WO2022124053A1

WO2022124053A1 - Information processing device, computer program, information processing method, and simulation information provision method

Info

Publication number: WO2022124053A1
Application number: PCT/JP2021/042597
Authority: WO
Inventors: 高史佐藤; 裕貴塚本; 松辺
Original assignee: 国立大学法人京都大学
Priority date: 2020-12-10
Filing date: 2021-11-19
Publication date: 2022-06-16
Also published as: JP2022092491A

Abstract

Provided are an information processing device, a computer program, an information processing method, and a simulation information provision method with which it is possible to estimate the distribution of model parameters.　This information processing device comprises: a distribution information acquisition unit that acquires distribution information representing the distribution of a first parameter related to manufactured goods; and a probability density information generation unit that, on the basis of model information that represents the first parameter using a second parameter related to the manufactured goods, generates probability density information of the second parameter so that the distribution information can be reproduced.

Description

Information processing equipment, computer programs, information processing methods and simulation information provision methods

The present invention relates to an information processing apparatus, a computer program, an information processing method, and a simulation information providing method.

There is a processing limit in the production of artificial objects, and it is not possible to avoid variations (errors) due to the processing limit. Such variability affects the characteristics of the product and the products in which it is incorporated. For this reason, a variation consideration simulation that generates a model including model parameters and evaluates the influence of variation in advance using the generated model is widely performed.

Non-Patent Document 1 points out that the conventional method for extracting model parameters is limited to model parameters that follow a normal distribution, and discloses a statistical extraction method that can also extract model parameters that follow a lognormal distribution. ing.

However, since the distribution of model parameters is limited to a normal distribution or a lognormal distribution, the method of Non-Patent Document 1 cannot handle model parameters that follow an arbitrary distribution or model parameters whose distribution is unknown in the first place. , It is a strong practical constraint when performing a variation consideration simulation.

The present invention has been made in view of such circumstances, and an object of the present invention is to provide an information processing apparatus, a computer program, an information processing method, and a simulation information providing method capable of estimating the distribution of model parameters.

The present application includes a plurality of means for solving the above problems, and to give an example thereof, the information processing apparatus of the present embodiment is a distribution information acquisition unit that acquires distribution information representing the distribution of a first parameter relating to a product. And, based on the model information expressing the first parameter using the second parameter related to the product, the probability density information generation unit that generates the probability density information of the second parameter so that the distribution information is reproduced. And prepare.

According to the present invention, the distribution of model parameters can be estimated.

It is explanatory drawing which shows an example of the structure of the information processing apparatus of 1st Embodiment. It is explanatory drawing which shows an example of the model parameter in MOSFET. It is a schematic diagram which shows an example of the measured value of a characteristic parameter. It is a schematic diagram which shows an example of the probability density distribution of a characteristic parameter. It is a schematic diagram which shows the concept of the estimation method of the probability density function P (p) of a model parameter p. It is a flowchart which shows an example of the processing procedure of the information processing apparatus of 1st Embodiment. It is a flowchart which shows an example of the processing procedure of the information processing apparatus of 1st Embodiment. It is explanatory drawing which shows an example of the structure of the information processing apparatus of 2nd Embodiment. It is a schematic diagram which shows an example of fitting using the model formula of the measured characteristic parameter. It is a schematic diagram which shows an example of the probability density distribution of a model parameter. It is a flowchart which shows an example of the processing procedure of the information processing apparatus of 2nd Embodiment. It is a flowchart which shows an example of the processing procedure of the information processing apparatus of 2nd Embodiment. It is a circuit diagram which shows an example of the SRAM cell circuit as a simulation target. It is a schematic diagram which shows an example of the simulation result of the SRAM cell circuit. It is a schematic diagram which shows an example of the simulation result of the SRAM cell circuit. It is a schematic diagram which shows the variation of the model parameter of 500 virtual devices. It is a schematic diagram which shows an example of the variation of the current which is a characteristic parameter of 500 virtual devices. It is a schematic diagram which shows an example of the variation of the current which is a characteristic parameter of 500 virtual devices. It is a schematic diagram which shows an example of the generation result of a model parameter by a comparative example. It is a schematic diagram which shows an example of the generation result of the model parameter by 1st Embodiment. It is a schematic diagram which shows an example of the variation of the current which is a characteristic parameter of a fitting target. It is a schematic diagram which shows an example of the variation of the current which is a characteristic parameter of a fitting target. It is a schematic diagram which shows an example of the variation result of the current by the comparative example. It is a schematic diagram which shows an example of the variation result of the current by 1st Embodiment. It is a schematic diagram which shows an example of the use case of the variation consideration simulation in the case of 1st Embodiment. It is a schematic diagram which shows an example of the use case of the variation consideration simulation in the case of 2nd Embodiment. It is a schematic diagram which shows an example of the use case of the variation consideration simulation in the case of a comparative example. It is explanatory drawing which shows the other example of the structure of the information processing apparatus of 1st Embodiment and 2nd Embodiment.

(First Embodiment)
Hereinafter, the present invention will be described with reference to the drawings showing the embodiments thereof. FIG. 1 is an explanatory diagram showing an example of the configuration of the information processing apparatus 100 of the first embodiment. The information processing device 100 includes a control unit 10, an input unit 11, a distribution information generation unit 12, a probability density information generation unit 13, an output unit 14, a simulation unit 15, a storage unit 16, a display panel 17, and an operation that control the entire device. A unit 18 is provided. The probability density information generation unit 13 includes a sampling unit 131, a conversion unit 132, and a model parameter generation unit 133.

Applicants are often uncertain as to what distribution the model parameters required to model the variability of the product during processing will follow, and when compared to measuring the distribution of the model parameters, the product We focused on the fact that it is easy to measure the distribution of performance and characteristics. The information processing apparatus 100 is difficult to measure (for example, when the measurement takes a long time or only inside the product) based on the distribution of the first parameter (distribution of the performance and characteristics of the product) which is relatively easy to measure. It is possible to estimate the distribution of the second parameter (such as when it is an observed quantity). The first parameter is also called a characteristic parameter, and is relatively dependent on a so-called measuring instrument such as current, voltage, charge, frequency, impedance, length, area, volume, mass, pressure, velocity, acceleration, concentration, density, and luminosity. It can be a physical quantity that can be easily measured. On the other hand, the second parameter is also referred to as a model parameter and is used in a model formula expressing the performance and characteristics of the product, and is a parameter that affects the performance and characteristics of the product due to an error during processing of the product. be able to.

Manufactured products are artificially manufactured products and include semiconductor devices, electronic parts, electrical parts, mechanical parts, optical parts, etc. used in products in various fields. For example, semiconductor devices include various devices such as MOSFETs, bipolar transistors, diodes, light emitting devices, light receiving devices, memories, logic ICs, analog ICs, sensors, etc., but in the present specification, MOSFETs (as an example of products) are used as examples of products. Hereinafter, a description will be given by taking (also referred to as a “device”) as an example.

FIG. 2 is an explanatory diagram showing an example of model parameters in MOSFET. A device model (also referred to as a “model”) representing the voltage / current characteristics of a MOSFET, which is one of the typical circuit elements, can be represented by, for example, (Equation 1).

In (Equation 1), bold letters represent model parameters, and model parameter K is a current gain parameter, which is represented by the product of carrier mobility and insulating film capacity. The model parameter VTH represents the threshold voltage. W represents the channel width and L represents the channel length. The dimensions of the MOSFET are reflected by the channel length L and the channel width W.

Further, since the linear region and the saturated region are loosely connected, the device model can be expressed by the equation (2) using the model parameter DELTA. Furthermore, the model parameter CLM (channel length modulation effect coefficient), model parameter MD (mobility deterioration coefficient), and model parameter MDV (mobility deterioration start voltage) are used to determine the bias voltage dependence of the channel length modulation effect and carrier mobility. Considering this, the device model can be expressed by the equation (3). As shown in equation (3), the drain current Id can be expressed as a function of the gate-source voltage Vgs and the drain-source voltage Vds. Equations (1) to (3) are model equations expressing a device model (model) as model information. The model formula is an example and has different expressions depending on the type of the product. Hereinafter, in the present specification, for convenience, the model parameters K (current gain parameter) and VTH (threshold voltage) will be focused on, and other model parameters CLM, MD, MDV, and DELTA will be described assuming constant values. .. The model parameters are not limited to the parameters illustrated in FIG. 2.

The input unit 11 can acquire input data. Specifically, the input unit 11 has a function as a measured value acquisition unit, and can acquire the measured value of the characteristic parameter I. Further, the input unit 11 has a function as a distribution information acquisition unit, and can acquire a probability density function Q (I) representing the distribution of characteristic parameters (also referred to as “first parameters”) related to the product. Here, I represents a characteristic parameter. The control unit 10 can determine in advance whether the input unit 11 acquires the measured value of the characteristic parameter I or the probability density function Q (I).

FIG. 3 is a schematic diagram showing an example of measured values of characteristic parameters. As shown in FIG. 3, it is assumed that M devices (MOSFETs) # 1, # 2, ..., #M are manufactured from a semiconductor wafer. FIG. 3 shows voltage / current characteristics showing the relationship between the drain current Id and the gate / source voltage Vgs of each of the devices # 1 to #M. The voltage / current characteristics are actual measured values, and are shown for cases where the drain / source voltage Vds is Vds = Vds1 and Vds = Vds2. Further, it is assumed that the model parameters K and VTH of the device # 1 are K = K1 and VTH = VTH 1, respectively, and the model parameters K and VTH of the device # 2 are K = K2 and VTH = VTH 2, respectively. It is assumed that the model parameters K and VTH of M are K = Km and VTH = VTH, respectively. That is, the variation in the voltage / current characteristics of the devices # 1 to #M is expressed by the difference in the model parameters K and VTH of each device.

In the voltage / current characteristics of device # 1, when Vgs = Vgs1 and Vds = Vds1, Id = Id1, and when Vgs = Vgs2 and Vds = Vds2, Id = Id2. The same applies to the other devices # 2, ... # M. The voltage / current characteristics of each device can be related as Id1 = (Vgs1, Vds1), Id2 = (Vgs2, Vds2). Assuming that the current value under the first bias condition (Vgs1, Vds1) is Id1 and the current value under the second bias condition (Vgs2, Vds2) is Id2, the distribution of the drain current of each device is the current Id1. It can be represented by the distribution of points in the current space (also referred to as "characteristic parameter space") composed of and Id2. In the example of FIG. 3, the distribution of the measured values of the characteristic parameters (that is, the distribution of the drain currents at the two bias points) is illustrated. The input unit 11 can acquire the measured values of the characteristic parameters I (Id1, Id2) as schematically shown in FIG. The number of bias points is not limited to two, and may be three or more.

The distribution information generation unit 12 generates a probability density function Q (I) (also referred to as “distribution information”) representing the distribution of the characteristic parameters I (Id1, Id2) using the measured values acquired via the input unit 11. can do.

FIG. 4 is a schematic diagram showing an example of the probability density distribution of characteristic parameters. The distribution information generation unit 12 can estimate the density distribution by using, for example, Kernel Density Estimation (KDE). The kernel function and the optimum bandwidth (smoothing parameter) can be set as appropriate. For example, a standard Gaussian function can be used as the kernel function. This allows you to extrapolate the population data using kernel density estimation given the sample data for a population. That is, the probability density can be estimated even when there is no measured value of the characteristic parameter. FIG. 4 shows the probability density distribution for the characteristic parameter I (Id1, Id2), and for convenience, the difference in density is expressed by the difference in pattern. For example, the central part of the elliptical contour represents the highest probability density. The use of kernel density estimation is not mandatory. For example, it can be replaced by another method of approximating the density of measured values of characteristic parameters.

When the input unit 11 acquires the probability density function Q (I) representing the distribution of the characteristic parameters related to the product, the distribution information generation unit 12 does not have to generate the probability density function Q (I).

The probability density information generation unit 13 is a probability of expressing the distribution of the characteristic parameter I based on a model formula (also referred to as “device model” or “model information”) expressing the characteristic parameter I using the model parameter p related to the product. The probability density function P (p) (also referred to as “probability density information”) of the model parameter p can be generated so that the density function Q (I) is reproduced. The details of the probability density information generation unit 13 will be described later.

The simulation unit 15 can evaluate the performance of the simulation target including the product by using the probability density function P (p) of the model parameter p generated by the probability density information generation unit 13 and the model formula. Although FIG. 1 shows a configuration in which the simulation unit 15 is incorporated in the information processing device 100, the simulation unit 15 may be configured as an external simulator and separated from the information processing device 100. The details of the simulation unit 15 will be described later.

The output unit 14 can output the probability density function P (p) of the model parameter p and the simulation result performed by the simulation unit 15 as output data.

The storage unit 16 can be composed of a hard disk, a semiconductor memory, or the like, and stores required information. The storage unit 16 can store the input data acquired via the input unit 11. Further, the storage unit 16 can store the processing result of each processing in the information processing apparatus 100 and the information in the middle of processing. Further, the storage unit 16 can store one or a plurality of models (model formulas) in association with the model ID that identifies the device model. Here, the model ID can identify different device models of the same manufacturer, or can identify device models generated by different manufacturers.

The control unit 10 has a function as an update unit, and when a new model is provided for the model stored in the storage unit 16 and a new model is acquired via the input unit 11, the acquired new model is used. The model stored in the storage unit 16 can be updated. This allows the latest model to be used.

The display panel 17 can be composed of a liquid crystal panel, an organic EL (Electro Luminescence) display, or the like.

The operation unit 18 is composed of, for example, a hardware keyboard, a mouse, or the like, and can operate an icon or the like displayed on the display panel 17 or input characters or the like. The operation unit 18 may be configured with a touch panel.

Next, the model parameter estimation method will be described.

The probability density information generation unit 13 includes a sampling unit 131, a conversion unit 132, and a model parameter generation unit 133. The sampling unit 131 samples candidates for the model parameter p using a Markov chain. A Markov chain is a stochastic process in which the future state is determined only by the present state, is irrelevant to the past state, and the possible states are discrete values. The conversion unit 132 converts the sampled candidate into the candidate of the characteristic parameter I by using the model formula. The model parameter generation unit 133 applies the Monte Carlo method to the probability density function Q (I) representing the distribution of the converted characteristic parameter I, and generates the model parameter p from the sampled candidates. The Monte Carlo method is one of the numerical calculation methods, and is a method of finding an approximate solution by repeating trials using random numbers. Hereinafter, a method of generating model parameters will be described.

FIG. 5 is a schematic diagram showing the concept of an estimation method of the probability density function P (p) of the model parameter p. Since it is difficult to directly measure the model parameters of the product (for example, MOSFET, etc.) (for example, current gain parameter K, threshold voltage parameter VTH, etc.), it is not possible to know the probability density function that each model parameter follows. .. On the other hand, the characteristic parameters of the product (for example, current I) can be easily measured, and the probability density function Q (I) of the current distribution can be calculated. The probability density information generation unit 13 reproduces the distribution of model parameters using the probability density function Q (I) of the current distribution. That is, the probability density information generation unit 13 approximates the distribution including the correlation of the model parameters by randomly generating a set of model parameters through a process of reproducing the distribution of the model parameters based on the probability density of the current distribution. be able to.

As shown in FIG. 5, in the method of this embodiment, the model parameter space and the characteristic parameter space are associated with each other by using the model f (model formula). In the present specification, for convenience, the model parameter space is composed of two model parameters p1 and p2, and the characteristic parameter space is a two-dimensional space composed of characteristic parameters Id1 and Id2 (here, currents Id1 and Id2). The model parameter space and the characteristic parameter space are not limited to two dimensions, and the same procedure can be used even if the model parameter space and the characteristic parameter space are higher in dimension. Further, let P be the density distribution of the model parameters, and let Q be the density distribution of the measurement results of the characteristic parameters.

The point p ⁽ⁱ⁾ in the model parameter space represents the model parameter of one device and corresponds to the point I ⁽ⁱ⁾ in the characteristic parameter space. The points p ⁽ⁱ⁾ and the points I ⁽ⁱ⁾ in the two spaces are associated with each other by the model f. The points p ⁽ⁱ⁾ and p'in the model parameter space represent two different sets of model parameters. That is, these two points represent two different devices. Due to the difference in model parameters, the characteristic parameters (current) I ⁽ⁱ⁾ and I'of these two devices are also different.

The probability density function Q of the characteristic parameter in the characteristic parameter space is known by measuring the characteristic parameter (current) of many devices. In this embodiment, the probability density function P in the model parameter space can be defined so as to reproduce the probability density function Q through the transformation of the model f. This can be achieved by sampling the model parameters via the model f so that the density function of the sample of characteristic parameters is reproduced. Hereinafter, specific processing will be described.

6 and 7 are flowcharts showing an example of the processing procedure of the information processing apparatus 100 of the first embodiment. Hereinafter, for convenience, the main body of the process will be described as the control unit 10. The control unit 10 determines whether the input data is the probability density function Q (I) of the characteristic parameter I or the measured value of the characteristic parameter I (S11). When the input data is a measured value (measured value in S11), the control unit 10 acquires the measured value of the characteristic parameter I (here, the measured value of the drain electricity of the MOSFET) (S12).

The control unit 10 generates the probability density function Q (I) (S13) and performs the process of step S15 described later. Here, the probability density function Q (KDE) is applied to the measured value of the drain current in the J-dimensional characteristic parameter space (also referred to as "current space") stretched by the currents at the J bias points. I) can be calculated. If the number of devices N for current measurement is sufficiently large and the probability density at a certain point in the characteristic parameter space can be directly obtained from the measurement result, the provision of KDE may be omitted. Further, the probability density may be obtained by using an appropriate method other than KDE.

When the input data is a probability density function (probability density function in S11), the control unit 10 acquires the probability density function Q (I) (S14) and sets the initial value of the model parameter set p ⁽¹⁾ (S). S15). The control unit 10 sets the counter i = 1 (S16) and sets the current model parameter set in the model parameter space to p ⁽ⁱ⁾ (S17).

The control unit 10 calculates the current characteristic parameter (drain current) I ⁽ⁱ⁾ corresponding to p ⁽ⁱ⁾ with the current model parameter set using the model formula (S18). The control unit 10 moves the model parameter set p ⁽ⁱ⁾ , which is the current sample in the model parameter space, using the proposed distribution q (p'/ p ⁽ⁱ⁾ ), and moves the next sample candidate to the next. A candidate model parameter set p'is generated (S19). Here, as the proposed distribution, for example, a normal distribution can be used in which the current sample p ⁽ⁱ⁾ is centered and the variance is σp, and the sample x from this normal distribution can be obtained from p ^(i). Let it be the distance traveled to p'. The proposed distribution is not limited to the normal distribution, and various distributions satisfying the detailed equilibrium condition can be used. The detailed equilibrium condition is a condition that the existence probabilities of each are equal even if the states transition according to the transition probabilities. Here, in the model parameter space, Markov chains are used to sample model parameter candidates. The control unit 10 calculates the characteristic parameter (drain current) I'corresponding to the candidate model parameter set p'using the model formula (S20).

The control unit 10 calculates the probability ratio r by the formula r = Q (I ′) / Q (I ⁽ⁱ⁾ ) (S21). Here, P (p') / P (p ⁽ⁱ⁾ ) is approximated by Q (I') / Q (I ⁽ⁱ⁾ ). Since the probability density function Q is known by density estimation by KDE or the like, it can be calculated immediately, whereas the probability density function P is P (p') / P (p) because it is difficult to measure. This is because it is difficult to obtain ⁽ⁱ⁾ ). The validity of approximating the probability ratio in the model parameter space by the probability ratio in the characteristic parameter space is that the model equation f is injective (or injective) (this is usually satisfied), and the parameter variation is f. Obviously if is small enough to be considered linear. If f has a strong non-linearity in the range where variation is taken into consideration, it is necessary to correct it. The control unit 10 generates a uniform random number R (0 ≦ R <1) (S22).

The control unit 10 determines whether or not r> R (S23). When r> R (YES in S23), the control unit 10 sets the next candidate model parameter set p'as the next model parameter set p ^{(i + 1)} (p ^{(i + 1)} ← p'). (S24), the process of step S27 described later is performed. If r> R (NO in S23), the control unit 10 discards the next candidate model parameter set p'(S25) and sets the current model parameter set p ⁽ⁱ⁾ to the next model parameter set p ⁽ⁱ ). ⁺¹⁾ (p ^{(i + 1)} ← p ⁽ⁱ⁾ ) (S26). The processing of steps S23 to S26 applies the Monte Carlo method to the probability density function of the characteristic parameter in the characteristic parameter space to generate a model parameter.

The control unit 10 determines whether or not the counter is i ≦ (N-1), and if i ≦ (N-1) (YES in S27), that is, the processing is completed for all the devices. If not, 1 is added to the counter i (S28), the next model parameter set in step S24 or S26 is set as the current model parameter set in step S17, and the processing after step S17 is repeated. Each time it is repeated, a set of model parameter sets is generated.

If i≤ (N-1) (NO in S27), the control unit 10 generates a random set of model parameters {p ⁽¹⁾ , p ⁽²⁾ , ..., P ^(N) } (S29). .. The set of generated model parameters follows the probability density function P (p).

The control unit 10 evaluates the performance of the simulation target using the model formula and the generated model parameters (S30), outputs the probability density function P (p), outputs the simulation result (S31), and ends the process.

For practical purposes, it is more desirable to use a procedure called burn-in, which eliminates the correlation caused by the algorithm by rejecting the initial sample and thinning out the sample. As described above, according to the present embodiment, it is possible to obtain a random number of a model parameter set of an arbitrary distribution without assuming any distribution according to the model parameters. That is, the distribution of model parameters can be estimated. Also, non-linear correlations between model parameters can be considered. In the above example, the model parameters were generated to reproduce the current distribution, but are not limited to the current distribution, for example, to reproduce variations in other measurable electrical properties such as capacitance. Model parameters can be defined and a highly versatile method can be provided.

In addition to the methods described so far, it is also possible to generate random numbers that follow the distribution of model parameters more directly. This point will be described below.

(Second Embodiment)
FIG. 8 is an explanatory diagram showing an example of the configuration of the information processing apparatus 100 of the second embodiment. The difference from the first embodiment illustrated in FIG. 1 is that the input data is the measured value of the characteristic parameter I, and the distribution information generation unit 12 for generating the probability density function Q (I) of the characteristic parameter It is unnecessary and includes a fitting unit 19.

FIG. 9 is a schematic diagram showing an example of fitting using a model formula of measured characteristic parameters. As shown in FIG. 9, it is assumed that M devices (MOSFETs) # 1, # 2, ..., #M are manufactured from a semiconductor wafer. FIG. 9 shows voltage / current characteristics showing the relationship between the drain current Id and the gate / source voltage Vgs of each of the devices # 1 to #M. The voltage / current characteristics are actual measured values, and are shown for cases where the drain / source voltage Vds is Vds = Vds1 and Vds = Vds2.

The fitting unit 19 fits the model parameters of each device # 1 to #M using the model formula, and the model parameters p1 and p2 (in the figure, the model parameters pk1 and pk2 (here, k)) constituting the model formula. = 1, 2, ..., m)) is obtained. Fitting is to find a model parameter that represents a curve that best fits the measured characteristic parameter data (curve). By fitting the model parameters p1 and p2 to a plurality of devices, the distribution of the fitted model parameters in the model parameter space can be directly obtained. The model parameters p1 and p2 can be, for example, the current gain parameter K and the threshold voltage parameter VTH, but are not limited thereto. Fitting is effective as a method for extracting the majority of parameters. For some parameters, it is also possible to measure directly without fitting if it is permissible to use destructive measurements. However, in this case, the device itself is destroyed, so it is desirable to guess the parameters by fitting.

FIG. 10 is a schematic diagram showing an example of the probability density distribution of model parameters. The probability density information generation unit 13 can estimate the density distribution by using, for example, kernel density estimation (KDE: Kernel Density Estimation). The kernel function and the optimum bandwidth (smoothing parameter) can be set as appropriate. For example, a standard Gaussian function can be used as the kernel function. This allows you to extrapolate the population data using kernel density estimation given the sample data for a population. That is, the probability density can be estimated even when there is no calculated value of the model parameter. FIG. 10 shows the probability density distribution for the model parameters p1 and p2, and for convenience, the difference in density is expressed by the difference in pattern. For example, the central part of the elliptical contour represents the highest probability density. As described above, by executing KDE on the model parameters of a plurality of devices, the probability density function P (p) according to the model parameters can be obtained. Alternatively, the probability density function P (p) can be approximated by another method, for example, a value proportional to the probability density function in pj can be obtained by using the number of parameters around a certain model parameter pj.

11 and 12 are flowcharts showing an example of the processing procedure of the information processing apparatus 100 of the second embodiment. The control unit 10 acquires the measured value of the characteristic parameter I (here, the measured value of the drain current of the MOSFET) (S41). The control unit 10 fits the model parameters using the model formula (S42). The control unit 10 determines the presence / absence of another device (S43), and if there is another device (YES in S43), repeats the processes after step S41.

When there is no other device (NO in S43), the control unit 10 generates a probability density function P (p) of the model parameter (S44). The control unit 10 sets the initial value of the model parameter set p ⁽¹⁾ (S45). The control unit 10 sets the counter i = 1 (S46) and sets the current model parameter set in the model parameter space to p ⁽ⁱ⁾ (S47).

The control unit 10 moves the model parameter set p ⁽ⁱ⁾ , which is the current sample in the model parameter space, using the proposed distribution q (p'/ p ⁽ⁱ⁾ ), and moves the next sample candidate to the next. Generate a candidate model parameter set p'(S48). Here, as the proposed distribution, for example, a normal distribution can be used in which the current sample p ⁽ⁱ⁾ is centered and the variance is σp, and the sample x from this normal distribution can be obtained from p ^(i). Let it be the distance traveled to p'. The proposed distribution is not limited to the normal distribution, and various distributions satisfying the detailed equilibrium condition can be used. Here, in the model parameter space, Markov chains are used to sample model parameter candidates.

The control unit 10 calculates the probability ratio r by the formula r = P (p') / P (p ⁽ⁱ⁾ ) (S49). The control unit 10 generates a uniform random number R (0 ≦ R <1) (S50). The control unit 10 determines whether or not r> R (S51). When r> R (YES in S51), the control unit 10 sets the next candidate model parameter set p'as the next model parameter set p ^{(i + 1)} (p ^{(i + 1)} ← p'). (S52), the process of step S55 described later is performed.

If r> R (NO in S51), the control unit 10 discards the next candidate model parameter set p'(S53), and sets the current model parameter set p ⁽ⁱ⁾ to the next model parameter set p ⁽ⁱ ). ⁺¹⁾ (p ^{(i + 1)} ← p ⁽ⁱ⁾ ) (S54). The control unit 10 determines whether or not the counter is i ≦ (N-1), and if i ≦ (N-1) (YES in S55), that is, the processing is completed for all the devices. If not, 1 is added to the counter i (S56), the next model parameter set in step S52 or S54 is set as the current model parameter set in step S47, and the processing after step S47 is repeated. Each time it is repeated, a set of model parameter sets is generated.

If i≤ (N-1) (NO in S55), the control unit 10 generates a random set of model parameters {p ⁽¹⁾ , p ⁽²⁾ , ..., P ^(N) } (S57). .. The set of generated model parameters follows the probability density function P (p). The control unit 10 performs performance evaluation of the simulation target using the model formula and the generated model parameters (S58), outputs the probability density function P (p), outputs the simulation result (S59), and ends the process.

Using the probability density function P (p) or its approximation, the probability ratio r = P (p') / P (p ⁽ⁱ⁾ at any two points (p ⁽ⁱ⁾ and p') in the model parameter space. ) Is obtained, the probability ratio r can be evaluated while moving p using the proposed distribution, and model parameter candidates can be sampled using a Markov chain that repeats its adoption and rejection.

As described above, the information processing apparatus 100 of the second embodiment acquires the measured value of the first parameter (characteristic parameter indicating the characteristic of the product) relating to the product, and applies the measured value of the acquired first parameter to the measured value. The distribution information of the second parameter can be obtained by applying the model information expressing the first parameter using the second parameter (model parameter of the product) relating to the product. The information processing apparatus 100 can generate the probability density information (probability density function) of the second parameter based on the distribution information of the second parameter. More specifically, the information processing apparatus 100 samples the candidates of the second parameter using the Markov chain, applies the Monte Carlo method to the distribution information representing the distribution of the second parameter, and second from the sampled candidates. Parameters can be generated. The generated second parameter follows a probability density function.

Next, the circuit simulation performed by the simulation unit 15 will be described.

FIG. 13 is a circuit diagram showing an example of an SRAM cell circuit as a simulation target. The SRAM cell circuit shown in FIG. 13 uses the above-mentioned MOSFET and its device model. In the SRAM cell circuit, L1 and L2 are p MOSFETs, and D1, D2, A1 and A2 are n MOSFETs. Device models polyclonal1 and EtOAc1 representing the characteristics of each of the p MOSFET and n MOSFET used in manufacturing the circuit are prepared, and photoresist1 is used for L1 and L2, and IGMP1 is used for D1, D2, A1 and A2. Here, due to the symmetry of the SRAM cell circuit, L1 and L2 are designed using the same MOSFET with the same dimensions. That is, on the circuit diagram, the exact same model including the model parameters is used. Similarly, D1 and D2 have the same dimensions as each other, and A1 and A2 also have the same dimensions as each other. When performing a circuit simulation, a netlist including a model definition statement and an element definition statement is generated.

14A and 14B are schematic views showing an example of the simulation result of the SRAM cell circuit. FIG. 14 shows the evaluation result of the static noise margin (SNM), which is one of the circuit characteristics of the SRAM cell circuit. SNM represents the amount of voltage fluctuation required for reversing the value stored in the memory cell when the voltage at the nodes N ₀ and N ₁ fluctuates, and is an index for evaluating the stability of the value stored in the memory cell. It is one. FIG. 14A shows a state of normal operation. That is, the state in which two gaps (indicated to include the largest square whose one side length is SNM ₀ and SNM ₁ ) exist in two curves called butterfly curves is 0/1. Represents a normal operating state that can be stably stored. In the memory cell design, min (SNM ₀ , SNM ₁ ) is maximized.

On the other hand, FIG. 14B shows a state of malfunction. Due to variations in model parameters, for example, if the threshold voltage is different, the circuit characteristics will also be different. FIG. 14B shows an example in which the circuit does not operate normally due to a large variation in model parameters. In this example, SNM ₀ , that is, the gap on the left side of the butterfly curve does not exist. By repeating such a simulation many times in response to variations in model parameters, it is possible to obtain the yield of the SRAM cell circuit using the static noise margin as an index.

Next, the evaluation results for the generation of the probability density function of the model parameters by the information processing apparatus 100 of the first embodiment will be described. Model parameters such as thresholds are often difficult to measure directly. Therefore, two methods are used as the evaluation method. The first evaluation method assumes a virtual device and shows how accurately it can be estimated with respect to variations in model parameters of the virtual device. The second evaluation method shows how accurately the current characteristic parameters of the actually measured device can be estimated. First, the first evaluation method will be described.

FIG. 15 is a schematic diagram showing variations in model parameters of 500 virtual devices. In the figure, the vertical axis indicates the threshold voltage VTH, and the horizontal axis indicates the current gain K. The virtual device assumes a situation where two lots are mixed and the model parameters are divided into two clusters. In the following, the above equations (1) to (3) are used as the device model, and the variation of the two model parameters of the threshold voltage VTH and the current gain K is considered among the model parameters.

For each model parameter, the parameter is generated using a pseudo-random number assuming that it follows a normal distribution with two peaks. Model parameters other than these two are fixed to constant values. When generating model parameters using random numbers, the average value, variance, and correlation for each model parameter K and VTH may be appropriately set. We generated 500 bivariate normal random numbers as model parameters for 500 virtual devices. Of the 500, 70% of 350 are one cluster and 30% of 150 are the other cluster.

16A and 16B are schematic views showing an example of current variation, which is a characteristic parameter of 500 virtual devices. For the generated 500 model parameters exemplified in FIG. 15, the drain current of the device is calculated using the model formula. Here, the voltage-current characteristic data of 500 virtual devices were calculated. FIG. 16A shows the distribution of drain current under two bias conditions (bias voltage). Here, two points (Vgs, Vds) = (10V, 1V) and (18V, 5V) are selected as the bias conditions of the current data constituting the characteristic parameter space. These correspond to Id1 and Id2 in FIG. 16A, respectively.

FIG. 16B shows the probability density distribution of the drain currents of 500 virtual devices estimated using KDE with respect to the variation of the drain currents.

FIG. 17 is a schematic diagram showing an example of the generation result of the model parameter by the comparative example. FIG. 17 shows a scatter plot of model parameters K and VTH generated by the comparative example, and a histogram for each parameter K and VTH. In the figure, black circles indicate the true values of the model parameters, and ◇ indicates the model parameters generated by the comparative example. Since the parameters generated by the comparative example assume only one normal distribution, it can be seen that the variation of the given parameters cannot be reproduced and the error is large. This situation is also clear in the histogram for each model parameter. The true distribution represented by the solid line has two peaks, whereas in the comparative example, this is approximated by a normal distribution, so that the most frequent parts of the model parameters are completely different. Here, a method based on a comparative example will be described below.

In the comparative example, the model parameters are generated by the following procedure. (1) Generate a model formula that expresses the performance of the product by a function of parameters (model parameters) at the time of processing, (2) Fit the measured value (for example, current, etc.) of the product to the model formula. The variation of the parameters in the model formula is expressed by a normal distribution or the like. (3) The realization value of the parameter expressed by the normal distribution or the like is generated as a random number according to the normal distribution. Furthermore, when evaluating the performance of the product, a simulation is performed using the generated realization value and the model formula.

In the comparative example, the model parameters are represented as a normal distribution, but in reality, they often do not follow the normal distribution. In addition, it can be difficult to directly measure variability in model parameters. Since it is assumed that parameters that are difficult to measure and whose distribution is unknown follow a normal distribution, the generated model parameters may not be sufficiently accurate.

FIG. 18 is a schematic diagram showing an example of the generation result of the model parameter according to the first embodiment. FIG. 18 shows a scatter plot of the model parameters K and VTH generated by the above-described embodiment, and a histogram for each of the parameters K and VTH. In the figure, black circles indicate the true values of the model parameters, and Δ indicates the model parameters generated by the present embodiment. In the method of this embodiment, a random number created from a two-dimensional normal distribution having an average of 0 and a variance of (0.2) ² is used as a random number (proposal distribution) when creating a next sample candidate from the current sample. board. That is, if Δ _K and Δ _VTH to N (0, 0.2 ² ), the next sample candidate can be generated from the current sample as follows.
(K', VTH') ^T = (K ⁽ⁱ⁾ , VTH ⁽ⁱ⁾ ) ^T + ( _{ΔK, ΔVTH} ₎ ^T
The number of samples is 55,000. However, the first 5000 samples were discarded as burn-ins, leaving 50,000. Further, the samples were thinned out at intervals of 100 samples to finally obtain 500 samples.

As shown in FIG. 18, in the histogram of the model parameters generated by the method of this embodiment, the distribution of the model parameters is not assumed, but as a result, it can be seen that the two peaks are well reproduced. From this, it can be seen that this embodiment is useful for a variation consideration simulation with a small error.

Next, the second evaluation method will be described.

19A and 19B are schematic views showing an example of variation in current, which is a characteristic parameter of the fitting target. As in the case of the first evaluation method, for the sake of simplicity, the variation of the two model parameters of the threshold voltage VTH and the current gain K is considered among the model parameters. The bias conditions to be fitted are (Vgs, Vds) = (18V, 1V) and (12V, 3V) at two points, which are Id1 and Id2, respectively. FIG. 19A shows actual measurement data (current variation data) of the current under this bias condition. FIG. 19B shows the probability density of the current obtained using KDE.

FIG. 20 is a schematic diagram showing an example of the current variation result according to the comparative example. FIG. 20 is an evaluation in which variations in current characteristics are reproduced by simulation and compared with measured values (actual measurement data). It can be seen that the current simulation using the model parameters generated by the comparative example described in FIG. 17 cannot reproduce the distortion of the current distribution appearing in the measured values because it is assumed that the model parameters follow a normal distribution. ..

FIG. 21 is a schematic diagram showing an example of the current variation result according to the first embodiment. In the case of this embodiment, it can be seen that the measured value (actual measurement data) can be sufficiently reproduced in the current characteristic variation simulation using the generated model parameters. That is, it can be seen that in the present embodiment, more accurate current simulation is possible without assuming the distribution of model parameters. In addition, the same evaluation result as in the first embodiment can be obtained also in the second embodiment.

Next, a use case of the variation consideration simulation when the information processing apparatus 100 of the first embodiment and the second embodiment is used will be described.

FIG. 22 is a schematic diagram showing an example of a use case of the variation consideration simulation in the case of the first embodiment. When the information processing apparatus 100 of the first embodiment is used, the variation consideration simulation can be performed as follows, as shown in FIG. 22.
(1) A manufacturer (a company that manufactures circuits (FAB)) manufactures a large number of devices (for example, MOSFETs) and measures characteristic parameters (for example, voltage / current characteristics) of the manufactured devices.
(2) The manufacturer determines the device model (model formula) of the device to be manufactured, and applies, for example, kernel density estimation to the measured characteristic parameters to generate a probability density function of the characteristic parameters. ..
(3) The manufacturer provides the user with a device model and a probability density function of the generated characteristic parameter. In addition, instead of the probability density function of the characteristic parameter, the measured value of the characteristic parameter may be provided.
(4) The user uses the device model provided by the manufacturer and the probability density function of the characteristic parameter to use the method of the present embodiment (that is, the Markov chain in the model parameter space and the characteristic parameter space. Model parameters are generated using the model parameter generation method based on the Monte Carlo method). When the user acquires the measured value of the characteristic parameter from the manufacturer, the user can generate the probability density function of the characteristic parameter using the acquired measured value.
(5) The user performs a circuit simulation considering variation using the provided device model and the generated model parameters.

Here, the manufacturer can perform the following simulation information provision method. That is, the server that realizes the simulation information providing method acquires information about the simulation target (for example, a memory cell circuit) from the terminal on the user side, and determines the characteristics of the product (for example, MOSFET) included in the simulation target. Distribution information (probability density function) representing the distribution of the characteristic parameters to be shown is output to the terminal on the user side, and model information (for example, device model, model formula, etc.) expressing the characteristic parameters using the model parameters of the product is output to the user. It can be output to the terminal on the side. Here, the simulation information is information necessary for executing the simulation, and includes the above-mentioned distribution information (probability density function) and model information.

FIG. 23 is a schematic diagram showing an example of a use case of the variation consideration simulation in the case of the second embodiment. When the information processing apparatus 100 of the second embodiment is used, the variation consideration simulation can be performed as follows, as shown in FIG. 23.
(1) A manufacturer (for example, a company that manufactures a circuit (FAB)) manufactures a device (for example, MOSFET), measures the voltage / current characteristics of the device, and collects measurement data.
(2) The manufacturer determines the model formula of the device to be used, and extracts the model parameters so as to approximate the measured voltage / current characteristics (fitting). This makes it possible to obtain the distribution of model parameters.
(3) The manufacturer provides the user with a model formula and a distribution of model parameters extracted using the model formula.
(4) The user applies, for example, kernel density estimation to the model parameters to generate a probability density function of the model parameters.
(5) The user generates model parameters by using the probability density function of the model parameters and the model parameter generation method based on the Markov chain Monte Carlo method (MCMC) in the model parameter space. Here, the generated model parameters follow the same distribution as the model parameter distribution provided by the manufacturer, but the sample points are different.
(6) The user performs a circuit simulation considering variation using the provided device model and the generated model parameters.

FIG. 24 is a schematic diagram showing an example of a use case of the variation consideration simulation in the case of the comparative example. The comparative example shows an example in the case where the information processing apparatus 100 of this embodiment is not used. In the case of the comparative example, the variation consideration simulation can be performed as follows, as shown in FIG. 24.
(1) A manufacturer (for example, a company that manufactures a circuit (FAB)) manufactures a device (for example, MOSFET), measures the voltage / current characteristics of the device, and collects measurement data.
(2) The manufacturer determines the model formula of the device to be used, and extracts the model parameters so as to approximate the measured voltage / current characteristics (fitting). The manufacturer approximates the distribution of the extracted model parameters with a normal distribution, and calculates the mean value and standard deviation.
(3) The manufacturer provides the user with a model formula and a distribution of model parameters (mean value and standard deviation when approximated to a normal distribution) extracted using the model formula as a statistical device model.
(4) The user performs a circuit simulation using the provided model formula and distribution of model parameters.

In the case of the above comparative example, in the circuit simulator used by the user, it is necessary to read the model formula provided by the manufacturer, and the model formula and the model parameter need to be used as a set. For example, if a model expression is not available, the user will not be able to perform a circuit simulation even if the model parameters are provided. Moreover, since the variation in characteristics is expressed as the distribution of model parameters, it is necessary to obtain the distribution of model parameters for each model formula. Therefore, when it becomes necessary to perform a circuit simulation using a different model formula, it is necessary to re-extract the model parameters according to the model formula, and the expression of variation is independent of the model formula. That is, it is desirable that the model formula and the model parameters are separated. According to the first embodiment, as illustrated in FIG. 22, the variation in the characteristics can be summarized as the variation in the model parameters, and the circuit simulation can be performed by the same procedure as in the case where there is no variation. ing. Further, according to the second embodiment, it is possible to generate a large number of new model parameters that are larger than the number of measurement data regarding the model parameters provided by the manufacturer, and the model formula and the model parameters are substantially separated. It can be performed.

FIG. 25 is an explanatory diagram showing another example of the configuration of the information processing apparatus of the first embodiment and the second embodiment. In FIG. 25, reference numeral 200 is a computer. The computer 200 includes a control unit 30, an input unit 40, an output unit 50, an external I / F (interface) unit 60, a display panel 70, an operation unit 80, and the like. The control unit 30 includes a CPU 31, a ROM 32, a RAM 33, an I / F (interface) 34, and the like.

The input unit 40 acquires input data. The output unit 50 outputs output data. The I / F 34 has an interface function between the control unit 30, the input unit 40, the output unit 50, the external I / F unit 60, the display panel 70, and the operation unit 80, respectively.

The external I / F unit 60 can read the computer program from the recording medium M (for example, a medium such as a DVD) on which the computer program is recorded.

Although not shown, the computer program recorded on the recording medium M is not limited to the one recorded on the freely portable medium, and the computer program transmitted via the Internet or another communication line is also included. Can be included. The computer also includes a single computer equipped with a plurality of processors or a computer system composed of a plurality of computers connected via a communication network.

As described above, according to the present embodiment, the distribution of the model parameters used in the model (model formula) is accurately estimated from the distribution of characteristic parameters such as the performance of the product, which is relatively easy to measure. be able to. Since the distribution of model parameters can be estimated, more accurate variation-considered simulation can be performed using model parameters and model formulas. Further, based on the performance distribution of the product, it is possible to evaluate the performance of the product without explicitly giving the distribution of model parameters to the simulator.

Further, according to the present embodiment, it is possible to solve the following causes of deterioration in accuracy of the variation consideration simulation. That is,
(1) Degree of freedom of distribution representing variation: Normally, a normal distribution is assumed because of the ease of random number generation and statistical handling. However, the distribution that each model parameter follows may not always be clear and often does not follow a normal distribution. According to this embodiment, an arbitrary distribution can be expressed as the distribution of model parameters.
(2) Handling of correlations between model parameters: Statistical correlations are often seen between model parameters, but only linear correlations represented by Pearson's product moment correlation coefficient can be handled. According to this embodiment, any correlation between model parameters can be expressed.
(3) Statistical device models may contain (often large) errors if the distribution of model parameters extracted by fitting is distorted or if the current model cannot accurately represent the measured current characteristics. .. In this embodiment, it is not necessary to use the model parameters extracted by the fitting.
(4) Since the variation is expressed as the distribution of model parameters, it is necessary to obtain the distribution of model parameters for each device model. If the circuit simulator used by the user does not support the device model provided by the manufacturer, etc., or if it becomes necessary to perform a simulation using a different device model, the model parameters are reset according to the model formula. It is necessary to perform extraction and obtain its distribution. According to this embodiment, the expression of variation can be made independent of the device model.

As described above, the model parameter generation method of the present embodiment can be, for example, as follows. The model formula of the product is I = f (p). Here, p represents a set of second parameters that are relatively difficult to measure. The second parameter is also referred to as a product model parameter. I represents a set of first parameters that are easy to measure. The first parameter is also referred to as a characteristic parameter indicating the characteristics of the product. Here, we can think of two spaces. One is the model parameter space, which is the space in which the model parameter p is distributed. The other one is a characteristic parameter space, which is a space in which characteristic parameters I such as electric current are distributed. The model parameter generation method of the present embodiment generates a set of model parameters in the model parameter space by repeating a process of alternately performing a Markov chain and a Monte Carlo method in two spaces via a model formula. Is. In the general Markov chain Monte Carlo method (MCMC), when the density distribution of the random variable x is f (x), the random variable x is sampled (x _{t + 1} = x _t + Δ) using the Markov chain. A set of random variables is generated based on the probability ratio of f (x) of the density distribution, for example, {f (x _{t + 1} ) / f (x _t )}. It's completely different.

In the above-described embodiment, MOSFET, which is one element of a semiconductor device, has been described as an example as a product, but the product is not limited to MOSFET, and as described above, I = f (p). As long as it can be expressed by the model formula, it may be a product in various fields.

The information processing apparatus of the present embodiment has a distribution information acquisition unit that acquires distribution information that represents the distribution of the first parameter related to the product, and model information that expresses the first parameter using the second parameter related to the product. Based on the above, the probability density information generation unit that generates the probability density information of the second parameter is provided so that the distribution information is reproduced.

The computer program of the present embodiment acquires distribution information representing the distribution of the first parameter with respect to the product from the computer, and uses the second parameter with respect to the product to represent the first parameter based on the model information. , The process of generating the probability density information of the second parameter so that the distribution information is reproduced is executed.

In the information processing method of the present embodiment, distribution information representing the distribution of the first parameter related to the product is acquired, and the first parameter is expressed by using the second parameter related to the product, based on the model information. Probability density information of the second parameter is generated so that the distribution information is reproduced.

The simulation information providing method of the present embodiment acquires information about a simulation target, outputs distribution information indicating a distribution of characteristic parameters indicating the characteristics of the product included in the simulation target, and outputs model parameters of the product. The model information expressing the characteristic parameter is output by using.

The information processing apparatus of the present embodiment includes an evaluation unit that evaluates the performance of a simulation target including the product by using the probability density information of the second parameter generated by the probability density information generation unit and the model information. ..

The information processing apparatus of the present embodiment has a measurement value acquisition unit that acquires the measurement value of the first parameter and a distribution information generation unit that generates distribution information representing the distribution of the first parameter using the acquired measurement value. And prepare.

The information processing device of the present embodiment includes a model information acquisition unit for acquiring the model information and a storage unit for storing the acquired model information.

The information processing apparatus of the present embodiment includes an update unit that updates the model information stored in the storage unit with the acquired model information.

In the information processing apparatus of the present embodiment, the probability density information generation unit uses a Markov chain to sample the second parameter candidate, and the model information to sample the sampled candidate first. It is provided with a conversion unit for converting into parameter candidates and a parameter generation unit for generating a second parameter from sampled candidates by applying the Monte Carlo method to distribution information representing the converted distribution of the first parameter.

In the information processing apparatus of the present embodiment, the first parameter includes a characteristic parameter indicating the characteristic of the product, and the second parameter includes a model parameter of the product.

10, 30

Control unit

11, 40 Input unit 12 Distribution information generation unit 13 Probability density information generation unit 131 Sampling unit 132 Conversion unit 133 Model

parameter generation unit

14, 50 Output unit 15 Simulation unit 16

Storage unit

17, 70

Display panel

18, 80 Operation unit 19 Fitting unit 31 CPU
32 ROM
33 RAM
34 I / F
60 External I / F section 100 Information processing device 200 Computer

Claims

A distribution information acquisition unit that acquires distribution information that represents the distribution of the first parameter related to the product,
A probability density information generation unit that generates probability density information of the second parameter so that the distribution information can be reproduced based on model information expressing the first parameter using the second parameter related to the product. Information processing device to be equipped.
A measurement value acquisition unit that acquires the measurement value of the first parameter,
The information processing apparatus according to claim 1, further comprising a distribution information generation unit that generates distribution information representing the distribution of the first parameter using the acquired measured values.
The probability density information generation unit is
A sampling unit that samples the candidates for the second parameter using a Markov chain,
A conversion unit that converts sampled candidates into candidates for the first parameter using the model information, and
It is provided with a parameter generator that applies the Monte Carlo method to the distribution information representing the converted distribution of the first parameter and generates the second parameter from the sampled candidates.
The information processing apparatus according to claim 1 or 2.
A measurement value acquisition unit that acquires the measurement value of the first parameter related to the product,
A probability density information generation unit that generates probability density information of the second parameter by applying model information expressing the first parameter to the acquired measured value of the first parameter using the second parameter related to the product. Information processing device to be equipped.
The probability density information generation unit is
A sampling unit that samples the candidates for the second parameter using a Markov chain,
It is provided with a parameter generation unit that generates a second parameter from sampled candidates by applying the Monte Carlo method to the distribution information representing the distribution of the second parameter.
The information processing apparatus according to claim 4.
It is provided with an evaluation unit for evaluating the performance of a simulation target including the product by using the probability density information of the second parameter generated by the probability density information generation unit and the model information.
The information processing apparatus according to any one of claims 1 to 5.
The model information acquisition unit that acquires the model information and
The information processing apparatus according to any one of claims 1 to 6, further comprising a storage unit for storing acquired model information.
It is provided with an update unit that updates the model information stored in the storage unit with the acquired model information.
The information processing apparatus according to claim 7.
The first parameter includes a characteristic parameter indicating the characteristic of the product.
The second parameter includes the model parameter of the product.
The information processing apparatus according to any one of claims 1 to 8.
On the computer
Obtain distribution information representing the distribution of the first parameter for the product,
Based on the model information expressing the first parameter using the second parameter related to the product, the probability density information of the second parameter is generated so that the distribution information is reproduced.
A computer program that executes processing.
Obtain distribution information representing the distribution of the first parameter for the product,
Based on the model information in which the first parameter is expressed using the second parameter related to the product, the probability density information of the second parameter is generated so that the distribution information is reproduced.
Information processing method.
Get information about the simulation target and
Distribution information representing the distribution of characteristic parameters indicating the characteristics of the product included in the simulation target is output.
Outputs model information expressing the characteristic parameter using the model parameter of the product.
Simulation information provision method.