JPH1056167A - Semiconductor simulation method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a semiconductor simulation method which enables statistic prediction of a change in a semiconductor characteristic corresponding to a change in a parameter accurately and in a short time. SOLUTION: First, for one or more parameters affecting a semiconductor characteristic, variation information indicative of extents of variations in the respective parameters are set. Next, on the basis of the variation information, a plurality of sampling points are generated. Values of the semiconductor characteristic at the plurality of generated sampling points are calculated. Based on the calculated characteristic values at the sampling points, an interpolation function is found showing a relationship between the parameters and semiconductor characteristic. After this, a value of the semiconductor characteristic at a given sampling point is calculated in accordance with the interpolation function.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a semiconductor simulation method for predicting, by a statistical method, changes in semiconductor characteristics when values of various parameters affecting semiconductor characteristics are changed.

[0002]

2. Description of the Related Art In the course of semiconductor development and design, parameters related to various controls in the semiconductor manufacturing process, parameters related to the shape and dimensions such as the gate length, and the like are changed so as to follow variations occurring during the manufacturing process. Then, to simulate the semiconductor,
This is important for predicting and analyzing variations in characteristic values such as threshold voltage _Vth of a semiconductor element, or for grasping current distribution and the like.

Conventionally, as a method of such a simulation, a method of modeling a carrier transport phenomenon in a solid using a concept of mobility has been mainly used. However, with the recent miniaturization of semiconductor processing technology, the accuracy of models has become a problem. Therefore, the importance of methods for simulating semiconductors by performing statistical processing without directly using models has been increasing. I have.

As a method of such a statistical simulation, for example, a plurality of sampling points in which some parameter values are combined are set discretely, and the semiconductor characteristics at each sampling point are converted into a physical equation relating to semiconductor physics. , And then calculate the result using the response surface method (RSM).
A method is known in which semiconductor characteristics at an arbitrary sampling point are predicted by interpolating using the same.

[0005] As computer software for simulating a semiconductor by such a technique, for example, “PDF PDF” manufactured by PDF Solution is used.
AB "and" VWF "of SILVACO are commercially available.

[0006]

By the way, in the above-described simulation, it is necessary to appropriately set sampling points that are the basis of interpolation. That is, if the number of sampling points to be interpolated is too small, or if an appropriate number of sampling points is not selected, interpolation cannot be performed properly, and the semiconductor characteristics at an arbitrary sampling point will be reduced. You will not be able to lead correctly. Further, if there are too many sampling points to be interpolated, the calculation is performed even for information that is more than necessary, so that useless time is spent in the simulation.

As described above, in a simulation in which the semiconductor characteristics are actually calculated at some sampling points and the other semiconductor characteristics are predicted by interpolation, it is important to appropriately set the sampling points that are the basis of the interpolation. It is. However, conventionally, the user has arbitrarily set the sampling point that is the source of the interpolation, and therefore, trial and error is required to set the sampling point that is the source of the interpolation. Therefore,
Conventionally, it has been difficult to set an appropriate sampling point immediately, and it has been difficult to perform a simulation in a short time.

The present invention has been proposed in view of such conventional circumstances, and aims to accurately and quickly predict a change in a semiconductor characteristic corresponding to a change in a parameter by a statistical method. It is an object of the present invention to provide a method of simulating a semiconductor that can be performed.

[0009]

SUMMARY OF THE INVENTION A semiconductor simulation method according to the present invention, which has been completed to achieve the above-mentioned object, provides a semiconductor device having one or more parameters that affect semiconductor characteristics. Setting information, based on the variation information, generating a plurality of sampling points, calculating the semiconductor characteristics at each of the plurality of sampling points, and based on the semiconductor characteristics at each of the sampling points, The method is characterized by including at least a step of obtaining an interpolation function indicating a relationship between each parameter and a semiconductor characteristic, and a step of calculating a semiconductor characteristic at an arbitrary sampling point from the interpolation function.

Here, as the variation information, for example, for each parameter, at least a center value which is a value at the center of the variation, a maximum variation value which is a value when the variation becomes the largest, and A minimum variation value which is a value when the value becomes small, a maximum value which is a maximum value assumed as a value of the parameter, and a minimum value which is a minimum value assumed as a value of the parameter are set. To

At this time, assuming that the number of types of parameters is N, a plurality of sampling points, for example, one sampling point consisting of the center value of each parameter, one parameter consisting of the maximum value, and the other parameters Is a combination of N sampling points consisting of center values, minimum values for one parameter, N sampling points consisting of center values for other parameters, and maximum and minimum variation values for each parameter. And at least 2 ^N sampling points.

In the semiconductor simulation method according to the present invention as described above, a plurality of sampling points are generated from variation information indicating the degree of variation of each parameter. Only the variation information indicating the degree of variation of the parameter is sufficient.
Then, only by setting the variation information of each parameter, an appropriate sampling point is generated.

That is, in the semiconductor simulation method according to the present invention, there is no need for the user to perform trial and error to set sampling points, and appropriate sampling points are immediately generated. Therefore, in the semiconductor simulation method according to the present invention, accurate processing can be performed in a short time.

Further, the semiconductor simulation method according to the present invention employs a statistical method of obtaining an interpolation function indicating a relationship between a parameter and a semiconductor characteristic and calculating a semiconductor characteristic at an arbitrary sampling point from the interpolation function. Used. Therefore, a simulation can be performed with high accuracy even for an extremely miniaturized semiconductor element or the like in which it is difficult to accurately model a carrier transport phenomenon in a solid.

[0015]

Embodiments of the present invention will be described below in detail with reference to the drawings. The present invention is not limited to the following examples, and it goes without saying that changes can be made without departing from the scope of the present invention.

First, a simulation apparatus for performing a semiconductor simulation by applying the present invention will be described with reference to a block diagram shown in FIG.

As shown in FIG. 1, the simulation apparatus 1 includes an input setting module 2, an automatic sampling point generation module 3, and a simulator input module 4.
, A simulation calculation module 5, an output / display module 6, and a database management module 7. These modules are realized on a computer such as a workstation, for example, and are controlled by a central processing unit (CPU) of the computer.

The input setting module 2 is for receiving an input from the input device 8 connected to the simulation device 1. Here, as the input device 8, a keyboard for inputting operation instructions and the like to the simulation device 1 and information about various parameters and the like are read from a recording medium in which information is previously recorded and supplied to the simulation device 1. A data reading device or the like is appropriately used.

Then, from the input device 8 via the input setting module 2, parameters affecting the semiconductor characteristics to be simulated, data on variation information indicating the degree of variation of those parameters, and the like are input. . That is, the input setting module 2 functions as a unit for inputting information necessary for analyzing the influence of the process or device on the operating characteristics of the semiconductor by simulation.

The parameters input via the input setting module 2 are parameters used for semiconductor simulation, and specifically, include process parameters relating to various controls in the semiconductor manufacturing process, and gate lengths. Device parameters relating to the shape and dimensions to be used.

The data input from the input device 8 via the input setting module 2 is supplied from the input setting module 2 to the database management module 7, stored in the database by the database management module 7, and stored in the database management module. 7 to the sampling point automatic generation module 3.

The automatic sampling point generation module 3
Based on the data received from the database management module 7 such as parameters and their variation information, a plurality of sampling points necessary for performing a simulation are generated. Here, the sampling point is a point at which semiconductor characteristics are calculated, and specifically, is a combination of values of parameters to be evaluated. The method of generating a plurality of sampling points in the sampling point automatic generation module 3 will be described later in detail.

The plurality of sampling points generated by the sampling point automatic generation module 3 are supplied to the database management module 7 and stored in the database by the database management module 7.
Simulation calculation module 5 from database management module 7 via simulator input module 4
It is thrown into. Then, as described later, the semiconductor characteristics at these sampling points are calculated by the simulation calculation module 5. That is, the sampling point automatic generation module 3 functions as means for automatically generating appropriate data to be input to the simulation calculation module 5 based on the data input via the input setting module 2.

As described above, the simulator input module 4 receives a plurality of sampling points generated by the automatic sampling point generation module 3 from the database management module 7 and supplies the sampling points to the simulation calculation module 5. Also,
The simulator input module 4 receives the calculation result from the simulation calculation module 5 and supplies the calculation result to the database management module 7.

The simulation calculation module 5 receives a plurality of sampling points from the simulator input module 4 and calculates semiconductor characteristics at each sampling point.
It is calculated by solving a physical equation relating to semiconductor physics. That is, the simulation calculation module 5
By solving the physical equations related to semiconductor physics,
It functions as a means for calculating the characteristics of the semiconductor.

The result of the calculation by the simulation calculation module 5, that is, the semiconductor characteristics at each sampling point is supplied from the simulation calculation module 5 to the database management module 7 via the simulator input module 4. Then, the calculation result by the simulation calculation module 5 is stored in the database by the database management module 7 and supplied from the database management module 7 to the output / display module 6.

The output / display module 6 receives the calculation result by the simulation calculation module 5 from the database management module 7 and, based on the calculation result, calculates an interpolation function indicating the relationship between each parameter and the semiconductor characteristics by a response surface method. Determine using That is, the output / display module 6 functions as a means for estimating the semiconductor characteristics at an arbitrary sampling point where the physical equation has not been solved, based on the calculation result by the simulation calculation module 5.

The output / display module 6 calculates a semiconductor characteristic at an arbitrary sampling point based on the interpolation function according to an instruction input from the input device 8 by the user, and sends the calculation result to the simulation device 1. Output to the connected output device 9. In addition, as the output device 9, various displays, printers, plotters, and the like can be used as appropriate.

Next, a method for simulating a semiconductor to which the present invention is applied, which is performed by the simulation apparatus 1 as described above, will be described in detail.

In this simulation, changes in semiconductor characteristics when the values of various parameters affecting semiconductor characteristics are changed are predicted by using a response surface method. That is,
In this simulation, a plurality of sampling points are set for parameters to be analyzed, and semiconductor characteristics at those sampling points are calculated by solving a physical equation relating to semiconductor physics. From these calculation results, the semiconductor characteristics at the sampling points where the physical equations have not been solved are predicted using the response surface method.

Here, the parameters are, as described above,
Process parameters related to various controls in the semiconductor manufacturing process, device parameters related to the shape and dimensions such as the gate length, and the like. In the present invention, even if simulation is performed for only one parameter, a plurality of parameters are combined. Simulation may be performed.

Incidentally, the response surface method is a method of estimating the value of a point that does not actually exist by performing interpolation from a set of discrete points. Therefore, in the simulation using the response surface method, a calculation result of the semiconductor characteristics at a sufficient number of sampling points is necessary, and thereby correct interpolation can be performed for the first time. However, if the number of sampling points is too large, it is meaningless. If the number of sampling points is excessively large, extra calculations are performed and time is wasted. Therefore, in a simulation using the response surface method, it is important to appropriately set sampling points. Thus, in the present simulation, as described below, the sampling point that is the source of the interpolation by the response surface method is always set appropriately based on the parameter variation information.

Hereinafter, this simulation will be described in detail with reference to the flowchart shown in FIG.

First, in step S1, information necessary for analyzing the influence of a process or a device shape on the operating characteristics of a semiconductor by simulation through the input setting module 2 is input, and based on the information, For parameters to be analyzed, variation information indicating the degree of variation of each parameter is set.

Here, as the parameter variation information, a central value of the variation, a normal range of the variation, and a worst value are set for each parameter to be analyzed. That is, as the parameter variation information, for each parameter, a center value that is the center value of the variation, a maximum variation value that is the value when the variation becomes the largest, and a value that is the smallest when the variation is made. Five points are set: a certain minimum variation value, a maximum value that is the maximum value assumed as the value of the parameter, and a minimum value that is the minimum value assumed as the value of the parameter. Note that these values are input device 8
Alternatively, information necessary for obtaining these values may be set in advance, and the input setting module 2 may calculate the information as needed.

Next, in step S2, the sampling point automatic generation module 3 generates a plurality of sampling points required for performing a simulation based on the parameter variation information set in step S1.

Here, assuming that the number of types of parameters to be analyzed is N, the plurality of sampling points generated are one sampling point consisting of the center value of each parameter and the maximum value for one parameter. , The other parameters are composed of N sampling points each having a center value, one parameter is composed of a minimum value, and the other parameters are composed of N sampling points each having a center value. Values and the minimum variation value are combined and 2 ^N sampling points.

As a specific example, FIG. 3 schematically shows the distribution of sampling points when there are two types of parameters, and FIG. 4 schematically shows the distribution of sampling points when there are three types of parameters. Show. These FIGS. 3 and 4
In the figure, the circles indicate sampling points. As shown in FIG. 3, when there are two parameters, the number of sampling points is nine, and as shown in FIG. 4, when there are three parameters, the number of sampling points is fifteen. In FIG. 4, for convenience, the maximum value, the maximum variation value, the center value, the minimum variation value, and the minimum value are plotted only for the first parameter.

Next, in step S3, step S
The plurality of sampling points generated in 2 are input to the simulation calculation module 5 by the simulator input module 4, and the semiconductor characteristics at each sampling point are calculated by the simulation calculation module 5. That is, in step S3, the semiconductor characteristics at the plurality of sampling points generated in step S2 are calculated.

In step S3, the simulation calculation module 5 calculates semiconductor characteristics at each sampling point by solving a physical equation relating to semiconductor physics. Here, the physical equations related to semiconductor physics include, for example, Poisson's equation shown in the following equation (1), electron current continuation equation shown in the following equation (2), and hole current continuation equation shown in the following equation (3). And so on.

∇ (ε∇ψ) = q (n−p−C) (1) −∇ · J _n + qR = 0 (2) −∇ · J _p −qR = 0 (3) Here, ε is a dielectric constant of a substrate made of silicon or the like, ψ is an electrostatic potential, q is a unit charge, n is an electron concentration, p is a hole concentration, C is an n-type substrate impurity concentration and a p-type substrate. Difference from impurity concentration, _Jn is electron current density, _Jp is hole current density, R
Is the concentration of electrons or holes generated or annihilated per unit time.

Next, in step S4, the calculation result of the semiconductor characteristics calculated by the simulation calculation module 5 is supplied to the database management module 7 through the simulator input module 4, and the database management module 7 Stored in the database.

Next, in step S5, based on the calculation results of the semiconductor characteristics at a plurality of sampling points stored in the database, the output / display module 6 interpolates the relationship between each parameter and the semiconductor characteristics. The function is calculated by the response surface methodology. That is, in step S5, an interpolation function indicating the relationship between each parameter to be analyzed and the semiconductor characteristics is calculated by the response surface method based on the calculation result in step S3.

Here, the interpolation function is represented by N parameters x
_{When there are 1} , x ₂ ,..., X _N , it is expressed as the following equation (4).

Semiconductor characteristic value = f (x ₁ , x ₂ ,..., X _N ) (4) Therefore, if this interpolation function is obtained, any combination of values (X ₁ , X _2, ···, a value of the semiconductor characteristics for _{X N), f (X 1} , X 2, .., X N)
Will be represented by Therefore, if this interpolation function is obtained, it is possible to immediately calculate the semiconductor characteristics at an arbitrary sampling point without solving a new physical equation.

Therefore, after the interpolation function shown in the above equation (4) is obtained in step S5, the semiconductor characteristic at a desired arbitrary sampling point is calculated using the interpolation function. That is, in step S6, according to an instruction input from the input device 8, the output / display module 6 calculates semiconductor characteristics at an arbitrary sampling point based on the interpolation function obtained in step S5. And the calculation result is
It is output to an output device 9 connected to the simulation device 1 as appropriate.

The processing in step S6 is repeated by changing sampling points as needed. In the process of step S6, the value of the semiconductor characteristic is calculated only by inputting the sampling point to the interpolation function, so that the semiconductor characteristic at an arbitrary sampling point can be calculated very quickly.

In the above simulation, a plurality of appropriate sampling points are automatically generated from the parameter variation information. Therefore, the semiconductor characteristics at an arbitrary sampling point can be accurately predicted by the interpolation using the response surface method performed based on the calculation results of the semiconductor characteristics at those sampling points.

Moreover, in the above simulation, a necessary and sufficient number of sampling points are generated as a plurality of sampling points generated from the parameter variation information. That is, in the above simulation, there are no cases where more sampling points are set than necessary,
The time required for the calculation is minimized.

Next, the principle of calculating an interpolation function by the response surface method in the above simulation will be described.

The form of the interpolation function obtained in this simulation is expressed by the following equation ₁ using x ₁ , x ₂ ,..., X _n as variables.

[0052]

(Equation 1)

Here, (x ₁ , x ₂ ,
···, x _n, y _exp) has m sets of data sets as a unit, the calculated value y ⁱ _{c al} for the i-th response value y ⁱ _exp is the given by the number of following 2.

[0054]

(Equation 2)

At this time, the following equation 3 is defined as an evaluation function.

[0056]

(Equation 3)

Then, the coefficient a of the interpolation function shown in the equation (1)
_0, a _1, ···, as a combination of a _nn, determine the combination that minimizes the ω evaluation function shown in Equation 3. This is because the simultaneous equations obtained by partially differentiating the evaluation function shown in Equation 3 with the respective coefficients, that is, a ₀ , a ₁ , and so on satisfying the simultaneous equations shown in Equation 4 below.
.., Ann is equivalent to _obtaining a combination.

[0058]

(Equation 4)

Incidentally, it can be seen from the interpolation function shown in equation (1).
As a₀ , A₁ , ..., a _nnAre all y_cal To
Equation 4 is shown in Equation 5 below because
Can be described using a matrix as follows.

[0060]

(Equation 5)

In Expression 5, for simplicity, for example, the expression is simplified as shown in Expression 6 below.

[0062]

(Equation 6)

Then, by solving the above equation (5), a combination of the coefficients a ₀ , a ₁ ,..., An _n is obtained, and the interpolation function shown in the equation (1) is obtained.

[0064]

EXAMPLES Hereinafter, examples of the present invention will be described more specifically. In the present embodiment, an example is described in which the effects of variations in ion implantation concentration and gate length on the characteristics of a MOS transistor are simulated.

In the present embodiment, the center value of the ion implantation concentration as the first parameter is 5e12,
The maximum variation value is 5.5e12, and the minimum variation value is 4.
6e12, the maximum value was 6e12, and the minimum value was 4e12. For the gate length, which is the second parameter, the center value is 1.0 μm and the maximum variation value is 1.1.
μm, minimum variation value is 0.9 μm, maximum value is 1.3 μm
m, and the minimum value was 0.7 μm.

Here, Table 1 shows an example of a format displayed on the output device 9 such as a display when inputting the variation information of these parameters.

[0067]

[Table 1]

In the above example, “DOPANT = B DO
"SE = 5e12 ENERGY = 30KEV" indicates that the ion species, standard concentration and energy in the ion implantation are set, and "DEV1 = DOSE" indicates that the ion implantation concentration of the implanted ion species (BORON) is to be parameterized. Then, "RSM = 4e
12 4.6e12 5e12 5.5e12 6e1
2 ”, the minimum value, the minimum variation value, the center value, the maximum variation value, and the maximum value of the ion implantation concentration are set.

The same applies to “MASK” and thereafter, and “MASK 1.0 2.0 PROP = GAT”
"E" sets that this mask is a gate and its position, and "DEVI = LENGTH" indicates that the gate length is used as a parameter. Then, “RSM = 0.7 0.9 1.0 1.
The minimum value, the minimum variation value, the center value, the maximum variation value, and the maximum value of the gate length are set by “1 1.3”.

When the above-described variation information is set, the sampling point automatic generation module 3 generates a plurality of sampling points in which respective parameters are appropriately combined.

Specifically, nine sampling points as shown in Table 2 below are generated.

[0072]

[Table 2]

Here, the first sampling point is a sampling point in which both the ion implantation concentration and the gate length are center values. The second and third sampling points are sampling points in which one of the ion implantation concentration and the gate length has a maximum value and the other has a center value.
The fourth and fifth sampling points are sampling points in which one of the ion implantation concentration and the gate length has a minimum value and the other has a center value. In addition, the sixth to ninth
Are sampling points obtained by combining the maximum variation value and the minimum variation value of the ion implantation concentration with the maximum variation value and the minimum variation value of the gate length.

Here, as an example of the format when the sampling points set as described above are displayed on the output device 9 such as a display, the first sampling in which both the ion implantation concentration and the gate length are center values is performed. Table 3 shows an example of a format in which dots are displayed.

[0075]

[Table 3]

Table 4 shows an example of a format when the fifth sampling point where the ion implantation concentration has the center value and the gate length has the minimum value is displayed.

[0077]

[Table 4]

Here, the example of the format when the first sampling point and the fifth sampling point are displayed has been described, but the other sampling points are also displayed in the same manner.

The nine sampling points set as described above are input to the simulation calculation module 5 via the simulator input module 4, and the threshold voltage V corresponding to each sampling point is input by the simulation calculation module 5. _th is calculated. In addition,
Here, the semiconductor characteristics to be analyzed are assumed to be the threshold voltage _Vth , and the simulation calculation module 5 calculates the threshold voltage _Vth. The voltage may be other than the voltage _Vth .

Thereafter, based on the result calculated by the simulation calculation module 5, the threshold voltage V
An interpolation function for _{th is} obtained by a response surface method. Here, the interpolation function for the threshold voltage V _th uses the ion implantation concentration and the gate length as variables, and is expressed, for example, in the form shown in the following equation (5).

[0081] _{V th (x 1, x 2} ) = a 0 + a 1 x 1 + a 2 x 2 + a 11 x 1 2 + a 12 x 1 x 2 + a 22 x 2 2 ··· (5) where, x ₁ Represents the value of the ion implantation concentration, and x
₂ represents the value of the gate length. A ₀ , a ₁ ,
a ₂ , a ₁₁ , a ₁₂ , and a ₂₂ are coefficients of the interpolation function, and are values calculated by the output / display module 6 by the response surface method.

[0082] Then, as shown in the above equation (5), after the interpolation function for the threshold voltage V _th is obtained, the threshold voltage V _th with respect to any ion implantation concentration and gate length, e.g. The threshold voltage V _th when the ion implantation amount is 4.8e12 and the gate length is 1.15 μm,
It can be quickly obtained by the above interpolation function.

The above-mentioned simulation technique is used to estimate characteristics having a plurality of variation factors, for example, when estimating the influence of variations in the thickness and dielectric constant of a wiring in a semiconductor on wiring capacitance. It can be widely applied to simulation.

[0084]

As is clear from the above description, in the semiconductor simulation method according to the present invention, since a plurality of sampling points are generated from the variation information of each parameter, the user sets the sampling points. Therefore, it is not necessary to perform trial and error in order to generate an appropriate sampling point immediately. Therefore, according to the present invention, it is possible to perform a simulation of a semiconductor in a short time.

Further, according to the present invention, since the user does not set sampling points by trial and error, but always generates appropriate sampling points from parameter variation information, simulation of semiconductor characteristics is always performed with high accuracy. It becomes possible.

Also, in the present invention, since a statistical method of calculating semiconductor characteristics at an arbitrary sampling point from an interpolation function is used, it is difficult to accurately model a carrier transport phenomenon in a solid. Also, simulation can be performed with high accuracy even for extremely miniaturized semiconductor elements and the like.

As described above, according to the present invention, a simulation of a semiconductor can be performed with high accuracy and in a short time, so that development and design of a semiconductor can be efficiently performed. As a result, costs required for semiconductor development, design, and the like can be significantly reduced.

[Brief description of the drawings]

FIG. 1 is a block diagram illustrating a configuration example of a simulation apparatus.

FIG. 2 is a flowchart showing a flow of a semiconductor simulation method to which the present invention is applied.

FIG. 3 is a diagram schematically showing distribution of sampling points when there are two types of parameters.

FIG. 4 is a diagram schematically showing distribution of sampling points when there are three types of parameters.

[Explanation of symbols]

1 simulation device, 2 input setting module, 3 sampling point automatic generation module, 4
Simulator input module, 5 Simulation calculation module, 6 Output / display module, 7
Database management module, 8 input devices, 9
Output device

Claims (4)

[Claims] A step of setting variation information indicating a degree of variation of each parameter for one or more parameters affecting semiconductor characteristics; a step of generating a plurality of sampling points based on the variation information; Calculating the semiconductor characteristics at each of the plurality of sampling points, based on the semiconductor characteristics at each of the sampling points,
A method for simulating a semiconductor, comprising: at least a step of obtaining an interpolation function indicating a relationship between each parameter and a semiconductor characteristic; and a step of calculating a semiconductor characteristic at an arbitrary sampling point from the interpolation function. 2. The variation information includes, for each parameter, at least a center value that is a value of the center of the variation, a maximum variation value that is a value when the variation becomes the largest, and a value that is the smallest when the variation is made. A minimum variation value that is the value of the parameter, a maximum value that is the maximum value assumed as the value of the parameter, and a minimum value that is the minimum value assumed as the value of the parameter. The method for simulating a semiconductor according to claim 1. 3. When the number of types of the parameters is N, the plurality of sampling points include at least one sampling point including a center value of each parameter, and one parameter includes a maximum value. For each parameter, N sampling points consisting of center values, one parameter consists of minimum values, and for the other parameters, N sampling points consisting of center values, and the maximum variation value and minimum variation value of each parameter 3. The method according to claim 2, wherein 2 ^N sampling points and the combination are generated. 4. The semiconductor simulation method according to claim 1, wherein said interpolation function is obtained by a response surface method.