A method for predicting the mechanical behavior of piezoelectric semiconductor devices under multi-physical field coupling

Abstract

The application discloses a kind of prediction methods of the mechanical behavior of piezoelectric semiconductor device multi-physics field coupling, and the prediction method is through grid inversion full connection neural network model prediction multi-physics field coupling mechanical behavior, there is significant advantage in solving piezoelectric semiconductor multi-field coupling nonlinear problem, both can realize the flexible modeling of complex coupling relationship, and can cope with nonlinear effect, realize efficient optimization;At the same time, by parallel training physical information neural network, under the condition of complex calculation problem, large amount of calculation, reduce the loss function in model training process, so that the trained model can more quickly predict the approximate solution of the problem, so as to improve the calculation efficiency and the accuracy of prediction.In addition, the prediction method fuses the law of physics in the process of training model, so that the designed model has strong generalization ability, can improve the precision of model prediction result in the case of lacking data, enhance the practical application value of the model designed by the application.

Description

Technical Field

[0001] This invention belongs to the field of multi-physics mechanical behavior prediction technology for piezoelectric semiconductors, and specifically relates to a method for predicting the multi-physics coupled mechanical behavior of piezoelectric semiconductor devices. Background Technology

[0002] Piezoelectric semiconductor devices are a class of semiconductor devices that utilize the piezoelectric effect to convert mechanical energy into electrical energy or vice versa. These devices can be used to fabricate optoelectronics, electronics, microelectronics, integrated circuits, chips, memory, and microwave devices, and have broad application potential in energy, communications, aerospace, and healthcare. With increasing demands for energy sustainability and smart technology, piezoelectric semiconductor technology will continue to be driven by research and application to meet evolving market needs.

[0003] Piezoelectric semiconductor devices often involve the coupling of multiple physical fields, including mechanical, electric, and thermal fields. Understanding the interactions between these physical fields is crucial for establishing multi-field coupling computational models. Currently, solving multi-field coupling nonlinear problems in piezoelectric semiconductors faces the following difficulties: (1) Piezoelectric semiconductor devices are simultaneously affected by electric, strain, and temperature fields, which are coupled with each other, leading to complex physical phenomena and nonlinear behaviors; (2) The nonlinear effects of piezoelectric semiconductor devices become more significant under multi-field coupling, such as geometric nonlinearity and nonlinear carrier transport, which require complex numerical methods to handle; (3) Due to the complexity of multi-field coupling nonlinear problems, numerical simulations often require high-precision numerical methods and large-scale computational resources, which places high demands on computational power and algorithms. Traditional multi-field coupling computational methods typically use finite element analysis (FEA) to establish physical models. This method can describe simple geometries and physical field distributions, but it is difficult to handle multi-physics coupling, nonlinearity, and multi-scale problems of piezoelectric semiconductor devices, which are piezoelectric dielectric devices. Furthermore, based on existing solvers, it requires a large amount of computational resources and time, sometimes resulting in unsolvable problems. Furthermore, finite element models require verification with actual test data, which may be difficult to obtain or too costly in complex systems. When the physical model and data are complex, traditional Physical Information Neural Networks (PINNs) suffer from low computational efficiency and accuracy, as well as inaccurate predictions, in handling high-dimensional multi-field nonlinear calculations. Therefore, there is an urgent need for an efficient computational method to solve the problem of multi-physics coupled nonlinear mechanical analysis of piezoelectric semiconductors. Summary of the Invention

[0004] This invention addresses the shortcomings of existing solution methods by providing a multi-field coupled nonlinear mechanical analysis method for piezoelectric semiconductors based on a gridded physical information neural network. This method solves the problem of traditional methods being unable to solve or handle the complex multi-physics nonlinearities of piezoelectric semiconductors. Therefore, it provides effective guidance for the design, optimization, and application of practical devices.

[0005] In a first aspect, the present invention provides a method for predicting the multiphysics coupled mechanical behavior of piezoelectric semiconductor devices, the prediction method comprising the following steps:

[0006] Step 1: Obtain experimental or simulation data of the piezoelectric semiconductor device as a dataset. The dataset includes the displacement, potential, and electron concentration of the piezoelectric semiconductor.

[0007] Step 2: Construct a gridded inverted fully connected neural network model; the gridded inverted fully connected neural network model consists of multiple parallel physical information neural networks with identical structures. The physical information neural network includes an input layer, hidden layers, and an output layer.

[0008] Step 3: Construct the loss function for the gridded inversion fully connected neural network model. This loss function includes the physical information error term and data error term for each physical information neural network. Train the gridded inversion fully connected neural network model constructed in Step 2 using the dataset.

[0009] Step 4: Collect the local displacement, potential, and electron concentration of the piezoelectric semiconductor device under test, and input them into the trained gridded inversion fully connected neural network model to predict the overall displacement, potential, and electron concentration of the piezoelectric semiconductor device.

[0010] Preferably, in step three, the loss function of the neural network for each physical information is Loss. k The expression is:

[0011]

[0012] in, This is the physical information error term; For data error terms; k = 1, 2, ..., M; M is the number of parallel physical information neural networks.

[0013] The expression for the loss function Loss of the entire model is:

[0014]

[0015] Preferably, the method for obtaining the physical information error term is as follows:

[0016] Based on the piezoelectric semiconductor governing equations, constitutive equations, and nonlinear strain-displacement equations, and considering the coupling of the three physical fields of force, charge, and charge carriers, a system of partial differential equations is constructed:

[0017] N a U a (x,y,z)-q=0

[0018] Where, N a U is the parameter matrix; a (x,y,z) is the physical quantity matrix; q is the external load; a = 1,2,...,A; A is the number of categories of the physical quantity matrix.

[0019] Error terms for obtaining physical information from partial differential equations The expression is:

[0020]

[0021] Where n is the size of the dataset; This is the matrix of predicted physical quantities.

[0022] Preferably, the data error term The method for obtaining it is as follows:

[0023]

[0024] in, This is the actual physical quantity matrix.

[0025] Preferably, the parameter matrix N a It includes an adaptive parameter λ, which can adaptively adjust the parameter λ during training to minimize the error term of physical information.

[0026] Preferably, in step two, each physical information neural network has 5 hidden layers and 50 neurons per layer.

[0027] In a second aspect, the present invention provides a computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the memory stores the computer program; and the processor executes the aforementioned method for predicting the multiphysics coupled mechanical behavior of a piezoelectric semiconductor device.

[0028] Thirdly, the present invention provides a readable storage medium storing a computer program; when the computer program is executed by a processor, it is used to implement the aforementioned method for predicting the multiphysics coupled mechanical behavior of a piezoelectric semiconductor device.

[0029] The beneficial effects of this invention are:

[0030] 1. This invention predicts multi-physics coupled mechanical behavior by using a gridded inversion fully connected neural network model, which has significant advantages in solving multi-field coupled nonlinear problems of piezoelectric semiconductors. This prediction method can flexibly model complex coupling relationships through data-driven methods, cope with nonlinear effects, and achieve efficient optimization. At the same time, by adding a parallel-trained physical information neural network, the loss function in the model training process is reduced when the computation problem is complex and the computational load is large, so that the trained model can predict the approximate solution of the problem more quickly, thereby improving computational efficiency and prediction accuracy.

[0031] 2. This invention uses a gridded physical information neural network to predict the mechanical behavior of multi-physics coupling, providing a new approach and tool for solving nonlinear problems of multi-field coupling in piezoelectric semiconductors, and mining hidden patterns and laws from a large amount of data. At the same time, this invention integrates physical laws during the training process, giving the designed model a strong generalization ability, improving the accuracy of the model's prediction results even in the absence of data, and enhancing the practical application value of the model designed in this invention. Attached Figure Description

[0032] Figure 1 This is a flowchart of the gridded physical information neural network in this invention.

[0033] Figure 2 This is a schematic diagram of the gridded physical information neural network model in this invention.

[0034] Figure 3 This is a schematic diagram of the electron displacement in the x-direction in Example 1.

[0035] Figure 4 This is a schematic diagram of the electron displacement in the z-direction in Example 1.

[0036] Figure 5 This is a schematic diagram of the potential distribution along the x-axis in Example 1.

[0037] Figure 6 This is a schematic diagram of the electron concentration distribution along the x-axis in Example 1. Detailed Implementation

[0038] To make the objectives, methods, and implementation of this invention clearer, this invention takes piezoelectric semiconductors as the research object, establishes a three-dimensional multi-field coupling nonlinear equation system by combining equilibrium equations, electrostatic Gauss's law, and semiconductor physics equations, and studies the multi-field coupling of piezoelectric semiconductors using Meshed Physics Informed Neural Networks (MPINNs). The invention will be further described below with reference to the accompanying drawings.

[0039] Example 1

[0040] like Figure 1 As shown, a method for predicting the multiphysics coupled mechanical behavior of piezoelectric semiconductor devices includes the following steps:

[0041] Step 1: Obtain the dataset of the three-dimensional piezoelectric semiconductor disc using the COMSOL three-dimensional finite element model. The dataset size is 2000; the dataset includes the displacement, potential, and electron concentration of the piezoelectric semiconductor structure. To improve the accuracy of the prediction results, the data is normalized using the following formula:

[0042]

[0043] Among them, a norm 'a' represents the normalized data; 'a' represents the original data. max and a min These are the maximum and minimum values ​​in the original data, respectively.

[0044] Step 2, as follows Figure 2 As shown, a gridded inversion fully connected neural network model is constructed. This model comprises two parallel, identical physical information neural networks. Each physical information neural network includes an input layer, hidden layers, and an output layer, using the tanh function as the activation function. Each physical information neural network has 5 hidden layers, with 50 neurons in each layer.

[0045] Step 3: Construct the loss function for the gridded inversion fully connected neural network model. This model's loss function includes a physical information error term and a data error term. Physical information error term. and data error terms The method to obtain it is as follows:

[0046] Based on the piezoelectric semiconductor control equations, constitutive equations, nonlinear strain-displacement relationships, and the relationships between electric field and electron concentration gradient, a set of partial differential equations is constructed using the three physical fields of coupling force, electric field, and charge carrier.

[0047] The governing equation for piezoelectric semiconductors is:

[0048]

[0049]

[0050]

[0051]

[0052]

[0053] Among them, T xx Tyy T zz T xy T xz T yz D represents the stress component; x D y D z J is the electric displacement component; x J y J z ρ is the electron current density; ρ is the mass density; is the second derivative of the displacement component; n is the electron concentration; q represents the doping concentration; q represents the external load.

[0054] The constitutive equation is:

[0055] T ij =c ijkl S kl -e kij E k ,

[0056] D k =e kiji ε ij +ε kl E k ,

[0057] J k =qnμ ij E k +qD ij n ，k ,

[0058] Among them, c ijkl S is the elastic stiffness coefficient; kl For strain; E k For electric field; electric potential; e ij ε is the piezoelectric constant; ij μ is the dielectric constant. ij D represents electron mobility. ij is the electron diffusion coefficient.

[0059] The nonlinear strain-displacement relationship is as follows:

[0060]

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[0065]

[0066] The relationship between the electric field and the electron concentration gradient is as follows:

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[0070]

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[0073] The constructed system of partial differential equations is as follows:

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[0078]

[0079] Transform the constructed system of partial differential equations into matrix form:

[0080]

[0081] Where U is the physical quantity matrix; K is the parameter matrix. Specifically, the physical quantity matrix U and the parameter matrix K are:

[0082]

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[0100]

[0101]

[0102]

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[0104]

[0105] Introducing an adaptive parameter λ into the parameter matrix K transforms the original matrix-form partial differential equation system into:

[0106]

[0107] Where N is the parameter matrix, it is represented as:

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[0110]

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[0117]

[0118]

[0119]

[0120]

[0121] Through parameter matrix N a An adaptive parameter λ is defined, which can adaptively adjust the parameter λ during training to minimize the physical information error term. The physical information error term is obtained based on the transformed partial differential equation. The expression is:

[0122]

[0123] Where n is the size of the dataset; denoted as the predicted physical quantity matrix; k = 1, 2, ..., M; M is the number of parallel physical information neural networks; a = 1, 2, ..., A; A is the number of categories of the physical quantity matrix.

[0124] Data error term The expression is:

[0125]

[0126] in, This is the actual physical quantity matrix.

[0127] Loss function for each grid k The expression is:

[0128]

[0129] The expression for the loss function Loss of the entire model is:

[0130]

[0131] The gridded inversion fully connected neural network model constructed in step two was trained using the dataset for 50,000 training iterations. The loss function value was continuously updated using the gradient optimization algorithm. If the loss function Loss < ε, it means that the model training is complete; where ε is a preset threshold.

[0132] Step 4: Input the local displacement, potential, and electron concentration of the piezoelectric semiconductor device under test into the trained gridded inversion fully connected neural network model to predict the overall displacement, potential, and electron concentration of the piezoelectric semiconductor device. The distribution results of each physical quantity along the x-axis diameter are shown below. Figures 3-6 As shown.

[0133] Step 5: Predict the overall displacement, potential, and electron concentration of the piezoelectric semiconductor device using PINNs and MPINNs respectively. Evaluate the prediction results of the two methods using the mean square error and prediction time. The evaluation results are shown in Table 1. As can be seen from Table 1, the method provided by this invention not only has high efficiency, but also high accuracy of prediction results.

[0134] Table 1

[0135]

[0136] Example 2

[0137] A multi-physics coupled mechanical behavior prediction method for piezoelectric devices is disclosed in this embodiment. The prediction object is piezoelectric devices other than piezoelectric semiconductor devices. In this embodiment, a gridded inversion fully connected neural network model with the same structure as in Embodiment 1 is used to predict the overall displacement and potential of the piezoelectric device based on the local displacement and potential of the device. During the prediction process, the physical information error term used in the loss function of the gridded inversion fully connected neural network model is constructed based on the displacement and potential of the piezoelectric device.

Claims

1. A method for predicting the multiphysics coupled mechanical behavior of piezoelectric semiconductor devices, characterized in that: The prediction method includes the following steps: Step 1: Obtain experimental or simulation data of the piezoelectric semiconductor device as a dataset. The data in the dataset contains the key physical quantities of the piezoelectric semiconductor device. In Step 1, the key physical quantities include: displacement, electric potential, and electron concentration of the piezoelectric semiconductor device. Step 2: Construct a gridded inversion fully connected neural network model; the gridded inversion fully connected neural network model includes multiple parallel physical information neural networks with identical structures; the physical information neural network includes an input layer, hidden layers, and an output layer; Step 3: Construct the loss function of the gridded inversion fully connected neural network model. This loss function is obtained by averaging the loss functions of each physical information neural network. The loss function of each physical information neural network includes the physical information error term and the data error term of each physical information neural network. Train the gridded inversion fully connected neural network model constructed in Step 2 using the dataset. The physical information error term is obtained by transforming the multiphysics nonlinear equations related to displacement, potential, and electron concentration. The method for obtaining the physical information error term is as follows: Based on the governing equations, constitutive equations, nonlinear strain-displacement relationships, and the relationships between the electric field and electron concentration gradient in piezoelectric semiconductors, a system of partial differential equations is constructed by coupling the three physical fields of force, charge, and charge carriers. This system of partial differential equations is then transformed into a matrix form consisting of physical quantity matrices and parameter matrices, as follows: ； Where, N a U is the parameter matrix; a (x,y,z) is the physical quantity matrix; q is the external load; a=1,2,...,A; A is the number of categories of the physical quantity matrix; An adaptive parameter λ is introduced into the parameter matrix to transform the matrix-form partial differential equations. The physical information error term is then obtained from the transformed partial differential equations. The expression is: ； Where n is the size of the dataset; This is the matrix of predicted physical quantities; Step 4: Collect the local displacement, potential, and electron concentration of the piezoelectric semiconductor device under test, and input them into the trained gridded inversion fully connected neural network model to predict the overall displacement, potential, and electron concentration of the piezoelectric semiconductor device.

2. The method for predicting the multiphysics coupled mechanical behavior of a piezoelectric semiconductor device according to claim 1, characterized in that: In step three, the loss function of the neural network for each physical information is Loss. k The expression is: ； in, This is the physical information error term; For data error terms; k=1,2,...,M; M is the number of parallel physical information neural networks; The expression for the loss function Loss of the entire model is: 。 3. The method for predicting the multiphysics coupled mechanical behavior of a piezoelectric semiconductor device according to claim 2, characterized in that: The data error term The method for obtaining it is as follows: ； in, This is the actual physical quantity matrix.

4. The method for predicting the multiphysics coupled mechanical behavior of a piezoelectric semiconductor device according to claim 1, characterized in that: In step two, each physical information neural network has 5 hidden layers, and each layer has 50 neurons.

5. A computer device, characterized in that: It includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the memory stores the computer program; and the processor executes the multiphysics coupling mechanical behavior prediction method for a piezoelectric semiconductor device as described in claim 1.

6. A readable storage medium, characterized in that: The computer program is stored therein; when executed by a processor, the computer program is used to implement the multiphysics coupling mechanical behavior prediction method for a piezoelectric semiconductor device as described in claim 1.

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