has a horizontal distance b and a vertical distance c. Thus, the pixel of interest C has a horizontal distance a and a vertical distance d, and the pixel of interest D has a horizontal distance b and a vertical distance d.

In this case, if the feature value x of the evaluation point E is represented by the same reference symbols A, B, C, and D as the pixel values of the respective target pixels A, B, C, and D, and the pixel size u (pixel pitch) is 1, As shown in FIG. 22 (b),
G = (A · b + B · a) / 2
H = (C · b + D · a) / 2
x = (G · d + H · c) / 2
Can be obtained by the following calculation.

Of course, the method of calculating the feature amount x from the pixel values of the four target pixels A, B, C, and D is not limited to the method illustrated in FIG. Various other calculation methods can be employed as long as the feature amount x reflecting the pixel value can be calculated. In the calculation methods illustrated in FIGS. 21 and 22, four pixels located in the vicinity of the evaluation point E are selected as the target pixels. However, the number of target pixels used for calculating the feature amount x is as follows. The number is not limited to four. For example, nine pixels constituting a 3 × 3 pixel array located in the vicinity of the evaluation point E are selected as the target pixels, and the pixel values of these nine target pixels are set according to the distance from the evaluation point E. It is also possible to obtain a weighted average in consideration of the weight and use this as the feature quantity x for the evaluation point E.

In general terms, when calculating the feature value x for a specific evaluation point E on the specific hierarchical image P, the feature value calculating unit 123 calculates the specific evaluation from the pixels constituting the specific hierarchical image P. A total of j pixels are extracted as the target pixel in the order close to the point E, and the weight of the extracted pixel values of the j target pixels in consideration of the weight according to the distance between the specific evaluation point E and each target pixel An arithmetic operation for obtaining an average is performed, and the obtained weighted average value can be used as the feature amount x.

<2.4 Modification of Feature Extraction Process>
Here, some modified examples of the procedure of the feature amount extraction processing described so far will be described.

(1) Modified Example Using Difference Image Dk as Hierarchical Image In §2.2, the processing of steps S33 to S36 shown in the flowchart of FIG. 7 is exemplified as the image pyramid PP creation processing procedure by the image pyramid creation unit 122. In this process, starting from the original image Q1 (first preparation image), the filtering process and the reduction process are executed alternately, and n images (by the procedure shown in FIG. (Hereinafter referred to as “filtered image”) is used as it is as the hierarchical images P1 to Pn to create the image pyramid PP.

On the other hand, the modification described here is based on the processing of steps S33 to S36 shown in the flowchart of FIG. 7, and further, when the filtering processing of step S33 is completed, the k-th obtained by the filtering processing. The difference calculation “Pk−Qk” is performed by subtracting the k-th preparation image Qk from the filtered image Pk (the image called the k-th layer image Pk in §2.2) to obtain the k-th difference image Dk. The required processing is added. In other words, in the modification described here, the processing of steps S33 to S36 shown in the flowchart of FIG. 7 is executed as it is, but furthermore, from the kth filtered image Pk to the kth prepared image Qk. The difference calculation “Pk−Qk” for subtracting is reduced.

Here, the difference calculation “Pk−Qk” defines pixels arranged at the same position on the pixel array for the k-th filtered image Pk and the k-th prepared image Qk as corresponding pixels. This is a process for subtracting the pixel value of the corresponding pixel on the image Qk from the pixel value of each pixel to obtain a difference, and obtaining a difference image Dk composed of a new pixel aggregate with the obtained difference as the pixel value.

FIG. 23 is a plan view showing a procedure for creating an image pyramid PD composed of n kinds of difference images D1 to Dn by such a difference calculation “Pk−Qk”. Here, the first hierarchical image D1 shown on the upper right side is a difference image obtained by the difference calculation “P1-Q1”, and specifically, the first filtered image P1 ( In FIG. 20, the difference is calculated by subtracting the first preparation image Q1 shown on the upper left side (referred to as the first hierarchical image P1) (subtraction of pixel values of pixels at corresponding positions).

Similarly, the second hierarchical image D2 shown on the right side of the middle stage in FIG. 23 is a difference image obtained by the difference calculation “P2-Q2”. Specifically, the second filter processing shown on the right side of the middle stage in FIG. The difference is calculated by subtracting the second preparation image Q2 shown on the left side of the middle stage from the image P2 (referred to as the second hierarchical image P2 in FIG. 20). Further, the third hierarchical image D3 shown on the lower right side of FIG. 23 is a difference image obtained by the difference calculation “P3-Q3”. Specifically, the third filtered image shown on the lower right side of FIG. The difference is calculated by subtracting the third preparation image Q3 shown on the left side of the lower stage from P3 (referred to as the third hierarchical image P3 in FIG. 20). Thereafter, the same difference calculation is performed, and finally, the difference image obtained by the difference calculation “Pn−Qn” is the n-th layer image Dn.

In the embodiment described in §2.2, as shown in FIG. 20, the image pyramid PP is generated by the first hierarchical image (first filtered image) P1 to the nth hierarchical image (nth filtered image) Pn. However, in the modification described here, as shown in FIG. 23, an image pyramid is formed by the first layer image (first difference image) D1 to n-th layer image (n-th difference image) Dn. The PD is configured.

As described above, in order to implement the modification example described here, a difference calculation procedure may be added to the procedure of the example described in §2.2. Specifically, the image pyramid creation unit 122 uses the original image created by the original image creation unit 121 as the first preparation image Q1, and obtains it by filtering the kth preparation image Qk (where k is a natural number). The difference image Dk between the filtered image Pk and the kth preparation image Qk is obtained, the difference image Dk is set as the kth hierarchical image Dk, and the image obtained by the reduction processing on the kth filtered image Pk is the ( As the preparation image Q (k + 1) of (k + 1), the first hierarchical image D1 to the nth hierarchical image Dn are included by alternately executing the filtering process and the reduction process until the nth hierarchical image Dn is obtained. An image pyramid PD composed of a plurality of n hierarchical images may be created.

After all, in this modification, the k-th layer image Dk constituting the k-th layer of the image pyramid PD is an image after the filter process (filtered image Pk) and an image before the filter process (prepared image Qk). This is a difference image, and the pixel value of each pixel corresponds to the difference between the pixel values before and after the filtering process. That is, the k-th hierarchical image Pk in the embodiment described in §2.2 shows the image after the filtering process, whereas the k-th hierarchical image Dk in the modification described here is a filter. It shows the difference caused by the process. As described above, the image pyramid PP created in the embodiment described in §2.2 and the image pyramid PD created in the modification described here are significantly different in the meaning of the hierarchical image as a component. As a matter of course, there is no change in the points that are images showing some characteristics about the evaluation point E. Therefore, it is possible to extract feature amounts from each of the hierarchical images D1 to Dn created in the modified example described here, and the feature amount calculating unit 123 in this modified example has the hierarchical images D1 to Dn. Thus, processing for extracting the feature amounts x1 to xn is performed.

(2) Modified Example of Creating Plural Image Pyramids Using Plural Algorithms In the embodiment described in §2.2, as shown in FIG. 20, the original image (first prepared image Q1) is filtered. By alternately executing the reduction processing and the reduction processing, the respective filtered images P1 to Pn are obtained, and the image pyramid PP is created by the algorithm that uses these filtered images P1 to Pn as n hierarchical images P1 to Pn as they are. Yes. On the other hand, in the modified example in which the difference image Dk described in §2.4 (1) is a hierarchical image, as shown in FIG. 23, each difference operation between the filtered image Pk and the preparation image Qk is performed. Difference pyramids D1 to Dn are obtained, and an image pyramid PD is created by an algorithm that uses the difference images D1 to Dn as n hierarchical images D1 to Dn.

Further, there are various types of image filters used for the filter processing as shown in FIGS. 16 and 17, and there are various types of reduction processing (pooling processing) methods as shown in FIGS. is there. Thus, even if the starting point is the same original image (first preparation image Q1), the contents of the hierarchical images constituting the obtained image pyramid differ depending on the algorithm employed. Moreover, in order to execute the present invention, the number of image pyramids to be used is not necessarily one, and a plurality of image pyramids can be created by a plurality of algorithms, and feature amounts can be extracted from individual image pyramids. Is possible.

That is, the image pyramid creation unit 122 has a function of performing image pyramid creation processing based on a plurality of different algorithms for one original image (first preparation image Q1), thereby creating a plurality of image pyramids. You may be made to do. In this case, the feature amount calculation unit 123, for each hierarchical image constituting each of the plurality of image pyramids, based on the pixel value of a pixel (a pixel located around the evaluation point) corresponding to the evaluation point position. What is necessary is just to perform the process which calculates a feature-value.

For example, when the image pyramid creation unit 122 performs the image pyramid creation process, if the algorithm of the embodiment described in §2.2 is adopted as the main algorithm, as shown in FIG. A main image pyramid PP composed of P1 to Pn (filtered images) can be created, and as a sub-algorithm, a modified algorithm using the difference image Dk described in §2.4 (1) ２ as a hierarchical image is used. If it is adopted, as shown in FIG. 23, a sub-image pyramid PD composed of n sub-layer images D1 to Dn (difference images) can be created. Therefore, if the image pyramid creation unit 122 performs image pyramid creation processing using the above two algorithms, it is possible to create two types of image pyramids, the main image pyramid PP and the sub image pyramid PD. .

Here, the main image pyramid PP created by the filter processing using the Gaussian filter illustrated in FIG. 14 can be called a Gaussian pyramid. Further, the sub-image pyramid PD configured using the difference image can be called a Laplacian pyramid. Since the Gaussian pyramid and the Laplacian pyramid are image pyramids that are greatly different from each other, they are adopted as the main image pyramid PP and the sub image pyramid PD, and feature amounts are extracted using two image pyramids. This makes it possible to extract feature values with more diversity.

On the other hand, the feature amount calculation unit 123 sets the pixel values of the pixels in the vicinity of the evaluation point E for the main layer images P1 to Pn constituting the main image pyramid PP and the sub layer images D1 to Dn constituting the sub image pyramid PD, respectively. If the process of calculating the feature amount is performed based on the feature amounts, the feature amounts xp1 to xpn calculated from the main layer images P1 to Pn and the feature amounts xd1 to xdn calculated from the sub layer images D1 to Dn are obtained. . That is, a total of 2n feature amounts are extracted for one evaluation point E. In this case, since the feature amount for one evaluation point E is given to the estimation calculation unit 132 as a 2n-dimensional vector, more accurate estimation calculation can be performed.

Eventually, in order to implement the above-described modification, the image pyramid creation unit 122 sets the original image created by the original image creation unit 121 as the first preparation image Q1, and the kth preparation image Qk (where k is The image obtained by the filtering process for (natural number) is the k-th main layer image Pk, the image obtained by the reduction process for the k-th main layer image Pk is the (k + 1) th preparation image Q (k + 1), and the nth By alternately executing the filtering process and the reduction process until the main hierarchy image Pn is obtained, a main image pyramid including a plurality of n hierarchy images including the first main hierarchy image P1 to the nth main hierarchy image Pn. Further, a difference image Dk between the k-th main hierarchy image Pk and the k-th preparation image Qk is obtained, and the difference image Dk is set as the k-th sub-layer image Dk. It is sufficient to create a sub image pyramid consisting of hierarchy images of a plurality n as including a sub-hierarchy image Dn image D1 ~ No. n.

The feature amount calculation unit 123 may calculate the feature amount based on the pixel values of the pixels near the evaluation point E for each hierarchical image constituting the main image pyramid PP and the sub image pyramid PD. . If it does so, it will become possible to extract a 2n-dimensional vector as a feature-value about one evaluation point E, and it will become possible to perform a more exact estimation calculation.

(3) Modified example of creating multiple image pyramids by creating multiple image originals In §2.4 (2) above, multiple algorithms are applied to the same original image. A modification of creating multiple image pyramids was described. Here, a modified example in which a plurality of original images are created to create a plurality of image pyramids will be described.

In the figure pattern shape estimation apparatus 100 ′ according to the present invention, as shown in FIG. 1, the original image creation unit 121 performs a process of creating an original image based on the given original figure pattern 10. As the original image created here, as described in §2.1, the area density map M1 (FIG. 10), the edge length density map M2 (FIG. 11), the dose density map M3 (FIG. 13), etc. Various forms of images can be employed.

In other words, the original image creation unit 121 can employ various creation algorithms when creating an original image based on the original graphic pattern 10, and the contents differ depending on which algorithm is employed. Various original images can be created. For example, the area density map M1 shown in FIG. 10, the edge length density map M2 shown in FIG. 11, and the dose density map M3 shown in FIG. 13 are all images created based on the same original figure pattern 10. The pixel values of the individual pixels are different from each other, and each has a different image. Alternatively, based on the same original figure pattern 10, a plurality of density maps (in other words, a plurality of maps having different resolutions) having different pixel sizes (dimensions of one pixel) and map sizes (numbers of pixels arranged vertically and horizontally) are prepared. Then, a plurality of image pyramids may be created using each of the plurality of density maps as an original image. Of course, theoretically, it is ideal to use a density map with a small pixel size and a large map size (high-resolution density map) as the original image. However, since the memory of a computer is limited, it is practically used. Preferably, a plurality of density maps having different pixel sizes and map sizes are used as the original image.

Therefore, the original image creation unit 121 has a function of performing original image creation processing based on a plurality of different algorithms to create a plurality of types of original images, and the image pyramid creation unit 122 has a plurality of types of original images. A plurality of image pyramids can be created by providing a function of performing processing for creating separate image pyramids based on images. Then, if the feature amount calculation unit 123 has a function of calculating the feature amount based on the pixel values of the pixels in the vicinity of the evaluation point E for each hierarchical image constituting each of the plurality of image pyramids, It is possible to extract a feature amount composed of a higher-dimensional vector, and it is possible to perform a more accurate estimation calculation.

For example, the original image creation unit 121 performs a first original image composed of the area density map M1 shown in FIG. 10, a second original image composed of the edge length density map M2 shown in FIG. 11, and a dose density shown in FIG. If the function of creating the third original image composed of the map M3 is provided, the image pyramid creation unit 122 creates three sets of independent image pyramids based on the three original images. Can do. All of the image pyramids are image pyramids created based on the same original graphic pattern 10. The feature amount calculation unit 123 can perform a process of calculating a feature amount based on the pixel values of pixels in the vicinity of the evaluation point E for each hierarchical image constituting each of the three image pyramids. If n feature amounts x1 to xn are extracted from one image pyramid, a total of 3n feature amounts can be extracted for the same evaluation point E. That is, since a 3n-dimensional vector can be given as a feature amount for one evaluation point E, it is possible to perform more accurate estimation calculation.

Of course, it is also possible to combine the above-described modification of §2.4 (2) に with the modification described here. As described in §2.4 (2) IV, if the image pyramid creation unit 122 employs two different types of algorithms when creating the image pyramid, the main image pyramid PP and the sub-image pyramid PD An image pyramid can be created. Therefore, if two image pyramids of the main image pyramid PP and the sub image pyramid PD are created based on each of the above three original images, a total of six image pyramids based on the same original graphic pattern 10 are created. Therefore, a 6n-dimensional vector can be given as a feature amount for one evaluation point E.

<<< §3. Bias estimation unit details >>
Here, a detailed processing operation of the bias estimation unit 130 will be described. As shown in FIG. 1, the bias estimation unit 130 includes a feature amount input unit 131 and an estimation calculation unit 132, and has a function of executing the process bias estimation process in step S4 in the flowchart of FIG. . In the case of the embodiment shown in FIG. 6, for one evaluation point E, feature quantities (n-dimensional vectors) x1 to xn are input to the feature quantity input unit 131, and an estimation calculation by the estimation calculation unit 132 is executed. An estimate y of the process bias for E is determined. In the embodiment shown in FIG. 6, a neural network is used as the estimation calculation unit 132. Therefore, the detailed configuration and operation of this neural network will be described below.

<3.1 Estimate calculation by neural network>
In recent years, neural networks have attracted attention as a technology that forms the basis of artificial intelligence, and are used in various fields including image processing. This neural network is a computer-like structure that mimics the structure of a biological brain, and is composed of neurons and edges that connect them.

FIG. 24 is a block diagram showing an embodiment using a neural network as the estimation calculation unit 132 shown in FIG. As shown in the figure, an input layer, an intermediate layer (hidden layer), and an output layer are defined in the neural network, and predetermined information processing is performed on the information given to the input layer in the intermediate layer (hidden layer). The result is output to the output layer. In the case of the present invention, as shown in the figure, feature quantities x1 to xn for one evaluation point E are given to the input layer as n-dimensional vectors, and an estimated value of the process bias for the evaluation point E is given to the output layer. y is output. Here, the estimated value y of the process bias is an estimated value indicating the amount of deviation in the normal direction of the contour line for the evaluation point E located on the contour line of the predetermined graphic as described in §1. .

In the case of the embodiment shown in FIG. 24, the estimation calculation unit 132 has a neural network having the feature amounts x1 to xn input by the feature amount input unit 131 as input layers and the process bias estimate y as an output layer. The intermediate layer of this neural network is composed of N hidden layers, which are a first hidden layer, a second hidden layer,. These hidden layers have a large number of neurons (nodes), and edges connecting these neurons are defined.

The feature values x1 to xn given to the input layer are transmitted as signals to each neuron via the edge. Finally, a signal corresponding to the estimated value y of the process bias is output from the output layer. A signal in the neural network is transmitted from one hidden layer neuron to the next hidden layer neuron through computation via an edge. The calculation via the edge is performed using learning information L (specifically, parameters W and b described later) obtained in the learning stage.

FIG. 25 is a diagram showing a specific calculation process executed by the neural network shown in FIG. The part shown by the bold line in the figure shows the first hidden layer, the second hidden layer,..., The Nth hidden layer, and each circle in each hidden layer is a neuron (node) and connects each circle. Lines indicate edges. As described above, feature values x1 to xn for one evaluation point E are given to the input layer as n-dimensional vectors, and an estimated value y of the process bias for the evaluation point E is scalar in the output layer. It is output as a value (a dimension value indicating the amount of deviation in the normal direction of the contour line).

In the case of the illustrated example, the first hidden layer is an M (1) -dimensional layer, and is composed of a total of M (1) neurons h (1,1) to h (1, M (1)). The second hidden layer is an M (2) -dimensional layer and is configured by a total of M (2) neurons h (2,1) to h (2, M (2)), and the Nth hidden layer is M (N ) Dimension layer, and is composed of a total of M (N) neurons h (N, 1) to h (N, M (N)).

Here, the calculation values of the signals transmitted to the neurons h (1,1) to h (1, M (1)) of the first hidden layer are respectively expressed as the calculation values h (1,1) using the same symbols. .., H (1, M (1)), the values of these calculated values h (1, 1) to h (1, M (1)) are given by the matrix equation shown in the upper part of FIG. It is done. As the function f (ξ) on the right side of this equation, the sigmoid function shown in FIG. 27A, the normalized linear function ReLU shown in FIG. 27B, the normalized linear function Leakey 線形 ReLU shown in FIG. The activation function can be used.

Further, ξ described as an argument of the function f (ξ) is a matrix [W] and a matrix [x1 to xn] (features given to the input layer as n-dimensional vectors, as shown in the middle of FIG. ) And the product of the matrix [b]. Here, the contents of the matrix [W] and the matrix [b] are as shown in the lower part of FIG. 26, and each component of the matrix (weight parameter W (u, v) and bias parameter b (u, v)). Is learning information L obtained by a learning stage described later. That is, the values of the individual components (parameters W (u, v), b (u, v)) constituting the matrix [W] and the matrix [b] are given as learning information L, and are shown in FIG. By using the calculated equation, the calculation values h (1,1) to h (1, M (1)) of the first hidden layer are calculated based on the feature values x1 to xn given to the input layer. Can do.

On the other hand, FIG. 28 is a diagram showing an arithmetic expression for obtaining each value of the second hidden layer to the Nth hidden layer in the diagram shown in FIG. Specifically, the same sign is used for the operation value of the signal transmitted to the neurons (i + 1, 1) to h (i + 1, M (i + 1)) of the (i + 1) th hidden layer (1 ≦ i ≦ N). Thus, if expressed as operation values h (i + 1,1) to h (i + 1, M (i + 1)), the values of these operation values h (i + 1,1) to h (i + 1, M (i + 1)) are It is given by the matrix equation shown in the upper part of FIG. As the function f (ξ) on the right side of this equation, as described above, each function shown in FIG. 27 can be used.

Also, ξ described as an argument of the function f (ξ) is a matrix [W] and a matrix [h (i, 1) to h (i, M (i))] as shown in the middle part of FIG. It is a value obtained by adding the matrix [b] to the product of (the calculated value of the neuron h (i, 1) to h (i, M (i)) of the previous i-th hidden layer). Here, the contents of the matrix [W] and the matrix [b] are as shown in the lower part of FIG. 28, and the individual components of the matrix (parameters W (u, v), b (u, v)) are This is learning information L obtained by a learning stage described later.

Again, the values of the individual components (parameters W (u, v), b (u, v)) constituting the matrix [W] and the matrix [b] are given as learning information L, and are shown in FIG. Using the arithmetic expression shown, based on the arithmetic values [h (i, 1) to h (i, M (i))] obtained in the i-th hidden layer, the arithmetic values in the (i + 1) -th hidden layer h (i + 1, 1) to h (i + 1, M (i + 1)) can be calculated. Therefore, each value of the second hidden layer to the Nth hidden layer in the diagram shown in FIG. 25 can be obtained sequentially based on the arithmetic expression shown in FIG.

FIG. 29 is a diagram showing an arithmetic expression for obtaining the output layer value y in the diagram shown in FIG. Specifically, the output value y (estimated value of process bias for the evaluation point E: scalar value) is given by the matrix equation shown in the upper part of FIG. That is, the output value y is expressed as matrix [W] and matrix [h (N, 1) to h (N, M (N))] (Nth hidden layer neurons h (N, 1) to h (N, M (N)) and the scalar value b (N + 1). Here, the contents of the matrix [W] are as shown in the lower part of FIG. 29, and the individual components (parameters W (u, v)) and the scalar value b (N + 1) of the matrix [W] are also described later. This is the learning information L obtained by the learning stage.

In this way, the values of the first hidden layer in the diagram shown in FIG. 25 are the parameters W (1, v), b prepared in advance as learning information L for the feature amounts x1 to xn given as the input layers. (1, v) can be obtained by applying each parameter of the second hidden layer to each value of the first hidden layer using parameters W (2, v), b (2, v) can be obtained by applying ..., each value of the Nth hidden layer is prepared in advance as learning information L in each value of the (N-1) th hidden layer. The values of the output layer y are prepared in advance as learning information L for each value of the Nth hidden layer. Parameter Parameter W (N + 1, v), b (N + 1) It can be obtained by. Specific arithmetic expressions are as shown in FIGS.

In addition, as described in §2.4 (2) and (3), when adopting a modified example of creating a plurality of image pyramids, the feature value given as the input layer is an n-dimensional vector ( x1 to xn), but a vector of V · n dimensions (V is the total number of image pyramids), but the numerical value of the input layer in the diagram shown in FIG. There is no change in the basic configuration and operation.

The calculation for obtaining the estimated value y of the process bias for a certain evaluation point E has been described above using the neural network shown in FIG. 25. In practice, however, the calculation is performed on the outline of the figure included in the original figure pattern 10. The same calculation is performed for a large number of defined evaluation points, and an estimated value y of the process bias is obtained for each evaluation point. In the figure pattern shape correction apparatus 100 shown in FIG. 1, the pattern correction unit 140 corrects the pattern shape based on the estimated value y of the process bias for each evaluation point thus obtained (step S5 in FIG. 4). Will be executed.

<3.2 Learning stage of neural network>
As described above, in the case of the embodiment shown in FIG. 24, the estimation calculation unit 132 is configured by a neural network, and uses the learning information L set in advance to calculate the signal value transmitted to each neuron. Will do. Here, the substance of the learning information L is the parameters W (u, v), b () described as the components of the matrices [W], [b] in the lower part of FIG. 26, the lower part of FIG. 28, and the lower part of FIG. u, v) and the like. Therefore, in order to construct such a neural network, it is necessary to obtain learning information L by a learning stage executed in advance.

That is, the neural network included in the estimation calculation unit 132 includes dimension values obtained by actual dimension measurement of the actual figure pattern 20 actually formed on the actual substrate S by a lithography process using a large number of test pattern figures. Process bias estimation processing is performed using, as learning information L, parameters W (u, v), b (u, v), and the like obtained in the learning stage using the feature amounts obtained from each test pattern figure. become. Such a process in the learning stage of the neural network is a known technique, but here, an outline of a process suitable for the learning stage of the neural network used in the present invention will be briefly described.

FIG. 30 is a flowchart showing a learning stage procedure for obtaining learning information L used by the neural network shown in FIG. First, in step S81, a test pattern graphic creation process is executed. Here, the test pattern figure corresponds to, for example, the original figure pattern 10 as shown in FIG. 2A, and a simple figure such as a rectangle or an L-shaped figure is usually used. Actually, thousands of test pattern figures having different sizes and shapes are created.

Subsequently, in step S82, an evaluation point E is set on each test pattern figure. Specifically, a process of defining a large number of evaluation points E at predetermined intervals on the contour lines of individual test pattern figures may be performed. In step S83, a feature amount is extracted for each evaluation point E. The feature quantity extraction process in step S83 is the same as the process described in §2, and is executed by a unit having a function equivalent to that of the feature quantity extraction unit 120. According to the procedure described in §2, the feature quantities x1 to xn are extracted for each evaluation point E.

The estimation calculation unit learning process in step S84 is a process of determining learning information L (that is, parameters W (u, v), b (u, v), etc.) using the feature amount extracted in step S83. is there. In order to execute this learning process, actual dimensions obtained by an actual lithography process are required. Therefore, in step S85, the lithography process is actually executed based on the test pattern graphic created in step S81, and the actual substrate S is created. In step S86, the actual dimension of each figure is measured for the actual figure pattern formed on the actual substrate S. This measurement result is used for the learning process in step S84.

As described above, the learning stage process shown in FIG. 30 includes a process executed on the computer composed of steps S81 to S84 (a process executed by the computer program) and a process executed on the actual substrate composed of steps S85 and S86. And composed of In the estimation calculation unit learning process in step S84, learning information L used for the neural network is determined based on the feature amounts x1 to xn obtained by the processing on the computer and the actual dimensions measured on the actual board. It will be processing.

FIG. 31 is a flowchart showing a detailed procedure of learning of the estimation calculation unit in step S84 in the flowchart shown in FIG. First, in step S841, the design position and feature amount of each evaluation point are input. Here, the design position of the evaluation point is a position on the test pattern figure of the evaluation point set in step S82, and the feature amount of the evaluation point is the feature amount x1 to xn extracted in step S83. Subsequently, in step S842, the actual position of each evaluation point is input. Here, the actual position of the evaluation point is determined based on the actual dimension of each figure on the actual substrate S actually measured in step S86. In step S843, the actual bias of each evaluation point is calculated. This actual bias corresponds to the amount of deviation between the design position of the evaluation point input in step S841 and the actual position of the evaluation point input in step S842.

For example, when a rectangle such as the original graphic pattern 10 shown in FIG. 3 (a) is created as a test pattern graphic in step S81, evaluation points E11, E12, E13, etc. are formed on the outline of the rectangle in step S82. In step S83, feature amounts x1 to xn are extracted for each of the evaluation points E11, E12, and E13. The position and feature amount of each evaluation point E11, E12, E13 are input in step S841.

On the other hand, the actual figure pattern 20 as shown in FIG. 3B, for example, is formed on the actual substrate S by the lithography process in step S85, and the actual figure pattern 20 is formed by measuring the actual dimension in step S86. The actual dimensions are measured for each side of the rectangle. By this measurement, the actual positions E21, E22, and E23 of the evaluation points are determined as the points where the evaluation points E11, E12, and E13 are moved in the normal direction of the contour line, respectively. The actual positions E21, E22, E23 of each evaluation point are input in step S842.

Therefore, in step S843, as shown in FIG. 3B, the actual bias y11, y12, y13 is calculated as the difference between the design position of each evaluation point E11, E12, E13 and the actual position E21, E22, E23. The Actually, for example, the difference “b−” between the horizontal width b of the rectangle forming the actual graphic pattern 20 shown in FIG. 3B and the rectangular horizontal width a forming the original graphic pattern 10 shown in FIG. The actual bias may be determined by obtaining a value y obtained by dividing “a” by 2. Of course, in practice, test pattern figures having a scale of several thousand are created, and a large number of evaluation points are set on the contour lines of each figure. Therefore, the procedure of steps S841 to S843 is a huge number of evaluation points. Will be executed for each. Here, focusing on one evaluation point E, for the evaluation point E, a combination of the feature amounts x1 to xn and the actual bias y is prepared as a learning material.

Subsequently, in step S844, the parameters W and b are set to initial values. Here, the parameters W and b are the parameters W (u, v) and b (u described as the components of the matrices [W] and [b] in the lower part of FIG. 26, the lower part of FIG. 28, and the lower part of FIG. , V) and the like, and becomes a value constituting the learning information L. As an initial value, a random value may be given by a random number. In other words, at the initial stage before learning, the parameters W and b that constitute the learning information L have frank values.

Each of the subsequent steps S845 to S848 is an actual learning process, and by performing this learning process, the parameters W and b that were initially set to frank values are gradually updated. Eventually, the value is corrected to an accurate value that sufficiently functions as the learning information L. First, in step S845, an operation for estimating the process bias y from the feature amounts x1 to xn is executed.

Specifically, a neural network as shown in FIG. 24 is prepared. Of course, at this stage, random numbers are given as initial values to the parameters W and b constituting the learning information L, and this neural network cannot perform a normal function as the estimation calculation unit 132. Is something. The feature values x1 to xn input in step S841 are given to the input layer of this incomplete neural network, the calculation using the learning information L consisting of incomplete values is performed, and the estimated value y of the process bias is output as the output layer. calculate. Of course, the estimated value y of the process bias obtained initially is far from the observed actual bias.

Therefore, in step S846, a residual with respect to the actual bias at that time is calculated. That is, a difference between the estimated value y of the process bias obtained in step S845 and the calculated actual bias value obtained in step S843 is obtained, and this difference is set as a residual for the evaluation point E. If this residual is less than or equal to a predetermined tolerance, the learning information L at that time (that is, parameters W (u, v), b (u, v), etc.) is sufficiently practical learning information. Therefore, the learning stage can be completed.

Step S847 is a procedure for determining whether or not the learning stage can be completed. Actually, since a residual is obtained for each of a large number of evaluation points, in practice, for example, if the amount of improvement in the residual sum of squares is below a specified value, a determination is made to end learning. A determination method may be adopted. If it is not determined that the learning has ended, the parameters W (u, v), b (u, v), etc. are updated in step S848. Specifically, updating is performed to increase or decrease the values of the parameters W (u, v), b (u, v), etc. by a predetermined amount so that the effect of reducing the residual occurs. As for the specific update method, methods based on various algorithms are known as learning methods in neural networks, so the explanation is omitted here, but the basic policy is to evaluate the evaluation points of many test pattern figures. An algorithm is employed that comprehensively considers the residuals and performs a total adjustment such that each residual is reduced overall.

Thus, the steps S845 to S848 are repeatedly executed until a positive determination is made in step S847. As a result, the values of the parameters W (u, v), b (u, v), etc. constituting the learning information L are gradually corrected in the direction of decreasing the residual, and finally in step S847. A positive determination is made and the learning phase ends. The learning information L (parameters W (u, v), b (u, v), etc.) obtained at the learning end stage is information suitable for obtaining an estimated value y of the process bias close to the actual bias in the output layer. It has become. Therefore, the neural network including the learning information L obtained at the learning end stage functions as the estimation calculation unit 132 in the present invention.

<<< §4. Figure pattern shape estimation method >>
The present invention has been described as the figure pattern shape estimation apparatus 100 ′ or the figure pattern shape correction apparatus 100 having the structure shown in FIG. Here, a brief description will be given of the present invention as a method invention called a figure pattern shape estimation method.

When the present invention is grasped as an invention of a figure pattern shape estimation method, the method estimates the shape of an actual figure pattern formed on an actual substrate by simulating a lithography process using the original figure pattern. It will be a method. Then, in this method, the computer inputs the original graphic pattern input stage in which the original graphic pattern 10 including the contour line information indicating the boundary between the inside and the outside of the graphic is input (the pattern created in step S1 in FIG. 4 is input). And an evaluation point setting step (step S2 in FIG. 4) in which the computer sets an evaluation point E at a predetermined position on the contour line of the input graphic, and each evaluation for the original graphic pattern 10 input by the computer. A feature amount extraction stage (step S3 in FIG. 4) for extracting feature amounts x1 to xn indicating features around the point E, and the original figure of each evaluation point E based on the extracted feature amounts x1 to xn A process bias estimation step (step S4 in FIG. 4) for estimating a process bias y indicating the amount of deviation between the position on the pattern 10 and the position on the actual graphic pattern 20; Constructed.

Here, in the feature amount extraction stage (step S3 in FIG. 4), based on the original figure pattern 10, an original image creation stage (see FIG. 4) that creates an original image Q1 composed of a collection of pixels U each having a predetermined pixel value. 7 and step S32) and image pyramid creation processing including reduction processing (step S35 in FIG. 7) for creating a reduced image Qk (preparation image) based on the original image Q1. An image pyramid creation stage (steps S33 to S35 in FIG. 7) for creating an image pyramid PP composed of the hierarchical images P1 to Pn, and each evaluation point E for each of the hierarchical images P1 to Pn constituting the created image pyramid PP. And a feature amount calculating step (step S37 in FIG. 7) for calculating feature amounts x1 to xn based on pixel values of pixels in the vicinity of.

Here, in the process bias estimation stage (step S4 in FIG. 4), the estimated values corresponding to the feature quantities x1 to xn for the evaluation point E are calculated based on the learning information L obtained in the learning stage performed in advance. And an estimation calculation step of outputting the calculated estimated value as the estimated value y of the process bias for the evaluation point E.

When the feature amount extraction unit 120 described in §2 is used, a filter processing stage that performs a filter process using a predetermined image processing filter on the original image Q1 or the reduced image Qk in the image pyramid creation stage. By alternately executing (step S33 in FIG. 7) and a reduction processing stage (step S35 in FIG. 7) for performing reduction processing on the image Pk after the filter processing, a plurality of hierarchical images P1 to Pn are executed. An image pyramid PP consisting of can be created.

Specifically, in the procedure described in §2.2, images in which the filtered image (filtered image Pk obtained in step S33 in FIG. 7) is set as hierarchical images P1 to Pn at the image pyramid creation stage. A pyramid PP has been created. On the other hand, in the procedure of the modified example described in §2.4 (1) IV, at the image pyramid creation stage, the image after filtering (filtered image Pk) and the image before filtering (prepared image Qk) Difference image Dk is created, and an image pyramid PD is created with the created difference images as hierarchical images D1 to Dn.

<<< §5. Additional embodiments of the invention >>>
So far, in §1 to §4, the figure pattern shape estimation apparatus and shape correction apparatus according to the basic embodiment of the present invention have been described, but here, still another embodiment of the present invention will be described. For convenience, the embodiments described in §5 are referred to as “additional embodiments of the present invention”.

<5.1 Basic Configuration and Basic Operation of Additional Embodiment>
FIG. 32 is a block diagram showing a configuration of a figure pattern shape correcting apparatus 200 according to an additional embodiment of the present invention. As shown in the figure, the figure pattern shape correction apparatus 200 includes an evaluation point setting unit 110, a feature amount extraction unit 220, a bias estimation unit 130, and a pattern correction unit 140. Here, a figure pattern shape estimation apparatus 200 ′ according to an additional embodiment of the present invention is configured by the three units of the evaluation point setting unit 110, the feature amount extraction unit 220, and the bias estimation unit 130. The shape correction apparatus 200 is configured by further adding a pattern correction unit 140 as a fourth unit to the figure pattern shape estimation apparatus 200 ′.

The difference between the figure pattern shape correcting apparatus 100 according to the basic embodiment shown in FIG. 1 and the figure pattern shape correcting apparatus 200 according to the additional embodiment shown in FIG. In the latter, only the feature amount extraction unit 220 is replaced. In other words, the evaluation point setting unit 110, the bias estimation unit 130, and the pattern correction unit 140 shown in FIG. 32 are exactly the same as the units having the same reference numerals shown in FIG.

Therefore, the figure pattern shape estimation apparatus 200 ′ shown in FIG. 32 simulates the lithography process using the original figure pattern 10 in the same manner as the figure pattern shape estimation apparatus 100 ′ shown in FIG. It has a function of estimating the shape of the real graphic pattern 20 formed on S. For this purpose, the figure pattern shape estimation apparatus 200 ′ shows an evaluation point setting unit 110 for setting an evaluation point E on the original figure pattern 10, and features around the individual evaluation points E for the original figure pattern 10. A feature amount extraction unit 220 that extracts a feature amount x, and a process bias that indicates a deviation amount between the position on the original graphic pattern 10 and the position on the actual graphic pattern 20 of each evaluation point E based on the feature amount x. and a bias estimation unit 130 for estimating y.

Here, the evaluation point setting unit 110 sets a plurality of evaluation points E at predetermined positions on the contour line based on the original graphic pattern 10 including the contour line information indicating the boundary between the inside and the outside of the figure. The specific evaluation point setting process is as already described in §1.

The feature quantity extraction unit 220 extracts a feature quantity x indicating a feature around the evaluation point E on the original graphic pattern 10 for each evaluation point E set in this way. In the embodiment described here, a plurality of n feature amounts x1 to xn are extracted for each evaluation point E. As will be described in detail later, in the case of the additional embodiment described here, the feature amounts x1 to xn are actually calculated by an operation based on a predetermined calculation function defined in advance.

On the other hand, the bias estimation unit 130, based on the feature amount input unit 131 for inputting the feature amounts x1 to xn calculated for the individual evaluation points E in this way, and the learning information L obtained by the learning stage performed in advance, An estimation calculation unit 132 that calculates an estimated value according to the feature amounts x1 to xn and outputs the calculated estimated value as the estimated value y of the process bias for the evaluation point E. The specific estimation calculation method is as already described in §3.

The figure pattern shape correction apparatus 200 according to the additional embodiment is an apparatus having a function of correcting the shape of the original figure pattern 10 by using the figure pattern shape estimation apparatus 200 ′ described above. A pattern correction unit 140 is further added to the evaluation point setting unit 110, the feature amount extraction unit 220, and the bias estimation unit 130 that constitute the estimation device 200 ′. The pattern correction unit 140 performs processing for correcting the original graphic pattern 10 based on the estimated value y of the process bias output from the bias estimation unit 130. Then, the corrected graphic pattern 15 obtained by the correction by the pattern correction unit 140 is given as a new original graphic pattern to the graphic pattern shape estimation device 200 ′, thereby repeatedly performing correction on the graphic pattern. The specific method of such correction processing is as already described in §1.

Of course, all of the evaluation point setting unit 110, the feature amount extraction unit 220, the bias estimation unit 130, and the pattern correction unit 140 shown in FIG. 32 are configured by incorporating a predetermined program into a computer. Therefore, the graphic pattern shape estimation device 200 ′ and the graphic pattern shape correction device 200 according to this additional embodiment are actually realized by incorporating a dedicated program into a general-purpose computer.

As described above, the shape correction apparatus 100 (or shape estimation apparatus 100 ′) shown in FIG. 1 and the figure pattern shape correction apparatus 200 (or shape estimation apparatus 200 ′) shown in FIG. is doing. However, the feature extraction mechanism is different between the two. Therefore, in order to explain this difference, the basic configuration and basic operation of the feature quantity extraction unit 220 shown in FIG. 32 will be described below.

As shown in FIG. 6, the feature quantity extraction unit 120 shown in FIG. 1 performs image pyramid creation processing including reduction processing on the original image Q1, and uses a plurality of n hierarchical images P1 to Pn having different sizes. The image pyramid PP is created, and the feature amount for the evaluation point E is calculated based on the pixel value of the pixel corresponding to the position of the evaluation point E using each of the hierarchical images P1 to Pn. .

On the other hand, the feature quantity extraction unit 220 shown in FIG. 32 uses n calculation functions Z1 (X, Y) to Zn (X, Y) instead of using n hierarchy images P1 to Pn. Then, a process of calculating n feature values x1 to xn for the evaluation point E (X, Y) located at the coordinates (X, Y) is performed.

Here, n calculation functions Z1 (X, Y) to Zn (X, Y) are obtained from the evaluation point E (X, Y) from the feature amount x1 in consideration of a narrow range in the vicinity of the evaluation point E (X, Y). The calculation function is suitable for calculating a plurality of n types of feature quantities x1 to xn with different consideration ranges up to the feature quantity xn taking into account a wide range including Y). Therefore, it is possible to obtain individual features that show various features from the vicinity of each evaluation point to the distance, and accurate simulation that takes into account the effects of various phenomena with different scales, such as proximity effects and etching loading phenomena. It becomes possible to do.

In this way, by extracting a plurality of n types of feature amounts x1 to xn indicating various features from the vicinity of the evaluation point to the distant place, an accurate simulation is performed in consideration of the effects of various phenomena having different scales. This is the technical idea adopted in the basic embodiment described in §1 to §4, and is also the technical idea adopted in the additional embodiment described in §5. In other words, the basic embodiment and the additional embodiment are common in that an accurate simulation is performed using such a technical idea, and in any of the embodiments, it can be obtained. The feature amounts x1 to xn include information obtained by multiplexing various phenomena having different influence ranges.

As described above, the basic embodiment described in §1 to §4 and the additional embodiment described in §5 are based on a common technical idea, and perform an accurate simulation considering the effects of various phenomena of different scales. Although it is an invention to be performed, the specific methods for extracting the feature amounts x1 to xn are slightly different. In other words, in the basic embodiment, the feature amounts x1 to xn are extracted using the image pyramid PP including a plurality of n kinds of hierarchical images P1 to Pn, whereas in the additional embodiment described here, a plurality of feature quantities x1 to xn are extracted. Feature amounts x1 to xn are extracted using n calculation functions Z1 (X, Y) to Zn (X, Y). Hereinafter, a feature amount extraction method in the additional embodiment will be described in detail with reference to a specific example.

32, the feature quantity extraction unit 220 includes a rectangular aggregate replacement unit 221, a feature quantity calculation unit 222, and a calculation function provision unit 223. Here, the rectangular aggregate replacement unit 221 performs processing for replacing a graphic included in the original graphic pattern 10 with a rectangular aggregate. The calculation function providing unit 223 provides a calculation function for calculating a feature amount for one evaluation point based on a positional relationship with respect to a rectangle positioned around the evaluation point. Then, the feature amount calculation unit 222 performs a process of calculating the feature amount for each evaluation point set by the evaluation point setting unit 110 using the calculation function provided from the calculation function providing unit 223.

The rectangular aggregate replacement unit 221 performs the process of replacing a graphic included in the original graphic pattern 10 with a rectangular aggregate because the feature amount calculation unit 222 has a rectangular evaluation point around a certain evaluation point. This is to perform a process of calculating the feature amount based on the positional relationship with respect to the four sides. FIG. 33 is a plan view showing an example of processing for replacing the original graphic pattern 10 with the rectangular aggregate 50 by the rectangular aggregate replacing unit 221. FIG. In the case of this example, the original figure pattern 10 including a figure having an arbitrary shape as shown in FIG. 33 (a) has four rectangles as shown in FIG. 33 (b) (each shown by hatching). Is replaced by a rectangular assembly 50 made of As shown in the figure, the outline of the entire rectangular aggregate 50 obtained by this replacement processing matches the outline of the figure included in the original figure pattern 10.

Such replacement can be performed by a process of dividing the graphic included in the original graphic pattern 10 into a plurality of rectangles. In the case of the example shown in FIG. 33 (a), when an XY two-dimensional orthogonal coordinate system is defined and the original figure pattern 10 is arranged thereon, the figure included in the original figure pattern 10 has sides parallel to the X axis and Y It can be seen that the polygon has a side parallel to the axis. As described above, a pattern used in a semiconductor integrated circuit is often constituted by a regular polygon having a side parallel to the X axis and a side parallel to the Y axis. If such a regular polygon is divided by a straight line parallel to the X axis or a straight line parallel to the Y axis, two sides parallel to the X axis and 2 parallel to the Y axis are obtained as shown in FIG. A plurality of regular rectangles having sides can be formed.

As described above, since a specific method using various algorithms is known as a method of dividing an arbitrary regular polygon to form an aggregate of a plurality of regular rectangles, detailed description is omitted here. To do. Of course, the figure included in the original figure pattern 10 is not necessarily a regular figure consisting of sides parallel to the X-axis or the Y-axis. By approximating the outline, it can be divided into a plurality of regular rectangles.

FIG. 34 is a plan view showing an example of a process of replacing the arbitrarily shaped figure included in the original figure pattern 10 with the rectangular set 50 made of regular rectangles by the rectangular set replacing unit 221. FIG. 34A shows an example of the original graphic pattern 10 including two sets of graphics. Specifically, the original figure pattern 10 includes a pentagon having an arbitrary shape drawn in the upper part of the figure and a circle drawn in the lower part of the figure. Each side of the pentagon shown in the upper part faces an arbitrary direction and is not necessarily a side parallel to the X axis or the Y axis. In addition, in the circle shown in the lower part, the boundary line is not a side but a circumference.

In this way, even if the original figure pattern 10 includes a figure of arbitrary shape, as shown in FIG. 34 (b), the outline (indicated by a broken line in the figure) is a regular figure outline. Can be divided into a plurality of regular rectangles (indicated by solid lines in the figure). As described above, the outline of the rectangular aggregate 50 obtained by the replacement processing by the rectangular aggregate replacement unit 221 does not need to exactly match the outline of the graphic included in the original graphic pattern 10, and the outline of both It is sufficient if the lines are approximately matched.

The rectangular aggregate 50 obtained by the replacement processing of the rectangular aggregate replacement unit 221 is not necessarily a regular rectangle (two sides parallel to the X axis and two parallel to the Y axis when an XY two-dimensional orthogonal coordinate system is defined). Although it is not necessary to reduce the calculation burden of the feature amount calculation unit 222, it is preferable to use a regular rectangular aggregate. Therefore, an embodiment in the case where a rectangular aggregate 50 composed of regular rectangles is obtained by the rectangular aggregate replacement unit 221 will be described below.

In the basic embodiment described in §1 to §4, it is necessary to create an image pyramid PP composed of a plurality of n types of hierarchical images P1 to Pn having different sizes. Thus, it is necessary to create an original image (raster image) composed of a collection of pixels, but in the additional embodiment described in this section 5, it is not always necessary to create a raster image composed of a collection of pixels. The original graphic pattern 10 can be handled as a vector image, and the rectangular aggregate 50 obtained by the replacement processing by the rectangular aggregate replacement unit 221 may be in the form of a vector image.

In other words, each rectangle constituting the rectangular aggregate 50 can be expressed by vector data indicating its four sides. In particular, in the embodiment described below, since the rectangular aggregate 50 is a set of regular rectangles arranged in an XY two-dimensional orthogonal coordinate system, each rectangle has two diagonal points (for example, an upper left corner point and a lower right corner point). It can be defined by the XY coordinate value of point).

The feature amount calculation unit 222 calculates a feature amount for a certain evaluation point based on a positional relationship with respect to a rectangle positioned around the evaluation point. FIG. 35A is a diagram illustrating the principle of feature amount calculation by the feature amount calculation unit 222. Here, it is assumed that the rectangular aggregate replacement unit 221 defines a rectangular aggregate 50 having five regular rectangles F1 to F5 as shown in the figure on the XY two-dimensional orthogonal coordinate system. Is used to explain the principle of calculating the feature quantity x for one evaluation point. More specifically, for example, consider a case where the feature amount x is calculated for the evaluation point E (X, Y) set on the right side of the rectangle F3.

In the present application, since the lowercase letter x is used as the code indicating the feature amount and the lowercase letter y is used as the code indicating the process bias, uppercase X and Y are used as the coordinate values of the XY two-dimensional orthogonal coordinate system. To. In the case of the example shown in FIG. 35A, the feature amount x for the evaluation point E (X, Y) set at the coordinate (X, Y) on the XY two-dimensional orthogonal coordinate system is the evaluation point E (X, Y) is calculated based on the positional relationship between the individual rectangles F1 to F5.

As described above, actually, a plurality of n feature amounts x1 to xn are calculated as the feature amount x for the evaluation point E (X, Y). FIG. 35 (b) is a diagram showing an example of the n feature values x1 to xn and a calculation function used to calculate them. Specifically, in order to calculate the first feature quantity x1, the first calculation function Z1 (X, Y) is used, and in order to calculate the second feature quantity x2, the second feature quantity x1 is calculated. The calculation function Z2 (X, Y) is used,..., And the nth calculation function Zn (X, Y) is used to calculate the nth feature quantity xn. Each of the calculation functions is a function that gives a predetermined function value using the coordinate values X and Y of the evaluation point E (X, Y) as variables.

For example, the first calculation function Z1 (X, Y) is
Z1 (X, Y) = Σ _{i = 1 to 5} [K · fhi (σ1) · fvi (σ1)]
Is a function represented by the following expression. Here, i is a parameter indicating a rectangle number, and in the example shown in FIG. 35 (a), since it is necessary to calculate the positional relationship with respect to a total of five rectangles F1 to F5, i = 1 to 5 Is set in the range.

In the above formula, fhi (σ1) on the right side is a horizontal function for the i-th rectangle Fi, and the horizontal direction between the evaluation point E (X, Y) and the rectangle Fi (example shown in FIG. 35 (a)). In the case of (3), it plays a role of indicating the positional relationship with respect to the X-axis direction) as a numerical value. For example, the horizontal function fh1 (σ1) when i = 1 indicates the positional relationship in the X-axis direction between the evaluation point E (X, Y) and the rectangle F1 in the example shown in FIG. This is a function that gives a numerical value.

Actually, as described later, the function value of the horizontal function fh1 (σ1) depends on the deviation between the X coordinate values of the left and right sides of the rectangle F1 and the X coordinate value of the evaluation point E (X, Y). Will be determined. Similarly, the horizontal function fh2 (σ1) in the case of i = 2 is a function that gives a numerical value indicating the positional relationship in the X-axis direction between the evaluation point E (X, Y) and the rectangle F2. As will be described later, σ1 is a spreading coefficient, and is a parameter that determines the degree of function spreading in the X-axis direction.

On the other hand, fvi (σ1) on the right side is a vertical direction function for the i-th rectangle Fi, and the vertical direction between the evaluation point E (X, Y) and the rectangle Fi (in the case of the example shown in FIG. 35A) , Y-axis direction) as a numerical value. For example, the vertical function fv1 (σ1) in the case of i = 1 is a function that gives a numerical value indicating the positional relationship in the Y-axis direction between the evaluation point E (X, Y) and the rectangle F1.

Actually, as will be described later, the function value of the vertical function fv1 (σ1) depends on the deviation between the Y coordinate values of the upper and lower sides of the rectangle F1 and the Y coordinate value of the evaluation point E (X, Y). Will be determined. Similarly, the vertical function fv2 (σ1) in the case of i = 2 is a function that gives a numerical value indicating the positional relationship in the Y-axis direction between the evaluation point E (X, Y) and the rectangle F2. In this case as well, σ1 is a spread coefficient, and is a parameter that determines the extent of the function spread in the Y-axis direction.

The coefficient K on the right side is a predetermined constant for adjusting the scaling of the finally obtained feature quantity x, and is referred to as a feature quantity calculation coefficient here. In the embodiment described later, the feature amount calculation coefficient K is set to 1/4, but the value of K may be set to an arbitrary constant. After all, the first calculation function Z1 (X, Y) indicates the horizontal direction function fhi (σ1) that indicates the positional relationship in the horizontal direction as a numerical value and the positional relationship in the vertical direction as a numerical value for the i-th rectangle Fi. The product of the vertical function fvi (σ1) and the feature amount calculation coefficient K is obtained for each of the five rectangles F1 to F5, and the sum is obtained.

In other words, the first calculation function Z1 (X, Y) is in the horizontal direction between the individual rectangles F1 to F5 constituting the rectangular aggregate 50 with respect to a certain evaluation point E (X, Y). This is a function for calculating the sum of numerical values indicating the positional relationship in the vertical direction. As will be described later, the horizontal direction function fh1 (σ1) and the vertical direction function fv1 (σ1) include the coordinate values X and Y of the evaluation point E (X, Y) as variables, and the function values are The coordinate values X and Y of the evaluation point E (X, Y) are given as variables. The function value calculated using the first calculation function Z1 (X, Y) in this way is used as the first feature amount x1.

On the other hand, the second calculation function Z2 (X, Y) is
Z2 (X, Y) = Σ _{i = 1 to 5} [K · fhi (σ2) · fvi (σ2)]
Is a function represented by the following expression. The difference between the first calculation function Z1 (X, Y) and the second calculation function Z2 (X, Y) described above is that the former function fhi (σ1) and fvi ( Whereas σ1) is used, the latter is only the point where fhi (σ2) · fvi (σ2) is used. Here, fhi (σ1) and fvi (σ1) are functions using the spread coefficient σ1, whereas fhi (σ2) and fvi (σ2) are functions using the spread coefficient σ2.

The same applies to the third calculation function Z3 (X, Y) and thereafter, and the calculation functions Z1 (X, Y) to Zn (X, Y) are defined in total by changing the spread coefficient σ. Can do. As will be described in detail later, these calculation functions can be referred to as calculation functions for calculating a feature quantity x based on a positional relationship with respect to four sides of a rectangle positioned around one evaluation point E.

The substance of the expansion coefficient σ and its role will be described later. The calculation function providing unit 223 uses n calculation functions Z1 (X, Y) to Zn (X, Y) using n expansion coefficients σ1 to σn. Fulfills the function of providing). Then, the feature quantity calculation unit 222 calculates n feature quantities x1 to xn for one evaluation point E by an arithmetic process using the n calculation functions Z1 (X, Y) to Zn (X, Y). calculate. That is, each function value obtained by giving the coordinate values X and Y of the evaluation point E (X, Y) as variables to the respective calculation functions Z1 (X, Y) to Zn (X, Y) is a characteristic. Calculated as quantities x1 to xn.

As described above, the expansion coefficient σ is a parameter that determines the degree of expansion of the function in the X-axis direction or the Y-axis direction. Accordingly, n calculation functions Z1 (X, Y) to Zn (n) are used by using n expansion coefficients σ1 to σn from a expansion coefficient σ1 indicating a narrow expansion condition to an expansion coefficient σn indicating a wide expansion condition. If X, Y) is provided, a wide range including from a feature amount x1 considering a narrow range near the evaluation point E (X, Y) to a distance from the evaluation point E (X, Y) is considered. A plurality of n feature amounts x1 to xn with different consideration ranges can be calculated until the feature amount xn is reached.

As a result, as in the basic embodiment described in §1 to §4, it is possible to perform an accurate simulation in consideration of the effects of various phenomena of different scales such as proximity effects and etching loading phenomena. In other words, the n calculation functions Z1 (X, Y) to Zn (X, Y) provide the same operational effects as the image pyramid PP including the n hierarchical images P1 to Pn shown in FIG. Will be able to.

In short, in the additional embodiment described here, the calculation function providing unit 223 moves from the feature amount x1 considering a narrow range in the vicinity of the evaluation point E (X, Y) to a distance of the evaluation point E (X, Y). In order to calculate a plurality of n feature amounts x1 to xn with different consideration ranges up to a feature amount xn that takes into account a wide range, a plurality of n calculation functions Z1 (X, Y) to Zn (X , Y). Then, the feature amount calculation unit 222 uses the plurality of n types of calculation functions to calculate a plurality of n types of feature amounts x1 to xn for each evaluation point.

The basic configuration and basic operation of the feature quantity extraction unit 220 shown in FIG. 32 have been described above. The n feature quantities x1 to xn calculated by the feature quantity extraction unit 220 are given to the bias estimation unit 130. The configuration and operation of the bias estimation unit 130 are as described in section 3 above.

That is, as shown in FIG. 32, the bias estimation unit 130 includes a feature amount input unit 131 that inputs feature amounts x1 to xn for a specific evaluation point E extracted by the feature amount extraction unit 220, and predetermined learning information L. And an estimation calculation unit 132 that outputs an estimated value corresponding to the feature amount x1 to xn as an estimated value y of a process bias for the specific evaluation point E.

In the case of the embodiment shown here, the estimation calculation unit 132 has a neural network having the feature amounts x1 to xn input by the feature amount input unit 131 as input layers and the process bias estimate y as an output layer. . As described in §3, this neural network includes the dimension value obtained by the actual dimension measurement of the actual figure pattern 20 formed on the actual substrate S by the lithography process using a large number of test pattern figures, and each test. Process bias estimation processing is performed by using, as learning information L, a parameter obtained in a learning step using a feature amount obtained from a pattern figure. In addition, the estimation calculation unit 132 obtains an estimated value of the deviation amount of the evaluation point E in the normal direction of the contour line as the estimated value y of the process bias for the evaluation point E located on the contour line of the predetermined graphic. Process.

In addition, when the additional embodiment described here is regarded as a method invention, the method can be realized by simulating a lithography process using the original graphic pattern 10 to form a real graphic pattern formed on the real substrate S. This is a figure pattern shape estimation method for estimating 20 shapes. Then, the method includes an original graphic pattern input stage for inputting an original graphic pattern 10 including information on a contour line indicating the boundary between the inside and the outside of the graphic, and an evaluation for setting an evaluation point E at a predetermined position on the contour line. A point setting stage, a feature quantity extraction stage for extracting a feature quantity x indicating features around the evaluation point E for the original figure pattern 10, and a position of the evaluation point E on the original figure pattern 10 based on the feature quantity x And a process bias estimation stage for estimating a process bias y indicating the amount of deviation between the position and the position on the actual graphic pattern 20 is realized by causing the computer to execute.

In addition, the feature quantity extraction stage is based on a rectangular aggregate replacement stage that replaces the graphic included in the original graphic pattern 10 with a rectangular aggregate, and a feature quantity based on the positional relationship of each evaluation point E with respect to the surrounding rectangle. a feature amount calculation stage for calculating x, and the process bias estimation stage obtains an estimated value corresponding to the feature quantity x based on the learning information L obtained by the learning stage performed in advance. In this case, an estimation calculation stage for outputting the estimated value as the estimated value y of the process bias for the evaluation point E is included.

<5.2 Specific examples of calculation functions>
FIG. 35 (b) shows an example of the basic form of n calculation functions Z1 (X, Y) to Zn (X, Y) provided by the calculation function providing unit 223. Here, a more detailed configuration of these calculation functions will be described.

In the case of the example shown in FIG. 35 (b), the k-th (1 ≦ k ≦ n) calculation function Zk (X, Y) is as shown in the first line of FIG.
Zk (X, Y) = Σ _{i = 1 to q} [K · fhi (σk) · fvi (σk)]
The function value of the function Zk (X, Y) is output from the feature amount calculation unit 222 as the value of the kth feature amount xk. Here, q is the total number of surrounding rectangles for which the positional relationship with the evaluation points is to be obtained, i is a parameter indicating a rectangle number (1 ≦ i ≦ q), σk is the kth expansion coefficient, and K is a feature amount It is a calculation coefficient. In the embodiment shown here, K is set to 1/4, but the feature quantity calculation coefficient K is a coefficient that determines the scaling factor of the feature quantity x, and may be set to an arbitrary value.

As described above, in the above equation, fhi (σk) is a horizontal function for the i-th rectangle Fi and relates to the horizontal direction (X-axis direction) between the evaluation point E (X, Y) and the rectangle Fi. This is a factor indicating the positional relationship. On the other hand, fvi (σk) is a vertical function for the i-th rectangle Fi, and is a factor indicating the positional relationship in the vertical direction (Y-axis direction) between the evaluation point E (X, Y) and the rectangle Fi. . Here, a specific example of the horizontal function fhi (σk) and the vertical function fvi (σk) will be described.

In the second row of FIG. 36, as an example of the horizontal function fhi (σk),
fhi (σk) = erf [(X−Li) / σk] −erf [(X−Ri) / σk]
A specific function is shown. In the third row of FIG. 36, as an example of the vertical function fvi (σk),
fvi (σk) = erf [(Y−Bi) / σk] −erf [(Y−Ti) / σk]
A specific function is shown. As described above, i is a parameter indicating a rectangle number (1 ≦ i ≦ q), q is a total number of rectangles, k is a parameter indicating a calculation function number (1 ≦ k ≦ n), and n is a total number of feature values (calculation). (Total number of functions), σk is the kth spreading factor.

On the other hand, Li, Ri, Ti, and Bi are the coordinate values of the four sides of the i-th regular rectangle Fi, as shown in the lower part of FIG. Specifically, Li is the X coordinate value of the left side L of the rectangle Fi, Ri is the X coordinate value of the right side R of the rectangle Fi, Ti is the Y coordinate value of the upper side T of the rectangle Fi, Bi is Y of the lower side B of the rectangle Fi. It is a coordinate value. The regular rectangle Fi arranged on the XY two-dimensional orthogonal coordinate system can be represented by, for example, the coordinate value (Li, Bi) of the lower left corner point LB and the coordinate value (Ri, Ti) of the upper right corner point RT. In addition, X and Y assigned as variables to the above functions are the X coordinate value and the Y coordinate value of the evaluation point E (X, Y) that is the calculation target of the feature amount x, as shown in the lower part of FIG. is there.

The rectangular aggregate replacement unit 221 replaces the graphic included in the original graphic pattern 10 with a plurality of regular rectangles, and represents the data representing the individual regular rectangles with coordinate values (Li, Bi), (Ri, Ti). The amount can be given to the amount calculation unit 222. Therefore, the feature amount calculation unit 222 uses the coordinate values Li, Bi, Ri, Ti indicating the rectangle Fi given from the rectangle assembly replacement unit 221 for the horizontal direction function fhi (σk) and the vertical direction function fvi (σk). Each function value can be calculated by performing an operation in which the coordinate values X and Y indicating the evaluation point E (X, Y) given from the evaluation point setting unit 110 are respectively entered as variables.

Regarding the value of the spread coefficient σk, the value of the spread coefficient σ1 in the first (k = 1) calculation function Z1 (X, Y) is set to σ1 = 1, for example, and as k increases, σk also increases. What is necessary is just to set so that it may become large. A specific numerical example of σk will be described later.

The function erf included in the horizontal function fhi (σk) and the vertical function fvi (σk) is a function generally called an error function. FIG. 37 is a diagram for explaining the error function erf (ξ). The error function erf (ξ) is a function defined by the mathematical formula shown in FIG. 37 (a), and takes a function value in a range of −1 ≦ erf (ξ) ≦ + 1 with respect to an arbitrary variable ξ. Then, + erf (ξ) becomes a function whose function value monotonously increases from −1 to +1 as the variable ξ increases, as shown in FIG. 37 (b), and −erf (ξ) As shown in, the function value monotonically decreases from +1 to −1 as the variable ξ increases.

Next, the meaning of the horizontal function fhi (σk) will be described with reference to FIG. 38 based on the above characteristics of the error function erf (ξ). FIG. 38 (a) is a diagram showing a mutual positional relationship between the i-th rectangle Fi arranged on the XY two-dimensional orthogonal coordinate system and the evaluation point E arranged at an arbitrary position. Since the rectangle Fi is a regular rectangle, the upper and lower sides are parallel to the X axis, and the left and right sides are parallel to the Y axis. Since the horizontal function fhi (σk) is a factor indicating the positional relationship in the horizontal direction, eleven evaluation points E1 to E11 arranged at the same interval on the horizontal line indicated by the broken line are shown in FIG. Illustrated. Points Li and Ri on the coordinate axis X indicate the X coordinate values of the left and right sides of the rectangle Fi.

The positional relationship in the horizontal direction between the specific evaluation point E and the rectangle Fi includes the left side position deviation indicating the distance between the left side L of the rectangle Fi and the evaluation point E, and the right side indicating the distance between the right side R of the rectangle Fi and the evaluation point E. Quantified using position deviation. Here, let us first consider quantifying the left side position deviation. The left side position deviation of each of the evaluation points E1 to E11, when focusing on the left side L of the rectangle Fi (in the figure, the left side L is indicated by a thick line), the X coordinate value Li of the left side L and each evaluation point E1 The horizontal function fhi (σk) takes a function value corresponding to the distance from the X coordinate value of E11 to E11.

Here, let us consider k = 1 and the horizontal function fhi (σ1) included in the first calculation function Z1 (X, Y). σ1 can be set to an arbitrary value. For example, if σ1 = 1 is set,
fhi (σ1) = erf (X-Li) -erf (X-Ri)
become. Therefore, first consider the function of + erf (X−Li) in the first term on the right side of the above equation.

FIG. 38 (b) shows a state in which the graph of the error function + erf (X−Li) is arranged with reference to the position of the left side L of the rectangle Fi shown in FIG. 38 (a). As described above, the error function + erf (ξ) is a function whose function value monotonously increases from −1 to +1 as ξ increases, as shown in FIG. ) Is arranged so that the function value becomes 0 at the position of the left side L of the rectangle Fi, a graph as shown in FIG. The horizontal axis of this graph is “X-Li”, and the evaluation point E (evaluation at in FIG. 38 (a)) arranged at the position of X-Li = 0, that is, the position of the left side L where the X coordinate value is Li The value of + erf (X−Li) for point E3) is zero.

On the other hand, for the evaluation points located on the left side of the left side L like the evaluation points E2 and E1, the value of + erf (X−Li) is negative. For example, for the evaluation points E2 and E1, negative function values e2 and e1 can be obtained by substituting the X coordinate value into the error function + erf (X−Li). On the other hand, the value of + erf (X−Li) is positive for evaluation points located on the right side of the left side L, such as evaluation points E4, E5,. For example, for the evaluation points E4 and E5, positive function values e4 and e5 are obtained by substituting the X coordinate value into the error function + erf (X−Li) (the value e1 etc. is the point e1 etc. on the graph). The ordinate value of.)

However, as the variable value “X−Li” increases, the function value + erf (X−Li) eventually reaches the upper limit value + 1 and becomes saturated. Therefore, in the case of the illustrated example, the function values e8, e9, e10, e11 are all the upper limit value +1, and the function value is also +1 for the evaluation point (not shown) arranged on the right side. Conversely, as the variable value “X−Li” decreases, the function value + erf (X−Li) eventually reaches the lower limit value−1 and becomes saturated.

Now, next
fhi (σ1) = erf (X-Li) -erf (X-Ri)
Let us consider what function is -erf (X-Ri) in the second term on the right side of the equation. FIG. 39A shows the positional relationship in the horizontal direction between the i-th rectangle Fi arranged on the XY two-dimensional orthogonal coordinate system and the eleven evaluation points E1 to E11, as in FIG. FIG. As described above, the positional relationship in the horizontal direction is quantified by the left side position deviation indicating the distance from the left side L and the right side position deviation indicating the distance from the right side R. Here, let us consider quantifying the right side position deviation. The right side position deviation of each of the evaluation points E1 to E11 is the X coordinate value Ri of the right side R and each evaluation point E1 when the right side R of the rectangle Fi is noticed (in the figure, the right side R is indicated by a thick line). The horizontal function fhi (σ1) corresponds to a distance from the X coordinate value of E11 to E11, and takes a function value corresponding to the distance.

FIG. 39 (b) shows a state in which the graph of the error function −erf (X−Ri) is arranged with reference to the position of the right side R of the rectangle Fi shown in FIG. 39 (a). As described above, the error function −erf (ξ) is a function whose function value monotonously decreases from +1 to −1 as ξ increases, as shown in FIG. If the graph of -Ri) is arranged so that the function value becomes 0 at the position of the right side R of the rectangle Fi, a graph as shown in FIG. The horizontal axis of this graph is “X-Ri”, and the evaluation point E (evaluation at in FIG. 39 (a)) is arranged at the position of X-Ri = 0, that is, the position of the right side R where the X coordinate value is Ri. The value of -erf (X-Ri) for point E8) is zero.

On the other hand, for the evaluation points located on the right side of the right side R, such as the evaluation points E9 and E10, the value of -erf (X-Ri) is negative. For example, for the evaluation points E9 and E10, the negative function values e9 and e10 are obtained by substituting the X coordinate values into the error function -erf (X-Ri). On the other hand, for the evaluation points located on the left side of the right side R, such as the evaluation points E7, E6, E5,..., The value of -erf (X-Ri) is positive. For example, for the evaluation points E7 and E6, positive function values e7 and e6 are obtained by substituting the X coordinate values into the error function -erf (X-Ri).

However, as the variable value “X−Ri” increases, the function value −erf (X−Ri) eventually reaches the lower limit value−1 and becomes saturated. Conversely, as the variable value “X−Ri” decreases, the function value −erf (X−Ri) eventually reaches the upper limit value + 1 and becomes saturated. Therefore, in the case of the illustrated example, the function values e1, e2, e3 are all the upper limit value +1.

After all,
fhi (σ1) = erf (X-Li) -erf (X-Ri)
The horizontal function fhi (σ1) defined by the following formula is based on the function value + erf (X−Li) corresponding to the left side position deviation indicating the distance from the left side L and the right side position deviation indicating the distance from the right side R. The function value −erf (X−Ri) and the sum of the function value −erf (X−Ri) and the function + erf (X−Li) shown in FIG. 38 (b) and FIG. 39 (b) when σ1 = 1. This is the sum of the function -erf (X-Ri). Here, assuming that σ1 = 1, the horizontal function fhi (σ1) is simply described as fhi.

FIG. 40 (a) is similar to FIG. 38 (a) and FIG. 39 (a), the i-th rectangle Fi arranged on the XY two-dimensional orthogonal coordinate system, and eleven evaluation points E1 to E11. It is a figure which shows the positional relationship regarding horizontal direction. Here, the left side L, which is the reference for the left side position deviation, and the right side R, which is the reference for the right side position deviation, are indicated by bold lines. 40 (b) b is a graph showing the sum of the function + erf (X−Li) shown in FIG. 38 (b) and the function −erf (X−Ri) shown in FIG. 39 (b). The horizontal function fhi is shown in FIG. (The horizontal axis is the coordinate value X that is a variable of the horizontal function fhi).

The graph of the horizontal function fhi is a bilaterally symmetric graph with the position of the center of gravity G of the rectangle Fi as shown in the figure. As shown in FIG. 38 (b), the left and right ends of the function + erf (X−Li) take a saturation value of −1 or +1, and as shown in FIG. 39 (b), the function −erf (X−Ri) The left and right ends of the signal take a saturation value of +1 or -1. Therefore, in the graph of the horizontal function fhi shown in FIG. 40 (b), the peak in the vicinity of the center is a peak (the center position may be depressed), and a mountain-like curve that gradually decreases as it goes to the left and right. Draw and the left and right edges are zero. The width of this mountain-shaped curve changes according to the lateral width dX (X-axis direction width) of the rectangle Fi.

The horizontal direction function fhi shown by the graph having such a curve is a function that gives a larger value to the evaluation point E closer to the peak position of the graph with respect to the horizontal positional relationship. For example, in the case of the example shown in FIG. 40, the larger the X coordinate value is closer to the X coordinate value of the center of gravity G, such as the evaluation points E5 and E6, the larger function values such as values e5 and e6 are given (upper limit value). Becomes 2). Conversely, the smaller the X coordinate value is from the X coordinate value of the center of gravity G, such as the evaluation points E1 and E11, the smaller function values such as the values e1 and e11 are given (the graph value is negative). In some cases, the lower limit is -2.

Although the meaning of the horizontal function fhi has been described above, the meaning of the vertical function fvi is the same. That is, the horizontal function fhi is a factor indicating the positional relationship in the horizontal direction (X-axis direction) for the specific evaluation point E of interest and the i-th rectangle Fi, whereas the vertical function fvi is This is a factor indicating the positional relationship in the vertical direction (Y-axis direction) between the specific evaluation point E of interest and the i-th rectangle Fi.

That is, fhi (σk) = erf [(X−Li) / σk] −erf [(X−Ri) / σk] described in the second row of FIG.
For the horizontal function fhi (σk), if the variable X is replaced with the variable Y, the coordinate value Li of the left side L is replaced with the coordinate value Bi of the lower side B, and the coordinate value Ri of the right side R is replaced with the coordinate value Ti of the upper side T 36, fvi (σk) = erf [(Y−Bi) / σk] −erf [(Y−Ti) / σk] described in the third line of FIG.
A vertical function fvi (σk) is obtained. Here, assuming that σ1 = 1 is set, the vertical function fvi (σ1) is
fvi (σ1) = erf (Y−Bi) −erf (Y−Ti)
become. Here again, assuming that σ1 = 1, the vertical function fvi (σ1) is simply described as fvi.

Similarly to the graph of the horizontal function fhi shown in FIG. 40 (b) の, the graph of the vertical function fvi also has a mountain-like curve that has a peak in the vicinity of the center and gradually decreases toward the left and right. . However, the horizontal axis of the graph is the Y axis, and the width of this mountain-shaped curve changes according to the vertical width dY (Y-axis direction width) of the rectangle Fi.

FIG. 41 is a diagram showing a positional relationship between the rectangle Fi, the graph of the horizontal function fhi, and the graph of the vertical function fvi. As shown in the lower part of the figure, the graph of the horizontal function fhi is a graph of a function that gives the function value fhi using the X coordinate value as a variable, and is a symmetric graph centered on the X coordinate of the gravity center G of the rectangle Fi ( The center of the graph is indicated by a one-dot chain line), and a mountain-like curve showing a peak in the vicinity of the center is drawn. On the other hand, the graph of the vertical function fvi is a reverse graph in which the direction of the Y axis is reversed in order to match the coordinate system in which the rectangle Fi is arranged as shown on the left side of the figure. It is a graph of a function that gives a function value fvi with the coordinate value as a variable, and is a symmetric graph centered on the Y coordinate of the center of gravity G of the rectangle Fi (the center of the graph is indicated by a one-dot chain line), which also has a peak approximately at the center. A mountain-shaped curve is drawn.

In the example shown in FIG. 41, the width of the graph of the horizontal function fhi is larger than the width of the graph of the vertical function fvi, because the horizontal width of the rectangle Fi is wider than the vertical width. It is. In other words, the width of the graph of the horizontal function fhi corresponds to the horizontal width dX (X-axis direction width: dX = Ri−Li) of the rectangle Fi, and the width of the graph of the vertical function fvi is rectangular. This corresponds to the vertical width dY of Fi (Y-axis direction width: dY = Ti−Bi).

Here, the calculation function Zk (X, Y) = Σ _{i = 1 to q} [K · fhi (σk) · fvi (σk)] shown in FIG. 36 again.
Let's look back. The right side of this equation includes the product fhi (σk) · fvi (σk). Assuming that σ1 = 1 for the first calculation function Z1 (X, Y), the above equation is
Z1 (X, Y) = Σ _{i = 1 to q} [K · fhi · fvi]
Therefore, the right side calculates a product obtained by mutually multiplying the feature amount calculation coefficient K, the horizontal function fhi, and the vertical function fvi for each of the first rectangle F1 to the qth rectangle Fq, This is the formula for calculating the sum.

As described above, the horizontal direction function fhi is a factor indicating the positional relationship in the horizontal direction with respect to the specific evaluation point E of interest and the i-th rectangle Fi, and the vertical direction function fvi is related to the specific evaluation point E and Since this is a factor indicating the positional relationship in the vertical direction with respect to the i-th rectangle Fi, the product fhi · fvi (or K · fhi · fvi further multiplied by the feature amount calculation coefficient K) is the particular of interest. This is a factor indicating the positional relationship between the evaluation point E and the i-th rectangle Fi in both the horizontal direction and the vertical direction. Therefore, the value of the calculation function Z1 (X, Y) obtained as the sum is the horizontal and vertical directions of the specific evaluation point E of interest and all the q rectangles F1 to Fq positioned around it. This is an amount indicating the positional relationship between the two. In the additional embodiment described here, such an amount is adopted as the feature amount x for the specific evaluation point E.

For example, in the example shown in FIG. 41, the function value fhi, which is a factor indicating the positional relationship between the evaluation point E1 and the rectangle Fi in the horizontal direction, is obtained when the X coordinate value of the evaluation point E1 is entered in the horizontal function fhi. It is given as a function value fhi, that is, a value e11. On the other hand, the function value fvi serving as a factor indicating the positional relationship in the vertical direction is given as a function value fvi when the Y coordinate value of the evaluation point E1 is inserted into the vertical function fvi, that is, a value e12. In the example shown in the figure, e11> e12, but this is because the evaluation point E1 is close to the rectangle Fi in the horizontal direction but slightly apart in the vertical direction.

In this case, the two-dimensional positional relationship between the evaluation point E1 and the rectangle Fi can be quantified by the product fhi · fvi (in the above example, the product e11 · e12) (actually, the scaling factor) As a feature quantity calculation coefficient K).
Z1 (X, Y) = Σ _{i = 1 to q} [K · fhi · fvi]
The first calculation function is a function that obtains such a two-dimensional positional relationship with respect to all the q rectangles F1 to Fq and takes the sum thereof, and the function value is the evaluation point E1 and the surroundings. This is a value obtained by quantifying the total positional relationship with q rectangles. Then, the function value is output as the first feature amount x1 for the evaluation point E1.

The same applies to the second evaluation point E2 shown in FIG. That is, the function value fhi serving as a factor indicating the positional relationship between the evaluation point E2 and the rectangle Fi in the horizontal direction is a function value fhi when the X coordinate value of the evaluation point E2 is inserted into the horizontal function fhi, that is, the value The function value fvi which is given as e21 and is a factor indicating the positional relationship in the vertical direction is given as the function value fvi when the Y coordinate value of the evaluation point E2 is put in the vertical function fvi, that is, the value e22.

Of course, the same applies to the third evaluation point E3 shown in the upper right of FIG. However, since the evaluation point E3 shown in the figure is far away from the rectangle Fi, actually, fhi = 0 and fvi = 0, and the product thereof is also zero. In other words, the presence of the rectangle Fi at a distant position does not affect the feature amount for the evaluation point E3.

So far, the first calculation function Z1 (X, Y) including the expansion coefficient σ1 has been described by taking the case of σ1 = 1 as an example. Therefore, the role of the spread coefficient σk (1 ≦ k ≦ n) in the calculation function will be described with reference to FIG.

In the upper part of FIG. 42, the i-th rectangle Fi having a width dX is shown, the middle part shows a graph of the horizontal function fhi (σ1) including the expansion coefficient σ1, and the lower part shows the expansion coefficient σ2. A graph of the horizontal function fhi (σ2) including is shown. Here, the horizontal direction function fhi (σ1) is
fhi (σ1) = erf [(X−Li) / σ1] −erf [(X−Ri) / σ1]
The horizontal function fhi (σ2) is
fhi (σ2) = erf [(X−Li) / σ2] −erf [(X−Ri) / σ2]
It is a function. The only difference is that the denominator on the right side is σ1 or σ2.

42 is a graph showing an example in which σ1 = 1 and σ2 = 2 are set. As shown in the drawing, the horizontal width of the fhi (σ2) graph shown in the lower part is wider than that of the fhi (σ1) shown in the middle part. As described above, the horizontal width of the mountain-shaped graph basically corresponds to the horizontal width dX of the rectangle Fi. However, the horizontal width can be increased or decreased by the expansion coefficient σ. That is, if the spread coefficient σ is doubled, the horizontal width of the mountain-shaped graph is doubled.

In the example shown in FIG. 41, when the first calculation function Z1 (X, Y) including a spread coefficient of σ1 = 1 is used, the feature value of the evaluation point E3 has the presence of a rectangle Fi at a far position. I explained that it has no effect. However, when the second calculation function Z2 (X, Y) including the spread coefficient σ2 = 2 is used, the horizontal width of the mountain-shaped graph is doubled, so that the feature amount of the evaluation point E3 is far from the feature amount. The presence of the rectangle Fi at the position will have an effect. For example, when the third calculation function Z3 (X, Y) including the spread coefficient σ3 = 4 is used, the influence of the existence of the rectangle Fi on the feature amount of the evaluation point E3 is further increased.

In FIG. 35 (b), in order to calculate n feature values x1 to xn for the evaluation point E, calculations using the calculation functions Z1 (X, Y) to Zn (X, Y) are performed. Explained. Here, the difference between the calculation functions Z1 (X, Y) to Zn (X, Y) is only that the included spread coefficients are σ1 to σn, respectively. As the spreading coefficients σ1 to σn, any values may be set as long as they are different from each other, but in practice, the kth (1 ≦ k ≦ n) spreading coefficient σk is set. It is preferable to set σk = 2 ^(k−1) . That is, σ1 = 1, σ2 = 2, σ3 = 4, σ4 = 8,...

The feature quantity x1 calculated using the first calculation function Z1 (X, Y) having a small value of the spread coefficient σ is a value considering only the positional relationship with the rectangle located in the vicinity of the evaluation point E. The feature amount xn calculated using the nth calculation function Zn (X, Y) having a large value of the spread coefficient σ is a value that takes into account the positional relationship with a rectangle positioned far from the evaluation point E. .

As described above, the n calculation functions Z1 (X, Y) to Zn (X, Y) provided by the calculation function providing unit 223 are characteristics considering a narrow range in the vicinity of the evaluation point E (X, Y). Suitable for calculating a plurality of n feature quantities x1 to xn with different consideration ranges from the quantity x1 to the feature quantity xn that takes into account a wide range including the distance from the evaluation point E (X, Y). It is a calculation function.

After all, in the basic embodiment, the technique of extracting the feature amounts x1 to xn using the image pyramid PP composed of a plurality of n kinds of hierarchical images P1 to Pn is adopted, whereas the additional embodiment described here is used. In this case, a method of extracting the feature amounts x1 to xn using a plurality of n types of calculation functions Z1 (X, Y) to Zn (X, Y) having different values of the spread coefficient σ is employed. Regardless of which method is used, individual feature quantities indicating various features from the vicinity of each evaluation point to the distance can be obtained, and various phenomena with different scales such as proximity effects and etching loading phenomena can be obtained. It becomes possible to perform an accurate simulation considering the influence.

The calculation function used in the additional embodiment of the present invention has been described above by presenting a specific example. The summary of this example is summarized as follows. First, the rectangular aggregate replacement unit 221 shown in FIG. 32 has a graphic included in the original graphic pattern 10 in an XY two-dimensional orthogonal coordinate system in which the X-axis positive direction is the right direction and the Y-axis positive direction is the upward direction. A rectangular aggregate 50 of regular rectangles Fi having an upper side T and a lower side B parallel to the X axis and a left side L and a right side R parallel to the Y axis is replaced. This is because when the feature amount calculation unit 222 performs an operation for calculating a feature amount x based on the positional relationship with respect to the four sides of the rectangle Fi positioned around one evaluation point E, the rectangle Fi is a regular rectangle. This is because the burden of calculation can be reduced.

Then, the calculation function providing unit 223 determines, for each regular rectangle Fi defined on the XY two-dimensional orthogonal coordinate system, the left side position deviation “X-Li” indicating the distance from the left side L in the X-axis direction of the evaluation point E. And the right side position deviation “X-Ri” indicating the distance from the right side R, and the upper side position deviation “Y-Ti” indicating the distance from the upper side T in the Y-axis direction of the evaluation point E and the distance from the lower side B. A calculation function for calculating the feature amount x may be provided based on the lower side position deviation “Y−Bi”.

More specifically, for a certain target rectangle Fi, the function value monotonously increases as the variable value increases, and the function value becomes 0 when the X coordinate value Li of the left side L of the target rectangle Fi is given as a variable. When the X-axis monotonically increasing function (for example, + erf [(X−Li / σk)]) and the function value monotonously decrease as the variable value increases, the X coordinate value Ri of the right side R of the target rectangle Fi is given as a variable. A horizontal function fhi (σk) that is the sum of an X-axis monotonically decreasing function (for example, −erf [(X−Ri / σk)]) for which the function value of is defined as 0 is defined. Similarly, the function value monotonously increases as the variable value increases, and a Y-axis monotonically increasing function (for example, + erf [(Y -Bi / σk)]), and the function value monotonously decreases as the variable value increases, and the Y-axis monotonically decreasing function becomes 0 when the Y coordinate value Ti of the upper side T of the target rectangle Fi is given as a variable. (For example, −erf [(Y−Ti / σk)]) and a vertical direction function fvi (σk) that is the sum of these.

Then, the amount indicating the positional relationship with respect to the target rectangle Fi for one target evaluation point E, the function value of the horizontal function fhi (σk) with the X coordinate value X of the target evaluation point E as a variable, and the target evaluation point Calculated based on the product of the function value of the vertical function fvi (σk) with the Y coordinate value Y of E as a variable (if necessary, it may be multiplied by a feature value calculation coefficient K for scaling). ), The sum of the amounts indicating the positional relationship with respect to each rectangle located around the target evaluation point E may be calculated as the feature amount x for the target evaluation point E.

In order to perform an accurate simulation in consideration of the effects of various phenomena with different scales, n types of feature amounts x1 to xn indicating various features from the vicinity of each evaluation point E to the far side are calculated. Is preferred. For this purpose, the calculation function providing unit 223 changes a plurality of n types of calculation functions Z1 (X, Y) to Zn (X, Y) using functions having different monotonic increases or monotonic decreases, with different consideration ranges. It is sufficient to provide a calculation function for calculating a plurality of n types of feature amounts x1 to xn.

Specifically, the calculation function providing unit 223 expands the left side position deviation “X-Li”, the right side position deviation “X-Ri”, the upper side position deviation “X-Ti”, and the lower side position deviation “X-Bi”. A calculation function including a monotonically increasing function or a monotonically decreasing function having a value divided by σ as a variable is prepared, and a plurality of n calculation functions are obtained by changing the value of the spread coefficient σ into a plurality of n values (σ1 to σn). Z1 (X, Y) to Zn (X, Y) may be provided. The values of a plurality of n types of spread coefficients σ1 to σn are expressed as σk = 2 ^(k− when the kth spread coefficient is expressed as σk using a parameter k that takes a range of 1 ≦ k ≦ n. ^It is preferable to set to ¹⁾ .

<5.3 Modification of Calculation Function>
In §5.2 described above, the basic specific example of the calculation function is shown, but the calculation function used in the additional embodiment of the present invention is not limited to the specific example described above. For example, the error function erf (ξ) is not necessarily used as the monotonically increasing function or the monotonically decreasing function, and other functions may be used. Here, some modified examples of this calculation function will be described.

(1) Calculation Function Considering Dose Amount In §2.1, refer to FIG. 12 and FIG. 13 for a method of extracting a feature amount when the original figure pattern 10 with a dose amount is given in the basic embodiment. Explained. Here, in an additional embodiment, a method for extracting a feature amount when an original figure pattern 10 with a dose amount is given will be described with reference to FIG.

FIG. 43 (a) is a plan view of the rectangular aggregate 60 created based on the graphic included in the original graphic pattern 10 with the dose amount. As shown, five regular rectangles F1d to F5d are defined on the XY two-dimensional orthogonal coordinate system. The shapes of the regular rectangles F1d to F5d constituting the rectangular aggregate 60 are exactly the same as the shapes of the regular rectangles F1 to F5 constituting the rectangular aggregate 50 shown in FIG. 35 (a). A predetermined dose amount is defined for each of the regular rectangles F1d to F5d constituting the body 60. These dose amounts are information added to the graphic originally included in the original graphic pattern 10.

The original figure pattern 10 with a dose amount includes information on a dose amount for each figure in the lithography process in addition to information on a contour line indicating the boundary between the inside and the outside of the figure. Therefore, the rectangular aggregate replacement unit 221 recognizes the internal area and the external area of each graphic based on the original graphic pattern 10, and further recognizes the dose amount for each graphic, and corresponds to each graphic. A process for setting a dose amount may be performed for each of the rectangles F1d to F5d. The rectangular aggregate 60 shown in FIG. 43 (a) is created by such processing, and the information on the dose amount of the original figure is added as it is to the individual rectangles F1d to F5d.

As described above, when the rectangular aggregate 60 having the rectangles F1d to F5d with the dose amount is created by the rectangular aggregate replacement unit 221, the calculation function providing unit 223 sets the dose amount set to each of the rectangles F1d to F5d. Is provided as a variable, and the feature amount calculation unit 222 calculates the feature amount x of the desired evaluation point E (X, Y) based on the calculation function including the dose amount as a variable. Good.

An example of a calculation function including such a dose amount as a variable is shown in FIG. The calculation function Zk (X, Y) shown here is the kth (1 ≦ k ≦ n) calculation function, and the function value calculated by this calculation function is output as the kth feature amount xk. The The calculation function Zk (X, Y) = Σ _{i = 1 to q} [Di · K · fhi (σk) · fvi (σk)] shown in FIG.
Is the calculation function Zk (X, Y) = Σ _{i = 1 to q} [K · fhi (σk) · fvi (σk)] shown in the first line of FIG.
The feature amount calculation coefficient K is further multiplied by the dose amount Di for the i-th rectangle.

The feature amount calculation coefficient K is a common constant for scaling, whereas the dose amount Di is an individual value set for each rectangle. For example, in the example shown in FIG. 43A, doses D1 and D2 used for calculations (i = 1, 2, and 3) for rectangles F1d, F2d, and F3d for which a 100% dose is set. , D3 are both 1, but the dose amount D4 used for the calculation (i = 4 calculation) for the rectangle F4d for which the 50% dose is set is 0.5, and the dose is 10%. The dose amount D5 used for the computation (i = 5 computation) for the rectangle F5d for which the amount is set is 0.1.

As a result, in the case of the example shown in FIG. 43 (a) 演算, a specific arithmetic expression of the calculation function Zk (X, Y) is as shown in FIG. 43 (c). The expression for the i-th rectangle includes an operation of multiplying the dose amount Di, and a feature amount xk in consideration of the dose amount of each rectangle is obtained. In the basic embodiment described in §2.1, the process of extracting the feature amount xk in consideration of the dose amount has been performed by creating the image pyramid PP using the dose density map M3 shown in FIG. . On the other hand, in the additional embodiment described here, as shown in FIG. 43B, the feature quantity xk taking the dose amount into consideration is calculated by an operation based on a calculation function including the dose amount as a variable. It will be.

(2) Calculation function based on a rectangular aggregate corresponding to the edge of a figure In §2.1, as a modification of the basic embodiment, an image pyramid PP is used by using an edge length density map M2 as shown in FIG. The process of extracting the feature amount x by creating the above has been described. The edge length density map M2 is information that focuses on the arrangement of the outlines (edges) of the graphic included in the original graphic pattern 10, not the information on the area inside / outside the graphic.

As for the additional embodiment described here, it is possible to handle a figure as outline information instead of handling the figure as area information. In the embodiments described so far, the rectangular aggregate replacement unit 221 performs a process of dividing the area of the graphic included in the original graphic pattern 10 and replacing it with the rectangular aggregate 50. For example, if the original figure pattern 10 includes a figure as shown in FIG. 44 (a), the figure is divided into two parts, and two pieces as shown in FIG. 44 (b) are shown by hatching. It was replaced with a rectangular aggregate consisting of rectangles F1 and F2. Such a replacement method is based on the idea of handling graphics as area information.

In the case of the modification described here, the rectangular aggregate replacement unit 221 recognizes the unit line segments that form the outline of each graphic based on the original graphic pattern 10, and sets a minute width for each unit line segment. Then, a process of replacing the graphic included in the original graphic pattern 10 with a rectangular aggregate having the minute width is performed. Such a replacement method is a method based on the idea of handling a graphic as contour line information.

FIG. 45 is a plan view showing a process of replacing the rectangular aggregate by setting a minute width to the unit line segment constituting the outline of the figure by the rectangular aggregate replacing unit 221. FIG. 45 (a) and (b) are shown by broken lines in FIG. 44 (a). This figure is composed of six sides. In the modification described here, these six sides are replaced with rectangles each having a very small width. As a result, this figure is replaced with a collection of six elongated rectangles.

Of the six sides constituting the outline of the figure, three are sides facing the horizontal direction (direction parallel to the X axis when arranged in the XY two-dimensional coordinate system). Here, the horizontal unit line segment Call it. The remaining three are sides facing the vertical direction (the direction parallel to the Y axis when arranged in the XY two-dimensional coordinate system), and are called vertical unit line segments here. In the case of the original graphic pattern 10 used for a semiconductor integrated circuit or the like, it is often the case that a contour is composed of only horizontal unit line segments and vertical unit line segments.

Therefore, the rectangular assembly replacement unit 221 sets the horizontal unit line segment to a horizontal rectangle by setting a minute width in the vertical direction, and sets the vertical unit line segment to a vertical rectangle by setting a minute width in the horizontal direction. Perform replacement processing. FIG. 45A is a plan view showing a state in which three horizontal unit line segments are replaced with horizontal rectangles Fh1, Fh2, and Fh3 (rectangles that form hatched areas), respectively. FIG. 5 is a plan view showing a state in which three vertical unit line segments are replaced with vertical rectangles Fv1, Fv2, and Fv3 (rectangles that form hatched regions), respectively.

Since the data constituting the original figure pattern 10 includes information indicating the geometric position of the outline of each figure (for example, the coordinate values of the end points of the unit line segment), each horizontal rectangle Fh1, Data indicating Fh2 and Fh3 and the respective vertical rectangles Fv1, Fv2 and Fv3 can be created based on the data constituting the original graphic pattern 10.

For example, in the case of the horizontal rectangle Fh1 shown in FIG. 45 (a) 座標, the X coordinate value of the left side can be defined as the X coordinate value of the left end of the horizontal unit line segment constituting the upper side of the original figure indicated by the broken line. The X coordinate value of the right side can be defined as the X coordinate value of the right end of this horizontal unit line segment. The Y coordinate value of the upper side can be defined as T1 + w where the Y coordinate value of this horizontal unit line segment is T1, and the Y coordinate value of the lower side is the Y coordinate value of the horizontal unit line segment. When B1, it can be defined as B1-w. Here, w is a value corresponding to half of the minute width, and may be set to an arbitrary numerical value.

Similarly, in the case of the vertical rectangle Fv1 shown in FIG. 45 (b) Ｙ, the Y coordinate value of the upper side can be defined as the Y coordinate value of the upper end of the vertical unit line segment constituting the left side of the original figure indicated by the broken line. The Y coordinate value of the lower side can be defined as the Y coordinate value of the lower end of this vertical unit line segment. Further, the X coordinate value of the right side can be defined as R1 + w when the X coordinate value of the vertical unit line segment is R1, and the X coordinate value of the left side is the X coordinate value of the vertical unit line segment. When L1, it can be defined as L1-w. Here, w is a value corresponding to half of the minute width, and may be set to an arbitrary numerical value.

After all, in the case of the modification shown here, the figure having the six sides shown in FIG. 44 (a) 、 has six regular rectangles Fh1, Fh2, Fh3 shown in FIGS. 45 (a) and 45 (b) with hatching. It is replaced with Fv1, Fv2, and Fv3. These regular rectangles are elongate rectangles having a minute width 2w, and are arranged along the unit line segments constituting the contour line of the original figure. The feature amount calculation unit 222 may calculate the feature amount x for a certain evaluation point E based on the positional relationship with these six rectangles.

Next, a specific example of a calculation function provided from the calculation function providing unit 223 to the feature amount calculating unit 222 in order to perform such calculation operation will be described. FIG. 46 is a diagram illustrating an example of a calculation function Zk (X, Y) applied to the rectangular aggregate illustrated in FIG. 45 (aggregate including six rectangles illustrated by hatching). This calculation function Zk (X, Y) is a function for extracting the k-th (1 ≦ k ≦ n) feature quantity xk. As shown in the upper part of FIG.
Zk (X, Y)
= Σ _{i = 1 to qh} [K · fhi (σk) · fvi ′ (σk)]
+ Σ _{i = 1 to qv} [K · fhi ′ (σk) · fvi (σk)]
Takes the form Here, the first term on the right side is an arithmetic term relating to the horizontal rectangles Fh1, Fh2, and Fh3 shown in FIG. 45A, and the second term on the right side is the vertical rectangles Fv1, Fv2, and Fb2, shown in FIG. This is an operation term related to Fv3.

And as shown in the middle of FIG.
fhi (σk) = erf [(X−Li) / σk]
-Erf [(X-Ri) / σk]
fvi (σk) = erf [(Y−Bi) / σk]
-Erf [(Y-Ti) / σk]
fhi ′ (σk) = erf [(X− (Li−w)) / σk]
−erf [(X− (Ri + w)) / σk]
fvi ′ (σk) = erf [(Y− (Bi−w)) / σk]
−erf [(Y− (Ti + w)) / σk]
It is.

Here, Li, Ri, Bi, and Ti are coordinate values indicating the end point position or line segment position of the i-th horizontal unit line segment or the i-th vertical unit line segment, as shown in FIG. For example, in the case of the horizontal rectangle Fh1 shown in FIG. 45 (a) (when i = 1), the X coordinate value of the left end of the horizontal unit line segment indicated by the broken line is L1, the X coordinate value of the right end is R1, and the Y of the line segment. The coordinate values are T1 and B1. Similarly, in the case of the vertical rectangle Fv1 shown in FIG. 45 (b) (when i = 1), the Y coordinate value of the upper end of the vertical unit line segment indicated by the broken line is T1, the Y coordinate value of the lower end is B1, and the line segment. The X coordinate values are L1 and R1.

46, qh is the total number of horizontal rectangles and qv is the total number of vertical rectangles (in the example shown in FIG. 45, qh = 3 and qv = 3). The parameter i in the calculation terms relating to the horizontal rectangles Fh1, Fh2, Fh3 (second line in FIG. 46) takes a range of i = 1 to qh, and the calculation terms relating to the vertical rectangles Fv1, Fv2, Fv3 (in FIG. 46). The parameter i in the third line) takes a range of i = 1 to qv. k is a parameter indicating the number of the calculation function, and the k-th spread coefficient σk is used for the k-th calculation function Zk (X, Y). The coefficient K is a feature amount calculation coefficient for scaling as described above. It can be easily understood that the feature quantity xk for the specific evaluation point E (X, Y) can be calculated by such a calculation function Zk (X, Y) in view of the contents of §5.2.

(3) Calculation Method for Reducing the Load Here, a method for reducing the calculation load when the feature amount calculation unit 222 calculates the feature amount xk by the calculation using the calculation function Zk (X, Y) will be described. . In §5.1, with reference to the example shown in FIG. 35 (a), as a method of calculating the feature amount x for a predetermined evaluation point E (X, Y), evaluation points E (X, Y) and 5 The procedure for calculating a value indicating the positional relationship with the individual rectangles F1 to F5 and setting the sum to the feature amount x has been described. However, actually, it is not always necessary to calculate a value indicating the positional relationship with all the rectangles F1 to F5.

For example, in the case of the example shown in FIG. 41, when calculating the feature quantity x for the evaluation point E1, it is meaningful to calculate a value indicating the positional relationship with the rectangle Fi taking into account the rectangle Fi. That is. This is because the evaluation point E1 is located in the vicinity of the rectangle Fi, and the values of the horizontal direction function fhi and the vertical direction function fvi do not become zero. However, it is not necessary to take the rectangle Fi into consideration when calculating the feature value x for the evaluation point E3. As shown in the figure, since the evaluation point E3 is located far from the rectangle Fi, the values of the horizontal function fhi and the vertical function fvi are both 0, so the value indicating the positional relationship with the rectangle Fi is This is because it does not contribute to the value of the calculation function Zk (X, Y).

Thus, given that the graph of the horizontal function fhi and the vertical function fvi draws a mountain-shaped curve and the function values at the left and right ends are 0, the feature amount for one evaluation point E It can be seen that rectangles that are too far away need not be considered when calculating x. Therefore, in practice, when the feature quantity calculation unit 222 calculates the feature quantity x for the evaluation point E, a reference circle C having a predetermined radius r around the evaluation point E is defined. It is only necessary to perform the calculation considering only the positional relationship with the rectangle belonging to the predetermined neighborhood range corresponding to C.

FIG. 47 is a plan view showing an example in which a reference circle C having a predetermined radius r is defined on a rectangular aggregate in order to make the calculation operation efficient in this way. In the illustrated example, the rectangular aggregate includes a total of 12 rectangles F1 to F12. Here, it is assumed that the k-th feature amount xk for the evaluation point E set on the right side of the rectangle F6 is calculated using the k-th calculation function Zk (X, Y). In the embodiments described so far, all the 12 rectangles F1 to F12 are subject to calculation. However, in the case of the modification described here, a reference having a predetermined radius r around the evaluation point E as shown in the figure. A calculation is performed in which a circle C is defined and only rectangles belonging to a predetermined neighborhood range corresponding to the reference circle C are considered.

In the case of the illustrated example, the rectangle to be calculated is selected based on the selection criterion that “the rectangle in which at least a part is included in the reference circle C” is to be calculated. As a result, only the seven rectangles F2, F5 to F10 indicated by hatching in the figure are selected as calculation targets. Therefore, the calculation function Zk (X, Y) is calculated only for these seven rectangles. Of course, other selection criteria may be used. For example, if the selection criterion “a rectangle that is entirely contained in the reference circle C” is used as the calculation target, only four rectangles F5, F6, F9, and F10 are selected as the calculation targets. Alternatively, if the selection criterion “the rectangle whose position of the center of gravity G is included in or on the circumference of the reference circle C” is selected, only six rectangles F5 to F10 are selected for calculation. The

Of course, if a rectangle to be calculated is selected on the basis of such a selection criterion, a rectangle that contributes to the value of the calculation function Zk (X, Y) may be included in the rectangle that is not selected. However, since the degree of contribution due to the rectangle that is not selected is not so large, even if the rectangle that is not selected is excluded from the calculation target, there is no significant problem. As described above, by removing a rectangle having a small degree of contribution to the value of the calculation function Zk (X, Y) from the calculation target, the feature amount calculation calculation by the feature amount calculation unit 222 can be made efficient, and the calculation burden is reduced. Mitigation can be achieved.

Note that the radius r of the reference circle C used to determine whether or not each rectangle is to be calculated is a peak of the horizontal function fhi and the vertical function fvi included in the calculation function Zk (X, Y). It is preferable to determine according to the width (width of the skirt) of the shape graph. As described above, since the width of the mountain graph is determined by the expansion coefficient σk, it is preferable to set the radius r of the reference circle C to be larger as the expansion coefficient σk is larger. Practically, it is preferable to set the value of the radius r to a range of 5σk <r <10σk, that is, a value about 5 to 10 times the spread coefficient σk.

<5.4 Comparison of processing time required for feature extraction processing>
Finally, verification of the basic embodiment described in §1 to §4 and the additional embodiment described in §5 by comparing the processing time required for feature quantity extraction for several original figure patterns 10 Present the results. For the basic embodiment, the verification results using the area density map M1 shown in FIG. 10 are shown, and for the additional embodiment, the calculation method for reducing the burden described in §5.3 (3) is adopted. The verification result is shown.

First, FIG. 48 is a diagram showing a verification result obtained by performing a feature amount extraction process on a predetermined number of evaluation points E using the original graphic pattern 10 including the Line & Space pattern. FIG. 48A is a plan view showing a graphic configuration of the original graphic pattern 10 actually used for verification. The original figure pattern 10 is a pattern of a number of parallel lines generally called “Line & Space” patterns. More specifically, linear rectangles having a width of 100 nm and a length of 65 μm are arranged in the horizontal direction with an interval of 100 nm. The entire pattern is formed in a 65 μm square area.

48 (b) b shows the processing time required when the feature amount extraction processing for a predetermined number of evaluation points E is performed on the original graphic pattern 10 shown in FIG. 48 (a), in addition to the basic embodiment. It is the graph compared about embodiment. The bar graph described as “density map” in the figure shows the processing time according to the basic embodiment (processing time by the feature quantity extraction unit 120 shown in FIG. 1), and the bar graph described as “function calculation” The processing time (processing time by the feature-value extraction unit 220 shown in FIG. 32) by embodiment is shown.

Each bar graph is divided into a plurality of sections, and each section has a predetermined circle number. This circled number corresponds to various individual processes as described in the right column, and each section of the bar graph indicates the processing time required for each individual process. For example, in the bar graph of “density map”, a section marked with a circle number 5 indicates a time required for the image pyramid creation process, and a section marked with a circle number 6 is necessary for the area density map M1 creation process. Show time. Similarly, the section marked with the circled number 3 in the “function calculation” bar graph indicates the time required for the calculation processing of the calculation function Zk (X, Y) described above.

比較 Comparing both bar graphs, the overall processing time is shorter for “Function calculation” than for “Density map”. This is because, in the basic embodiment, a long time is required for the process of creating the area density map M1 (the process of the section marked with the circled number 6). Therefore, it can be seen that the Line & Space pattern as shown in Fig. 48 (a) is more efficient than using the basic embodiment as far as the processing time is concerned.

FIG. 49 is a diagram showing a verification result obtained by performing a feature amount extraction process on a predetermined number of evaluation points E using the original figure pattern 10 including an Array Hole pattern. FIG. 49A is a plan view showing a graphic configuration of the original graphic pattern 10 actually used for verification. The original figure pattern 10 is a pattern in which a large number of squares generally called an Array Hole pattern are arranged in a matrix. More specifically, squares of 100 nm in length and breadth are arranged vertically and horizontally with an interval of 100 nm. The entire pattern is formed in a 65 μm square area.

FIG. 49 (b) を shows the processing time required when the feature amount extraction processing for a predetermined number of evaluation points E is performed on the original graphic pattern 10 shown in FIG. 49 (a) と. It is the graph compared about embodiment. Again, the bar graph labeled “Density Map” in the figure represents the processing time according to the basic embodiment, and the bar graph labeled “Functional calculation” represents the processing time according to the additional embodiment. The point that each section constituting these bar graphs indicates individual processing is the same as the bar graph of FIG. 48 (b).

When comparing both bar graphs, the overall processing time is shorter for the “density map” than for the “function calculation”. This is because in the additional embodiment, the calculation process of the calculation function Zk (X, Y) takes a long time. In the case of the Array Hole pattern shown in FIG. 49 (a), the number of rectangles created by the rectangle assembly replacing unit 221 is enormous, and the calculation processing load of the calculation function Zk (X, Y) inevitably increases. It will be. Therefore, for a pattern in which the number of rectangles created by the rectangular aggregate replacement unit 221 is large, such as this Array Hole pattern, it is better to use the basic embodiment than the additional embodiment as far as the processing time is concerned. It turns out to be efficient.

FIG. 50 shown at the end is a diagram showing a verification result obtained by performing the feature amount extraction process for a predetermined number of evaluation points E using the original graphic pattern 10 including the ISO-Space IV pattern. FIG. 50A is a plan view showing a graphic configuration of the original graphic pattern 10 actually used for verification. The original figure pattern 10 is a single elongated linear pattern generally called an ISO-Space IV pattern. More specifically, it is a very simple pattern composed of one linear rectangle elongated in the vertical direction with a width of 100 nm and a length of 65 μm. The entire pattern is formed in a 65 μm square area.

50 (b) shows the processing time required when the feature amount extraction processing for a predetermined number of evaluation points E is performed on the original figure pattern 10 shown in FIG. It is the graph compared about embodiment. Again, the bar graph labeled “Density Map” in the figure represents the processing time according to the basic embodiment, and the bar graph labeled “Functional calculation” represents the processing time according to the additional embodiment. The point that each section constituting these bar graphs indicates individual processing is the same as the bar graph of FIG. 48 (b).

比較 Comparing both bar graphs, the overall processing time is much shorter for “Functional calculation” than for “Density map”. This is because, in the basic embodiment, the density map creation process and the image pyramid creation process take a long time, whereas in the additional embodiment, the calculation process of the calculation function Zk (X, Y) is extremely difficult. This is because it takes a short time. In the case of the ISO-Space pattern shown in FIG. 50 (a) た め, the number of rectangles created by the rectangular aggregate replacement unit 221 can be relatively small, so that the calculation processing load of the calculation function Zk (X, Y) is inevitably required. Will be reduced. Therefore, as for the pattern in which the number of rectangles created by the rectangular aggregate replacement unit 221 is reduced as in this ISO-Space IV pattern, as long as processing time is concerned, the additional embodiment is used rather than the basic embodiment. Can be seen to be efficient.

As described above, the basic embodiment described in §1 to §4 and the additional embodiment described in §5 have a difference in processing time required for feature amount extraction depending on the feature of the original graphic pattern 10 to be handled. It will be. Therefore, in practice, it is preferable to perform more efficient feature amount extraction processing by properly using the basic embodiment and the additional embodiment according to the type of the original graphic pattern 10 to be handled. .

The figure pattern shape estimation apparatus according to the present invention simulates a lithography process using an original figure pattern in a field where a specific material layer needs to be finely patterned, such as a semiconductor device manufacturing process. Thus, it can be widely used as a technique for estimating the shape of a real graphic pattern formed on a real substrate.

10: Original graphic pattern 15: Corrected graphic pattern 20: Real graphic pattern 50: Rectangular aggregate 60: Rectangular aggregate (with dose)
100: figure pattern shape correction apparatus 100 ′: figure pattern shape estimation apparatus 110: evaluation point setting unit 120: feature quantity extraction unit 121: original image creation section 122: image pyramid creation section 123: feature quantity calculation section 130: bias Estimation unit 131: Feature value input unit 132: Estimation operation unit 140: Pattern correction unit 200: Graphic pattern shape correction device 200 ': Graphic pattern shape estimation device 220: Feature value extraction unit 221: Rectangle aggregate replacement unit 222: Feature quantity calculation unit 223: calculation function providing units A to D: individual pixels / pixel values of individual pixels B: lower side of rectangle Bi: lower side of i-th rectangle / Y coordinate values a to d thereof: evaluation point E And the horizontal distance or vertical distance b, b (1, 1) to b (i + 1, M (i + 1)), b (N + 1) between the pixel and the center point of each pixel: Ral network parameters C: reference circles C1, C2: reference circles D1 to Dn: difference image Di: dose amount for the i-th rectangle dX: rectangular X-axis direction width dY: rectangular Y-axis direction widths E, E1 E23: Evaluation point E (X, Y): Evaluation points e1 to e22 on the XY two-dimensional orthogonal coordinate system F1 to F12 on the graph: Figures (rectangles) constituting the original figure pattern 10
F1d to F5d: Rectangles with doses Fh1 to Fh3: Horizontal rectangles Fv1 to Fv3: Vertical rectangles Fi: i-th rectangle f (ξ): Function used for calculation of neural network fhi: Horizontal function fhi (σk): Horizontal function fvi using the kth expansion coefficient σk for the i-th rectangle: Vertical function fvi (σk): Vertical function using the kth expansion coefficient σk for the i-th rectangle G: apportioned value / centroid GF33, GF55: Gaussian filter H: apportioned values h (1, 1) to h (N, M (N)): neurons in the hidden layer of the neural network / calculated values i: hidden of the neural network A parameter indicating the number of layers / a parameter indicating a rectangle number K: a feature amount calculation coefficient k: a parameter indicating an image number / a parameter indicating a calculation function number L: Learning information / Left side of rectangle Li: Left side of i-th rectangle / X coordinate value LB: Lower left corner point LF33, LF55: Laplacian filter M1: Area density map M2: Edge length density map M3: Dose Density maps M (1) to M (N): dimensions of each hidden layer of the neural network N: number of hidden layers of the neural network n: number of layers of the image pyramid / total number of feature quantities (calculation functions) O: XY two-dimensional Origin P1 to Pn of Cartesian coordinate system: hierarchical image Pk: kth hierarchical image PC: corrected image PD: image pyramid (sub-image pyramid)
PP: Image pyramid (main image pyramid)
Q1: First preparation image (original image)
Qk: k-th prepared image q, qh, qv: total number of rectangles R: right side of rectangle Ri: right side of i-th rectangle / its X coordinate value RT: upper right corner point of rectangle r: radius of reference circle C S: Actual substrates S1 to S848: Steps in flowchart T: Upper side Ti of rectangle: Upper side of i-th rectangle / Y coordinate value U: Pixel u: Pixel dimensions W, W (1, 11) to W (N + 1) , 1M (N)): Neural network parameter w: Half of minute width X: Horizontal coordinate axis x, x1 to xn of XY two-dimensional orthogonal coordinate system: Feature amount Y: Vertical coordinate axis y of XY two-dimensional orthogonal coordinate system , Y11 to y13: Process bias Zk (X, Y): k-th calculation function ξ: arguments σ, σ1, σ2 of function f: spread coefficient σk: k-th spread coefficient

Claims (40)

A figure pattern shape estimation device (100 ′) that estimates the shape of the actual figure pattern (20) formed on the actual substrate (S) by simulating a lithography process using the original figure pattern (10). There,
An evaluation point setting unit (110) for setting an evaluation point (E) on the original figure pattern (10);
A feature amount extraction unit (120) for extracting feature amounts (x1 to xn) indicating features around the evaluation point (E) for the original figure pattern (10);
Based on the feature quantities (x1 to xn), a process bias (y indicating the amount of deviation between the position of the evaluation point (E) on the original figure pattern (10) and the position on the actual figure pattern (20) ) A bias estimation unit (130) for estimating
With
The evaluation point setting unit (110) sets an evaluation point (E) at a predetermined position on the contour line based on the original graphic pattern (10) including the contour line information indicating the boundary between the inside and the outside of the graphic. And
The feature quantity extraction unit (120)
Based on the original figure pattern (10), an original image creation unit (121) that creates an original image composed of an aggregate of pixels (U) each having a predetermined pixel value;
An image pyramid for performing an image pyramid creation process including a reduction process for creating a reduced image by reducing the original image to create an image pyramid (PP) composed of a plurality of hierarchical images (P1 to Pn) having different sizes. Creating unit (122);
Feature amount calculation for calculating feature amounts (x1 to xn) based on pixel values of pixels corresponding to the positions of the evaluation points (E) for each hierarchical image (P1 to Pn) constituting the image pyramid (PP) Part (123);
Have
The bias estimation unit (130) is
A feature amount input unit (131) for inputting feature amounts (x1 to xn) calculated for the evaluation point (E);
Based on learning information (L) obtained in advance by a learning stage, an estimated value (y) corresponding to the feature amount (x1 to xn) is obtained, and the obtained estimated value is obtained for the evaluation point (E). An estimation calculation unit (132) that outputs an estimated value of the process bias of
An apparatus for estimating the shape of a graphic pattern, comprising: In the figure pattern shape estimation apparatus (100 ') according to claim 1,
The original image creation unit (121) superimposes the original figure pattern (10) on a mesh composed of a two-dimensional array of pixels (U), and positions of individual pixels and figures (F1 to F5) constituting the original figure pattern A shape estimation apparatus for a graphic pattern, wherein the pixel value of each pixel (U) is determined based on the relationship with the position of the contour line. The figure pattern shape estimation apparatus (100 ') according to claim 2,
Based on the original graphic pattern (10), the original image creation unit (121) recognizes the internal area and the external area of each graphic (F1 to F5), and determines the occupancy rate of the internal area in each pixel. An apparatus for estimating a shape of a graphic pattern, wherein an area density map (M1) having pixel values is created as an original image. The figure pattern shape estimation apparatus (100 ') according to claim 2,
The original image creation unit (121) recognizes the contour lines of the respective graphics (F1 to F5) based on the original graphic pattern (10), and determines the length of the contour line existing in each pixel as the pixel value of the pixel. An edge length density map (M2) is created as an original image. The figure pattern shape estimation apparatus (100 ') according to claim 2,
An original graphic pattern (10) including information on a contour line indicating the boundary between the inside and the outside of the graphic (F1 to F5) and information on a dose amount for each graphic in the lithography process. Based on the internal area and external area of each figure, and further, the dose amount for each figure is recognized, and for each figure existing in each pixel, the occupancy of the internal area and the dose amount of the figure The figure pattern shape estimation apparatus is characterized in that a dose density map (M3) in which a sum of the products is obtained as a pixel value is generated as an original image. In the figure pattern shape estimation apparatus (100 ') according to any one of claims 1 to 5,
The image pyramid creation unit (122) has a function of performing a filter process using a predetermined image processing filter (GF33) on the original image or the reduced image, and alternately executes the filter process and the reduction process. Thus, a graphic pattern shape estimation device for creating an image pyramid (PP) composed of a plurality of hierarchical images (P1 to Pn). In the figure pattern shape estimation apparatus (100 ') according to claim 6,
The image pyramid creation unit (122) uses the original image created by the original image creation unit (121) as the first preparation image Q1, and is obtained by filtering the kth preparation image Qk (where k is a natural number). Filtering is performed until the nth layer image Pn is obtained, assuming that the image is the kth layer image Pk, the image obtained by the reduction process on the kth layer image Pk is the (k + 1) th preparation image Q (k + 1). By alternately executing reduction processing, an image pyramid (PP) composed of a plurality of n hierarchical images (P1 to Pn) including the first hierarchical image P1 to the nth hierarchical image Pn is created. A shape pattern shape estimation apparatus. In the figure pattern shape estimation apparatus (100 ') according to claim 6,
The image pyramid creation unit (122) uses the original image created by the original image creation unit (121) as the first preparation image Q1, and is obtained by filtering the kth preparation image Qk (where k is a natural number). A difference image Dk between the filter-processed image Pk and the k-th preparation image Qk is obtained, the difference image Dk is set as the k-th layer image Dk, and an image obtained by the reduction process on the k-th filter-process image Pk is the (( As the preparation image Q (k + 1) of (k + 1), the first hierarchical image D1 to the nth hierarchical image Dn are included by alternately executing the filtering process and the reduction process until the nth hierarchical image Dn is obtained. An apparatus for estimating a shape of a graphic pattern, which creates an image pyramid (PD) composed of a plurality of n hierarchical images (D1 to Dn). In the figure pattern shape estimation apparatus (100 ') according to claim 6,
The image pyramid creation unit (122)
The original image created by the original image creation unit (121) is defined as the first preparation image Q1, and an image obtained by filtering the kth preparation image Qk (where k is a natural number) is the kth main layer image Pk. The image obtained by the reduction process for the k-th main layer image Pk is defined as the (k + 1) th preparation image Q (k + 1), and the filter process and the reduction process are alternately performed until the n-th main layer image Pn is obtained. By executing, a main image pyramid (PP) composed of a plurality of n kinds of layer images (P1 to Pn) including the first main layer image P1 to the nth main layer image Pn is created,
Further, a difference image Dk between the k-th main layer image Pk and the k-th preparation image Qk is obtained, and the difference image Dk is set as the k-th sub-layer image Dk, whereby the first sub-layer image D1. A sub-image pyramid (PD) composed of a plurality of n hierarchical images (D1 to Dn) including the n-th sub-hierarchical image Dn,
A feature amount calculation unit (123) performs a feature on each hierarchical image constituting the main image pyramid (PP) and the sub image pyramid (PD) based on the pixel value of the pixel corresponding to the position of the evaluation point (E). A figure pattern shape estimation apparatus for calculating a quantity (y). The figure pattern shape estimation apparatus (100 ') according to any one of claims 6 to 9,
An image pyramid creation unit (122) executes a filtering process by a convolution operation using a Gaussian filter or a Laplacian filter as an image processing filter to create an image pyramid (PP), and a shape estimation apparatus for a graphic pattern . The figure pattern shape estimation apparatus (100 ') according to any one of claims 1 to 10,
The image pyramid creation unit (122) performs, as a reduction process, an average pooling process in which a plurality of m adjacent pixels are replaced with a single pixel having an average value of pixel values of the m adjacent pixels as a pixel value. An apparatus for estimating a shape of a graphic pattern, wherein a reduced image is created by execution. The figure pattern shape estimation apparatus (100 ') according to any one of claims 1 to 10,
The image pyramid creation unit (122) performs, as a reduction process, a max pooling process in which a plurality of m adjacent pixels are replaced with a single pixel having a maximum pixel value of the plurality of m adjacent pixels as a pixel value. An apparatus for estimating a shape of a graphic pattern, wherein a reduced image is created by execution. The figure pattern shape estimation apparatus (100 ') according to any one of claims 1 to 12,
An original image creation unit (121) performs an original image creation process based on a plurality of different algorithms, creates a plurality of original images,
An image pyramid creation unit (122) performs image pyramid creation processing based on the plurality of original images to create a plurality of image pyramids (PP),
A feature value calculation unit (123) calculates a feature value (y) for each hierarchical image constituting each of the plurality of image pyramids based on the pixel value of the pixel corresponding to the position of the evaluation point (E). An apparatus for estimating the shape of a graphic pattern characterized by the above. The figure pattern shape estimation apparatus (100 ') according to any one of claims 1 to 13,
An image pyramid creation unit (122) performs image pyramid creation processing based on a plurality of different algorithms for one original image, creates a plurality of image pyramids (PP, PD),
A feature amount calculation unit (123) calculates a feature amount for each hierarchical image constituting each of the plurality of image pyramids (PP, PD) based on the pixel value of the pixel corresponding to the position of the evaluation point (E). An apparatus for estimating a shape of a graphic pattern, characterized by calculating. The figure pattern shape estimation apparatus (100 ') according to any one of claims 1 to 14,
When the feature quantity calculation unit (123) calculates the feature quantity (y) for the specific evaluation point (E) on the specific hierarchical image, the specific evaluation is performed from the pixels constituting the specific hierarchical image. A total of j pixels are extracted as the target pixels (A to D) in the order close to the point, and a weight corresponding to the distance between the specific evaluation point and each target pixel is assigned to the pixel values of the extracted j target pixels. An apparatus for estimating a shape of a graphic pattern, which performs an operation for obtaining a weighted average in consideration. The figure pattern shape estimation apparatus (100 ') according to any one of claims 1 to 15,
The estimation calculation unit (132) includes a neural network having the feature amounts (x1 to xn) input by the feature amount input unit (131) as input layers and the process bias estimate (y) as an output layer. A shape pattern shape estimation apparatus. The figure pattern shape estimation apparatus (100 ') according to claim 16,
The neural network included in the estimation calculation unit (132) uses the dimension value obtained by measuring the actual dimension of the actual figure pattern formed on the actual substrate by the lithography process using a large number of test pattern figures, and each test pattern figure. A shape estimation apparatus for a graphic pattern, characterized in that a process bias estimation process is performed by using, as learning information (L), a parameter obtained from a learning step using The figure pattern shape estimation apparatus (100 ') according to claim 16 or 17,
The estimation calculation unit (132) uses the estimated value (y) of the process bias for the evaluation point (E) located on the contour line of the predetermined graphic as the deviation amount of the evaluation point in the normal direction of the contour line. An apparatus for estimating a shape of a graphic pattern, wherein an estimated value is obtained. A figure pattern shape correction apparatus (100) for correcting the shape of an original figure pattern (10) using the figure pattern shape estimation apparatus (100 ') according to any one of claims 1 to 18, comprising:
In addition to the evaluation point setting unit (110), the feature quantity extraction unit (120), and the bias estimation unit (130) that constitute the figure pattern shape estimation apparatus (100 ′),
A pattern correction unit (140) for correcting the original figure pattern (10) based on the estimated value (y) of the process bias output from the bias estimation unit (130);
The corrected graphic pattern (15) obtained by the correction by the pattern correction unit (140) is given as a new original graphic pattern to the graphic pattern shape estimation device (100 '), thereby repeatedly performing correction on the graphic pattern. A figure pattern shape correction apparatus having a function of: A program that causes a computer to function as the figure pattern shape estimation apparatus (100 ') according to any one of claims 1 to 18 or the figure pattern shape correction apparatus (100) according to claim 19. A figure pattern shape estimation method for estimating the shape of an actual figure pattern (20) formed on an actual substrate (S) by simulating a lithography process using an original figure pattern (10),
An original graphic pattern input step (S1) in which a computer inputs an original graphic pattern (10) including information on a contour line indicating the boundary between the inside and the outside of the graphic;
An evaluation point setting step (S2) in which the computer sets an evaluation point (E) at a predetermined position on the contour line;
A feature amount extraction step (S3) in which the computer extracts feature amounts (x1 to xn) indicating features around the evaluation point (E) for the original figure pattern (10);
A process in which the computer indicates a deviation amount between the position on the original graphic pattern (10) of the evaluation point (E) and the position on the actual graphic pattern (20) based on the feature values (x1 to xn). A process bias estimation step (S4) for estimating the bias (y);
Have
In the feature quantity extraction step (S3),
Based on the original graphic pattern (10), an original image creating step of creating an original image composed of a collection of pixels each having a predetermined pixel value;
An image pyramid for performing an image pyramid creation process including a reduction process for creating a reduced image by reducing the original image to create an image pyramid (PP) composed of a plurality of hierarchical images (P1 to Pn) having different sizes. The creation stage,
Feature amount calculation for calculating feature amounts (x1 to xn) based on pixel values of pixels corresponding to the positions of the evaluation points (E) for each hierarchical image (P1 to Pn) constituting the image pyramid (PP) Stages,
Including
In the process bias estimation step (S4), an estimated value (y) corresponding to the feature amount (x1 to xn) is obtained based on learning information (L) obtained in a learning step performed in advance. A method for estimating a shape of a graphic pattern, comprising: an estimation calculation step of outputting an estimated value as an estimated value of a process bias for the evaluation point. The shape estimation method for a graphic pattern according to claim 21,
In the image pyramid creation stage, a filter process stage that performs a filter process using a predetermined image processing filter on the original image or the reduced image, and a reduction process stage that performs a reduction process on the image after the filter process A method for estimating a shape of a graphic pattern, characterized in that an image pyramid (PP) composed of a plurality of hierarchical images (P1 to Pn) is created by performing alternately. The shape estimation method for a graphic pattern according to claim 22,
In the image pyramid creation stage, an image pyramid (PD) is created in which the image after filtering, or the difference image (D1 to Dn) between the image after filtering and the image before filtering, is used as a hierarchical image. Shape estimation method of figure pattern to be performed. A figure pattern shape estimation apparatus (200 ′) that estimates the shape of the actual figure pattern (20) formed on the actual substrate (S) by simulating a lithography process using the original figure pattern (10). There,
An evaluation point setting unit (110) for setting an evaluation point (E) on the original figure pattern (10);
A feature amount extraction unit (220) for extracting feature amounts (x1 to xn) indicating features around the evaluation point (E) for the original figure pattern (10);
Based on the feature quantities (x1 to xn), a process bias (y indicating the amount of deviation between the position of the evaluation point (E) on the original figure pattern (10) and the position on the actual figure pattern (20) ) A bias estimation unit (130) for estimating
With
The evaluation point setting unit (110) sets an evaluation point (E) at a predetermined position on the contour line based on the original graphic pattern (10) including the contour line information indicating the boundary between the inside and the outside of the graphic. And
The feature quantity extraction unit (220)
A rectangular aggregate replacement unit (221) that replaces a graphic included in the original graphic pattern (10) with a rectangular aggregate (50);
A calculation function providing unit that provides a calculation function (Zk (X, Y)) for calculating feature quantities (x1 to xn) based on a positional relationship with respect to a rectangle positioned around one evaluation point (E) (223),
Using the calculation function (Zk (X, Y)) provided from the calculation function providing unit (223), the feature amount for each evaluation point (E) set by the evaluation point setting unit (110) is calculated. A feature amount calculation unit (222) to perform,
Have
The bias estimation unit (130) is
A feature amount input unit (131) for inputting feature amounts (x1 to xn) calculated for the evaluation point (E);
Based on learning information (L) obtained in advance by a learning stage, an estimated value (y) corresponding to the feature amount (x1 to xn) is obtained, and the obtained estimated value is used as a process bias for the evaluation point. An estimation calculation unit (132) that outputs an estimated value of
An apparatus for estimating the shape of a graphic pattern, comprising: The figure pattern shape estimation apparatus (200 ') according to claim 24,
From the feature amount (x1) considering the narrow range in the vicinity of the evaluation point (E) to the feature amount (xn) considering the wide range including the distance from the evaluation point, the calculation function providing unit (223) In order to calculate a plurality of n feature quantities (x1 to xn) with different consideration ranges, a plurality of n calculation functions are provided,
A feature amount calculation unit (222) uses the plurality of n types of calculation functions to calculate a plurality of n feature amounts (x1 to xn) for each evaluation point (E). Shape estimation device. In the figure pattern shape estimation apparatus (200 ') according to claim 25,
The calculation function providing unit (223) provides a calculation function for calculating a feature amount (x1 to xn) based on a positional relationship with respect to four sides of a rectangle positioned around one evaluation point (E). An apparatus for estimating the shape of a featured graphic pattern. In the figure pattern shape estimation apparatus (200 ') according to claim 26,
In the XY two-dimensional orthogonal coordinate system in which the rectangular aggregate replacement unit (221) takes the X axis positive direction as the right direction and the Y axis positive direction as the upward direction, the figure included in the original figure pattern (10) is converted into the X axis. Is replaced by a rectangular collection (50) having upper and lower sides parallel to, and left and right sides parallel to the Y-axis,
The calculation function providing unit (223) has a left side positional deviation indicating a distance from the left side in the X-axis direction of the evaluation point (E) and a right side positional deviation indicating a distance from the right side on the XY two-dimensional orthogonal coordinate system. And a calculation function for calculating feature quantities (x1 to xn) based on an upper side position deviation indicating a distance from the upper side in the Y-axis direction of an evaluation point and a lower side position deviation indicating a distance from the lower side An apparatus for estimating a shape of a graphic pattern, characterized in that: In the figure pattern shape estimation apparatus (200 ') according to claim 27,
The calculation function providing unit (223)
For one particular rectangle of interest,
As the variable value increases, the function value increases monotonously, and when the X coordinate value of the left side of the target rectangle is given as a variable, the function value becomes 0, and the function value increases monotonically as the variable value increases. A horizontal function that is the sum of an X-axis monotonically decreasing function that decreases and gives a function value of 0 when the X coordinate value of the right side of the target rectangle is given as a variable;
The function value monotonously increases with the increase of the variable value, and the Y-axis monotonically increasing function when the Y coordinate value of the lower side of the target rectangle is given as a variable, and the function value monotonously with the increase of the variable value A vertical function that is the sum of a Y-axis monotonically decreasing function that decreases and gives a function value of 0 when the Y coordinate value of the upper side of the rectangle of interest is given as a variable;
, And an amount indicating a positional relationship with respect to the target rectangle with respect to a certain target evaluation point, a function value of the horizontal function using the X coordinate value of the target evaluation point as a variable, and a value of the target evaluation point Based on the product of the function value of the vertical function with the Y coordinate value as a variable,
An apparatus for estimating a shape of a graphic pattern, characterized in that a calculation function is provided in which a sum of amounts indicating positional relationships with respect to rectangles positioned around the target evaluation point is used as a characteristic amount for the target evaluation point. In the figure pattern shape estimation apparatus (200 ') according to claim 28,
The calculation function providing unit provides a plurality of n types of calculation functions using functions having different degrees of monotonic increase or monotonic decrease as calculation functions for calculating a plurality of n types of feature quantities with different consideration ranges. An apparatus for estimating the shape of a graphic pattern characterized by the above. The figure pattern shape estimation apparatus (200 ') according to claim 29,
The calculation function providing unit (223) prepares a calculation function including a monotone increasing function or a monotone decreasing function having a variable obtained by dividing the left side position deviation, the right side position deviation, the upper side position deviation, and the lower side position deviation by the spread coefficient σ. An apparatus for estimating the shape of a graphic pattern, which provides a plurality of n types of calculation functions by changing the value of the spread coefficient σ into a plurality of n types. The shape estimation apparatus (200 ') for graphic patterns according to claim 30,
The calculation function providing unit (223) sets σk = 2 ^(k−1) when the k-th expansion coefficient is expressed as σk using the parameter k in the range of 1 ≦ k ≦ n. An apparatus for estimating the shape of a graphic pattern characterized by the above. The figure pattern shape estimation apparatus (200 ') according to any one of claims 24 to 31,
Based on the original graphic pattern (10), the rectangular aggregate replacement unit (221) includes information on a contour line indicating the boundary between the inside and the outside of the graphic, and information on a dose amount for each graphic in the lithography process. Recognize the internal area and external area of each figure, further recognize the dose amount for each figure, set the dose amount for each rectangle corresponding to each figure,
A shape estimation device for a graphic pattern, characterized in that a calculation function providing unit (223) provides a calculation function including a dose amount set for each rectangle as a variable. The figure pattern shape estimation apparatus (200 ') according to any one of claims 24 to 31,
The rectangular aggregate replacement unit (221) recognizes the unit line segment constituting the contour line of each figure based on the original figure pattern (10), and sets a minute width for each unit line segment, whereby the original figure An apparatus for estimating a shape of a graphic pattern, wherein a graphic included in the pattern is replaced with a rectangular aggregate having the minute width. The figure pattern shape estimation apparatus (200 ') according to any one of claims 24 to 33,
When the feature quantity calculation unit (222) calculates the feature quantities (x1 to xn) for the evaluation point (E), a reference circle (C) having a predetermined radius around the evaluation point (E) is defined. And a figure pattern shape estimation apparatus that performs a calculation considering only a positional relationship with a rectangle belonging to a predetermined neighborhood range corresponding to the reference circle. The figure pattern shape estimation apparatus (200 ') according to any one of claims 24 to 34,
The estimation calculation unit (132) includes a neural network having the feature amounts (x1 to xn) input by the feature amount input unit (131) as input layers and the process bias estimate (y) as an output layer. A shape pattern shape estimation apparatus. In the figure pattern shape estimation apparatus (200 ') according to claim 35,
The neural network included in the estimation calculation unit (132) uses the dimension value obtained by measuring the actual dimension of the actual figure pattern formed on the actual substrate by the lithography process using a large number of test pattern figures, and each test pattern figure. A shape estimation apparatus for a graphic pattern characterized in that process bias estimation processing is performed by using, as learning information (L), the parameters obtained in the learning step using the feature amounts (x1 to xn) obtained from the above. In the figure pattern shape estimation device (200 ') according to claim 35 or 36,
The estimation calculation unit (132) uses the estimated value (y) of the process bias for the evaluation point (E) located on the contour line of the predetermined graphic as the deviation amount of the evaluation point in the normal direction of the contour line. An apparatus for estimating a shape of a graphic pattern, wherein an estimated value is obtained. A figure pattern shape correction apparatus (200) for correcting the shape of an original figure pattern (10) using the figure pattern shape estimation apparatus (200 ') according to any one of claims 24 to 37,
In addition to the evaluation point setting unit (110), the feature quantity extraction unit (220), and the bias estimation unit (130) that constitute the figure pattern shape estimation apparatus (200 ′),
A pattern correction unit (140) for correcting the original figure pattern (10) based on the estimated value (y) of the process bias output from the bias estimation unit (130);
A function of repeatedly executing correction on a graphic pattern by giving the corrected graphic pattern obtained by the correction by the pattern correction unit (140) as a new original graphic pattern to the graphic pattern shape estimation device (200 '). A shape correction apparatus for a graphic pattern, comprising: A program that causes a computer to function as the figure pattern shape estimation apparatus (200 ') according to any one of claims 24 to 37 or the figure pattern shape correction apparatus (200) according to claim 38. A figure pattern shape estimation method for estimating the shape of an actual figure pattern (20) formed on an actual substrate (S) by simulating a lithography process using an original figure pattern (10),
An original graphic pattern input stage in which a computer inputs an original graphic pattern (10) including information on a contour line indicating the boundary between the inside and the outside of the graphic;
An evaluation point setting step in which the computer sets an evaluation point (E) at a predetermined position on the contour line;
A feature amount extraction step in which a computer extracts feature amounts (x1 to xn) indicating features around the evaluation point (E) for the original figure pattern (10);
A process in which the computer indicates a deviation amount between the position on the original graphic pattern (10) of the evaluation point (E) and the position on the actual graphic pattern (20) based on the feature values (x1 to xn). A process bias estimation stage for estimating the bias (y);
Have
The feature extraction step includes:
A rectangular aggregate replacement step of replacing a graphic included in the original graphic pattern (10) with a rectangular aggregate (50);
For each evaluation point (E), a feature amount calculating step for calculating feature amounts (x1 to xn) based on the positional relationship with respect to the rectangle positioned around the evaluation point (E);
Including
In the process bias estimation step, an estimated value (y) corresponding to the feature amount (x1 to xn) is obtained based on learning information (L) obtained in a learning step performed in advance, and the obtained estimated value is obtained. A method for estimating a shape of a graphic pattern, comprising: an estimation calculation step of outputting as an estimated value of a process bias for the evaluation point.

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