KR100402339B1 - Physical model parameter extraction method and storage medium thereof, and non-linear element manufacturing method - Google Patents

Abstract

Provides a technique to efficiently extract the parameters of the physical property model.

Extraction of the parameters of the physical property model results in finding the minimum value of the error function S. First, in step 121, an enumeration method is performed in which the parameter is updated while maintaining the probability that the parameter update having the error function S increases is positive (+). Next, as a procedure condition of the enumerated method, it is determined in step 122b whether or not the error function S has decreased for successive t. If YES is determined in step 122b, the flow advances to step 123, where a Newtonian method solution is executed in which the parameter update with decreasing error function S is performed.

Description

Parameter extraction method and recording medium of physical property model, and manufacturing method of nonlinear element {PHYSICAL MODEL PARAMETER EXTRACTION METHOD AND STORAGE MEDIUM THEREOF, AND NON-LINEAR ELEMENT MANUFACTURING METHOD}

The present invention corresponds to the physical properties from which the characteristic quantity group g _i composed of at least one characteristic quantity, respectively, corresponds to each of a plurality of vi (i = 1, 2, ..., m) of the external factor group composed of at least one external factor. And a function of a parameter group P consisting of said external factor v _s and a plurality of parameters, each of the calculated values corresponding to each characteristic amount g _s (s represents any one value employed by i). In the physical property model provided as f (v _s , P), the present invention relates to a technique for extracting a parameter group P.

A technique for extracting model parameters, for example for circuit simulation used in the design of large scale integrated circuits (LSIs).

In the production of LSIs, the process is roughly divided into a design process for designing the circuit and a semiconductor process process for realizing the circuit as a semiconductor device based on the information obtained by the design process. And in the design process, circuit simulation is performed in advance in order to predict the function which the LSI circuit (henceforth "LSI apparatus") implemented as a semiconductor device should exhibit.

There are two important aspects of circuit simulation: formulation of circuit equations and device modeling. In device modeling, for example, electrical characteristics of a nonlinear device such as a transistor are simulated by an analysis formula obtained by modeling the device. This equation contains parameters that are determined physically or intermediate empirically.

In order to execute the circuit simulation with precision, it is necessary to appropriately determine the parameters in these device modeling. And as an index for this determination, the error of the calculated value based on the measured characteristic and the analysis model of an LSI apparatus is normally selected normally. Alternatively, the results of device simulations for simulating phenomena occurring inside devices such as transistors may be used instead of the measured characteristics of the LSI device.

In order to find a combination of parameters in which the value of this error is minimum, the Newton method has conventionally been adopted, for example.

In Newton's method, however, the parameter is searched only in the direction in which the error value decreases. Therefore, the local minimum value is obtained without obtaining a minimum value (hereinafter, referred to as a "true solution") of the overall physical property model to be analyzed. There is a possibility that the parameter is determined as a true solution (hereinafter referred to as a "local solution").

On the other hand, there are also global search algorithms that can use random number generation to avoid falling into local solutions, but the computational load required to reach a true solution is enormous.

SUMMARY OF THE INVENTION The present invention has been made in view of the above circumstances, and an object thereof is to provide a technique for efficiently extracting a parameter for obtaining a true solution, that is, extracting a parameter.

It is another object of the present invention to provide a medium for storing a program for efficiently extracting parameters from a computer.

It is another object of the present invention to provide a method for manufacturing a nonlinear device including physical property simulation employing such a parameter extraction technique.

According to the present invention, (a) the characteristic quantity group g each consisting of at least one characteristic quantity corresponding to each of a plurality of v _i (i = 1, 2, ..., m) of the external factor group consisting of at least one external factor _The physical properties of _i are obtained, and each of the calculated values corresponding to each of the characteristic quantities g _s (s represents any one value adopted by i) corresponds to the external factor group v _s and a plurality of parameters. Applying a physical property model provided as a function f (v _s , P) of the parameter group P consisting of (b) each of the characteristic quantities g _s and the corresponding function f (v _s , P) Extracting the parameter group P that provides a minimum for the error function S that sums a square of a difference multiplied by a weight function w _s over a plurality of external factor groups; In the extraction method, the step ( b) (b-1) repeatedly calculating the value of the error function S while updating the parameter group P while keeping the probability Q at which the value of the error function S increases is positive (+), and the error function S And stopping when the value of is decreased a predetermined number of times.

According to the present invention, in the parameter extraction method of the physical property model, the step (b) is (b-2) the error function S with the parameter group P last updated in the step (b-1) as an initial value. Updating the parameter group P only in a monotonically decreasing direction.

According to the present invention, in the parameter extraction method of the physical property model, the probability Q is obtained based on a predetermined amount monotonously varying each time the parameter group P is updated, and the predetermined amount is updated by the parameter group P. Each time contributes to the tendency to decrease the probability Q, and the step (b-1) 'stops as the predetermined amount reaches a predetermined value.

According to the present invention, a computer-readable recording medium in which a program to be executed by the computer is recorded, either alone or in addition to a program provided in the computer in advance.

According to the present invention, there is provided a method of manufacturing a non-linear device, in which a characteristic simulation employing device modeling using a parameter extraction method of a physical property model and a non-linear device are produced by performing a physical process based on the property simulation.

1 is a flowchart illustrating an outline of a manufacturing process of an LSI device according to the present invention.

2 is a flowchart showing the operation of the parameter extraction apparatus according to the present invention;

3 is a flowchart showing the decomposition of the process of the embodiment of the present invention.

4 is a flowchart showing a Newton method solution.

<Explanation of symbols for main parts of drawing>

1: circuit simulator

903: Circuit Design Process

A. Basic Thoughts

Before giving a detailed description of the embodiments, the basic idea of the present invention will be described. As described by taking device modeling included in a circuit simulation that is part of the design process of the LSI as an example, there is conventionally a method of setting a physical property model. This physical property model includes an external factor group v _i (i represents a change in the external factor group, where i = 1, 2, 3, ..., m), which is composed of at least one external factor, and at least obtained for them. The characteristic quantity group g _i which consists of one characteristic quantity is set by obtaining the physical property of the nonlinear element which has a nonlinear relationship. This physical property model is set as a function f (v _i , P) of the parameter group P composed of a plurality of parameters and the external factor group v _i . And the square of the value of the characteristic quantity group g _s (s represents any one value adopted by i) and the value of the calculated function f (v _s , p) multiplied by the weight function w _s The total over the variation i of the external factor group, and the error function S is obtained. The parameter is extracted by finding a combination of parameters whose minimum value of the error function S is the minimum.

For example, when a MIS transistor is used as the nonlinear element, for example, when the gate length is larger than about 1 µm, the Frohman-Bentchkowsky model can be listed as the physical property model. As an external factor, the operating temperature τ, the potential of the gate electrode (gate voltage V _gs ) to the source electrode, and the potential of the drain electrode (drain voltage V _ds ) are used as characteristics, and the current flowing between the source electrode and the drain electrode (drain current I _ds ) can be enumerated respectively. And as a parameter, the threshold voltage _Vth and the coefficient (beta) mentioned later are mentioned, for example. In this way, the number of external factors constituting the external factor group, the number of characteristic quantities constituting the characteristic quantity group, and the number of parameters constituting the parameter group generally do not coincide.

In order to find the parameter group P which minimizes the value of the error function S, the value of the error function S is repeatedly obtained while updating the value of the parameter group P. At this time, in the step of obtaining the first solution, the value of the parameter group P is updated while maintaining the probability Q at which the value of the error function S increases is positive (+). For updating such predicates, the generation of random numbers is used as described above. As described above, in updating the value of the parameter group P aimed at the minimum value of the error function S, the error probability falls into a local solution by maintaining the positive probability Q of the value of the error function S positive. Can be avoided.

However, only by calculating the first solution, which is such a global search algorithm, the computational load necessary to reach the true solution is enormous. Therefore, after the execution of the step for finding the first solution, the step for finding a second solution for updating the parameter group P only in the direction in which the error function S monotonically decreases is adopted.

The step of finding the first solution is less likely to fall into the local solution, but it takes a lot of calculation time, and the step of obtaining the second solution takes a short time to calculate, but may fall into the local solution. Therefore, appropriately setting the conditions for switching from the first solution finding step to the second solution finding step is important for improving accuracy and shortening the calculation time in parameter extraction.

As the first switching condition, the value of the error function S decreases by a predetermined number of times as the value of the parameter group P is updated in the step of obtaining the first solution. The fact that the value of the error function S tends to decrease even though the probability Q of increasing the value of the error function S is kept positive (+) can be judged that the updating of the parameter group P is performed near the true solution. Because there is. Therefore, the technique of ending the step of obtaining the first solution using the first switching condition is also effective in parameter extraction.

As a 2nd switching condition, the probability Q which the value of the error function S increases becomes low, for example is mentioned. This is because the probability that the parameter is searched in the direction in which the value of the error function S decreases increases, so that the use of the step for obtaining the second solution can suppress the calculation amount. For example, the probability Q has a predetermined amount which monotonously fluctuates every time the parameter group P is updated, and this predetermined amount is set to contribute to the tendency to decrease the probability Q each time the parameter group P is updated. And as the predetermined amount reaches a predetermined value, the step of obtaining the first solution is stopped.

The present invention can be applied not only to the semiconductor field but also to other fields, for example, the fields of electricity, mechanical and chemistry, as long as the technology employs a physical property model set as a function having parameters as described above. Hereinafter, the field of the semiconductor manufacturing method will be described as an example.

In addition, Japanese Patent Application Laid-Open No. 7-295959 discloses an algorithm that converts a nonlinear circuit into a divisional linear circuit, gradually reduces the division interval, and has wide area convergence, and a simulation using the Newton method.

B. Application to Manufacturing Method of Semiconductor:

b1) overview of the method of manufacturing a semiconductor

1 is a flowchart illustrating an outline of a manufacturing process of an LSI apparatus to which the present invention is applicable. The manufacturing process is roughly divided into a design process group 90 and a semiconductor process process 905 which is a physical process. The design process group 90 is roughly divided into a functional design process 901, a logic design process 902, a circuit design process 903, and a layout design process 904. The semiconductor process process 905 performs a semiconductor process based on the information obtained from the design process group 90, and the LSI device 300 is obtained.

The circuit design process 903 is executed by employing the circuit simulator 1 and the parameter extraction device 3. In addition, for example, the timing simulator 201 may be employed. The circuit simulator 1 is a main body that performs circuit simulation, and the measured value of the manufactured LSI device 300 and the simulation result from the device simulator 202 are input to the parameter extraction apparatus 3 which supplies the parameter used therein. . The parameter database 2 in which the parameters determined by the parameter extraction device 3 are stored may also be employed in the circuit design process 903. In FIG. 1, the circuit design process 903 employs the circuit simulator 1, the parameter database 2, the parameter extraction apparatus 3, and the timing simulator 201 in the circuit design process 903. It is enclosed by the block shown.

1 is schematically shown, and each process 901 to 904 of the design process group 90 does not need to exist independently, and the parameter extraction apparatus 3 needs to be realized separately as hardware. none. For example, the whole design process group 90 may be implement | achieved with the single calculator which operates based on a predetermined program. As a matter of course, dedicated software for executing the processing of the parameter extraction device 3 may be used, and a parameter extraction device (for example, by a patch program for software for operating the entire design process group 90), which is conventionally present, The process of 3) may be executed. These programs can be recorded on a computer readable recording medium.

2 is a flowchart showing the operation of the parameter extraction device 3 according to the present invention. First, the measured value measured using a measuring instrument, such as a parameter analyzer and an LCR meter, is input into the initial value determination part 11. These meters are preferably operated under automatic control. Alternatively, the device simulation result obtained from the device simulator 202 may be input.

Since parameters in device modeling are determined, iterative calculation is usually performed. In order to perform this iteration efficiently, the initial value determination part 11 determines the initial value of a parameter. Properly selecting this initial value is largely concerned with the precision of the finally obtained parameter. Therefore, the initial value determining unit 11 adopts a simple model that defines the operating area and the shape of the device, and determines the initial value of some of the parameters in a quantitative manner, thus eliminating the need for iterative calculation.

For example, in the operation of the MIS transistor, the drain current I _ds in the linear region where the drain voltage V _ds is small is almost obtained with β (V _gs -V _th -V _ds / 2) V _ds . Here, the coefficient β is a value obtained by subtracting the product of the gate insulating film capacitance C _ox per unit area, the carrier mobility μ and the channel width W by the channel length L (β = C _ox μW / L). Based on this model, the dependence of the drain current I _{ds on} the gate voltage V _gs is obtained from the measured value, the extrapolation and the slope are calculated to obtain the threshold voltage V _th and the coefficient β, respectively.

The initial values of some parameters determined as described above are provided to the parameter optimizer 12 together with the measured values or the device simulator results to determine the parameters. Details of the operation of the parameter optimizer 12 will be described later.

The device characteristics calculated using the parameters obtained from the parameter optimizer 12 are displayed by overlapping on the display device 13 with the device characteristics obtained from the measured values, for example, the dependence on the drain voltage V _ds of the drain current I _ds . Visually confirm the precision of the determined parameters. In FIG. 2, the case where the dependence of the drain current I _{ds on} the drain voltage V _ds is _floated with respect to various gate voltages V ₁ , V ₂ , and V ₃ is illustrated.

When it is confirmed that the accuracy of the parameter can be satisfied, the parameter is stored in the parameter database 2 so that it can be reused.

In addition, FIG. 2 is shown typically and it is not necessary for each part 11-13 to exist independently. For example, the entirety of the parameter extraction device 3 may be realized by a single calculator that operates based on a predetermined program. Of course, a dedicated software for executing the processing of the parameter optimization unit 12 may be used, and the parameter optimization unit 12 may be used by a patch program for software for operating the entire design process group 90 that has existed conventionally. May be executed. These programs can be recorded on a computer readable recording medium.

b2) Overview of parameter extraction

3 is a flowchart showing the decomposition of the processing of the parameter optimizer 12. First, in step 121, a parameter search is performed using a combinatorial optimization method. The enumerated technique here is to find the first solution described in section A. The process proceeds to step 123 via the solution switching step 122, where a parameter search using the Newtonian method is executed. The Newtonian solution here refers to the step of finding the second solution described in section A.

Step 122 returns to the process of step 121 if it is determined that the parameter found in step 121 is not an initial value when executing step 123, and proceeds to step 123 if it is determined appropriate. Step 122 includes steps 122b and 122a corresponding to each of the first and second switching conditions described above.

The error function S of a nonlinear device, for example a MIS transistor, is represented by equation (1).

External factor groups v ₁ , v ₂ , v ₃ ,. , v _m each has u (≧ 1) external factors. As shown in section A, for example, u = 3, and an operating factor τ, a gate voltage V _gs , and a drain voltage V _ds can be adopted as external factors. The characteristic quantity g _i is the physical quantity represented by the nonlinear element when the external factor group v _i is provided. As shown in section A, for example, the drain current I _ds can be employed. In this case, the number of characteristic quantities constituting the characteristic quantity group is 1, and the error function S is a scalar quantity. In addition, the characteristic quantity may be used as a result of device simulation, not as an actual measurement value. In that case, a function approximating a device is generally expressed by device simulation, and the characteristic quantity group can be expressed by g _i = g (v _i ).

The parameter group P is composed of n (≥2) parameters p ₁ , p ₂ , p ₃ ,. , p _n . As shown in section A, for example, n = 2, and the threshold voltage V _th and the coefficient β can be adopted as parameters. However, in step 121, the parameters already quantitatively obtained by the initial value determining unit 11 are also employed as initial values. In the example shown in section b1), either the threshold voltage V _th or the coefficient β is quantitatively determined as an initial value.

The weight function w _i is set corresponding to each of the other external factor groups v _i . As a special case, the weight function w _i is always set to 1 for any of the external factor groups v _i , and the error function S is defined as an absolute error. If w _i = 1 / g _i , the error function S is defined as the relative error.

The process of parameter extraction is the process of obtaining the parameter group P which minimizes the error function S or sets it to zero within a predetermined error. The parameter extraction proceeds by decreasing the value of the error function S while updating the parameter group P with a predetermined rule.

In FIG. 3, it is also possible to execute a computer by a program for integrally processing the processes described as steps 121, 122, and 123. In FIG. Alternatively, the processes described as steps 121, 122, and 123 may be integrally executed using hardware. In addition, it is also possible to execute it on a computer by a program which executes steps 121, 122, and 123 independently.

Alternatively, the parameter optimization unit 12 may be configured by using hardware which individually executes the processes described as steps 121, 122, and 123, respectively. In this case, the parameter optimization unit 12 is configured by using an enumerated method execution unit, a process switching determination unit, and a Newton method system solving unit as hardware for completing functions corresponding to steps 121, 122, and 123, respectively. The flowchart of FIG. 3 is read again as a block diagram showing a coupling relationship of blocks that complete the function disclosed in each step.

b3) enumeration.

As an example of the enumerated method, a method called Simulated Annealing and a method called Simulated Diffusion (hereinafter, referred to as "SA method" and "SD method", respectively) are already known. For example, an example of applying the SA method to a semiconductor device is referred to as “Modeling of Microwave Semiconductor Devices Using Simulated Annealing Optimization” (Man-Kuan Vai, et al., IEEE Trans. Electron Devices, Vol. ED-36, No4, pp761-762, Apr.1989, hereinafter referred to as "Document 1", and an example in which the SD method is applied to a semiconductor device is described as "Fast Simulated Diffusion: An Optimization Algorithm for Multiminimum Problems and Its Application to MOSFET Model Parameter Extraction" (T. Sakurai, et al. , IEEE Trans.computer-Aided Design, Vol. CAD-11, No2, pp228-233, Feb. 1992, hereinafter referred to as "Document 2".

In the SA method and the SD method, an error function S is obtained using a parameter provided with a predetermined update amount, and when the error function S increases, the parameter provided with the update amount in probability Q is employed as the updated parameter. For example, in Document 1, by using the base amount V ₀ and the random number R (0≤R≤1) the update, and the update amount as provided in the update of the parameters adopted ΔV = ₀ RV. As long as the parameter increased by [Delta] V does not exceed a predetermined range, it is employed in the following calculation as an updated parameter. In addition, in Document 2, if the update amount proportional to the slope of the error function S is added to the parameter, and the value of the error function S obtained by this added parameter becomes large, the parameter is adopted as the updated parameter along the probability Q. Specifically, when a parameter obtained by increasing the value of the error function S is obtained, a random number R is generated, and the parameter is adopted as an updated parameter provided that it is equal to or less than the probability Q. On the contrary, when the value of the obtained error function S becomes small, the parameter is adopted as the updated parameter.

The so-called Metropolis method is adopted in either the SA method or the SD method. The Metropolis method is introduced, for example, in "Simulated Annealing Algorithm: An Overview" (Rob A. Rutenbar, IEEE Circuits and Devices Magazine, Jan., 1989, PP19-25, hereafter referred to as Document 3). Based on the method and the SD method, the probability Q at which the error function S increases by the increase amount δS (> 0) is calculated as exp (−δS / T), and 0 <Q ≦ 1 is established.

Here, the divisor T is a predetermined amount that decreases and is updated when the parameter is updated to perform the iterative calculation. For example, in Document 1, it is called pseudo-temperature, and the initial value is set to 500 or more, and is updated to a value of 90% at the time of repetitive calculation.

As the procedure determination condition in the SA method and the SD method, for example, whether or not the parameter is within the size-determined range and whether or not the number of occurrences of the random number has reached a predetermined upper limit is adopted. Or whether the arbitrary temperature T is sufficiently cooled.

Also in this invention, whether arbitrary temperature T was fully cooled as a 2nd switching condition is employ | adopted. Since the predetermined amount T contributes to the reduction of the probability Q, the second switching condition can be realized by introducing this as a factor of the probability Q. Step 122a is a judgment corresponding to this. For example, if the arbitrary temperature T is smaller than 1 × 10 ⁻³ of the initial value, the arbitrary temperature T is judged to be sufficiently cooled, and the process proceeds to step 123, otherwise, the process proceeds to step 122b. Proceeding, determination of the first switching condition is performed.

However, in the present invention, as a procedure condition of the enumerated method, the judgment is mainly made by whether or not the error function S decreases a predetermined number of times as shown in section A. More preferably, when the error function S decreases continuously for a predetermined number of times, it is determined that the error function S decreases monotonically with respect to the iterative calculation involving the updating of the parameters, and ends the enumeration technique. That is, the magnitude | size of the error function S obtained by the iteration calculation of the kth time is made into the convergence determination condition by Equation 2 as Sk.

The number of times t of successively decreasing values of the error function S is set to, for example. This procedure determination condition corresponds to step 122b, which proceeds to step 123 when the error function S decreases between successive t states, that is, between t calculations performed by updating the parameter group P, and returns to step 122 otherwise. Goes. In other words, if it is determined that the procedure is performed under the first switching condition, the process proceeds to step 123.

As described above, step 122a corresponding to the determination of the second switching condition may be employed, or may be omitted.

In the SD method, in addition to the metropolis method, the Brownian motion is also employed as a part of the update amount of the parameter. For example, in Document 2, Equation 3 is interposed as an update amount dx provided for updating a parameter.

In Equation (3), the parameter x and the function f are employed as corresponding to the parameter group P and the error function S, respectively. The right side claim 1 is a drift term, and the second claim corresponds to a Brownian motion. Where dw is Gaussian random noise.

b4) Newtonian solution.

When the error function S becomes the minimum, Equation 4 can be satisfied.

This means that the parameters p ₁ , p ₂ ,... is a nonlinear system of equations of order _n with p _n as the unknown variable. In order to solve this simultaneous equation, iterative calculation is performed to update the parameter group P, and the Newton method is the most common numerical solution as the method of monotonically decreasing the error function S obtained based on the updated parameter group P. In this solution, the update amount ΔP for the parameter group P is calculated by the expression (6) using the expression of the expression (5).

Provided that k = 1,2,... , n, and J ^T represents the transpose matrix of J. In "", Hessian of the function f (v, P) is shown.

Various approximation methods are used to improve the calculation efficiency of obtaining the update amount ΔP. For example, the Gauss-Newton method ignores the terms of two or more layers of the function f,

To employ. From equation (7), parameter group P is sequentially obtained using QR decomposition.

In order to further improve the convergence, as an approximation of Hessian, a Levenberg-harquardt method is proposed in which diagonal terms are added to emphasize components in the direction in which the magnitude of the error function S decreases. This technique is described, for example, in “General Optimization and Extraction of IC Device Model Parameters” (K. Dogains and DLScharfetter, IEEE Trans. Electron Devices, Vol. ED-30, No9, pp1219-1228, Sep. 1983). Specifically, the update amount ΔP is calculated based on the equation (8).

Here, I is a unit matrix, diag () employs the diagonal component of the matrix in () as a diagonal component, and shows the matrix which has zero as other components. The coefficient λ is large at the beginning of the repetition calculation, for example, is set to about 0.1, and is set to be zero in the vicinity of the solution.

Fig. 4 is a flowchart showing the case where equation (7) is used in the Newton method. In step 124, the parameter group p ^{(r + 1)} obtained in the (r + 1) th time is increased by the update amount [A ^T A] ^-1 C with respect to the parameter group P ^(r) in the r th time. Calculate In step 125, the error function S is updated using the parameter group P ^{(r + 1)} . In step 126, it is determined whether the error function S is sufficiently small, i.e., zero in a predetermined error range. If the error function S is 0 within the predetermined error range, the optimization ends. Otherwise, in step 127, the number r is increased by one and then the process returns to step 124.

In step 126, if it is determined that the updated parameter group P ^{(r + 1)} falls within the predetermined range with the parameter group P ^(r) before the update, the accuracy of the parameter group P cannot be increased even if the calculation is continued further. Optimization ends. If it is not within the predetermined range, step 127 returns to step 124.

C. Variation:

Document 3 states the case in which the probability is handled in the form of the Boltzmann distribution in the Metropolis method, but the Lorentz distribution may be employed as introduced in Document 2. Further, the Boltzmann distribution may be series-developed and a function may be employed in which the predetermined number of terms after the lower order term are ignored.

According to the parameter extraction method of the physical property model according to the present invention, in step (b-1), the parameter group P is updated while maintaining the probability Q at which the error function S increases is positive (+). It is possible to avoid falling into a local solution. Moreover, the parameter group P obtained after the value of the error function S decreases a predetermined number of times while maintaining the probability Q at which the error function S increases is positive (+) exists near the true solution.

According to the parameter extraction method of the physical property model according to the present invention, since the parameter group P obtained in the step (b-1) is considered to exist near the true solution, the step of updating the parameter group P only in a monotonically decreasing direction The convergence property in (b-2) can be improved.

According to the parameter extraction method of the physical property model according to the present invention, the predetermined amount contributes to the decrease in the probability Q that the error function S increases each time the parameter group P is updated. Therefore, increasing the number of repetitions more than necessary in step (b-1) is avoided.

According to the recording medium of the present invention, a computer can execute a parameter extraction method of a physical property model.

According to the method for manufacturing a nonlinear element according to the present invention, since the physical process is executed based on a characteristic simulation with high precision and low computational cost, the produced nonlinear element can also be close to the design specification and can realize a low cost.

Claims (3)

(a) Corresponding to the physical properties from which the characteristic quantity group g _i which consists of at least one characteristic quantity respectively corresponds to each of the some external factor group v _i (i = 1, 2, ..., m) which consists of at least one external factor Each of the calculated values corresponding to each of the characteristic quantities g _s (where s represents any one value adopted by i) includes the corresponding external factor group v _s and a parameter group P composed of a plurality of parameters. Applying a physical property model given as a function f (v _s , P), (b) The square of the difference between the respective characteristic quantities g _s and the corresponding function f (v _s , P) multiplied by the weight function w _s is multiplied by the error function S that sums the plurality of external factor groups. Extracting the parameter group P providing the minimum value, Step (b) is (b-1) The value of the error function S is repeatedly obtained by updating the parameter group P while maintaining the probability Q at which the value of the error function S increases is positive (+), and the value of the error function S is preset. Steps to stop after decreasing by the number of times Parameter extraction method of the physical property model comprising a. A computer-readable recording medium in which a program to be executed by the computer is recorded, either alone or together with a program provided in a computer in advance. Characteristic simulation employing device modeling using the parameter extraction method of the physical property model according to claim 1, Physical process based on the property simulation Method for producing a non-linear device to produce a non-linear device by executing.