CN115437225A - Method for drawing photoetching process window - Google Patents

Abstract

The invention relates to the technical field of development of a photoetching process, in particular to a method for drawing a photoetching process window, which is used for obtaining exposure results and constraint conditions of a pattern with a specific characteristic size under different defocusing amounts and different exposure doses; drawing two Poisson curves based on the exposure result and the constraint condition; judging whether the two poisson curves and the head and tail points of the poisson curves form the concavity and the convexity of a closed area to obtain a judgment result; and based on the judgment result, drawing the maximum area ellipse in the new closed region according to the convex optimization principle to obtain the process window, wherein the method realizes the rapid drawing of the process window by dividing the irregular closed region into convex sets by utilizing the characteristics of rapidness and high efficiency of convex optimization, draws the elliptical process window at the speed of 0.11s, does not need to designate the starting point of elliptical search at any position, and meets the requirement of rapidly drawing the process window.

Description

A Method for Drawing Photolithography Process Window

technical field

The invention relates to the technical field of photolithography process development, in particular to a method for drawing a photolithography process window.

Background technique

Lithography technology is a key technology in integrated circuit manufacturing. It is responsible for transferring mask patterns to silicon wafers. The effect of photolithography pattern transfer is affected by many factors, among which the change of defocus amount and the change of exposure dose are two common ones. factors.

In the projection optical lithography system, for a given feature size, the imaging position that can obtain the ideal line width is called the best focal plane position. Similarly, the exposure dose that can obtain the ideal line width is called the optimal exposure dose. In the actual photolithography process, the position of the best focal plane is susceptible to certain changes due to aberrations, three-dimensional effects of the mask, etc., and the optimal exposure doses corresponding to different patterns are different.

In order to accurately obtain the optimal exposure dose and the optimal focal plane position, it is necessary to expose the same mask pattern under different exposure doses and different defocusing amounts, and the resulting photoresist feature size is expressed in a point diagram in the form of a Poisson curve. Since it is generally believed in engineering that the range of line width variation within 10% meets the imaging quality requirements, the exposure dose and defocus variation range that meets this quality requirement can be depicted from the Poisson curve, in order to quantitatively describe the process window Generally, an ellipse with the largest area is drawn in the above range, the width of the horizontal axis of the ellipse represents the depth of focus, and the height of the vertical axis represents the exposure dose range. In order to draw an ellipse in an irregular closed area, traditional methods mostly use fixed-point search and multiple rounds of trials, which has the problem of a long cycle.

Contents of the invention

The purpose of the present invention is to provide a method for drawing a photolithography process window, aiming at solving the problems of long period of traditional ellipse drawing process window and slow drawing speed.

To achieve the above object, the present invention provides a method for drawing a photolithographic process window, comprising the following steps:

Obtain the exposure results and constraints of specific feature size graphics under different defocus amounts and different exposure doses;

drawing two Poisson curves based on the exposure result and the constraints;

Judging the concavity and convexity of the closed area formed by the two Poisson curves and the first and last points of the Poisson curves to obtain a judgment result;

Based on the judgment result, an ellipse with the largest area in the new closed area is drawn according to the principle of convex optimization to obtain the process window.

Wherein, the constraint condition includes the unit of the data, the physical meaning represented by the horizontal and vertical distribution, and the line width constraint range.

Wherein, the line width restriction range is 0.225um˜0.275um.

Wherein, the judgment result includes any one of a convex polygon and a concave polygon.

Wherein, the specific way of obtaining the process window is to draw the maximum area ellipse in the new closed area according to the principle of convex optimization based on the judgment result:

If the judgment result is the convex polygon, then according to the principle of convex optimization, draw the largest area ellipse in the new closed area, if the judgment result is the concave polygon, then find the convexity from the concave polygon Polygon, and then according to the principle of convex optimization, describe the largest area ellipse in the new closed area.

A method for drawing a photolithography process window of the present invention obtains the exposure results and constraint conditions of graphics with specific feature sizes under different defocus amounts and different exposure doses; draws two Poisson graphs based on the exposure results and the constraint conditions curve; judging two described Poisson curves and the concavo-convexity of the closed area formed by the first and last points of the Poisson curve, and obtaining a judgment result; based on the judgment result, the maximum area ellipse in the new closed area is described according to the principle of convex optimization, The process window is obtained. This method establishes a method and process for drawing the lithography process window, which comprehensively considers the Poisson curve characteristics of the exposure results under different exposure doses and different defocus amounts during lithography imaging, and makes full use of convex optimization to quickly and efficiently The feature of dividing the irregular closed area into convex sets realizes the rapid drawing of the process window, and solves the dependence of the search results on the starting point position, and draws the ellipse process window at a speed of 0.11s, and does not need to be in the Specify the starting point of the ellipse search at any position, which meets the requirements of quickly drawing the process window. This method quickly analyzes the process window of the experimental data or simulation data, and combines the data analysis results to quickly obtain the overlapping process window size of multiple graphics. The problem of traditional ellipse drawing process window is long and drawing speed is slow.

Description of drawings

In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings that need to be used in the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description are only These are some embodiments of the present invention. Those skilled in the art can also obtain other drawings based on these drawings without creative work.

FIG. 1 is a schematic diagram of a Poisson curve of a method for drawing a photolithography process window provided by the present invention.

FIG. 2 is a schematic structural diagram of the judgment result of a method for drawing a photolithography process window provided by the present invention.

Fig. 3 is a schematic structural diagram of the distribution of elliptical process windows.

FIG. 4 is a flowchart of a method for drawing a photolithography process window provided by the present invention.

Fig. 5 is a graph of exposure results of a specific feature size pattern under different defocus amounts and different exposure doses.

detailed description

Embodiments of the present invention are described in detail below, examples of which are shown in the drawings, wherein the same or similar reference numerals designate the same or similar elements or elements having the same or similar functions throughout. The embodiments described below by referring to the figures are exemplary and are intended to explain the present invention and should not be construed as limiting the present invention.

Please refer to Fig. 1 to Fig. 5, the present invention provides a kind of method of drawing photolithography process window, comprises the following steps:

S1 Obtain the exposure results and constraints of a specific feature size pattern under different defocus amounts and different exposure doses;

Specifically, the constraints include the unit of data, the physical meaning represented by the horizontal and vertical distribution, and the line width constraint range. The exposure results of specific feature size graphics under different defocus amounts and different exposure doses are shown in Figure 5. In 5, the first line indicates the defocus amount, the unit is um, the first column indicates the exposure dose, the unit is mJ/cm2, and the rest of the data indicate the line width value of the exposure result, the unit is um, and the line width constraint range is ±10 %, the central line width is 0.25um, that is, the line width restriction range is 0.225um-0.275um.

S2 drawing two Poisson curves based on the exposure result and the constraints;

Specifically, first exclude the data in the first row and the first column of the data that has nothing to do with the line width value of the exposure result; then perform cubic spline interpolation on the line width value of the exposure result; The line width value between is set to 1, and the other values are set to 0; finally, the boundary of the area with a value of 1 is drawn, and the two Poisson curves meeting the requirements of 0.225um and 0.275um are obtained, and the line width inside the curve is between the two, as shown in Figure 1.

S3 judging the concavo-convexity of the closed area formed by the two Poisson curves and the first and last points of the Poisson curves, and obtaining a judgment result;

Specifically, the judgment result includes any one of a convex polygon and a concave polygon.

S4 Based on the judgment result, draw an ellipse with the largest area in the new closed area according to the principle of convex optimization to obtain the process window.

Specific ways:

S41 If the judgment result is the convex polygon, then according to the principle of convex optimization, draw the largest area ellipse in the new closed area, if the judgment result is the concave polygon, then find the concave polygon from the concave polygon. Convex polygon, and then according to the principle of convex optimization, describe the largest area ellipse in the new closed area.

Specifically, the vertex of the dot Poisson curve limits the concavo-convexity of the polygon. Using the vertex as the starting point, draw a straight line to convert the polygon into the convex polygon, as shown in Figure 2 below. According to the principle of convex optimization , depicting the largest area ellipse in the new closed area, the principle of convex optimization is as follows:

The general formula for an ellipsoid can be expressed as

ε＝{Bu+d|||u|| ₂ ≤ 1}

The enclosed area of a convex polygon can be expressed as

The solution to the ellipse with the largest area can be expressed as

maximize log det B

In the above formula, C represents a general closed area, i represents the serial number of the vertex, B represents the half-width of the major axis of the ellipse, d represents the translation distance of the center of the ellipse relative to the origin, x represents the vertex coordinates of the closed area, and a and b are According to the matrix and vector fitted by the inequality, T represents the transposition of the matrix, m represents the number of vertices in the closed area, and the distribution of the ellipse process window is shown in Figure 3.

The drawing time of the ellipse in the figure above is 0.11s, and there is no need to specify the starting point of the ellipse search at any position. As can be seen from Figure 3, using the new drawing process of the ellipse process window, the fast drawing of the ellipse can be realized, and the search result can be solved Dependency on the starting position.

What is disclosed above is only a preferred embodiment of the patent title of the present invention, and of course it cannot limit the scope of rights of the present invention. Those of ordinary skill in the art can understand the whole or part of the process of realizing the above embodiments, and according to this The equivalent changes made in the claims of the invention still belong to the scope covered by the invention.

Claims (5)

1. A method for drawing a photolithography process window, comprising the steps of:

acquiring exposure results and constraint conditions of the specific feature size graph under different defocus amounts and different exposure doses;

drawing two Poisson curves based on the exposure result and the constraint condition;

judging whether the two poisson curves and the head and tail points of the poisson curves form the concavity and the convexity of a closed area to obtain a judgment result;

and drawing the maximum area ellipse in the new closed region according to the convex optimization principle based on the judgment result to obtain a process window.

2. The method of drawing a photolithography process window of claim 1,

the constraint conditions comprise units of data, physical meanings represented by horizontal and vertical distribution and line width constraint ranges.

3. The method of drawing a photolithography process window of claim 2,

the line width constraint range is 0.225 um-0.275 um.

4. The method of drawing a photolithography process window of claim 1,

the judgment result includes any one of a convex polygon and a concave polygon.

5. The method of drawing a photolithography process window of claim 4,

the specific mode of describing the maximum area ellipse in the new closed region according to the convex optimization principle based on the judgment result to obtain the process window is as follows:

if the judgment result is the convex polygon, depicting the maximum area ellipse in the new closed region according to the convex optimization principle, if the judgment result is the concave polygon, searching the convex polygon from the concave polygon, and depicting the maximum area ellipse in the new closed region according to the convex optimization principle.

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