A neural network-based BSIM-BULK model parameter extraction method

Abstract

The application belongs to the technical field of parameter extraction, and discloses a BSIM-BULK model parameter extraction method based on a neural network, which comprises the following steps: step 1: automatically and intelligently completing parameter extraction through machine learning; introducing physical constraints and prior knowledge in the parameter extraction process by combining the advantages of physical modeling and data-driven models; step 2: constructing a parameter extraction model by adopting a CNN architecture: converting one-dimensional characteristic data into a two-dimensional matrix, utilizing the advantages of two-dimensional characteristic extraction of the CNN, combining multiple groups of device characteristics into multi-channel input, and enabling the CNN to simultaneously process multi-dimensional characteristics. The application uses a CNN neural network to replace an ANN neural network for fitting, thereby improving local fitting accuracy; the CNN significantly reduces the number of parameters through a convolution kernel, convolution and pooling operations are used to process local regions, thereby improving calculation efficiency, enhancing the generalization ability of the model, and improving the robustness of the model.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of parameter extraction, and particularly relates to a BSIM-BULK model parameter extraction method based on a neural network. BACKGROUND

[0002] With the development of semiconductor technology to deep submicron and nanometer level, the BSIM-BULK model provides a reliable device modeling basis. The BSIM-BULK model is a standard compact model of deep submicron CMOS devices. Compared with other BSIM models (such as BSIM3, BSIM4 and BSIM-CMG), the BSIM-BULK model provides higher modeling accuracy for key physical phenomena (including short channel effect and subthreshold characteristics), and is particularly suitable for advanced planar CMOS technology.

[0003] For parameter extraction of the BSIM-BULK model, the traditional parameter extraction method first processes the data, then builds a parameter extraction template, manually analyzes the curve characteristics, selects the characteristic parameter range, and extracts specific parameters through a fitting tool. Then, the extracted parameters are substituted into the model, and the simulation results are compared with the experimental results for further adjustment. The manual analysis and fitting need to consume a lot of time, and the efficiency is low. Moreover, the quality of parameter extraction is highly dependent on the experience level of engineers, which may lead to insufficient consistency and reliability. When dealing with high-dimensional and complex nonlinear problems, the efficiency and accuracy are insufficient. The parameter extraction method based on neural network provides a better solution for parameter extraction of complex models through its efficient nonlinear fitting capability, automation characteristics, adaptive ability and powerful data processing performance. Some articles propose to use the architecture of ANN to realize the parameter extraction of the BSIM-BULK model. Each parameter in the method is repeatedly adjusted until an acceptable error is reached. Using this method can directly generate a set of parameters without iteration. The method steps are as follows:

[0004] 1. A large number of initial data sets are obtained through simulation and testing, and the data are divided into current-voltage (IV) data and capacitance-voltage (CV) data. The discrete S parameters are converted into Y parameters, and Cgg.s (simulation result) and Cgg.m (test result) are calculated. Ids, Vgs and Vds (simulation and test results) are extracted, and Gm.s, Gds.s (simulation results) and Gm.m, Gds.m (test results) are calculated according to the results.

[0005] 2. Parameter value normalization processing

[0006] The normalization processing is performed in the following manner:

[0007]

[0008] where, θ min and θ max are the minimum and maximum values of the parameters, respectively. The normalized parameters are limited between 0 and 1, so that the algorithm can process these parameters more effectively.

[0009] 3. The ANN architecture is adopted. The current, voltage and capacitance of the input layer input device are input; the hidden layer is adopted to capture the nonlinear relationship in the data, and the activation function is selected as ReLU; the output layer outputs the target parameters (such as threshold voltage, saturation rate, etc.) of the HEMT model. A set of CV parameters are obtained to approximate Cgg.m, and a set of IV parameters are obtained to approximate IdVd.m, IdVg.m, Gm.m and Gds.m.

[0010] 4. The neural network is trained. The initial data is divided, 80% of the data is used as the training set, and 20% of the data is used as the test set. The trained model is saved, and the data in the test set is used as the input and output of the model to verify the effectiveness of the model training. The neural network is trained. The initial data is divided, 80% of the data is used as the training set, and 20% of the data is used as the test set. The trained model is saved, and the data in the test set is used as the input and output of the model to verify the effectiveness of the model training. By adjusting the weight (weight) of each optimization target (IdVd, IdVg, Gds, Gm, Cgg), a set of model parameters with the best overall effect can be obtained.

[0011] 5. The output parameters of the trained neural network are saved, and the parameter combination is brought back to the original model netlist for verification and comparison with the measured data to verify the fitting accuracy of the parameter combination.

[0012] However, the above method has the following technical defects:

[0013] 1. The input of the neural network is very long, and there are problems such as sequential dependence;

[0014] 2. The fully connected structure of the ANN needs to calculate the weight of all input features, which is low in calculation efficiency. SUMMARY

[0015] The present application aims to provide a BSIM-BULK model parameter extraction method based on neural network to solve the above technical problems.

[0016] To solve the above technical problems, the specific technical scheme of the BSIM-BULK model parameter extraction method based on neural network of the present application is as follows:

[0017] A BSIM-BULK model parameter extraction method based on a neural network, comprising the following steps: step 1: automatically and intelligently completing parameter extraction through machine learning; by combining the advantages of physical modeling and data-driven modeling, introducing physical constraints and prior knowledge in the parameter extraction process;

[0018] Step 2: Constructing a parameter extraction model using a CNN architecture: converting one-dimensional characteristic data into a two-dimensional matrix, using the advantages of CNN for two-dimensional characteristic extraction, combining multiple device characteristics into multi-channel input, and allowing CNN to process multiple-dimensional characteristics simultaneously.

[0019] Further, the step 1 comprises the following steps:

[0020] Step 1.1: Introducing a data-driven method;

[0021] Step 1.2: Hybrid modeling method and automated workflow.

[0022] Further, the step 1.1 specifically comprises:

[0023] Using CNN to automatically extract device characteristic curves instead of manual analysis, directly predicting the core parameters of the BSIM-BULK model from the characteristic data through the trained model, and improving the generalization ability of the model through data augmentation. Further, the step 1.2 specifically comprises:

[0024] Using a physical model to provide initial parameter estimation, and then using a neural network to fit the residual error to improve accuracy; adding physical consistency as a constraint in the trained model to ensure that the prediction results conform to the physical law; and through programming, realizing an integrated and automated process from data acquisition to parameter extraction, realizing the normalization preprocessing of characteristic data, and subsequently combining with the optimizer to convert the parameter extraction process into an optimization problem, and using genetic algorithm, particle swarm optimization or Bayesian optimization to automatically fit the parameters.

[0025] Further, the step 2 comprises the following specific steps:

[0026] Step 2.1: Obtain a large amount of simulation data by calling automatic simulation;

[0027] Step 2.2: Data processing: after obtaining a large amount of data through the netlist, divide the data into DC data and S parameter data, process the data to obtain the required C gg values, g ds and g m , and normalize the obtained data; Step 2.3: Implementation of CNN architecture: CNN captures the local correlation and spatial structure of data through convolution kernels, and in model parameter extraction, processes the I-V curve superposition under multiple bias conditions from two-dimensional characteristic data.

[0028] Further, the step 2.1 includes the following specific steps:

[0029] Step 2.1.1: Obtain the netlist of the BSIM-BULK model;

[0030] First, determine the circuit topology of the BSIM-BULK model netlist, which clearly lists the connection relationship of the components in the circuit, then determine the complete netlist according to the actual parameter adjustment experience, and then use the netlist for automatic simulation;

[0031] Step 2.1.2: Call automatic simulation to determine the model parameters to be modified; generate a large amount of simulation experiment data by automatically modifying the model parameters and mobilizing automatic simulation;

[0032] Given a certain change range of the parameters to be adjusted, obtain different IV data and CV data, which is difficult to obtain through actual testing, but the required data quantity can be easily obtained through automatic simulation, and then the data can be used as the training data and test data of the neural network.

[0033] Further, the step 2.2 includes the following specific steps:

[0034] First, convert the discrete S parameters to Y parameters, and then use the formula:

[0035]

[0036] Calculate C gg.s Simulation results and C gg.m Test results, where f is the frequency, Im(Y 11 ) is the imaginary part of (Y 11 ); then extract I ds , V gs , V ds Simulation and test results, calculated by the formula:

[0037]

[0038] g m.s , g ds.s Simulation results and g m.m , g ds.m Test results.

[0039] And the following method is used for normalization processing:

[0040]

[0041] Where θ min and θ maxThe minimum and maximum values of the parameters, respectively, and the normalized parameters are limited between 0 and 1, so that the algorithm can more effectively process the parameters.

[0042] Further, the step 2.3 comprises the following specific steps:

[0043] The basic structure of CNN is composed of input layer, convolution layer, pooling layer, full connection layer and output layer. The convolution operation in CNN can be regarded as the inner product operation of input sample and convolution kernel. Each element of the convolution kernel corresponds to a weight coefficient and a bias. It is similar to a neuron of a feedforward neural network. Each neuron in the convolution layer is connected to multiple neurons in the region close to the position in the previous layer. The size of the region depends on the size of the convolution kernel, which is called "receptive field". The meaning can be compared with the receptive field of the visual cortex cells. When the convolution kernel works, it will regularly scan the input features, do matrix element multiplication and sum in the receptive field, and add the bias:

[0044]

[0045] Where b is the bias, Z l and Z l+1 represent the convolution input and output of the l+1 layer, also known as feature map.

[0046] After the convolution operation of the input sample in the first convolution layer, the feature map can be obtained. The same convolution kernel is used to perform convolution operation on each input sample in the convolution layer. In the second and subsequent convolution layers, the feature map of the previous layer is used as input data, and the convolution operation is also performed.

[0047] The role of the pooling layer is to reduce the size of the feature map generated by the convolution layer. A region is selected, and a new feature map is obtained according to the feature map of the region. This process is called pooling operation, and its general form is:

[0048]

[0049] In the formula, the step is s0, and p is a pre-specified parameter. When p = 1, the pooling takes the mean value in the pooling region, which is called mean pooling. When p→∞, the pooling takes the maximum value in the region, which is called maximum pooling.

[0050] The full connection layer is the same as the multilayer perceptron. First, the activation value is calculated, and then the output value of each unit is calculated through the activation function. The activation function is selected as ReLU, which replaces all negative values in the feature map with 0 and keeps the positive values unchanged.

[0051] That is:

[0052] f(x) = max(0, x)

[0053] The output layer adopts different forms according to different tasks.

[0054] The BSIM-BULK model parameter extraction method based on the neural network has the following advantages:

[0055] The application provides a parameter extraction method through a neural network, and is particularly suitable for parameter extraction of a BSIM-BULK model.The application first extracts parameters of the BSIM-BULK model, uses a CNN neural network instead of an ANN neural network for fitting, and improves local fitting precision. The CNN significantly reduces the number of parameters through a convolution kernel, processes local regions through convolution and pooling operations, improves calculation efficiency, and enhances generalization ability and robustness of the model.

[0056] Experimental results show that the powerful nonlinear fitting capability of the neural network and the physicality of the BSIM-BULK model are combined to realize rapid and accurate extraction of device model parameters, and therefore the application is suitable for modeling requirements of complex semiconductor devices. BRIEF DESCRIPTION OF DRAWINGS

[0057] Figure 1 The application is a CNN structure schematic diagram.

[0058] Figure 2 The application is a characteristic curve diagram verified in an ICCAP. DETAILED DESCRIPTION

[0059] In order to better understand the purpose, structure and function of the application, the application will be further described in detail below in combination with the drawings.

[0060] As shown in the drawings, the application is a BSIM-BULK model parameter extraction method based on a neural network, which includes the following steps: Figure 1 Step 1: automatically and intelligently complete parameter extraction through machine learning; combine the advantages of physical modeling and data-driven models, and introduce physical constraints and prior knowledge in the parameter extraction process.

[0061] Step 1.1: introduce a data-driven method.

[0062]

[0063] The application changes the traditional parameter extraction process by machine learning technology, and automatically and intelligently completes parameter extraction. The specific improvement is to use CNN to automatically extract features of device characteristic curves (such as I-V and C-V curves) instead of manual analysis. The core parameters of the BSIM-BULK model are directly predicted from the characteristic data by training the model, and the generalization ability of the model can be improved by data augmentation to solve the problem of insufficient data.

[0064] Step 1.2: Mixed modeling method and automatic workflow

[0065] The application introduces physical constraints and prior knowledge in the parameter extraction process by combining the advantages of physical modeling and data-driven models. The specific improvement is to provide initial parameter estimation with a physical model, and then use a neural network to fit the residual error to improve accuracy. In the trained model, physical consistency is added as a constraint to ensure that the prediction results conform to the physical law. And through programming, an integrated and automated process from data acquisition to parameter extraction is realized, and the characteristic data is normalized and preprocessed. Subsequently, it can be combined with the optimizer to convert the parameter extraction process into an optimization problem, and automatically fit the parameters using genetic algorithms, particle swarm optimization or Bayesian optimization.

[0066] Step 2: Build a parameter extraction model using a CNN architecture

[0067] The application converts one-dimensional characteristic data (such as I-V curves and C-V curves) into a two-dimensional matrix, and uses the advantages of CNN for two-dimensional characteristic extraction to combine multiple device characteristics into multi-channel input, allowing CNN to process multiple dimensions of characteristics simultaneously. For I-V, C-V curve data, CNN can identify important patterns such as turning points, linear regions, and nonlinear regions.

[0068] Step 2.1: Obtain a large amount of simulation data by calling automatic simulation.

[0069] Step 2.1.1: Obtain the netlist of the BSIM-BULK model. During parameter tuning, the netlist provides a standardized input form, making it easy to quickly adjust parameters and observe their impact on circuit performance.

[0070] In this embodiment, the circuit topology of the netlist is first determined, and the connection relationship of the components in the circuit is clearly listed in the netlist. Then, based on actual parameter tuning experience, a complete netlist is determined, and the netlist is used for automatic simulation after being obtained.

[0071] Step 2.1.2: Call automatic simulation to determine the model parameters to be modified. Traditional model parameter tuning is done by manually simulating the results. This method automatically modifies model parameters to generate a large number of simulation experiment data through automatic simulation.

[0072] In this embodiment, the following table is the model parameters to be modified, given a certain range of variation of the parameters to be adjusted, different IV data and CV data can be obtained. The data required for the experiment is up to 100000, which is difficult to obtain through actual testing, while it can be easily obtained through automatic simulation, and then the data can be used as the training data and test data of the neural network.

[0073] IVParameters Description NFACTOR Subthreshold swing factor U0 Low field mobility ETAMOB Effective electric field parameter UA Acoustic phonon / surface roughness scattering parameter EU Acoustic phonon / surface roughness scattering parameter. RDW Zero bias drain extension resistance per width VSAT Saturation velocity PTWG Correction factor for velocity saturation in forward mode PSATX Correction parameter for PTWG effect

[0074]

[0075]

[0076] Step 2.2: Data processing. After obtaining a large amount of data through the netlist, the data is divided into DC data and S parameter data, and the data is processed to obtain the required C gg values, g ds and g m , and the obtained data is normalized.

[0077] In this embodiment, the discrete S parameter is first converted into Y parameter, and then the formula:

[0078]

[0079] C gg.s (simulation result) and C gg.m (test result) are calculated, wherein f is the frequency, and Im(Y 11 ) is the imaginary part of (Y 11 ).

[0080] I ds , V gs , and V ds (simulation and test results) are extracted, and the formula:

[0081]

[0082] g m.s , g ds.s (simulation result) and g m.m , g ds.m (test result) are calculated.

[0083] And the following method is used for normalization:

[0084]

[0085] Wherein, θ min and θ maxare the minimum and maximum values of the parameter, respectively. The normalized parameters are limited between 0 and 1, making the algorithm more efficient in handling these parameters.

[0086] Step 2.3: Implementation of CNN architecture. CNN can capture the local correlation and spatial structure of data through convolution kernel, and can process the I-V curve superposition under multi-bias conditions from two-dimensional characteristic data in model parameter extraction, which has higher applicability in parameter extraction task.

[0087] In this embodiment, the basic structure of CNN is shown in FIG. 1, which is composed of an input layer, a convolution layer, a pooling layer, a full connection layer and an output layer. Figure 1 The convolution operation in CNN can be regarded as the inner product operation of input samples and convolution kernel. Each element of the convolution kernel corresponds to a weight coefficient and a bias, which is similar to a neuron of a feedforward neural network. Each neuron in the convolution layer is connected to multiple neurons in the region close to the position in the previous layer, and the size of the region depends on the size of the convolution kernel, which is called "receptive field", which can be compared with the receptive field of visual cortex cells. When the convolution kernel works, it will regularly scan the input features, do matrix element multiplication and sum in the receptive field, and add the bias:

[0088]

[0089] where b is the bias, Z l and Z l+1 represent the convolution input and output of the l+1 layer, also known as feature map.

[0090] After the convolution operation of the input sample in the first layer of the convolution layer, the feature map can be obtained. The same convolution kernel is used to perform convolution operation on each input sample in the convolution layer. In the second layer and subsequent convolution layers, the feature map of the previous layer is used as input data, and the convolution operation is also performed.

[0091] The role of the pooling layer is to reduce the size of the feature map generated by the convolution layer. A region is selected, and a new feature map is obtained according to the feature map of the region, which is called pooling operation. Its general form is:

[0092]

[0093] In the formula, the step is s0, and p is a pre-specified parameter. When p = 1, the pooling takes the mean value in the pooling region, which is called mean pooling. When p→∞, the pooling takes the maximum value in the region, which is called maximum pooling. Mean pooling and maximum pooling are the pooling methods that have been used for a long time in the design of convolutional neural network. Pooling operation reduces the dimension of the feature map, making the feature representation robust to the position change of the input data.

[0094] The full connection layer, like the multi-layer perceptron, first calculates the activation value, and then calculates the output value of each unit through the activation function. The selected activation function of the present application is ReLU. It replaces all negative values in the feature map with 0 and keeps the positive values unchanged. That is:

[0095] f(x) = max(0, x)

[0096] The output layer can adopt different forms according to different tasks.

[0097] The embodiment provides a BSIM-BULK model parameter extraction method based on a neural network.

[0098] The parameter extraction through the neural network greatly shortens the parameter extraction time, Figure 2 The characteristic curve diagram of the parameter extracted through the neural network is put back into the original model netlist for verification in ICCAP, and the CNN can fully exert the advantages of the CNN in automatic feature extraction, spatial perception, multi-modal processing and the like, and is particularly suitable for the parameter extraction task of a complex physical model such as BSIM-BULK. In application, the model performance can be further improved and innovative applications can be realized by combining physical priori, data enhancement, network optimization and result interpretability design.

[0099] It can be understood that the present application is described through some embodiments, and those skilled in the art know that various changes or equivalent replacements can be made to the features and embodiments without departing from the spirit and scope of the present application. In addition, under the guidance of the present application, the features and embodiments can be modified to adapt to specific conditions and materials without departing from the spirit and scope of the present application. Therefore, the present application is not limited by the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of the present application belong to the scope of protection of the present application.

Claims

1. A method for extracting parameters of a BSIM-BULK model based on a neural network, characterized in that, The steps include:

1. Constructing a parameter extraction model using a CNN architecture: Transforming one-dimensional feature data into a two-dimensional matrix, leveraging the advantages of CNN in extracting two-dimensional features, combining multiple sets of device features into multi-channel inputs, allowing CNN to process multi-dimensional features simultaneously; Step 1.1: Obtain a large amount of simulation data by calling the automatic simulation function; Step 1.1.1: Obtain the netlist of the BSIM-BULK model; First, determine the circuit topology of the BSIM-BULK model netlist. The netlist clearly lists the connection relationships of the components in the circuit. Then, determine the complete netlist based on actual parameter tuning experience. After obtaining the netlist, use it for automated simulation. Step 1.1.2: Call the automated simulation to determine the model parameters to be modified; By automatically modifying model parameters, a large amount of simulation experimental data is generated through automated simulation. Given a defined range of variation for the parameters to be adjusted, different IV and CV data can be obtained. Obtaining this data through actual testing is quite difficult, but the required amount of data can be easily obtained through automated simulation. This data can then be used as training and testing data for the neural network. Step 1.2: Data Processing: After obtaining a large amount of data through the netlist, the data is divided into DC data and S-parameter data, and then processed to obtain the required data. C gg value, g ds and g m The obtained data is then normalized. First, convert the discrete S-parameters into Y-parameters, then use the formula: Calculated C gg.s Simulation results and C gg.m Test results, among which, It's frequency. yes The imaginary part; Re-extract I ds , V gs , V ds Simulation and test results are given by the formula: ， ， Calculated g m.s , g ds.s Simulation results and g m.m , g ds.m Test results; The normalization process was performed using the following method: ， in, and These are the minimum and maximum values ​​of the parameters, respectively. The normalized parameters are limited to between 0 and 1, which allows the algorithm to process these parameters more efficiently. Step 1.3: Implementation of CNN architecture: CNN captures the local correlation and spatial structure of data through convolutional kernels, and processes the superposition of IV curves under multiple bias conditions from two-dimensional characteristic data in model parameter extraction; Step 2: Parameter extraction is completed automatically and intelligently through machine learning; by combining the advantages of physical modeling and data-driven models, physical constraints and prior knowledge are introduced in the parameter extraction process.

2. The method for extracting parameters of a BSIM-BULK model based on a neural network according to claim 1, characterized in that, Step 2 includes the following steps: Step 2.1: Introduce a data-driven approach; Step 2.2: Hybrid modeling approach and automated workflow.

3. The method for extracting parameters of the BSIM-BULK model based on a neural network according to claim 2, characterized in that, Step 2.1 specifically includes: CNNs are used to automatically extract features from device characteristic curves, replacing manual analysis. The core parameters of the BSIM-BULK model are predicted directly from the characteristic data by training the model, and the generalization ability of the model is improved by data augmentation.

4. The method for extracting parameters of the BSIM-BULK model based on a neural network according to claim 2, characterized in that, Step 2.2 specifically includes: The initial parameter estimates are provided by a physical model, and the residuals are fitted by a neural network to improve accuracy. Physical consistency is added to the trained model as a constraint to ensure that the prediction results conform to physical laws. Furthermore, an integrated automated process from data acquisition to parameter extraction is implemented through programming, which realizes the normalization preprocessing of characteristic data. Subsequently, it is combined with an optimizer to transform the parameter extraction process into an optimization problem, and the parameters are automatically fitted using genetic algorithms, particle swarm optimization, or Bayesian optimization.

5. The method for extracting parameters of a BSIM-BULK model based on a neural network according to claim 1, characterized in that, Step 1.3 includes the following specific steps: The basic structure of a CNN consists of an input layer, convolutional layers, pooling layers, fully connected layers, and an output layer. The convolution operation in a convolutional neural network can be viewed as an inner product operation between the input sample and the convolutional kernel. Each element of the convolutional kernel corresponds to a weight coefficient and a bias, similar to a neuron in a feedforward neural network. Each neuron in a convolutional layer is connected to multiple neurons in a region located close to it in the previous layer. The size of this region depends on the size of the convolutional kernel and is called the "receptive field," analogous to the receptive field of visual cortex cells. When the convolutional kernel works, it systematically scans the input features, performing element-wise matrix multiplication and summation on the input features within the receptive field, and then adding the bias. ， in, b This is the deviation amount. and Indicates the first The convolutional input and output of a layer are also called feature maps; After performing convolution operations on the input samples in the first convolutional layer, a feature map is obtained. The same convolution kernel is used to perform convolution operations on each input sample in the convolutional layer. In the second and subsequent convolutional layers, the feature map of the previous layer is used as input data and convolution operations are performed in the same way. The purpose of pooling layers is to reduce the size of the feature maps generated by convolutional layers. By selecting a region and obtaining a new feature map based on the feature map of that region, this process is called pooling, and its representation is as follows: ， The step size in the formula is , These are pre-specified parameters, when When the pooling value is averaged within the pooling region, it is called mean pooling; when... When the pooling method reaches a maximum value within the region, it is called max pooling. Like multilayer perceptrons, fully connected layers first calculate activation values, then use an activation function to calculate the output value of each unit. ReLU is chosen as the activation function, which replaces all negative values ​​in the feature map with 0, while keeping positive values ​​unchanged. ， The output layer takes different forms depending on the task.

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