JP2010061190A - Model parameter extraction device and model parameter extraction method - Google Patents

Abstract

To improve the accuracy of circuit simulation.
An input unit for inputting measurement data indicating the electrical characteristics of a measurement point, and the electrical characteristics of the measurement point for the measurement point where the input measurement data exists are determined based on the input measurement data. A first approximate function formula creating unit 201 that creates a first approximate function formula to be approximated, and a first approximate function created by the first approximate function formula creating unit 201 for measurement points for which input measurement data is insufficient The second approximate function formula creating unit 202 that modifies the formula to create a second approximate function formula that approximates the electrical characteristics of the measurement point, and the first and second approximate function formula creating units 201 and 202 created by the first and second approximate function formula creating units 201 and 202. Based on the first and second approximate function formulas, an approximate value calculation unit 30 that calculates an approximate value of the electrical characteristic of the measurement point, and a model parameter set generation unit 8 that generates a model parameter set including the calculated approximate value Comprising the, an output unit 90 for outputting the generated model parameter set, a.
[Selection] Figure 1

Description

  The present invention relates to a model parameter extraction apparatus and a model parameter extraction method, and more particularly to a model parameter extraction apparatus and a model parameter extraction method for extracting model parameters of a SPICE (Simulation Program with Integrated Circuit Emphasis) model.

  The SPICE model parameter set of a MOSFET (Metal Oxide Semiconductor Field Effect Transistor) includes a global model and a binning model. The global model is a model that expresses the electrical characteristics of the entire region on the LW plane with respect to the gate length L and gate width W of the MOSFET by one model formula. On the other hand, the binning model divides the LW plane into a plurality of local regions, and the electrical characteristics in each local region on the LW plane with respect to the gate length L and gate width W of the MOSFET are effective only in each local region. This model is expressed by a local model expression. Each local region is called a bin, and creating a model divided into a plurality of bins is called binning.

  However, in general, the electrical characteristics of a fine MOSFET are nonlinear with respect to the gate length L and the gate width W, and have complicated dependencies on each other. Therefore, in the global model, it is difficult to express the electrical characteristics of the MOSFET with high accuracy.

  On the other hand, in the binning model, each local model expression represents only each bin, so that the electrical characteristics of the MOSFET can be expressed with high accuracy. For example, when a circuit simulation is executed, an appropriate local model is selected and used on the basis of the dimensions of a predetermined gate length L and gate width W, so that the electrical characteristics of the entire region on the LW plane can be accurately determined. Can be expressed.

  Here, a general procedure for creating a binning model will be described.

  First, a global model for the entire L / W area is created. The accuracy of this global model need not be high. Next, based on this global model, a local model of each measurement point arranged in a grid is created. The accuracy of this local model is preferably as high as possible. Next, a local model for each bin is created. This local model is created by solving a predetermined simultaneous equation using model parameters of four measurement points surrounding each bin.

Here, a method for creating a local model from a global model will be described. Incidentally, an example of a model parameter _{U 00.} The L / W dimensions (L _i , W _i ) at each measurement point are (L ₁ , W ₁ ), (L ₂ , W ₁ ), (L ₁ , W ₂ ), (L ₂ , W ₂ ). Assume that the value of the model parameter U ₀₀ at each measurement point is (U ₀₁ , U ₀₂ , U ₀₃ , U ₀₄ ), and the bin surrounded by each measurement point is “bin_A”. Using the values (U ₀₁ , U ₀₂ , U ₀₃ , U ₀₄ ) of these four model parameters U ₀₀ , the quaternary simultaneous linear equations of Expressions 1 to 4 are established. The solution (U ₀₁ , U ₀₂ , U ₀₃ , U ₀₄ ) of the simultaneous equations is a model parameter of “bin_A”.

[Expression 1] U ₀₁ = U ₀ + LU ₀ / L ₁ + WU ₀ / W ₁ + PU ₀ (L ₁ * W ₁ )
[Formula 2] U ₀₂ = U ₀ + LU ₀ / L ₁ + WU ₀ / W ₂ + PU ₀ (L ₁ * W ₂ )
[Equation 3] U ₀₃ = U ₀ + LU ₀ / L ₂ + WU ₀ / W ₁ + PU ₀ (L ₂ * W ₁ )
[Equation 4] _{U 04 = U 0 + LU 0} / L 2 + WU 0 / W 2 + PU 0 (L 2 * W 2)
That is, at the time of executing the circuit simulation, the solution of Equation 5 is calculated for an arbitrary gate length L and gate width W of “bin_A”.
[Formula 5] U ₀₀ = U ₀ + LU ₀ / L + WU ₀ / W + PU ₀ (L * W)
However, in the binning model, the model parameters of each bin are created by solving simultaneous equations as shown in Equations 1 to 4 using the model parameters of the four measurement points surrounding the bin. Therefore, in order to create a model parameter for a bin, measurement data indicating the electrical characteristics of four measurement points surrounding the bin is required. That is, the binning model requires measurement data at all measurement points. However, generally, measurement data may be insufficient (a TEG does not exist at a predetermined number or more measurement points) due to a lack of TEG (Test Element Group) or the like. In such a case, the area of one bin increases, and the error between the model parameters of each bin and the electrical characteristics of the MOSFET also increases. As a result, there arises a problem that the accuracy of circuit simulation is lowered.

Even if the measurement data is satisfied (the TEG exists at a predetermined number or more of measurement points), if the electrical characteristics change suddenly between the measurement points, the model parameter of the bin and the MOSFET The error between the electrical characteristics increases. As a result, there arises a problem that the accuracy of circuit simulation is lowered.
JP 2004-273903 A

  An object of the present invention is to provide a model parameter extraction device and a model parameter extraction method that improve the accuracy of circuit simulation.

According to the first aspect of the present invention,
A model parameter extraction device for extracting model parameters of a simulation model surrounded by measurement points arranged in a grid pattern in a gate length direction and a gate width direction of a transistor,
An input unit for inputting measurement data indicating the electrical characteristics of the measurement point;
A first approximation function formula that approximates the electrical characteristics of the measurement point is generated based on the measurement data input by the input unit for the measurement point that is satisfied by the measurement data input by the input unit. An approximate function formula creation unit;
For a measurement point for which measurement data input by the input unit is insufficient, the first approximate function formula created by the first approximate function formula creation unit is modified to approximate the electrical characteristics of the measurement point. A second approximate function formula creating unit for creating a two approximate function formula;
An approximate value calculation unit that calculates an approximate value of the electrical characteristics of the measurement point based on the first and second approximate function formulas created by the first and second approximate function formula creation units;
A model parameter set generation unit for generating a model parameter set including the approximate value calculated by the approximate value calculation unit;
And a model parameter extracting apparatus comprising: an output unit that outputs the model parameter set generated by the model parameter set generating unit.

According to a second aspect of the invention,
A model parameter extraction device for extracting model parameters of a simulation model surrounded by measurement points arranged in a grid in the gate length direction and gate width direction of a transistor,
A reading unit that reads electrical characteristics in the gate width or gate length direction at predetermined intervals;
A measurement point setting unit configured to set the measurement point to the gate width or the gate length corresponding to the electrical characteristic when the electrical characteristic read by the reading unit is outside an allowable range;
An estimated value calculation unit for calculating an estimated value of the electrical characteristics of the measurement point set by the measurement point setting unit;
A model parameter set generator for generating a model parameter set including the estimated value calculated by the estimated value calculator;
An output unit that outputs the model parameter set generated by the model parameter set generation unit.

According to a third aspect of the invention,
A model parameter extraction method for extracting a model parameter of a simulation model surrounded by measurement points arranged in a grid pattern in a gate length direction and a gate width direction of a transistor,
Input measurement data indicating the electrical characteristics of the measurement point,
For the measurement points satisfied by the measurement data, based on the measurement data, create a first approximate function equation that approximates the electrical characteristics of the measurement points,
For the measurement point for which the measurement data is insufficient, the first approximate function formula is corrected to create a second approximate function formula that approximates the electrical characteristics of the measurement point,
Based on the first and second approximation function equations, an approximate value of the electrical characteristics of the measurement point is calculated,
Generating a model parameter set including the approximation,
A model parameter extraction method is provided that outputs the model parameter set.

  According to the present invention, the accuracy of circuit simulation can be improved.

  Embodiments of the present invention will be described below with reference to the drawings. The following examples are one embodiment of the present invention and do not limit the scope of the present invention.

  First, Example 1 of the present invention will be described. The first embodiment of the present invention is an example of a model parameter extracting apparatus that calculates an approximate value or an estimated value of an electrical characteristic at a measurement point where no TEG exists and extracts a model parameter.

  First, the configuration of the model parameter extracting apparatus according to the first embodiment of the present invention will be described with reference to FIG. 1 and FIG. FIG. 1 is a block diagram illustrating a configuration of a model parameter extracting apparatus 1 according to the first embodiment of the present invention. FIG. 2 is a schematic diagram showing an outline of measurement data according to Example 1 of the present invention.

  As shown in FIG. 1, the model parameter extraction apparatus 1 according to the first embodiment of the present invention includes an input unit 10, an approximate function expression creation unit 20, an approximate value calculation unit 30, a reading unit 40, and a measurement point setting. Unit 50, binning model creation unit 60, estimated value calculation unit 70, model parameter set generation unit 80, and output unit 90.

As shown in FIG. 1, the input unit 10 is connected to an approximate function equation creation unit 20 and an input device (not shown). The input unit 10 also has measurement data indicating electrical characteristics (for example, an IV characteristic curve, a threshold voltage V _th , and a drain current I _on ) at a measurement point input by a user using an input device (not shown). It comes to input.

As shown in FIG. 2, the measurement data includes the measurement points at which TEGs exist for each MOSFET gate length L (= 0.04 to 10) in each of the MOSFET gate widths W (= W1 to W4). The measurement point where TEG does not exist is included. In FIG. 2, “o” indicates a measurement point where the TEG exists, and “x” indicates a measurement point where the TEG does not exist. That is, in FIG. 2, there is a TEG having a gate length L (= 0.1) at a gate width W (= W ₀ ), and a TEG having a gate length L (= 0.1) at a gate width W (= W ₁ ). Does not exist.

  Here, in the measurement data of FIG. 2, the gate width W has four stages and the gate length L has thirteen stages. Therefore, in order to create a binning model corresponding to the measurement data of FIG. 2, 52 (= 4 × 13) TEGs are required. However, in the measurement data of FIG. 2, since there are 19 TEGs, it is insufficient to create a binning model.

  As shown in FIG. 1, the approximate function formula creating unit 20 includes a first approximate function formula creating unit 201 and a second approximate function formula creating unit 202.

  As shown in FIG. 1, the first approximate function formula creating unit 201 is connected to the input unit 10, the second approximate function formula creating unit 202, the approximate value calculating unit 30, and the reading unit 40. In addition, the first approximate function formula creation unit 201 determines the gate width of the measurement data input by the input unit 10 for the measurement points where many TEGs with the same gate width W and different gate lengths L exist. An n-th order polynomial (hereinafter referred to as “first approximate function expression”) that approximates the electrical characteristics of W as a function of the gate length L is created. Note that n is a value determined by the required approximation accuracy, and the larger the value, the higher the accuracy.

  As shown in FIG. 1, the second approximate function formula creating unit 202 is connected to the first approximate function formula creating unit 201, the approximate value calculating unit 30, and the reading unit 40. In addition, the second approximate function formula creating unit 202 creates the first approximate function formula created by the first approximate function formula creating unit 201 for the measurement points where the TEG does not exist in the measurement data input by the input unit 10. Is modified to create an n-order polynomial (hereinafter referred to as “second approximate function expression”) that approximates the electrical characteristics of the gate width W as a function of the gate length L.

  As shown in FIG. 1, the approximate value calculation unit 30 is connected to the approximate function formula creation unit 20 and the model parameter set generation unit 80. In addition, the approximate value calculation unit 30 calculates the approximate value of the electrical characteristics of the measurement point based on the first and second approximate function formulas created by the first and second approximate function formula creation units 201 and 202. It has become.

  As shown in FIG. 1, the reading unit 40 is connected to the approximate function formula creation unit 20 and the measurement point setting unit 50. In addition, the reading unit 40 has a TEG in the measurement data input by the input unit 10 based on the first and second approximate function formulas created by the first and second approximate function formula creation units 201 and 202. The electrical characteristics of a point that has not been read are read, and the coordinates and electrical characteristics of the point are held when an error from a binning model described later is equal to or greater than an allowable value ε.

  As shown in FIG. 1, the measurement point setting unit 50 is connected to a reading unit 40, a binning model creation unit 60, and an estimated value calculation unit 70. The measurement point setting unit 50 sets the measurement point at the coordinates held by the reading unit 40.

  As shown in FIG. 1, the binning model creation unit 60 is connected to a measurement point setting unit 50. In addition, the binning model creation unit 60 creates a binning model using data obtained by combining the measurement data input by the input unit 10 and the approximate value calculated by the approximate value calculation unit 30.

  As shown in FIG. 1, the estimated value calculation unit 70 is connected to a measurement point setting unit 50 and a model parameter set generation unit 80. Further, the estimated value calculation unit 70 calculates an estimated value based on approximate function expressions (described later) shown in Expressions 6 to 9 for calculating the estimated value of the electrical characteristics, and is set by the measurement point setting unit 50. The electrical characteristics of the measured points are replaced with estimated values.

  As shown in FIG. 1, the model parameter set generation unit 80 is connected to the approximate value calculation unit 30, the estimated value calculation unit 70, and the output unit 90. The model parameter set generating unit 80 generates a model parameter set including the approximate value calculated by the approximate value calculating unit 30 or the estimated value calculated by the estimated value calculating unit 70.

  As shown in FIG. 1, the output unit 90 is connected to a model parameter set generation unit 80 and an output device (not shown). The output unit 90 outputs the model parameter set generated by the model parameter set generation unit 80 to an output device (not shown).

  Next, processing of the model parameter extracting apparatus according to the first embodiment of the present invention will be described with reference to FIGS. FIG. 3 is a flowchart illustrating a processing procedure of model parameter extraction processing according to the first embodiment of the present invention. FIG. 4 is a schematic diagram showing an outline of the measurement data of FIG. FIG. 5 is a flowchart showing a processing procedure of the approximate function formula creation processing (S302 in FIG. 3). FIG. 6 is a schematic diagram illustrating coefficient values of the first approximate function equation. FIG. 7 is a schematic diagram illustrating the coefficient values of the second approximate function equation. FIG. 8 is a flowchart showing the processing procedure of the estimated value calculation processing (S305 in FIG. 3). FIG. 9 is a schematic diagram showing an outline of the estimated value calculation process (S305 in FIG. 3).

First, as shown in FIG. 3, a measurement data input step (S301) is performed. In the measurement data input step (S301), the input unit 10 inputs measurement data indicating the electrical characteristics of the measurement points input by the user using an input device (not shown). For example, as shown in FIG. 4, the measurement data is a measurement value of the threshold voltage _{Vth and} a value of the first approximate function equation.

Next, as shown in FIG. 3, an approximate function formula creation process (S302) is performed. In the approximate function formula creation process (S302), first, as shown in FIG. 5, a first approximate function formula creation step (S501) is performed. In the first approximate function formula creation step (S501), the first approximate function formula creation unit 201 determines that the gate width W (for example, all of the measurement data input in the measurement data input step (S301 in FIG. 3) is satisfied. A first approximate function expression (see Expression 6 and Expression 7) for a gate width W _i in which a TEG for the gate length L of the current exists is created, and each coefficient A _{0 to} A ₅ and B _{0 to} B ₅ is created. The coefficient value of is calculated. For example, in the example of FIG. 4, the first approximate function formula creating unit 201 creates a first approximate function formula that approximates the threshold voltage V _th for the gate width W _i (i = 0) as a function of the gate length L. Then, the coefficient values of the coefficients A _{0 to} A ₅ as shown in FIG. 6 are calculated. FIG. 6 shows the coefficient values of the coefficients A _{0 to} A ₅ of the first approximate function equation when n = 5.

Next, as shown in FIG. 5, a second approximate function formula creation step (S502) is performed. In the second approximate function formula creating step (S502), the second approximate function formula creating unit 202 uses the gate width W (for example, at least the measurement data input in the measurement data input step (S301 in FIG. 3) is insufficient. create second approximate function expression for the gate width W _j) the TEG is not present for one gate length L (see equation 8 and equation 9), the coefficients a ₀ to a ₅ and B ₀ to B A coefficient value of ₅ is calculated. At this time, the second approximate function expression creation unit 202 of the gate width W _i of the first approximate function expression is created in the first approximate function expression generation step (S501), selects the one closest to the gate width W _j and, the number of gate length L of the second approximate function expression for the gate width W _j is to match the number of gate length L of the first approximate function expression for the gate width W _i, TEG is the gate width W _j The coefficients of the second approximate function formula are corrected from the lower order by the existing number, and the coefficient values of the coefficients A _{0 to} A ₅ and B _{0 to} B ₅ are calculated. For example, in the example of FIG. 4, as shown in FIG. 7, the second approximate function formula creating unit 202 creates the second approximate function formula for the gate width W _j (j = 1 to 3). Select W _i (i = 0), modify one coefficient (coefficient A ₀ ) for gate width W _j (j = 1), and two coefficients for gate width W _j (j = 2) (Coefficients A ₀ and A ₁ ) are corrected, and three coefficients (Coefficients A _{0 to} A ₂ ) are corrected for the gate width W _j (j = 3).

  As shown in FIG. 5, the approximate function formula creation process (S302 in FIG. 3) according to Embodiment 1 of the present invention ends after the second approximate function formula creation step (S502).

Next, as shown in FIG. 3, an approximate value calculation step (S303) is performed. In the approximate value calculating step (S303), the approximate value calculating unit 30 is based on the first and second approximate function formulas created in the first and second approximate function formula creating steps (S501 and S502 in FIG. 5). Approximate the electrical characteristics at the measurement point. As a result, in the example of FIG. 4, for each of the four gate widths W _i (i = 0 to 3), the electrical characteristics of 13 gate lengths L (= 0.04 to 10) (that is, 52 gates) Electrical characteristics).

  Next, as shown in FIG. 3, when an estimated value is calculated (S304—YES), an estimated value calculating process (S305) is performed. In the estimated value calculation process (S305), first, as shown in FIG. 8, a binning model creation step (S801) is performed. In the binning model creation step (S801), the binning model creation unit 60 combines the measurement data input in the measurement data input step (S301 in FIG. 3) and the approximate value calculated by the approximate value calculation unit 30. Create a binning model using. At this time, the binning model creation unit 60 divides the LW plane of the MOSFET into a lattice shape, selects any four points from each lattice point, and creates a local region surrounded by the vertices as a binning model. To do. Further, the binning model creation unit 60 creates a plurality of such binning models.

Next, as shown in FIG. 8, a reading step (S802) is performed. In the reading step (S802), the reading unit 40 obtains the electrical characteristics of the gate length L of the first and second approximate function formulas created in the first and second approximate function formula creation steps (S501 and S502 in FIG. 5). Read from the minimum value L _min of the gate length L at regular intervals ΔL (see FIG. 9A). At this time, the reading unit 40 reads the electrical characteristics of the read gate length L _min + kΔL (k = 0, 1, 2,...) And the electrical characteristics of the binning model created in the binning model creation step (S801). Compare

Next, as shown in FIG. 8, the electrical characteristics of the gate length L _min + kΔL (k = 0, 1, 2,...) Read in the reading step (S802) and the binning model generation step (S801). When a comparison result (hereinafter referred to as “electric characteristic error”) of the gate length L _min + kΔL (k = 0, 1, 2,...) Of the binning model on the way is equal to or greater than a predetermined allowable value ε (S803-YES), a holding process (S804) is performed. In the holding step (S804), the reading unit 40 holds the value of the gate length L _min + kΔL (k = 0, 1, 2,...) And its electrical characteristics.

  As shown in FIG. 8, in the reading process (S802) to the holding process (S804), the electrical characteristics for all the gate lengths L and the electrical characteristics for the gate lengths L of the first and second approximate function formulas are compared. It is repeated until completion (S805-NO).

Next, as shown in FIG. 8, when the comparison between the electrical characteristics for all the gate lengths L and the electrical characteristics for the gate lengths L of the first and second approximate function formulas is completed (YES in S805). As shown in FIG. 8, a measurement point setting step (S806) is performed. In the measurement point setting step (S806), the measurement point setting unit 50 sets the measurement point to the gate length L _min + kΔL (k = 0, 1, 2,...) Held in the holding step (S804). At this time, the measurement point setting unit 50 has the gate length L _m and the gate length L _min + kΔL at the maximum measurement point among those smaller than the gate length L _min + kΔL (k = 0, 1, 2,...). Paying attention to the gate length L _{m + 1} of the smallest measurement point among those larger than (k = 0, 1, 2,...), There are a plurality of candidates between the gate length L _m and the gate length L _{m + 1.} In this case, the measurement point is set to an arbitrary one (for example, the electric characteristic error is maximized) (see FIG. 9B).

  Next, as shown in FIG. 8, an estimated value calculating step (S807) is performed. In the estimation calculation step (S807), the estimated value calculation unit 70 calculates the estimated value of the electrical characteristic of the measurement point set in the measurement point setting step (S806) based on a predetermined approximate function equation.

As shown in FIG. 8, the reading step (S802) to the estimated value calculation step (S807) is repeatedly performed until the estimated value with the set measurement points of all the gate width _{W i} is calculated (S808-NO) . Also, the estimated value calculation processing according to the first embodiment of the present invention (S305 in FIG. 3) is terminated after the estimated value is calculated for the set measurement points of all the gate width W _i (S808-YES).

  Further, as shown in FIG. 3, when the estimated value is not calculated (S304-NO) or after the estimated value calculating process (S305), a model parameter set creating step (S306) is performed. In the model parameter set creation step (S306), the model parameter set generation unit 80 uses the IV characteristic curve of the measurement data input in the measurement data input step (S301) to make one entire LW plane. By creating a global model expressed by the model and solving Equations 1 to 4, each gate length L or each gate width W is adjusted so that it matches the measured value shown in FIG. 4 or the value of the first approximate function equation. A part of parameter values in the global model is corrected to create a model parameter set of 52 lattice points that reproduces the approximate value of the electrical characteristics calculated in the approximate value calculation step (S303). Based on the value of the model parameter set of any four lattice points among the 52 lattice points, the binaries formed by these four lattice points To create a Gumoderu.

  Next, as shown in FIG. 3, an output step (S307) is performed. In the output step (S307), the output unit 90 outputs the model parameter set group (hereinafter referred to as “binning model parameter set”) created in the model parameter set creation step (S306) to an output device (not shown). .

  As shown in FIG. 3, the model parameter extraction process according to the embodiment of the present invention ends after the output step (S307).

In the first embodiment of the present invention, as an approximate function that gives the relationship between the electrical characteristics and the gate length L, the gate length L is divided by the maximum gate length L _MAX and normalized, and the logarithm is taken. Expressed. Here, the coefficient of each term of the nth order polynomial is an adjustment parameter for approximating the electrical characteristics to be approximated. The maximum gate length L _MAX is the maximum value of the gate length L of the MOSFET assumed to be used. In the example of FIG. 2, the maximum gate length L _MAX = 10.

  The reason why the logarithm is taken is to improve the reproducibility of a sudden change in electrical characteristics when the gate length L is small.

The reason why the gate length L is normalized by dividing it by the maximum gate length L _MAX is to make the sign of the logarithmic evaluation value negative by setting the logarithm to 1 or less.

  The reason for adjusting the coefficient of each term using an nth-order polynomial is to increase the degree of freedom of the electrical characteristics expressed by the function and increase the accuracy of fitting to the electrical characteristics.

The approximate function equation to be used is not particularly limited as long as the electrical characteristics can be approximated with high accuracy, and it is preferable to select an appropriate one depending on the electrical characteristics to be approximated. For example, instead of Equation 6 and Equation 7, Equation 10 and Equation 11 or Equation 12 and Equation 13 may be used as other approximate function equations. Thus, as an approximate function expression, an intermediate variable (for example, log (L)) given as a function of the gate length L is raised to the 0th power, the first power, the second power,. The accuracy of approximation can be improved by using a function in the form of adding the functions or a function including such a function inside.

  In the first embodiment of the present invention, the entire range of the gate length L is represented by one function, but may be represented by a different function for each region of the gate length L.

  Further, in the first embodiment of the present invention, the first and second approximate function equation creation unit 201 calculates the electrical characteristics of the gate length L where the TEG is present in the measurement data input by the input unit 10 as the gate width W. It is also possible to create an nth-order polynomial that is prohibited as a function of. In this case, the reading unit 40 reads the electrical characteristics at predetermined intervals in the gate width W direction. In addition, the measurement point setting unit 50 sets the measurement point to the gate width W where the electrical characteristic read by the reading unit 40 is outside the allowable range.

In Embodiment 1 of the present invention, the reading unit 40 reads the electrical characteristics of the gate length L from the minimum value L _min of the gate length L at regular intervals ΔL for one of the first and second approximate function equations. Also good.

  According to the first embodiment of the present invention, as shown in FIG. 3, even if measurement data is insufficient, approximate values and estimated values are calculated, so that a highly accurate model parameter set can be extracted. Can do.

It is a block diagram which shows the structure of the model parameter extraction apparatus 1 which concerns on Example 1 of this invention. It is the schematic which shows the outline of the measurement data which concern on Example 1 of this invention. It is a flowchart which shows the process sequence of the model parameter extraction process which concerns on Example 1 of this invention. It is the schematic which shows the outline of the measurement data of FIG. It is a flowchart which shows the process sequence of an approximate function formula creation process (S302 of FIG. 3). It is the schematic which shows the coefficient value of a 1st approximation function type | formula. It is the schematic which shows the coefficient value of a 2nd approximation function type | formula. It is a flowchart which shows the process sequence of an estimated value calculation process (S305 of FIG. 3). It is the schematic which shows the outline of an estimated value calculation process (S305 of FIG. 3).

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Model parameter extraction apparatus 10 Input part 20 Approximate functional formula creation part 201 1st approximate function formula creation part 201 2nd approximate function formula creation part 30 Approximate value calculation part 40 Reading part 50 Measurement point addition part 60 Binning model creation part 70 Estimation Value calculation unit 80 Model parameter set generation unit 90 Output unit

Claims (5)

A model parameter extraction device for extracting model parameters of a simulation model surrounded by measurement points arranged in a grid pattern in a gate length direction and a gate width direction of a transistor,
An input unit for inputting measurement data indicating the electrical characteristics of the measurement point;
A first approximation function formula that approximates the electrical characteristics of the measurement point is generated based on the measurement data input by the input unit for the measurement point that is satisfied by the measurement data input by the input unit. An approximate function formula creation unit;
For a measurement point for which measurement data input by the input unit is insufficient, the first approximate function formula created by the first approximate function formula creation unit is modified to approximate the electrical characteristics of the measurement point. A second approximate function formula creating unit for creating a two approximate function formula;
An approximate value calculation unit that calculates an approximate value of the electrical characteristics of the measurement point based on the first and second approximate function formulas created by the first and second approximate function formula creation units;
A model parameter set generation unit that generates a model parameter set from data obtained by combining the measurement data input by the input unit and the approximate value calculated by the approximate value calculation unit;
An output unit that outputs a model parameter set generated by the model parameter set generation unit. A reading unit that reads the electrical characteristics in the gate width or the gate length direction at predetermined intervals based on at least one of the first and second approximate function formulas created by the first and second approximate function formula creation units; ,
When the error between the electrical characteristic read by the reading unit and the electrical characteristic of the binning model being created is outside the allowable range, the measurement point is set to the gate width or the gate length corresponding to the electrical characteristic. A measurement point setting section;
An estimated value calculation unit that calculates an estimated value of the electrical characteristics of the measurement point set by the measurement point setting unit,
The model parameter extraction device according to claim 1, wherein the model parameter set generation unit generates a model parameter set including the estimated value calculated by the estimated value calculation unit.   The model parameter extracting apparatus according to claim 2, wherein the reading unit reads the electrical characteristics in the gate width direction or the gate length direction at equal intervals. A model parameter extraction method for extracting a model parameter of a simulation model surrounded by measurement points arranged in a grid pattern in a gate length direction and a gate width direction of a transistor,
Input measurement data indicating the electrical characteristics of the measurement point,
For the measurement points satisfied by the measurement data, based on the measurement data, create a first approximate function equation that approximates the electrical characteristics of the measurement points,
For the measurement point for which the measurement data is insufficient, the first approximate function formula is corrected to create a second approximate function formula that approximates the electrical characteristics of the measurement point,
Based on the first and second approximation function equations, an approximate value of the electrical characteristics of the measurement point is calculated,
Generating a model parameter set including the approximation,
A model parameter extracting method, wherein the model parameter set is output. Based on the first and second approximate function equations, the electrical characteristics in the gate width or the gate length direction are read at predetermined intervals,
When the error between the read electrical characteristics and the electrical characteristics of the binning model being created is outside the allowable range, the measurement point is set to the gate width or the gate length corresponding to the electrical characteristics,
Calculate an estimated value of the electrical characteristics of the set measurement point,
The model parameter extraction method according to claim 4, wherein a model parameter set including the calculated estimated value is generated.

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