TSV electric heating multi-physics field coupling modeling method based on physical information neural network

Abstract

The invention discloses a TSV (Through Silicon Via) electric heating multi-physics field coupling modeling method based on a physical information neural network. The method comprises the following steps: acquiring a simulation data set of a plurality of material sub-regions of a TSV; a neural network integrating TSV design parameters is constructed, the network comprises a potential field neural network and a temperature field neural network, and the potential field neural network and the temperature field neural network respectively comprise a plurality of potential field sub-networks and a plurality of temperature field sub-networks; each material sub-region corresponds to a potential field sub-network and a temperature field sub-network, and a physical continuity constraint is arranged between the sub-networks corresponding to the adjacent material sub-regions; and training a potential field neural network on the basis of the simulation data set and the target loss function, and training a temperature field neural network on the basis of the trained potential field neural network, the simulation data set and the target loss function, so as to predict the electrothermal coupling temperature field of the target TSV under different design parameters by adopting the trained temperature field neural network. According to the invention, the efficiency and generalization ability of TSV electric heating multi-physics field coupling simulation can be improved.

Description

Technical Field

[0001] This invention belongs to the field of electrothermal multiphysics simulation technology, specifically involving a TSV electrothermal multiphysics coupling modeling method based on physical information neural network. Background Technology

[0002] Three-dimensional integrated circuit technology based on through-silicon vias (TSVs) is one of the important ways to achieve higher integration density and continue Moore's Law. However, TSVs generate Joule heat and chip self-heating during power-on and operation, forming a complex electrothermal coupling effect. If this effect is not fully evaluated and controlled during the design phase, it will lead to reliability problems such as local heat accumulation, thermal expansion mismatch, and structural delamination, seriously affecting the performance and lifespan of three-dimensional integrated circuits.

[0003] To address the aforementioned electrothermal coupling effect, traditional methods primarily employ numerical simulation techniques such as finite element analysis. While the finite element method offers high computational accuracy, its modeling process relies on meticulous mesh generation. When dealing with the complex geometry and multi-scale features of through-silicon via (TSV) arrays, mesh generation becomes challenging and computationally expensive. Furthermore, each design change necessitates remodeling and resimulation, leading to low design iteration efficiency. In addition, while purely data-driven neural network modeling methods have improved computational speed in recent years, they are entirely dependent on simulation data and lack physical constraints, resulting in poor model interpretability, limited generalization ability, and difficulty in ensuring physical consistency of predictions at untrained design points.

[0004] Therefore, how to improve the efficiency and generalization ability of multiphysics coupling simulation of through-silicon vias (TSVs) while ensuring computational accuracy and physical consistency, so as to support the efficient and reliable thermal design of 3D integrated circuits, is a technical problem that urgently needs to be solved. Summary of the Invention

[0005] To address the challenge of improving the efficiency and generalization ability of TSV electrothermal multiphysics coupling simulation while maintaining computational accuracy and physical consistency, this invention provides a TSV electrothermal multiphysics coupling modeling method based on a physical information neural network. The technical problem solved by this invention is achieved through the following technical solution: This invention provides a TSV electrothermal multiphysics coupling modeling method based on a physical information neural network, comprising: Obtain finite element simulation datasets for multiple material sub-regions of through-silicon vias; A physical information neural network model for the design parameters of integrated through-silicon vias (TSVs) is constructed. The physical information neural network model includes an electric potential field physical information neural network model and a temperature field physical information neural network model. The electric potential field physical information neural network model and the temperature field physical information neural network model each include multiple electric potential field sub-network models and multiple temperature field sub-network models. Each material sub-region corresponds to one electric potential field sub-network model and one temperature field sub-network model, and physical continuity constraints are set between the sub-network models corresponding to adjacent material sub-regions. First, a potential field physical information neural network model is trained based on the finite element simulation dataset and the target loss function. Then, a temperature field physical information neural network model is trained based on the trained potential field physical information neural network model, the finite element simulation dataset, and the target loss function. The trained temperature field physical information neural network model is then used for forward inference to predict the electrothermal coupling temperature field of the target through-silicon via under different design parameters. The target loss function includes a physical loss function and a data loss function.

[0006] In one embodiment of the present invention, a finite element simulation dataset of multiple material sub-regions of a through-silicon via (TSV) is obtained, including: Define the design parameters of through silicon vias as design variables, and determine the range of values ​​for the design variables to form the design space; Within the design space, multiple spatial coordinates are obtained using a preset sampling method; For each spatial coordinate, a corresponding parametric finite element model is established and simulation calculations are performed to obtain a finite element simulation dataset that includes each spatial coordinate and its corresponding physical field values.

[0007] In one embodiment of the present invention, a physical continuity constraint is used to constrain the physical field predicted by the corresponding sub-network model to satisfy the continuity condition at the interface of adjacent material sub-regions; the physical field includes electric potential and temperature, and the flux field corresponding to the electric potential and temperature includes current density and heat flux density.

[0008] In one embodiment of the present invention, the physical loss function includes physical equation residuals and boundary condition residuals. The physical equation residuals are used to constrain the control equations that satisfy electrothermal coupling within each material sub-region, and the boundary condition residuals are used to constrain the geometric boundaries of each material sub-region to satisfy preset electrical and thermal boundary conditions.

[0009] In one embodiment of the present invention, the governing equations for electrothermal coupling include: the Laplace equation for describing the potential distribution, and the Poisson equation for describing the temperature distribution with Joule heat as the source term.

[0010] In one embodiment of the present invention, a data loss function is used to constrain the difference between the predicted value of the physical information neural network model at the spatial coordinates of the finite element simulation dataset and the true value in the finite element simulation dataset.

[0011] In one embodiment of the present invention, a temperature field physical information neural network model is trained based on a pre-trained potential field physical information neural network model, a finite element simulation dataset, and a target loss function, including: The Joule heat distribution is calculated based on the potential distribution output by the trained neural network model of electric potential field physical information. By incorporating the Joule heat distribution as a heat source term into the target loss function, the updated target loss function is obtained. Based on the updated target loss function and the finite element simulation dataset, the temperature field physical information neural network model is trained iteratively. When the loss value of the updated target loss function is less than the loss threshold or the number of iterations reaches the preset number, the training stops, and the trained temperature field physical information neural network model is obtained.

[0012] In one embodiment of the present invention, the plurality of material sub-regions include a metal conductor region, an insulating layer region, and a silicon substrate region.

[0013] In one embodiment of the present invention, the design parameters include the insulation layer thickness, the conductor layer radius, and the through-silicon via spacing.

[0014] Another aspect of the present invention provides a storage medium storing a computer program for executing the steps of the TSV electrothermal multiphysics coupling modeling method based on physical information neural network described in any of the above embodiments.

[0015] Compared with the prior art, the beneficial effects of the present invention are as follows: (1) This invention provides a TSV electrothermal multiphysics coupling modeling method based on physical information neural network. By acquiring the finite element simulation dataset of multiple material sub-regions of through silicon via, and first training the electric potential field physical information neural network model based on the finite element simulation dataset and the target loss function, and then training the temperature field physical information neural network model based on the trained electric potential field physical information neural network model, the finite element simulation dataset and the target loss function. After training, the trained temperature field physical information neural network model can perform millisecond-level forward inference prediction for any new design parameters (including spatial coordinates that do not appear in the finite element simulation dataset). This realizes the transformation from "simulation one by one" to "train once and predict multiple times", shortening the simulation time of traditional methods from several hours or even several days to seconds, making large-scale, high-efficiency design space exploration and parameter optimization possible, while the prediction results maintain a level comparable to high-precision finite element solutions.

[0016] (2) This invention embeds governing equations (i.e., Laplace's equation and Poisson's equation), boundary conditions, and material interface continuity conditions as physical constraints into the target loss function. This hybrid driving mechanism ensures that while the neural network model learns the data patterns, its output strictly follows basic physical laws. Therefore, it can guarantee that the prediction results of the trained temperature field physical information neural network model have good physical interpretability and consistency. Even in regions where training data is sparse, its extrapolation predictions are more reliable, effectively avoiding the physically unreasonable predictions that may occur in purely data-driven models, and improving the output accuracy of the temperature field physical information neural network model.

[0017] (3) This invention adopts a decompositional neural network architecture based on material sub-regions. That is, each material sub-region is configured with an independent sub-network model for modeling, and physical continuity constraints are set between the sub-network models corresponding to adjacent material sub-regions. This design enables the sub-network model to accurately capture and characterize the complex coupling behavior at the material interface, solving the pain point that a single global neural network is difficult to converge or has insufficient accuracy, thereby significantly improving the modeling accuracy and convergence stability of multi-physics coupling problems, especially those involving strong heterogeneous material interfaces.

[0018] (4) The “domain decomposition + physical continuity constraint + two-stage training” framework proposed in this invention is not only applicable to the electrothermal coupling problem of TSV, but its design framework can be extended to other engineering simulation fields involving complex geometry, multiple materials, and multiple physical field coupling (such as microelectromechanical systems, packaging structures, composite materials, etc.). This framework provides a novel and effective technical path for achieving fast, accurate, and physically reliable digital simulation, and has broad engineering application prospects and important theoretical value.

[0019] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0020] Figure 1 This is a schematic diagram of a TSV structure provided in an embodiment of the present invention; Figure 2 This is a flowchart of a TSV electrothermal multiphysics coupling modeling method based on a physical information neural network provided in an embodiment of the present invention; Figure 3 This is a schematic diagram of a design space provided by an embodiment of the present invention; Figure 4 This is a schematic diagram of the boundary conditions of a TSV electrothermal coupling model provided in an embodiment of the present invention; Figure 5 This is a schematic diagram of finite element analysis solution and dataset splitting provided by an embodiment of the present invention; Figure 6 This is a schematic diagram of a physical information neural network architecture with integrated design parameters provided in an embodiment of the present invention. Detailed Implementation

[0021] To further illustrate the technical means and effects adopted by the present invention to achieve the intended purpose, the following describes in detail a TSV electrothermal multiphysics coupling modeling method based on a physical information neural network proposed in accordance with the present invention, in conjunction with the accompanying drawings and specific embodiments.

[0022] The foregoing and other technical contents, features, and effects of the present invention will be clearly presented in the following detailed description of specific embodiments in conjunction with the accompanying drawings. Through the description of the specific embodiments, a more in-depth and concrete understanding can be gained of the technical means and effects adopted by the present invention to achieve its intended purpose. However, the accompanying drawings are for reference and illustration only and are not intended to limit the technical solutions of the present invention.

[0023] It should be noted that, in this document, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations are intended to cover non-exclusive inclusion, such that an article or apparatus comprising a list of elements includes not only those elements but also other elements not expressly listed. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the article or apparatus that includes said element.

[0024] This invention addresses the problem of improving the efficiency and generalization ability of TSV electrothermal multiphysics coupling simulation while ensuring computational accuracy and physical consistency. It proposes a TSV electrothermal multiphysics coupling modeling method based on a physical information neural network. Before introducing this method, a schematic diagram of a cylindrical TSV structure is first presented; see [link to diagram]. Figure 1 ,like Figure 1 As shown, the TSV includes a silicon substrate from the inside out ( 101. Insulation layer ( )102 and the metal conductor layer ( 103. The thickness of the insulating layer 102 is expressed as... The TSV spacing is expressed as The radius of the metal conductor layer 103 is expressed as The height of TSV is represented as .

[0025] The following section introduces the TSV electrothermal multiphysics coupling modeling method based on a physical information neural network provided in this invention. Please refer to [link to relevant documentation]. Figure 2 ,like Figure 2 As shown, the method includes the following steps: Step (1): Obtain the finite element simulation dataset of multiple material sub-regions of the through silicon via.

[0026] The finite element simulation dataset includes multiple spatial coordinate points and the corresponding physical field values ​​for those spatial coordinate points.

[0027] It is understood that, in the embodiments of the present invention, the multiple material sub-regions include a metal conductor region, an insulating layer region, and a silicon substrate region.

[0028] In an embodiment of the invention, the specific implementation method for obtaining a finite element simulation dataset of multiple material sub-regions of a TSV includes: defining the design parameters of the TSV as design variables, determining the range of values ​​of the design variables to form a design space, then obtaining multiple spatial coordinates within the design space using a preset sampling method, and finally establishing a corresponding parameterized finite element model for each spatial coordinate and performing simulation calculations, thereby obtaining a finite element simulation dataset including each spatial coordinate and its corresponding physical field value.

[0029] It should be noted that in 3D integrated packaging, multiple TSVs are generally arranged in an array. This embodiment of the invention takes a single TSV as an example for analysis. When analyzing a single TSV, the side of the TSV model is assumed to be periodically symmetrical. Since the potential and temperature gradient at the interface of adjacent units at the symmetry plane are zero under the assumption of periodic symmetry, it is equivalent to electrical and thermal insulation boundary conditions. That is, the perimeter of the TSV model can be regarded as electrical and thermal insulation boundary conditions. At the same time, it is assumed that the manufacturing of the TSV is in an ideal state, that is, the metal filling is seamless and the materials are fully bonded together.

[0030] The parameters of the TSV array are shown in Table 1 below.

[0031] Table 1

[0032] Specifically, in the embodiments of the present invention, the present invention will... thickness , radius and TSV spacing As design variables, their values ​​range from [0.1,1], [1,5], to [15,40]um, respectively. Therefore, the design vector can be represented as: ,in, For design space, further, design space The expression is as follows:

[0033] Furthermore, to achieve a good design space filling effect using as few spatial coordinates as possible, this embodiment of the invention is based on the Latin Hypercube Sampling (LHS) method, which ensures that spatial coordinates are evenly distributed in the design space. For example, such as... Figure 3 As shown, N (e.g., N=27) spatial coordinates were collected from the design space. After collecting 27 spatial coordinates, the selected design parameters were used as parametric variables in the finite element model to facilitate simulations for different spatial coordinates. Subsequently, the geometric model of the TSV was constructed based on these parametric variables, and then... , and The three geometric regions were assigned corresponding electrical and thermal conductivity material properties, meshed, and finally boundary conditions were applied to obtain the parametric finite element model. For details on setting the boundary conditions, please refer to [link to relevant documentation]. Figure 4 ,like Figure 4 As shown, an excitation voltage of 0.03V is applied to the upper surface of the TSV, while the lower surface is grounded; that is, a voltage E=0.03V is applied across the TSV to simulate Joule heating. For heat transfer, the lower surface of the TSV is kept at a constant temperature. To simplify the geometric model, the TSV is set to be thermally insulated around its perimeter, and the heat flux density on the upper surface of the TSV is set to be [value missing]. The heat source is simulated to simulate chip heating. After obtaining the parameterized finite element model, the finite element method (FEM) can be used to simulate and solve only the 27 discrete spatial coordinates in the design space. This allows for the acquisition of a finite element simulation dataset including each spatial coordinate and its corresponding physical field value at a lower computational cost. This dataset is then used for data constraints in the subsequent training phase of the physical information neural network model. These data constraints enable the physical information neural network model to minimize the difference between the predicted values ​​at finite element nodes and the finite element method solution during training. To impose corresponding geometric region data constraints on the network model of each material sub-region, this embodiment of the invention splits the finite element simulation dataset obtained from the finite element simulation according to different material sub-regions. For details, please refer to... Figure 5 As shown.

[0034] Step (2): Construct a physical information neural network model for the design parameters of integrated through-silicon vias. The physical information neural network model includes a potential field physical information neural network model and a temperature field physical information neural network model. The potential field physical information neural network model and the temperature field physical information neural network model each include multiple potential field sub-network models and multiple temperature field sub-network models. Each material sub-region corresponds to one potential field sub-network model and one temperature field sub-network model, and physical continuity constraints are set between the sub-network models corresponding to adjacent material sub-regions.

[0035] The general expression for the physical information neural network model is:

[0036] in, It is a nonlinear partial differential operator. This represents the antiderivative of the physical information neural network model, i.e., the analytical solution of the partial differential equation (PDE). and These represent the spatial coordinates and design parameters within the material sub-region, respectively, when the computational domain is three-dimensional space. ,but .

[0037] The general expression for the boundary condition equations of the physical information neural network model is:

[0038] in, For constraint operators covering Dirichlet, Neumann, and Robin boundary conditions, Represents material sub-regions The boundary, For the boundary Spatial coordinates on.

[0039] It should be noted that the physical continuity constraint is used at the interface of adjacent material sub-regions to constrain the physical fields predicted by the corresponding sub-network model to satisfy the continuity condition. The physical fields include electric potential and temperature, and the flux fields corresponding to electric potential and temperature include current density and heat flux density.

[0040] Specifically, in any adjacent material sub-region (conductivity) thermal conductivity )and (conductivity) thermal conductivity ) interface Place, The electric potential field satisfies the following interface conditions: Electric potential continuity: ,in, and Representing material sub-regions respectively and material sub-region The internal electric potential.

[0041] Current density normal continuity: ,in, It is the unit normal vector, and its direction is from point to .

[0042] The temperature field satisfies the following interface conditions: Temperature continuity: ,in, and Representing material sub-regions respectively and material sub-region The internal temperature.

[0043] Heat flux density normal continuity: .

[0044] Furthermore, regarding the boundary conditions, an excitation voltage is set on the upper surface of the TSV according to step (1). The voltage is 0.03V, with the lower surface grounded. Set to 0. Heat flux density across the entire upper surface of the TSV. for The boundary condition equation for the heat flux density on the upper surface of its TSV is:

[0045] in, It is the unit normal vector outward from the boundary surface (i.e., the upper surface of the TSV). It is the thermal conductivity of solids. It is the temperature gradient inside the solid.

[0046] The boundary conditions around TSV are considered to be thermally and electrically insulating, and the expressions are as follows: and ,in, For thermal conductivity tensor, and These are the temperature gradient and the electric potential gradient, respectively. Let be the conductivity tensor.

[0047] It should be noted that, as can be seen from the continuity of the current density normal and the continuity of the heat flux density normal, due to the different physical properties of heterogeneous materials in the TSV array, abrupt changes in the gradient of physical quantities will occur at the interfaces of each material sub-region. Using a single physical information neural network model is difficult to converge. Therefore, to avoid this problem, this embodiment of the invention uses three sub-network models to fit the analytical solutions of the electric potential field and temperature field of each heterogeneous material sub-region, respectively, and uses the aforementioned interface conditions as constraints at the interfaces of each material sub-region to ensure physical continuity. It can be understood that this embodiment of the invention sets up two sets of physical information neural network models, each set including three sub-network models, for a total of six sub-network models. One set of physical information neural network models is the electric potential field physical information neural network model, including three electric potential field sub-network models, each used to predict the electric potential distribution of the corresponding material sub-region; the other set of physical information neural network models is the temperature field physical information neural network model, including three temperature field sub-network models, each used to predict the temperature distribution of the corresponding material sub-region. For each material sub-region, the interface condition can be considered as a special boundary condition. To reduce the number of weight hyperparameters, the loss function of the interface condition residual is also weighted with boundary condition weights. Weighting is applied.

[0048] Furthermore, such as Figure 6 As shown, in an embodiment of the invention, Subregion Subregions and The physical information network model of each sub-region includes an input layer, a hidden layer, and an output layer connected in sequence. Subregions and The sub-region's network model has 5 hidden layers, each containing 512 neurons. Because... Sub-regions are more complex and smaller in scale than other sub-regions, therefore, Figure 6 As shown, The network model for each sub-region has six hidden layers, each containing 512 neurons. The activation function for the physical information network model of each sub-region is a non-linear tanh function, expressed as follows: .

[0049] It should be noted that, by Figure 1 It can be seen that there are two types of interface conditions in this embodiment of the invention, namely: Subregion and Subregion Subregion and Sub-regions. Within each sub-region, the Laplace and Poisson equations are applied as domain constraints. At each interface, the aforementioned potential continuity condition, current density normal continuity condition, temperature continuity condition, and heat flux density normal continuity condition are applied as interface constraints. Simultaneously, the aforementioned temperature and potential boundary conditions are applied at the boundaries of adjacent sub-regions. Due to the similarity of the equations, the physical information neural network model architecture for solving the potential field and the temperature field is completely consistent. Specifically, when solving the potential field, the physical information neural network model outputs the predicted electric distribution, the physical equation residual term in the physical loss function is equal to 0, and the thermal conductivity in the interface constraints... Replace with conductivity When solving for the temperature field, the temperature field physical information neural network model outputs the predicted temperature distribution, and the residual terms of the physical equations are calculated from the output of the potential field physical information neural network model.

[0050] Step (3): First, based on the finite element simulation dataset and the target loss function, train the electric potential field physical information neural network model. Then, based on the trained electric potential field physical information neural network model, the finite element simulation dataset, and the target loss function, train the temperature field physical information neural network model. Use the trained temperature field physical information neural network model for forward inference to predict the electrothermal coupling temperature field of the target through silicon via under different design parameters. The target loss function includes the physical loss function and the data loss function.

[0051] The physical loss function includes physical equation residuals and boundary condition residuals. The physical equation residuals are used to constrain the control equations that satisfy electrothermal coupling in each material sub-region. The boundary condition residuals are used to constrain the geometric boundaries of each material sub-region to satisfy preset electrical and thermal boundary conditions.

[0052] Specifically, the expression for the residual term in the physical equation is:

[0053] in, For the spatial coordinates within each computational domain, To calculate the number of spatial coordinates within the domain, The model parameters for a neural network include weights and biases. , This refers to the predicted spatial coordinates within the computational domain output by the physical information neural network model. It is an L2 norm.

[0054] The expression for the boundary condition residual term is:

[0055] in, Spatial coordinates on the boundary The number of spatial coordinates on the boundary. For boundary condition operators, These are the predicted spatial coordinates on the boundary output by the physical information neural network model.

[0056] Furthermore, the governing equations for electrothermal coupling include: the Laplace equation for describing the potential distribution, and the Poisson equation for describing the temperature distribution with Joule heat as the source term.

[0057] As can be seen from the above embodiments, the TSV array comprises three different materials, namely , as well as Therefore, each material sub-region has its own electrical conductivity and thermal conductivity, that is: , , , , , The potential distribution and steady-state temperature field of the TSV array electrothermal coupling satisfy the Laplace equation and the Poisson equation in each material sub-region, respectively.

[0058] Specifically, the expression for the Laplace equation is:

[0059] in, For the Laplace operator, , These represent the electric potential and temperature of each material sub-region, respectively. This represents the sub-regions corresponding to the three materials.

[0060] The expression for the Poisson equation is:

[0061] in, This represents the thermal conductivity of each material sub-region. Indicates temperature The Laplace operator, This represents the Joule heat generated by the current in each material sub-region.

[0062] Furthermore, the Joule heating generated by the current in each material sub-region The calculation formula is:

[0063] in, The conductivity corresponding to each material sub-region is given. It is the current density vector. The electric field intensity vector, The potential gradient is denoted as .

[0064] In this embodiment of the invention, a data loss function is used to constrain the difference between the predicted value of the physical information neural network model at the spatial coordinates of the finite element simulation dataset and the true value in the finite element simulation dataset.

[0065] Specifically, the expression for the data loss function is:

[0066] in, Spatial coordinates in the finite element simulation dataset, The number of spatial coordinates in the finite element simulation dataset. The predicted values ​​of spatial coordinates in the finite element simulation dataset output by the physical information neural network model. These are the actual values ​​in the finite element simulation dataset.

[0067] Finally, to measure the difference between the physical information neural network model and the constraints, the objective loss function of the physical information neural network can be defined as a weighted sum of the sum of the physical equation residuals, the boundary condition residuals, and the squared L2 norms of the data residuals. That is, the expression for the objective loss function is:

[0068] Furthermore, it can be seen that, ,in, These are the optimal model parameters for the neural network. To make the target loss function Take the minimum value.

[0069] In embodiments of the invention, the parameters of a neural network model for the physical information of the electric potential field are trained based on a finite element simulation dataset and a target loss function, and by using a gradient-based optimizer (such as SGD, Adam, and L-BFGS) to minimize the target loss function. During the training process, automatic differentiation technology can be used to iteratively calculate the gradient information of the potential field physical information neural network model with respect to the input data. When the potential field physical information neural network model converges to an acceptable level of accuracy, the linear training can be stopped, and the trained potential field physical information neural network model can be obtained. That is, when the loss value of the target loss function is less than the loss threshold or the number of iterations reaches the preset number (such as 5000 times), the training is stopped, and the trained temperature field physical information neural network model is obtained.

[0070] Furthermore, after obtaining the trained temperature field physical information neural network model, the Joule heat distribution is calculated based on the potential distribution output by the trained potential field physical information neural network model. Then, the Joule heat distribution is introduced as a heat source term into the residual term of the physical equation of the target loss function to obtain the updated target loss function. Finally, based on the updated target loss function and the finite element simulation dataset, the weights and biases of the temperature field physical information neural network model are trained by minimizing the updated target loss function using a gradient-based optimizer. Similarly, during the training process, automatic differentiation technology can be used to iteratively calculate the gradient information of the temperature field physical information neural network model with respect to the input data. When the loss value of the updated target loss function is less than the loss threshold or the number of iterations reaches the preset number, training is stopped, and the trained temperature field physical information neural network model is obtained. The trained temperature field physical information neural network model is then used for forward inference to predict the electrothermal coupling temperature field of the target through-silicon via under different design parameters.

[0071] It should be noted that since the Joule heat distribution is already coupled into the trained temperature field physical information neural network model, when predicting the temperature field of the target through-silicon via, the design parameters of the target through-silicon via and the target spatial coordinates can be concatenated and input into the trained temperature field physical information neural network model for forward inference, so as to obtain the predicted temperature value of the target through-silicon via at the target spatial coordinates output by the model.

[0072] Specifically, the mathematical expression for forward reasoning is:

[0073] in, Indicates the first Layer The output value of each neuron This indicates the layer number of the neural network model. Represents the neuron index. and They represent the first The first in the layer The first neuron to the second The first in the layer The weights and biases of each neuron, Indicates the first Layer The output value of each neuron This represents the activation function (i.e., the tanh function).

[0074] In summary, the beneficial effects of the present invention are as follows: (1) This invention provides a TSV electrothermal multiphysics coupling modeling method based on physical information neural network. By acquiring the finite element simulation dataset of multiple material sub-regions of through silicon via, and first training the electric potential field physical information neural network model based on the finite element simulation dataset and the target loss function, and then training the temperature field physical information neural network model based on the trained electric potential field physical information neural network model, the finite element simulation dataset and the target loss function. After training, the trained temperature field physical information neural network model can perform millisecond-level forward inference prediction for any new design parameters (including spatial coordinates that do not appear in the finite element simulation dataset). This realizes the transformation from "simulation one by one" to "train once and predict multiple times", shortening the simulation time of traditional methods from several hours or even several days to seconds, making large-scale, high-efficiency design space exploration and parameter optimization possible, while the prediction results maintain a level comparable to high-precision finite element solutions.

[0075] (2) This invention embeds governing equations (i.e., Laplace's equation and Poisson's equation), boundary conditions, and material interface continuity conditions as physical constraints into the target loss function. This hybrid driving mechanism ensures that while the neural network model learns the data patterns, its output strictly follows basic physical laws. Therefore, it can guarantee that the prediction results of the trained temperature field physical information neural network model have good physical interpretability and consistency. Even in regions where training data is sparse, its extrapolation predictions are more reliable, effectively avoiding the physically unreasonable predictions that may occur in purely data-driven models, and improving the output accuracy of the temperature field physical information neural network model.

[0076] (3) This invention adopts a decompositional neural network architecture based on material sub-regions. That is, each material sub-region is configured with an independent sub-network model for modeling, and physical continuity constraints are set between the sub-network models corresponding to adjacent material sub-regions. This design enables the sub-network model to accurately capture and characterize the complex coupling behavior at the material interface, solving the pain point that a single global neural network is difficult to converge or has insufficient accuracy, thereby significantly improving the modeling accuracy and convergence stability of multi-physics coupling problems, especially those involving strong heterogeneous material interfaces.

[0077] (4) The “domain decomposition + physical continuity constraint + two-stage training” framework proposed in this invention is not only applicable to the electrothermal coupling problem of TSV, but its design framework can be extended to other engineering simulation fields involving complex geometry, multiple materials, and multiple physical field coupling (such as microelectromechanical systems, packaging structures, composite materials, etc.). This framework provides a novel and effective technical path for achieving fast, accurate, and physically reliable digital simulation, and has broad engineering application prospects and important theoretical value.

[0078] In the several embodiments provided by this invention, it should be understood that the apparatus and methods disclosed in this invention can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative. For example, the division of modules is merely a logical functional division, and in actual implementation, there may be other division methods. For example, multiple modules or components may be combined or integrated into another system, or some features may be ignored or not executed.

[0079] Furthermore, the functional modules in the various embodiments of the present invention can be integrated into one processing module, or each module can exist physically separately, or two or more modules can be integrated into one module. The integrated module can be implemented in hardware or in the form of hardware plus software functional modules.

[0080] Another embodiment of the present invention provides a storage medium storing a computer program for executing the steps of the TSV electrothermal multiphysics coupling modeling method based on physical information neural network described in the above embodiments.

[0081] Another aspect of the present invention provides an electronic device, including a memory and a processor. The memory stores a computer program, and when the processor invokes the computer program in the memory, it implements the steps of the TSV electrothermal multiphysics coupling modeling method based on physical information neural networks as described in the above embodiments. Specifically, the integrated modules implemented in the form of software functional modules can be stored in a computer-readable storage medium. The software functional modules stored in the storage medium include several instructions to cause an electronic device (which may be a personal computer, server, or network device, etc.) or processor to execute some steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0082] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A TSV electrothermal multiphysics coupling modeling method based on physical information neural network, characterized in that, include: Obtain finite element simulation datasets for multiple material sub-regions of through-silicon vias; A physical information neural network model integrating the design parameters of the through-silicon via (TSV) is constructed. The physical information neural network model includes an electric potential field physical information neural network model and a temperature field physical information neural network model. The electric potential field physical information neural network model and the temperature field physical information neural network model each include multiple electric potential field sub-network models and multiple temperature field sub-network models. Each material sub-region corresponds to one electric potential field sub-network model and one temperature field sub-network model, and physical continuity constraints are set between the sub-network models corresponding to adjacent material sub-regions. First, based on the finite element simulation dataset and the target loss function, the potential field physical information neural network model is trained. Then, based on the trained potential field physical information neural network model, the finite element simulation dataset, and the target loss function, the temperature field physical information neural network model is trained. The trained temperature field physical information neural network model is then used for forward inference to predict the electrothermal coupling temperature field of the target through-silicon via under different design parameters. The target loss function includes a physical loss function and a data loss function.

2. The TSV electrothermal multiphysics coupling modeling method based on physical information neural network according to claim 1, characterized in that, The finite element simulation dataset for obtaining multiple material sub-regions of through-silicon vias includes: The design parameters of the through silicon via are defined as design variables, and the range of values ​​for the design variables is determined to form a design space. Within the design space, multiple spatial coordinates are obtained using a preset sampling method; For each of the spatial coordinates, a corresponding parametric finite element model is established and simulation calculations are performed to obtain the finite element simulation dataset including each spatial coordinate and its corresponding physical field values.

3. The TSV electrothermal multiphysics coupling modeling method based on physical information neural network according to claim 1, characterized in that, The physical continuity constraint is used to constrain the physical field predicted by the corresponding sub-network model to satisfy the continuity condition at the interface of adjacent material sub-regions; the physical field includes electric potential and temperature, and the flux field corresponding to the electric potential and the temperature includes current density and heat flux density.

4. The TSV electrothermal multiphysics coupling modeling method based on physical information neural network according to claim 1, characterized in that, The physical loss function includes physical equation residuals and boundary condition residuals. The physical equation residuals are used to constrain the control equations that satisfy electrothermal coupling within each material sub-region. The boundary condition residuals are used to constrain the geometric boundaries of each material sub-region to satisfy preset electrical and thermal boundary conditions.

5. The TSV electrothermal multiphysics coupling modeling method based on physical information neural network according to claim 4, characterized in that, The governing equations for the electrothermal coupling include: the Laplace equation for describing the potential distribution, and the Poisson equation for describing the temperature distribution with Joule heat as the source term.

6. The TSV electrothermal multiphysics coupling modeling method based on physical information neural network according to claim 2, characterized in that, The data loss function is used to constrain the difference between the predicted value of the physical information neural network model at the spatial coordinates of the finite element simulation dataset and the true value in the finite element simulation dataset.

7. The TSV electrothermal multiphysics coupling modeling method based on physical information neural network according to claim 1, characterized in that, The training of the temperature field physical information neural network model based on the trained electric potential field physical information neural network model, the finite element simulation dataset, and the target loss function includes: The Joule heat distribution is calculated based on the potential distribution output by the trained potential field physical information neural network model. The Joule heat distribution is introduced as a heat source term into the target loss function to obtain the updated target loss function; Based on the updated target loss function and the finite element simulation dataset, the temperature field physical information neural network model is iteratively trained. When the loss value of the updated target loss function is less than the loss threshold or the number of iterations reaches the preset number, training is stopped, and the trained temperature field physical information neural network model is obtained.

8. The TSV electrothermal multiphysics coupling modeling method based on physical information neural network according to claim 1, characterized in that, The multiple material sub-regions include a metal conductor region, an insulating layer region, and a silicon substrate region.

9. The TSV electrothermal multiphysics coupling modeling method based on physical information neural network according to claim 1, characterized in that, The design parameters include the insulation layer thickness, conductor layer radius, and through-silicon via spacing.

10. A storage medium storing a computer program, characterized in that, The computer program is used to execute the steps of the TSV electrothermal multiphysics coupling modeling method based on physical information neural network as described in any one of claims 1 to 9.

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