A quasi-linear transformation method for machine learning training data

Abstract

The application discloses a quasi-linear transformation method for machine learning training data, comprising the following steps: 1, obtaining a data set, defining input X and output Y, simulating the relationship between the input X and the output Y of the data set, and obtaining the change form of Y with X; 2, defining a conversion function which can simulate the change relationship between the input X and the output Y; 3, optimizing the conversion function in step 2, substituting the input X to perform data transformation, and converting the same into Z as a new model input; and 4, constructing a machine learning model between the new input Z and the output Y. The input data is transformed by the conversion function, so that the input and the output in the machine learning model present a quasi-linear relationship, the complexity of the machine learning model can be reduced, and the simulation precision of the machine learning model is effectively improved.

Description

Technical Field

[0001] This invention relates to the field of EDA simulation of semiconductor devices, and in particular to a quasi-linear transformation method for machine learning training data. Background Technology

[0002] Electrical performance simulation is a crucial step in the design process of power semiconductor devices. Traditional device electrical performance simulation relies on simulation tools centered around Technology Computer Aided Design (TCAD), which primarily obtains the device's electrical performance by solving semiconductor equations using the finite element / finite difference method. However, this approach suffers from problems such as long simulation times and poor convergence. Accurate and efficient acquisition of electrical performance can effectively accelerate the design process.

[0003] In recent years, with the victory of AlphaGo, the success of autonomous driving, and breakthroughs in pattern recognition, artificial intelligence technology centered on machine learning has continued to develop. To date, in the field of semiconductor device modeling, machine learning algorithms can effectively model the relationship between device inputs (structural parameters, applied voltage) and outputs (electrical performance), providing corresponding electrical performance with advantages such as high accuracy and speed. Therefore, the technology of using machine learning algorithms to build simulation models and obtain the electrical performance of devices is constantly being proposed. In the process of building machine learning models, in order to effectively improve the prediction accuracy of the model, data preprocessing of the input and output data before model construction is a necessary means.

[0004] Currently, data preprocessing methods mainly include data normalization, which encompasses techniques such as min-max normalization, z-score normalization, linear proportional normalization, logarithmic normalization, arctangent normalization, and atan function transformation. These methods primarily utilize transformation formulas to scale input or output data of different dimensions or magnitudes, removing unit limitations. By normalizing input and output data, a prerequisite for the effective training of machine learning models is provided.

[0005] However, existing data normalization methods typically only normalize the input or output, neglecting the trend relationship between them. Therefore, the original input-output relationship is non-linear, and the normalized relationship remains non-linear. Machine learning algorithms suffer from high simulation complexity and low accuracy on data with large fluctuations in relationships. Summary of the Invention

[0006] The technical problem to be solved by the present invention is to address the shortcomings of the prior art by providing a quasi-linear transformation method for machine learning training data. This quasi-linear transformation method for machine learning training data transforms the input X by designing a transformation function, so that the transformed data and the output Y form a quasi-linear relationship, thereby optimizing the simulation accuracy of the machine learning model.

[0007] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0008] A quasi-linear transformation method for machine learning training data includes the following steps.

[0009] Step 1: Obtain the dataset, which includes the following steps.

[0010] Step 1-1: Determine the output Y: For various semiconductor devices, identify the electrical performance parameter Y that needs to be predicted. This electrical performance parameter Y is the output Y of the machine learning.

[0011] Step 1-2: Define the input X: For various semiconductor devices, define the input X that affects the output Y; where the input X includes N electrical parameters X1; where N≥1.

[0012] Steps 1-3: Obtain the dataset: Use experimental or simulation analysis methods to obtain a corresponding output Y for each input X.

[0013] Steps 1-4: Fitting the X1-Y curve: Based on the dataset obtained in Steps 1-3, fit the X1-Y curve for each electrical parameter and the functional form of Y with respect to X1, Y = f(X1).

[0014] Step 2, Define the transformation function: Define a function U = f(V) that varies with V; where V is the electrical parameter X1 or the normalized value X′ of the electrical parameter X1; U is the transformed value of the electrical parameter X1; U = f(V) has several undetermined coefficients.

[0015] Step 3: Optimize the transformation function, which includes the following steps.

[0016] Step 3-1, Convert electrical parameter X1: Substitute each electrical parameter X1 or the normalized value X′ of each input X in step 1 into the corresponding conversion function U = f(V) in step 2 to obtain U with undetermined coefficients.

[0017] Step 3-2: Determine the optimal undetermined coefficients: Fit the U value obtained in Step 3-1 with the output Y or the normalized value Y′ of the corresponding input X in Step 1; the undetermined coefficients when the fitted curve is close to a straight line are the determined optimal undetermined coefficients.

[0018] Step 4: Construct a machine learning model: The machine learning model has input X and output Y; where each electrical parameter X1 in the input X is converted to the value U by the conversion function U = f(V) optimized in step 3.

[0019] In step 3-2, the method for judging whether the fitted curve is close to a straight line is: when the numerical fluctuation of the first derivative of the fitted curve U value is less than the set threshold, it is judged that the current fitted curve is close to a straight line.

[0020] In step 4, the machine learning algorithm of the machine learning model is one or a combination of deep neural networks, Gaussian process regression, random forest, support vector machine linear regression, logistic regression, Lasso regression and CART regression tree.

[0021] In step 1, each input X consists of only N electrical parameters X1.

[0022] In step 1, each input X includes N electrical parameters X1 and M structural parameters; where M ≥ 1.

[0023] In step 1, each input X includes two electrical parameters X1 and three structural parameters; the three structural parameters are the channel length l, radius r, and gate oxide thickness t. ox The two electrical parameters X1 are the gate voltage v g and drain voltage v d The output Y is the drain current i of the transistor. d .

[0024] In step 2, the gate voltage v g The transformation function is U = G -1 / (m×V) Drain voltage v d The conversion function is U = -G -n*V +1; where G takes the value of 2, and m and n are undetermined coefficients.

[0025] In step 3-1, when converting electrical parameters, each electrical parameter X1 is normalized before being converted using the conversion function U = f(V); in step 3-2, the output Y is first normalized and then fitted with the U value obtained in step 3-1.

[0026] m = 10, n = 4.

[0027] The present invention has the following beneficial effects:

[0028] 1. This invention performs data preprocessing based on the relationship between input and output data, and quasi-linearizes the relationship between the input and output of the constructed model, which can effectively simplify the complexity of model construction.

[0029] 2. This invention performs data preprocessing based on the relationship between input and output data, thereby improving the accuracy of machine learning model predictions by simplifying the relationship between input and output. Attached Figure Description

[0030] Figure 1 A flowchart of a quasi-linear transformation method for machine learning training data according to the present invention is shown.

[0031] Figure 2 The diagram shows the overall curve change between the applied leakage voltage at the initial input and the output.

[0032] Figure 3 It shows the overall curve variation characteristics between the applied gate voltage at the initial input and the output.

[0033] Figure 4 The conversion function for handling leakage voltage is shown.

[0034] Figure 5 The conversion function for processing the gate voltage is shown.

[0035] Figure 6 The mapping relationship between the transformed leakage voltage and the output after quasi-linear transformation is shown.

[0036] Figure 7 The mapping relationship between the transformed gate voltage and the output after quasi-linear transformation is shown. Detailed Implementation

[0037] The present invention will now be described in further detail with reference to the accompanying drawings and specific preferred embodiments.

[0038] In the description of this invention, it should be understood that the terms "left side", "right side", "upper part", "lower part", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, and are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. "First", "second", etc. do not indicate the importance of the components, and therefore should not be construed as a limitation of this invention.

[0039] This embodiment takes an intelligent regression model for predicting the electrical performance of a gate-all-around (GAA) transistor based on a machine learning algorithm as an example for research, and does not limit the scope of protection of this invention.

[0040] like Figure 1 As shown, a quasi-linear transformation method for machine learning training data includes the following steps.

[0041] Step 1: Obtain the dataset, which includes the following steps.

[0042] Step 1-1: Determine the output Y: For various semiconductor devices, identify the electrical performance parameter Y that needs to be predicted. This electrical performance parameter Y is the output Y of the machine learning.

[0043] In this embodiment, the output Y is preferably the drain current i of the transistor. d Alternatively, it can be other electrical performance parameters that need to be predicted.

[0044] Step 1-2: Define the input X: For various semiconductor devices, define the input X that affects the output Y; where the input X includes N electrical parameters X1; where N≥1.

[0045] The above input X preferably has the following two combination modes:

[0046] Combination Mode 1: Each input X in each group includes only N electrical parameters X1.

[0047] Combination Mode 2: Each input X includes N electrical parameters X1 and M structural parameters; where M≥1.

[0048] In this embodiment, the second mode is preferably adopted, where each input X includes two electrical parameters X1 and three structural parameters; the three structural parameters are the channel length l, the radius r, and the gate oxide thickness t. ox The two electrical parameters X1 are the gate voltage v g and drain voltage v d .

[0049] The preferred range and step size of the input X are: l∈(10,20,1), r∈(2,5,0.5), t ox ∈(0.5,1.5,0.25), v g ∈(0,0.7,0.05), v d ∈(0,0.7,0.05), where the numbers in parentheses above represent the lower limit, upper limit, and step size in that order.

[0050] Steps 1-3: Obtain the dataset: Use experimental or simulation analysis methods to obtain a corresponding output Y for each input X.

[0051] Steps 1-4: Fitting the X1-Y curve: Based on the dataset obtained in Steps 1-3, fit the X1-Y curve for each electrical parameter and the functional form of Y with respect to X1, Y = f(X1).

[0052] Step 2, Define the transformation function: Define a function U = f(V) that varies with V; where V is the electrical parameter X1 or the normalized value X′ of the electrical parameter X1; U is the transformed value of the electrical parameter X1; U = f(V) has several undetermined coefficients.

[0053] In this embodiment, the gate voltage v is determined based on the corresponding X1-Y curve fitted in steps 1-4. g The transformation function is defined as U = G -1 / (m×V) Drain voltage v d The transformation function is defined as U = -G -n*V +1; where G takes the value of 2, and m and n are undetermined coefficients.

[0054] Step 3: Optimize the transformation function, which includes the following steps.

[0055] Step 3-1, Convert electrical parameter X1: Substitute each electrical parameter X1 or the normalized value X′ of each input X in step 1 into the corresponding conversion function U = f(V) in step 2 to obtain U with undetermined coefficients.

[0056] In this embodiment, each electrical parameter X1 is preferably normalized before being converted using the conversion function U = f(V). The preferred normalization formula is:

[0057] x′=(x-minx) / (maxx-minx)

[0058] In the formula, x is the gate voltage v before the conversion of electrical parameter X1. g or drain voltage v d value;

[0059] Minx is the gate voltage v in step 1. g or drain voltage v d The minimum value.

[0060] Max x is the gate voltage v in step 1. g or drain voltage v d The maximum value.

[0061] x′ is the gate voltage v after normalization of electrical parameter X1. g or drain voltage v d value.

[0062] Gate voltage v after normalization g As a variable V, input to the optimization function U = G -1 / (m×V) In this process, we obtain the U value (also known as v) containing the undetermined coefficient m. g_n Similarly, the normalized drain voltage v d As a variable V, input to the optimization function U = -G-n*V In +1, we obtain the U value (also known as v) containing the undetermined coefficient n. d_n ).

[0063] Step 3-2: Determine the optimal undetermined coefficients: The U value (i.e., v) obtained in step 3-1... d_n and v g_n The input Y of the corresponding group of input X in step 1 is fitted with the output Y or the normalized value Y′ of the output Y; the undetermined coefficients when the fitted curve is close to a straight line are the determined optimal undetermined coefficients.

[0064] In this embodiment, the output Y (i.e., the drain current i) is used. d First, normalization is performed to form i d_n Then, it is fitted with the U value obtained in step 3-1. The output Y is preferably log-normalized, specifically:

[0065] i d_n =lni d / lnQ

[0066] The above logarithmic processing can compress i d The size of the Q value makes its data distribution more stable, and Q is always set to 2.

[0067] Next, the new variable i obtained from the root d_n By using the method of controlling variables, we can determine i d_n With v d v g The curve, such as Figure 2 and Figure 3 As shown. Figure 2 The curve shown gives i d_n -v d The changing trend of the curve set Figure 3 The curve shown gives i d_n -v g The changing trend of the curve set.

[0068] Then, using the normalized v d_n with i d_n Plot a curve and calculate its first derivative. The magnitude of the fluctuation in the first derivative (i.e., the first derivative of the fitted curve U) is used to evaluate the effectiveness of the transformation function. The smaller the first derivative (preferably below a set threshold), the straighter the curve, and the better the function. By repeating steps 3-1 and 3-2, the optimal solutions for the undetermined coefficients m and n in the optimization function are found. In this embodiment, the optimal solutions for m and n are determined to be 10 and 4, respectively. Figure 4 and Figure 5 The voltages (V) after processing based on the optimized transfer function are given respectively. d_n and v g_nWith the initial applied voltage (v) d and v g The changing trend of ) can be seen. It is related to i d_n With the initial applied voltage (v) d and v g They exhibited a similar trend. Figure 6 and Figure 7 The target current (i) is further given. d_n ) with conversion voltage (v d_n v g_n The trend of change between ) is evident. It shows a good quasi-linear relationship, laying the foundation for accurate simulation by machine learning models.

[0069] Step 4: Build a machine learning model

[0070] The machine learning algorithm for the machine learning model is one or a combination of deep neural networks, Gaussian process regression, random forest, support vector machine linear regression, logistic regression, Lasso regression, and CART regression trees. In this embodiment, deep neural networks are preferably used to construct the model.

[0071] The machine learning model has input X and output Y; wherein each electrical parameter X1 in input X is converted to U value using the conversion function U=f(V) optimized in step 3.

[0072] The above-mentioned U value after transformation using the preferred transformation function U=f(V) and the three structural parameters are also called input Z.

[0073] In this embodiment, the construction process of the deep neural network preferably includes the following steps.

[0074] Step 41, Data Standardization: Z-Score standardization is preferably used to standardize the data obtained in Step 3. d_n and v g_n Standardize the process.

[0075] Step 42: Adjust the network model: In this embodiment, a deep neural network (DNN) is used as a representative deep neural network algorithm in machine learning. A suitable network model is selected based on the prediction target. The network input consists of 5 parameters, including 3 structural parameters (l, r, t). ox ), 2 electrical parameters (v) g v d The first hidden layer has 128 neurons with the Tanh activation function; the second hidden layer has 64 neurons with the sigmoid activation function; the output is 1(i d ).

[0076] Step 43: Set network hyperparameters, select the learning rate and optimization scheme.

[0077] Step 44: Determine the loss function: using i from step 3-2 d_n Let the actual value be `target`, and the network's output value be `predict`. Then the loss function is:

[0078]

[0079] In the formula, predict[i] represents the i-th element. d_n The network prediction value;

[0080] target[i] is the i-th element. d_n The actual value;

[0081] n is i d_n The total number.

[0082] Step 45, Model Training: Set the training period based on the target current (i d_n ) with conversion voltage (v d_n v g_n ), to train the model.

[0083] Table 1 presents the prediction results for the same test dataset with and without this technique, under the same training period. The results show that without quasi-linear data transformation, the neural network complexity is high; with quasi-linear data transformation, the neural network complexity is low. As can be seen from the data in Table 1, this method effectively simplifies model construction complexity under the same number of iterations and the same accuracy requirements. When the number of neurons in the two hidden layers is 128 and 64 respectively, the network model has 8192 weights; when the number of neurons in the two hidden layers is 96 and 48 respectively, the network model has 4608 weights. These data show that storage resources are saved by 43% after using this method.

[0084] Table 2 presents the prediction results for the same test dataset under the same machine learning algorithm framework and with the same training period, using the same model complexity with and without quasi-linear data transformation. As can be seen from the data in Table 2, this method achieves approximately a 20% accuracy improvement with the same number of iterations.

[0085] Table 1: Comparison of Complexity of Different Models

[0086]

[0087] Table 2: Accuracy Comparison for the Same Model Complexity

[0088]

[0089] The preferred embodiments of the present invention have been described in detail above. However, the present invention is not limited to the specific details in the above embodiments. Within the scope of the technical concept of the present invention, various equivalent transformations can be made to the technical solutions of the present invention, and these equivalent transformations all fall within the protection scope of the present invention.

Claims

1. A quasi-linear transformation method for machine learning training data, characterized in that: Includes the following steps: Step 1: Obtain the dataset, which includes the following steps: Step 1-1: Determine the output Y: For various semiconductor devices, identify the electrical performance parameter Y that needs to be predicted. This electrical performance parameter Y is the output Y of the machine learning. Step 1-2: Define the input X: For various semiconductor devices, define the input X that affects the output Y; each set of input X includes two electrical parameters. And three structural parameters; the three structural parameters are the channel length l, the radius r, and the gate oxide thickness t. ox ; 2 electrical parameters These are the gate voltages v g and drain voltage v d The output Y is the drain current i of the transistor. d ; Steps 1-3: Obtain the dataset: Use experimental or simulation analysis methods to obtain a corresponding output Y for each set of inputs X; Steps 1-4: Fitting Curve: Based on the dataset obtained in steps 1-3, the curve for each electrical parameter is fitted. Curve and Y about function form ; Step 2, Define the transformation function: Define a function that shows how U changes as V changes. Where V is an electrical parameter. or electrical parameters Normalized value ; Electrical parameters The value after function conversion; It contains several undetermined coefficients; Gate voltage v g The conversion function is Drain voltage v d The conversion function is Where G takes the value of 2, and m and n are undetermined coefficients; Step 3: Optimize the transformation function, which includes the following steps: Step 3-1: Convert electrical parameters : Input each electrical parameter in X from each group in step 1 or electrical parameters Normalized value Substitute each into the corresponding conversion function in step 2. Thus, we obtain the coefficients to be determined. ; Step 3-2: Determine the optimal undetermined coefficients: Combine the U value obtained in Step 3-1 with the output Y or the normalized value of the output Y corresponding to the input X in Step 1. The undetermined coefficients are then fitted; the undetermined coefficients that make the fitted curve close to a straight line are the optimal undetermined coefficients. Step 4: Construct a machine learning model: The machine learning model has input X and output Y; where each electrical parameter in input X... All use the optimized transformation function from step 3. The U value after conversion.

2. The quasi-linear transformation method for machine learning training data according to claim 1, characterized in that: In step 3-2, the method for judging whether the fitted curve is close to a straight line is: when the numerical fluctuation of the first derivative of the fitted curve U value is less than the set threshold, it is judged that the current fitted curve is close to a straight line.

3. The quasi-linear transformation method for machine learning training data according to claim 1, characterized in that: In step 4, the machine learning algorithm of the machine learning model is one or a combination of deep neural networks, Gaussian process regression, random forest, support vector machine linear regression, logistic regression, Lasso regression and CART regression tree.

4. The quasi-linear transformation method for machine learning training data according to claim 1, characterized in that: When converting electrical parameters in step 3-1, each electrical parameter When using the transformation function Before the transformation, normalization is performed. In step 3-2, the output Y is first normalized and then fitted with the U value obtained in step 3-1.

5. The quasi-linear transformation method for machine learning training data according to claim 1, characterized in that: m=10, n=4.

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