Standardized flow-based multi-parameter joint distribution modeling method for semiconductor devices

Abstract

The disclosure provides a semiconductor device multi-parameter joint distribution modeling method based on a standardized flow, comprising: S1: extracting a plurality of key model parameters from semiconductor device simulation data; S2: constructing an original model library containing a plurality of model cards based on the plurality of key model parameters; S3: processing model parameters based on the original model library to construct a training data set; S4: constructing a standardized flow model; and S5: training the standardized flow model based on the constructed training data to generate a complete model library including a large-scale model card, completing semiconductor device multi-parameter joint distribution modeling.

Description

Technical Field

[0001] This disclosure relates to the fields of semiconductors, semiconductor design technology collaborative optimization, electronic design automation, machine learning, and probability distribution generation, and in particular to a method for multi-parameter joint distribution modeling of semiconductor devices based on standardized flow. Background Technology

[0002] Design Technology Co-Optimization (DTCO) is a method that deeply integrates semiconductor technology development with circuit design to enhance key metrics such as performance, power efficiency, area, and cost. However, as transistor dimensions continue to shrink, atomic-level randomness caused by charge and material dispersion amplifies fluctuation effects. Ignoring these fluctuation effects in DTCO can lead to severe distortions in simulations and reliability assessments. These fluctuations intensify with advancements in process nodes, posing a fundamental challenge to DTCO. Therefore, a more accurate statistical assessment of these fluctuation effects in integrated circuits is urgently needed. Summary of the Invention

[0003] In view of this, in order to at least partially solve at least one of the aforementioned technical problems, this disclosure provides a method for multi-parameter joint distribution modeling of semiconductor devices based on normalized flow.

[0004] To achieve the above objectives, the technical solution disclosed herein is as follows:

[0005] According to one embodiment of this disclosure, a method for multi-parameter joint distribution modeling of semiconductor devices based on normalized flow is provided, comprising: S1: extracting multiple key model parameters from semiconductor device simulation data; S2: constructing an original model library containing multiple model cards based on the multiple key model parameters; S3: processing the model parameters based on the original model library to construct a training dataset; S4: constructing a normalized flow model; and S5: training the normalized flow model based on the constructed training data to generate a complete model library including a large number of model cards, thereby completing the multi-parameter joint distribution modeling of semiconductor devices.

[0006] According to embodiments of this disclosure, each model card includes multi-dimensional model parameters; the resulting complete model library has the same joint distribution of multi-parameters as the original model library.

[0007] According to an embodiment of this disclosure, in operation S3, the model parameters are normalized to eliminate the influence of dimensional differences.

[0008] According to an embodiment of this disclosure, in operation S4, when constructing the normalized flow model, a coupled rational quadratic neural spline flow is used as the basic architecture, including multiple layers of reversible transformation sequences. Each layer of reversible transformation sequence includes: a coupled rational quadratic spline transformation; a linear transformation of LU decomposition; and initialization of the basis distribution as a diagonal Gaussian distribution.

[0009] According to embodiments of this disclosure, Affine Coupling Layer or Planar Flow can also be used as the basic framework when constructing a standardized flow model.

[0010] According to an embodiment of this disclosure, in operation S5, the model is trained using the maximum likelihood estimation method, and the parameters are optimized using the Adam optimizer, dynamically adjusting the batch size and learning rate, and optimizing the network parameters using the backpropagation algorithm.

[0011] According to embodiments of this disclosure, the semiconductor device is a MOSFET, FinFET, FDSOI, or GAAFET; the various key model parameters are extracted from common semiconductor device simulation models. These key model parameters include at least two characteristic parameters selected from PHIG, DSUB, VSAT, DELTAVSAT, ETA0, KSATIV, CIT, CDSC, CDSCD, DVT0, DVT1, MEXP, ETAMOB, U0, UA, EU, UD, CGSL, WR, UP, LPA, PHIN, and LOVS.

[0012] The multi-parameter joint distribution modeling method for semiconductor devices also includes the validation and application of the completed multi-parameter joint distribution model. Validation includes calculating the KL divergence and energy distance between the model parameter samples of the original model library and the complete model library. Application involves integrating the trained model into the EDA toolchain and generating an arbitrary number of model card samples as needed for circuit stability analysis and yield prediction of semiconductor devices. Attached Figure Description

[0013] The above and other objects, features and advantages of this disclosure will become clearer from the following description of embodiments with reference to the accompanying drawings, in which:

[0014] Figure 1 This is a flowchart of a method for multi-parameter joint distribution modeling of semiconductor devices based on standardized flow, according to an embodiment of this disclosure.

[0015] Figure 2 This is a schematic diagram comparing the modeling results of bimodal and long-tailed distributions using different methods.

[0016] Figure 3This is a schematic diagram comparing the parameter distribution of an infinitely large model library generated based on a finite sample library of fully depleted silicon-on-insulator devices according to an embodiment of this disclosure with the original parameter distribution QQ diagram. Detailed Implementation

[0017] This disclosure provides a method for joint distribution modeling of multiple parameters of semiconductor devices based on normalizing flow. In the DTCO process of advanced nodes, an infinitely large model library is generated based on a finite model card to ensure that the joint distribution of parameters in the newly generated model library is consistent with the original model library. The modeling method of this disclosure mainly involves the semiconductor field, and more specifically involves semiconductor design technology co-optimization (DTCO), electronic design automation (EDA), and also involves the fields of machine learning and probability distribution generation. Specifically, it involves a method for joint modeling of semiconductor device model parameters based on normalizing flow, or it can also be called a method for joint modeling of semiconductor device model parameters based on normalizing flow generator (NFGen). Specifically: (1) This disclosure involves the co-optimization of semiconductor manufacturing process and integrated circuit design, especially for the parameter distribution modeling problem caused by device fluctuations in advanced process nodes. By constructing an accurate parameter joint distribution generation model, this invention can provide an infinitely large compact model library containing fluctuations for the DTCO process, which can be used to optimize process parameter selection and increase design margin, thereby improving chip performance, power consumption and yield. (2) This invention belongs to the statistical modeling module in the EDA toolchain and is compatible with mainstream simulation circuit simulators (Simulation Program with Integrated Circuit Emphasis, SPICE) and Berkeley short-channel insulated gate field-effect-transistor model (BSIM). By generating an infinitely large model parameter library that conforms to real statistical characteristics, this invention can be used in key design verification stages such as single device simulation and circuit stability analysis, helping designers to accurately assess circuit performance limits and yield risks in the early stages. (3) This invention adopts the normalized flow technique in deep generative models and realizes the nonlinear transformation from simple basis distribution to target high-dimensional joint distribution through a reversible neural network architecture. This method can accurately calculate probability density and retain the complex correlation between parameters, providing a machine learning solution for semiconductor parameter generation. (4) This invention proposes an innovative parameterized modeling method in the field of probability distribution generation, which can accurately capture the complex joint distribution characteristics of semiconductor device parameters (including non-Gaussian, long-tailed, multi-peaked distribution forms).By combining a rational quadratic neural spline flow (CRQ-NSF) with linear transformations, efficient sampling and density estimation of high-dimensional parameter spaces are achieved, overcoming the shortcomings of traditional methods in modeling complex joint distributions.

[0018] Existing technologies mainly rely on four methods: Gaussian fitting, Principal Component Analysis (PCA), Nonlinear Power Models (NPM), and Generalized Lambda Distribution (GLD), as detailed below:

[0019] (1) Gaussian fitting

[0020] Early research introduced Gaussian fitting to handle the statistical distribution of model parameters. This method simplifies calculations by assuming the parameters follow a Gaussian distribution and calculating the mean and covariance matrices of each parameter to construct a statistical model. However, Gaussian fitting struggles to accurately capture the tails of the device model parameter distribution and completely ignores potential nonlinear dependencies between parameters. This can lead to biases in predicting circuit performance under extreme conditions.

[0021] (2) PCA

[0022] PCA (Primary Principal Component Analysis) reduces the dimensionality of data by projecting a high-dimensional parameter space onto a low-dimensional principal component space using orthogonal transformations. However, PCA can only handle linear correlations and cannot capture complex nonlinear correlations. Furthermore, the dimensionality reduction process inevitably loses some higher-order statistical information, especially tail features. Finally, PCA requires the data to satisfy the Gaussian distribution assumption, which contradicts the actual parameter distribution characteristics.

[0023] (3) NPM

[0024] To improve the accuracy of marginal distributions, researchers have developed Non-Performing Motion (NPM) for seven-parameter statistical PSP models. NPM improves distribution modeling by introducing higher-order moments (skewness and kurtosis), providing better accuracy for device characteristics such as inverter delay. However, NPM faces challenges in preserving correlations, particularly in accurately capturing marginal distributions. Its correlation-preserving methods struggle to handle complex multi-parameter joint distributions.

[0025] (4) GLD

[0026] GLD uses rank correlation to approximate marginal distributions and has been widely used in performance modeling. While GLD performs well in modeling marginal distributions, it still primarily focuses on marginal distributions or simple correlations (such as pairwise correlations), neglecting complex joint distributions among multiple parameters. This limits the accuracy of the model card.

[0027] The proposed solution to the technical problems in the prior art involves using device-level simulation with fluctuations to extract parameters and obtain a model library containing a finite number of model cards. Circuit-level simulation using this sample library can directly reflect the impact of fluctuations on the circuit. However, typically limited by device simulation speed, only a limited number of model cards can be obtained. Circuit simulation with a finite number of model cards introduces subsampling problems, leading to unpredictable circuit performance under extreme conditions, ultimately resulting in chip failure. A better approach is to generate a comprehensive model library based on a finite set of model cards, while ensuring that the distribution of parameters in the generated model library is consistent with the original model library. Therefore, the main technical problem addressed by the modeling method in this application is how to generate an infinitely large model library based on a finite set of model cards in the DTCO process of advanced nodes, while ensuring that the joint distribution of parameters in the newly generated model library is consistent with the original model library.

[0028] To make the objectives, technical solutions, and advantages of this disclosure clearer, the following detailed description is provided in conjunction with specific embodiments and the accompanying drawings.

[0029] In the embodiments disclosed herein, such as Figure 1 As shown, a method for joint distribution modeling of multiple parameters in semiconductor devices based on normalized flow is provided, including operations S1-S5:

[0030] S1: Extracting various key model parameters from semiconductor device simulation data;

[0031] S2: Construct an original model library containing multiple model cards based on the aforementioned key model parameters;

[0032] S3: Process the model parameters based on the original model library to construct a training dataset;

[0033] S4: Construct a standardized flow model; and

[0034] S5: Based on the constructed training data, the standardized flow model is trained to generate a complete model library including large-scale model cards, thus completing the multi-parameter joint distribution modeling of semiconductor devices.

[0035] According to embodiments of this disclosure, each model card includes multi-dimensional model parameters; the resulting complete model library has the same joint distribution of multi-parameters as the original model library.

[0036] According to an embodiment of this disclosure, in operation S3, the model parameters are normalized by subtracting the mean and dividing by the standard deviation to eliminate the influence of dimensional differences and construct a training dataset.

[0037] According to an embodiment of this disclosure, in operation S4, when constructing the normalized flow model, a coupled rational quadratic neural spline flow is used as the basic architecture, including a multi-layer reversible transformation sequence. For example, a K-layer reversible transformation sequence is designed. Each layer contains: coupled rational quadratic spline transformation Linear transformation of LU decomposition Initialize the base distribution It follows a diagonal Gaussian distribution. It should be noted that other basic frameworks, such as AffineCoupling Layer or Planar Flow, can also be used when constructing the normalized flow model.

[0038] According to embodiments of this disclosure, in operation S5, the model is trained using the maximum likelihood estimation method, and parameters are optimized using the Adam optimizer, dynamically adjusting the batch size and learning rate, and optimizing network parameters using the backpropagation algorithm. For example, the model is trained using the maximum likelihood estimation (MLE) method, and the loss function L is defined as:

[0039] ;

[0040] The Adam optimizer is used to optimize parameters, dynamically adjusting the batch size and learning rate, and the network parameters are optimized through the backpropagation algorithm.

[0041] According to embodiments of this disclosure, the semiconductor device can be a planar metal-oxide-semiconductor field-effect transistor (MOSFET), a fin field-effect transistor (FinFET), a fully depleted silicon-on-insulator (FDSOI), or a gate all-around field effect transistor (GAAFET); various key model parameters are extracted from common semiconductor device simulation models, such as the BSIM-CMG model, the BSIM-IMG model, and the BSIM4 model. Taking the BSIM-CMG model as an example, this model is applicable to FinFET and GAAFET. Several key model parameters can include PHIG (work function), DSUB (drain-induced barrier reduction exponential coefficient), VSAT (saturation velocity in the saturation region), DELTAVSAT (saturation velocity in the linear region), ETA0 (drain-induced barrier reduction coefficient), KSATIV (long-channel saturation coefficient), CIT (interface trap coefficient), CDSC (coupling capacitance between source / drain and channel), CDSCD (drain bias sensitivity of CDSC), DVT0 (short-channel effect coefficient), DVT1 (short-channel effect exponential coefficient), and MEXP (smoothing function in the saturation region). The required parameters are at least two of the following: number factor, ETAMOB (effective field coefficient), U0 (low field mobility), UA (one of the phonon and surface scattering coefficients), EU (one of the phonon and surface scattering coefficients), UD (Coulomb scattering coefficient), CGSL (overlap capacitance between the gate and lightly doped source regions), WR (dependence of source / drain extension region resistance on channel width), UP (channel length dependence coefficient of carrier mobility), LPA (channel length dependence power coefficient of carrier mobility), and PHIN (influence coefficient of non-uniform vertical doping on surface potential). It should be noted that the type of parameters should be selected according to the actual application; for example, 5 or 15 characteristic parameters can be extracted. Different models extract different parameters. For example, for the BSIM-IMG model, its unique LOVS (source / drain overlap length for capacitance calculation) needs to be extracted.

[0042] According to embodiments of this disclosure, the method for multi-parameter joint distribution modeling of semiconductor devices further includes verifying and applying the completed multi-parameter joint distribution model of semiconductor devices. Verification includes calculating the Kullback-Leibler divergence and energy distance (ED) between model parameter samples of the original model library and the complete model library. For example, generating large-scale model card samples. ,in The verification method includes calculating the KL divergence and energy distance between the original samples and the generated samples. When applying the model, the trained model is integrated into the EDA toolchain, and an arbitrary number of model card samples are generated as needed for circuit stability analysis and yield prediction of semiconductor devices.

[0043] More specifically, key model parameters are extracted from semiconductor device simulation data, and model parameters are set. D is the dimension of model parameters, and the original model library containing N model cards is constructed. These model parameters need to be determined through device-level simulation. Due to the limitations of device simulation speed, only a limited number of model cards can be obtained. Using such model libraries can lead to undersampling issues, making it difficult to accurately predict circuit performance under high sigma conditions and even causing chip failure. To avoid undersampling and accurately capture the impact of process variations on circuits, our goal is to improve upon the original model libraries. This will generate a complete model library. M represents the number of model cards in the complete model library, and N represents the number of model cards in the original model library. Achieving this goal requires addressing the following key challenges:

[0044] 1. Marginal distribution of the generated model library The original edge distribution must be strictly matched. , where 1≤i≤D.

[0045] 2. The parameters are not completely independent, but have linear or non-linear correlations. These correlation characteristics must be accurately preserved in the generated data.

[0046] 3. Joint distribution of a new and complete model library It must be jointly distributed with the original model library. Totally consistent.

[0047] It is important to note that the difficulty of achieving these requirements increases progressively. Marginal distributions and the correlation between parameters (such as covariance) can both be calculated using the joint distribution, and their relationship is expressed as follows:

[0048] ;

[0049] ;

[0050] Where d, i, j, l represent indices, and x d x i x j x l Let and represent random variables. Therefore, constructing an accurate joint distribution ensures that the first two requirements are met simultaneously. However, establishing a complete and accurate joint distribution model still faces significant challenges. To our knowledge, existing research mainly focuses on modeling marginal distributions and correlations, and there are no precedents for successfully solving the joint distribution modeling problem. This critical gap directly affects the simulation accuracy of the impact of process variations on circuit performance.

[0051] Another key issue is the current lack of rigorous mathematical methods for evaluating generative model libraries. The quality of the generated model library is crucial. Directly using low-quality model libraries can lead to significant decision-making biases for circuit designers. Introducing statistical indicators that can intuitively reflect the quality of the generated model library will provide designers with quantitative references, thereby ensuring the reliability of design decisions.

[0052] To more accurately characterize the impact of process variations on circuit performance, we propose a joint generation model based on normalized flow to model the joint distribution of parameters. The basic principle of normalized flow is to use a reversible smooth mapping f: (its inverse mapping) satisfy To achieve probability density transformation. For the time elapsed... The distribution of the transformed random variable. It can be represented as:

[0053] ;

[0054] This means from Sampling is equivalent to prior to Sampling and then applying The mapping, f, denotes an invertible smooth mapping.

[0055] Standard streams are transformed through a series of reversible transformations Simple basis distribution ( (e.g., Gaussian distribution) is gradually transformed into the target distribution. This constitutes a standardized flow process. To construct complex distributions, multiple simple mappings can be combined and the "distribution" transformation can be applied iteratively. The initial distribution is... random variables After K transformations, the target variable It can be represented as:

[0056] ;

[0057] f1, f2…f K Represents a series of invertible transformations; its logarithmic probability distribution satisfies:

[0058] ;

[0059] As shown in the above formula, the core advantage of standardized flow lies in its ability to accurately calculate each point. The joint probability distribution. This capability is crucial for capturing the impact of process fluctuations on model parameters, representing a key breakthrough that traditional generation methods cannot achieve.

[0060] After testing various models (including autoregressive flow, affine coupled flow, and planar flow), we found that Coupled Rational Quadratic Neural Spline Flow (CRQ-NSF) performed best in modeling joint parameter distributions due to its greater flexibility compared to simple functions, and was therefore selected as the implementation scheme. In CRQ-NSF, Divided into two parts After transformation Defined as:

[0061] ;

[0062] in Therefore The neural network takes a certain input as input and outputs a spline mapping. The parameters. It is a monotonically rational quadratic spline, where each interval is defined as the ratio of two rational quadratic polynomials. Finally, through an invertible linear transformation to enhance expressive power and align with the target distribution, the overall flow sequence can be represented as:

[0063] ;

[0064] in This represents a coupled rational quadratic spline. Represents the LU decomposition permutation of a linear transformation. The samples are taken from a diagonal Gaussian distribution (assuming that each dimension is independent and follows a Gaussian distribution).

[0065] Assuming the original model library It is known that the parameter x needs to be normalized to eliminate the influence of dimensional differences on NFGen. After normalization by subtracting the mean and dividing by the standard deviation, the standardized flow model NFGen can be directly trained using maximum likelihood estimation (MLE), with its loss function defined as:

[0066] ;

[0067] The optimization process is implemented using the Adam optimizer.

[0068] After NFGen training is completed, new samples are generated by randomly sampling using a diagonal Gaussian distribution and applying a transformation to the trained flow model. After inverse normalization, these samples form a new model library. Their joint distribution is consistent with the original model library. Maintain consistency.

[0069] Model validation involves calculating the KL divergence and energy distance between the model parameter samples of the original model library and the complete model library.

[0070] The KL divergence between distributions P and Q is defined as follows:

[0071] ;

[0072] When only sample data is available and the densities of P and Q cannot be directly calculated, It can be estimated using k-nearest-neighbor (k-NN):

[0073] ;

[0074] in Sample points In the sample set of P The Euclidean distance from the k-th nearest neighbor. It is the same In the sample set of Q The Euclidean distance from the k-th nearest neighbor.

[0075] Energy distance between distributions P and Q The definition is as follows:

[0076] ;

[0077] in Represents Euclidean distance. Representative from and The expected value of the Euclidean distance between samples. and Represent and Expected self-distance of internal samples.

[0078] The alternative solutions involved in the above modeling method are as follows:

[0079] 1. Different Normalizing Flow model architectures.

[0080] The underlying architecture of other Normalizing Flow models that can replace CRQ-NSF, such as Affine Coupling Layer or Planar Flow.

[0081] These models may differ in complexity and flexibility, but the basic idea is the same: to approximate the joint distribution through invertible transformations.

[0082] 2. Different loss functions.

[0083] In addition to maximum likelihood estimation (MLE), other objective functions can be tried, such as minimizing the Wasserstein distance or using the objective function of a variational autoencoder (VAE).

[0084] 3. Different normalization methods.

[0085] Alternatives to standard deviation normalization can be found using other methods such as Min-Max normalization or RobustScaler to suit the characteristics of different data distributions.

[0086] The disclosed method for multi-parameter joint distribution modeling of semiconductor devices based on normalized flow has the following advantages and positive effects:

[0087] (1) It can accurately model non-normal distributions such as long-tailed and multimodal distributions.

[0088] Advantages: By gradually transforming the distribution through a reversible neural network, nonlinearity can be introduced at each step, ultimately fitting an arbitrarily complex target distribution.

[0089] Positive effects: Reduced errors when modeling long-tailed and multimodal distributions.

[0090] like Figure 2 The diagram shows the results of different methods for modeling bimodal and long-tailed distributions, with the top row representing bimodal distributions and the bottom row representing long-tailed distributions. It can be seen that the modeling method of this disclosure based on NFGen can accurately model bimodal distributions and achieves the best results in modeling long-tailed distributions.

[0091] (2) It can accurately capture joint distributions:

[0092] Advantages: Using standardized flow modeling naturally preserves the interaction relationships of all parameters, avoids a single fit to the marginal distribution, and the standardized flow directly approximates the joint distribution through reversible transformation.

[0093] Positive effects: Significantly reduces joint distribution modeling error, especially in high Sigma regions (such as ±4σ), making the generated model library more consistent with the actual process fluctuation characteristics.

[0094] Reference Figure 3 As shown, using the modeling method disclosed herein, a comparison is made between the Quantile-Quantile Plot of the parameter distribution of an infinitely large model library generated based on a finite sample library of a 22nm FDSOI device and the original parameter distribution Quantile Plot. Table 1 below shows the difference between the sample library generated by different methods and the original distribution. KL and ED are statistical indicators for measuring the difference: KL, or KL divergence, measures the information difference between the generated distribution and the true distribution; the smaller the value, the higher the similarity. ED, or energy distance, is a distribution difference measure based on the Euclidean distance between samples, which is sensitive to long-tailed distributions. Figure 3 As can be seen from Table 1, the parameter distribution generated based on NFGen is very close to the original distribution, and it outperforms traditional methods such as PCA, NPM, and GLD in terms of KL divergence and energy distance metrics.

[0095] Table 1

[0096]

[0097] The embodiments of this disclosure have been described in detail above with reference to the accompanying drawings. It should be noted that implementations not illustrated or described in the drawings or the main text of the specification are forms known to those skilled in the art and are not described in detail. Furthermore, the definitions of the various elements and methods described above are not limited to the specific structures, shapes, or methods mentioned in the embodiments, and those skilled in the art can easily modify or substitute them.

[0098] In this document, unless otherwise specified, the term "characteristic A" or "and / or" and "characteristic B" means that A exists alone, B exists alone, or A and B exist simultaneously; the term "characteristic A" and "and" or "and" and "and" and "characteristic B" means that A and B exist simultaneously; the terms "including", "containing", "having", and "containing" refer to, but are not limited to, these.

[0099] Furthermore, unless specifically described or required to occur in a specific order, the order of the above steps is not limited to those listed above and can be varied or rearranged according to the desired design. Moreover, the above embodiments can be used in combination with each other or with other embodiments based on design and reliability considerations; that is, technical features from different embodiments can be freely combined to form more embodiments.

[0100] The specific embodiments described above further illustrate the purpose, technical solutions, and beneficial effects of this disclosure. It should be understood that the above descriptions are merely specific embodiments of this disclosure and are not intended to limit this disclosure. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this disclosure should be included within the protection scope of this disclosure.

Claims

1. A semiconductor device multi-parameter joint distribution modeling method based on normalized flow, comprising: S1: extracting multiple key model parameters from semiconductor device simulation data; S2: constructing an original model library containing multiple model cards based on the multiple key model parameters; S3: processing model parameters based on the original model library to construct a training data set; S4: constructing a normalized flow model; and S5: training the normalized flow model based on the constructed training data to generate a complete model library including a large-scale model card, completing semiconductor device multi-parameter joint distribution modeling; When constructing the normalized flow model, a coupled rational quadratic neural spline flow is used as a basic framework, including a multi-layer reversible transformation sequence, each layer of the reversible transformation sequence including a coupled rational quadratic spline transformation, a linear transformation of LU decomposition, and an initialization basis distribution being a diagonal Gaussian distribution.

2. The semiconductor device multi-parameter joint distribution modeling method according to claim 1, each model card including multiple-dimensional model parameters; the generated complete model library is consistent with the joint distribution of multiple parameters in the original model library.

3. The semiconductor device multi-parameter joint distribution modeling method according to claim 1, in operation S3, the model parameters are normalized to eliminate the influence of dimensional differences.

4. The semiconductor device multi-parameter joint distribution modeling method according to claim 1, when constructing the normalized flow model, an Affine Coupling Layer or a Planar Flow can also be used as a basic framework.

5. The semiconductor device multi-parameter joint distribution modeling method according to claim 1, in operation S5, the model is trained using a maximum likelihood estimation method, and the parameters are optimized through an Adam optimizer, dynamically adjusting the batch size and learning rate, and optimizing the network parameters through a back propagation algorithm.

6. The semiconductor device multi-parameter joint distribution modeling method according to claim 1, the semiconductor device being a MOSFET, a FinFET, a FDSOI, or a GAAFET; the multiple key model parameters being extracted from a general semiconductor device simulation model.

7. The semiconductor device multi-parameter joint distribution modeling method according to claim 1, the multiple key model parameters including at least 2 characteristic parameters in PHIG, DSUB, VSAT, DELTAVSAT, ETA0, KSATIV, CIT, CDSC, CDSCD, DVT0, DVT1, MEXP, ETAMOB, U0, UA, EU, UD, CGSL, WR, UP, LPA, PHIN, and LOVS.

8. The semiconductor device multi-parameter joint distribution modeling method according to claim 1, further comprising verifying and applying the completed semiconductor device multi-parameter joint distribution model, the verification including calculating the KL divergence and energy distance between the model parameter samples of the original model library and the complete model library; when applied, the trained model is integrated into an EDA tool chain, and according to the demand, any number of model card samples are generated, which are used for circuit stability analysis and yield prediction of semiconductor devices.

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