TSV thermal modeling method based on physical information neural network

Abstract

The invention belongs to the technical field of three-dimensional integrated circuit thermal management. The invention provides a TSV thermal modeling method based on a physical information neural network. According to the embodiment of the invention, the PINN model is constructed, and the multi-stage training strategy and the systematized sensitivity analysis experiment are combined, so that high-precision and high-efficiency prediction of the TSV temperature field is realized. According to the method, the precision better than that of a traditional machine learning method can be achieved only through a small amount of training data, the extrapolation capability is excellent, the prediction result strictly follows the physical law, a novel technical means is provided for thermal reliability design of a three-dimensional integrated circuit, and the design efficiency and the model credibility are remarkably improved.

Description

Technical Field

[0001] This disclosure relates to the field of three-dimensional integrated circuit thermal management technology, and in particular to a TSV thermal modeling method based on physical information neural networks. Background Technology

[0002] With the continuous improvement of chip integration density, TSV-based 3D integration technology has become a key technology for realizing vertical interconnection of chips and improving integration density and performance. However, TSV structures are prone to significant heat accumulation effects in the vertical direction. The temperature field directly affects the thermal stress distribution and signal transmission reliability of the chip, leading to failure risks such as interface delamination and electromigration. Currently, thermal analysis of TSVs mainly relies on finite element simulation methods, which, although highly accurate, have huge computational costs and are time-consuming, making it difficult to support the design requirements of rapid iteration. In addition, analytical methods based on equivalent thermal conductivity, while improving computational efficiency, rely on too many simplification assumptions and have limited ability to capture complex temperature field characteristics. Although the pure data-driven machine learning methods that have emerged in recent years have strong nonlinear fitting capabilities, their prediction results lack physical consistency constraints and have insufficient extrapolation capabilities.

[0003] Therefore, there is an urgent need to develop a thermal modeling method that combines high precision, high efficiency, and physical consistency to improve the thermal reliability of three-dimensional integrated circuits.

[0004] It should be noted that this section is intended to provide background or context for the technical solutions of this disclosure as set forth in the claims. The description herein does not constitute an admission that it is prior art simply because it is included in this section. Summary of the Invention

[0005] The purpose of this disclosure is to provide a TSV thermal modeling method based on a physical information neural network, thereby overcoming, to at least some extent, one or more problems caused by the limitations and defects of related technologies.

[0006] According to embodiments of this disclosure, a TSV thermal modeling method based on a physical information neural network is provided, including: Construct a PINN model that integrates the physical information of TSVs; Construct the total loss function; where the total loss function includes the physical loss function, the data loss function, and the boundary loss function; A two-stage training strategy combining global optimization using a genetic algorithm and gradient descent is employed to collaboratively optimize the network parameters of the PINN model, resulting in an optimized PINN model. Sensitivity analysis was performed on the optimized PINN model to determine the optimal configuration of the PINN model; Based on the optimally configured PINN model, high-precision prediction of the temperature field of TSV in three-dimensional integrated circuits is achieved.

[0007] Furthermore, the method also includes: Establish a three-dimensional finite element model of TSV and set the physical parameters of copper, silicon dioxide and silicon. The physical parameters of copper, silicon dioxide and silicon should include at least the thermal conductivity, density and specific heat capacity of each material. Boundary conditions are set; the top boundary is set to a fixed temperature constraint to simulate the chip's heating state; the bottom boundary is set to a fixed temperature constraint to simulate the heat dissipation substrate; and the side boundaries are set to thermal insulation conditions to eliminate external environmental interference. Steady-state heat conduction simulation was performed to obtain temperature field distribution data of the TSV structure over the entire domain. Uniform sampling is performed within the space of the TSV three-dimensional finite element model. Preset coordinate points and corresponding temperatures are selected as the training set, and coordinate points and corresponding temperatures different from those in the training set are selected as the test set.

[0008] Furthermore, the steps in constructing the total loss function include: The residuals are calculated based on the steady-state heat conduction equation without internal heat source in cylindrical coordinates. The residuals are normalized and the physical loss function is obtained by combining the number of sampling points with physical constraints. A data loss function is constructed based on the error between the model-predicted temperature and the simulated temperature data. A boundary loss function is constructed based on boundary condition constraints of the TSV structure; where... The physical loss function, data loss function, and boundary loss function are weighted and summed to obtain the total loss function.

[0009] Furthermore, the expression for the total loss function is:

[0010] in, The weights of the physical loss function, The weights of the data loss function, The weights of the boundary loss function; The expression for the physical loss function is:

[0011] in, N The number of sampling points is the physical constraint. For the first i The result of normalizing the residuals of each physical constraint sampling point; The data loss function is:

[0012] in, M The total number of data points. For the firstj The normalized result of the predicted temperature for each data point. For the first j Normalized results of simulated temperatures for each data point; The boundary loss function is defined as:

[0013] in, For the top boundary loss, For the bottom boundary loss, For the side boundary thermal insulation loss, For central axis symmetric loss, This is due to the loss of temperature continuity at the copper-oxide interface. This is due to the loss of temperature continuity at the oxide-silicon interface.

[0014] Furthermore, the top boundary loss is based on a fixed temperature constraint; the bottom boundary loss is based on a fixed temperature constraint; the side boundary loss is based on thermal insulation conditions; the central axis loss is based on symmetry boundary conditions; and the material interface temperature continuity loss ensures the continuous distribution of temperature at different material interfaces. The material interface temperature continuity loss includes the copper-oxide interface temperature continuity loss and the oxide-silicon interface temperature continuity loss.

[0015] Furthermore, a two-stage training strategy combining global optimization using a genetic algorithm and gradient descent is employed to collaboratively optimize the network parameters of the PINN model, resulting in the optimized PINN model. This process includes: A smooth transition function is used to address the abrupt change in thermal conductivity at the material interface, ensuring a continuous distribution of thermal conductivity at the interface of multilayer materials. Design a dynamic weight adjustment mechanism to automatically adjust the weight ratios of physical loss, data loss, and boundary loss according to the iteration progress during training; A genetic algorithm is used for global optimization, and the population size, crossover rate and mutation rate are set to select the globally optimal initial weight combination. The Adam optimizer is used for fine-tuning, and the initial learning rate is set, combined with learning rate scheduling and gradient pruning techniques. A learning rate scheduling strategy is introduced: when the loss function does not decrease within a preset number of iterations, the learning rate is halved to avoid skipping the optimal solution; Gradient clipping technique is used to restrict the gradient norm in order to obtain an optimized PINN model.

[0016] Furthermore, the step of performing sensitivity analysis on the optimized PINN model to determine the optimal configuration of the PINN model includes: Sensitivity analysis was performed on the configuration parameters of the optimized PINN model to analyze the impact of the number of hidden layers, number of neurons, input dimension, and training data quality on model performance. Determine the number of hidden layers, the number of neurons, the input dimension, and the quality of the training data to obtain the optimal configuration of the PINN model.

[0017] The technical solutions provided by the embodiments of this disclosure may include the following beneficial effects: In the embodiments of this disclosure, the TSV thermal modeling method based on the physical information neural network described above achieves high-precision and high-efficiency prediction of the TSV temperature field by constructing a PINN model and combining a multi-stage training strategy with systematic sensitivity analysis experiments. Furthermore, this method requires only a small amount of training data to achieve accuracy superior to traditional machine learning methods, and possesses excellent extrapolation capabilities. The prediction results strictly follow physical laws, providing a novel technical means for the thermal reliability design of three-dimensional integrated circuits, significantly improving design efficiency and model reliability. Attached Figure Description

[0018] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this disclosure and, together with the description, serve to explain the principles of this disclosure. It is obvious that the drawings described below are merely some embodiments of this disclosure, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort.

[0019] Figure 1 The diagram illustrates the steps of a TSV thermal modeling method based on a physical information neural network in an exemplary embodiment of this disclosure. Figure 2 A flowchart illustrating the TSV thermal modeling method based on a physical information neural network in an exemplary embodiment of this disclosure is shown. Figure 3 This diagram illustrates the TSV structure in an exemplary embodiment of the present disclosure. Figure 4 A framework diagram of the PINN model in an exemplary embodiment of this disclosure is shown; Figure 5 The diagram illustrates the training flowchart for the two stages of global optimization and gradient descent in the exemplary embodiments of the present disclosure. Detailed Implementation

[0020] Exemplary embodiments will now be described more fully with reference to the accompanying drawings. However, these exemplary embodiments can be implemented in many forms and should not be construed as limited to the examples set forth herein; rather, they are provided so that this disclosure will be more comprehensive and complete, and will fully convey the concept of the exemplary embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0021] Furthermore, the accompanying drawings are merely illustrative diagrams of embodiments of this disclosure and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and therefore repeated descriptions of them will be omitted. Some block diagrams shown in the drawings are functional entities and do not necessarily correspond to physically or logically independent entities.

[0022] This example implementation provides a TSV thermal modeling method based on a physical information neural network. (Reference) Figure 1 As shown, the TSV thermal modeling method based on physical information neural networks may include: Step S101: Construct a PINN model that integrates the physical information of TSVs; Step S102: Construct the total loss function; wherein, the total loss function includes the physical loss function, the data loss function, and the boundary loss function; Step S103: Using a two-stage training strategy of global optimization of genetic algorithm and gradient descent, the network parameters of PINN model are jointly optimized to obtain the optimized PINN model; Step S104: Perform sensitivity analysis on the optimized PINN model to determine the optimal configuration of the PINN model; Step S105: Based on the optimally configured PINN model, achieve high-precision prediction of the temperature field of the three-dimensional integrated circuit TSV.

[0023] The TSV thermal modeling method based on the aforementioned physical information neural network achieves high-precision and high-efficiency prediction of the TSV temperature field by constructing a PINN model and combining a multi-stage training strategy with systematic sensitivity analysis experiments. Furthermore, this method requires only a small amount of training data to achieve accuracy superior to traditional machine learning methods, and possesses excellent extrapolation capabilities. The prediction results strictly adhere to physical laws, providing a novel technical means for the thermal reliability design of 3D integrated circuits, significantly improving design efficiency and model reliability.

[0024] Below, we will refer to Figures 1 to 5 The steps of the TSV thermal modeling method based on physical information neural networks described in this example embodiment will be explained in more detail.

[0025] In steps S101 and S102, a PINN model incorporating the physical information of TSVs is constructed; a total loss function is constructed; wherein the total loss function includes a physical loss function, a data loss function, and a boundary loss function.

[0026] Specifically, in the TSV temperature field modeling of three-dimensional integrated circuits, the traditional finite element method, while highly accurate, suffers from enormous computational costs and time-consuming simulations. While purely data-driven machine learning methods improve computational efficiency, their predictions lack physical constraints and heavily rely on large amounts of training data. Based on this, this application proposes a neural network modeling method that integrates physical information, constructing the PINN model. This model integrates spatial coordinates (radial coordinates) in cylindrical coordinates. r Axial coordinates z ) and material thermal conductivity k As a network input, temperature T As output, by introducing the residuals of the heat conduction equation, data fitting errors, and boundary condition constraints into the loss function, the model's prediction results are ensured to strictly follow physical laws. Through this method, physical laws and data features can be jointly integrated into the neural network's learning process. Compared to traditional purely data-driven methods, this approach not only significantly reduces the training data requirements but also guarantees the physical rationality of the prediction results. The model exhibits excellent extrapolation capabilities, effectively improving its practical value in the thermal reliability design of three-dimensional integrated circuits.

[0027] In step S103, a two-stage training strategy of global optimization using a genetic algorithm and gradient descent is adopted to jointly optimize the network parameters of the PINN model to obtain the optimized PINN model.

[0028] Specifically, to address the challenges of training PINN and its tendency to get trapped in local optima, this application proposes a two-stage collaborative training strategy, as shown in the training flowchart below. Figure 2 As shown, the first stage employs a genetic algorithm for global optimization, searching for the optimal initial weights through a population evolution mechanism, providing a good starting point for subsequent fine-tuning. Reasonable population size, crossover rate, and mutation rate are set to ensure global search capability. The second stage uses the Adam optimizer for local fine-tuning, combining an adaptive learning rate mechanism and gradient pruning techniques to effectively avoid gradient explosion and local optima problems. A learning rate scheduling strategy is introduced, automatically reducing the learning rate when the loss function stabilizes, improving convergence accuracy. This training strategy ensures both the global convergence of the model and the final prediction accuracy.

[0029] In steps S104 and S105, sensitivity analysis is performed on the optimized PINN model to determine the optimal configuration of the PINN model; based on the optimal configuration of the PINN model, high-precision prediction of the temperature field of the three-dimensional integrated circuit TSV is achieved.

[0030] Specifically, in PINN modeling, model configuration parameters directly affect its prediction accuracy and computational efficiency. Traditional parameter determination methods often rely on empirical selection and lack systematic analysis, easily leading to poor model performance. To address this issue, this application established the optimal configuration scheme for the PINN model through systematic sensitivity analysis experiments. Specifically, firstly, the impact of the number of hidden layers on the model's expressive power was analyzed, and the performance differences of different hidden layer networks were compared; secondly, the impact of the number of neurons on feature extraction capability was evaluated, comparing three network configurations with different numbers of neurons; then, the impact of input dimension on physical law learning was explored, comparing cases containing only spatial coordinates and cases containing both spatial coordinates and thermal conductivity; finally, the impact of training data quality on model accuracy was studied, examining performance under different grid partitioning levels. This optimized configuration significantly improves training efficiency and model stability while ensuring high prediction accuracy, providing a reliable modeling foundation for thermal management of 3D integrated circuits.

[0031] In a specific embodiment, such as Figure 1 As shown, this application provides a TSV thermal modeling method based on PINN, and the specific implementation steps are as follows: To verify the effectiveness of this method, a typical TSV structure in a three-dimensional integrated circuit was used as an example. Its structural schematic diagram and finite element model mesh are shown below. Figure 3 As shown in the figure, (a) is a schematic diagram of the TSV structure; (b) is the mesh generation diagram of the finite element model; (c) is the three-dimensional simulation result of the TSV finite element model; and (d) is the two-dimensional simulation result of the TSV finite element model. Finite element simulation and data acquisition were performed using COMSOL Multiphysics software. The TSV structure consists of three layers: a copper pillar at the center, an outer layer of silicon dioxide insulation, and an outermost layer of silicon dielectric. The radius of the copper pillar is... r 1=3μm, silicon dioxide layer thickness 0.1μm, silicon dielectric layer thickness 1μm, total TSV height h =30μm. In TSV thermal analysis, temperature field distribution is a core indicator for evaluating the effectiveness of thermal management. Accurately predicting the internal temperature distribution of the TSV is crucial for preventing thermal failure and ensuring the reliability of signal transmission.

[0032] For the heat conduction problem of TSV studied, the governing equations for heat conduction in cylindrical coordinates were first established. Under steady-state conditions and without internal heat sources, the heat conduction equations can be expressed as: (1) in, T Represents the temperature field distribution function. r Radial coordinates, z For axial coordinates, kThe thermal conductivity of the material. Boundary conditions are set as follows: fixed temperature at the top boundary. T top =333.15K, simulating chip heating; bottom boundary fixed temperature. T 0 = 293.15K, simulating a heat dissipation substrate; the side boundaries are thermally insulated. Based on the TSV structural characteristics, the constructed PINN model uses spatial coordinates ( r，z and material thermal conductivity k As input, temperature T As an output, the PINN model architecture diagram established in this application is as follows: Figure 4 As shown.

[0033] Analysis of the heat conduction equations reveals a complex nonlinear relationship between the TSV temperature field distribution and spatial coordinates and the material's thermal conductivity. However, traditional finite element methods are computationally expensive and time-consuming for single simulations; while purely data-driven machine learning methods lack physical constraints and have poor extrapolation capabilities. Therefore, it is necessary to use the PINN method proposed in this application to effectively describe the TSV temperature field distribution.

[0034] The loss function of the PINN model consists of three parts: the physical loss function, the data loss function, and the boundary loss function.

[0035] (1) Physical loss function The residual of the partial differential equation is: (2) in, ε =10 -12 This is a minimum value, used to avoid... r The division error when the result is equal to 0. To balance the influence of dimensions, the residuals are normalized. (3) in, r 0= r 3 represents the characteristic length. T scale Characteristic temperature difference, k 0= k silicon Characteristic thermal conductivity.

[0036] The final physical loss function is defined as follows: (4) in, N This represents the number of sampling points for physical constraints.

[0037] However, due to the multilayered material in TSV, the thermal conductivity is discontinuous. Therefore, a continuous thermal conductivity function should be constructed to calculate the physical losses, which can be expressed as: (5) in, r Radial coordinates, c For the transitional central position, w This is the width of the transition zone. x=c The width of the surrounding area is w Within the given interval, the transition function smoothly transitions from 0 to 1, effectively avoiding the problem of abrupt derivative changes. Therefore, the copper-silicon dioxide interface (…) is defined. c=r 1) Transition function and silicon dioxide-silicon interface ( c=r 2) Transition function: (6) (7) in, δ =0.005μm. A continuous distribution of thermal conductivity across different material regions is achieved through weighted averaging, mathematically expressed as: (8) in, k Cu , and k Si These are the thermal conductivity coefficients of copper, silicon dioxide, and silicon, respectively.

[0038] (2) Data loss function The data loss function is used to constrain the consistency between the model's predictions and the simulation data. The normalization of the model's predicted temperature and the simulation temperature is shown below: (9) (10) in, T pred The temperature predicted by the PINN model. T data For the temperature of the simulation data, T 0 represents the bottom boundary temperature of the model.

[0039] The final data loss function is defined as follows: (11) in, M This represents the total number of data points in the training set.

[0040] (3) Boundary loss function Boundary loss functions are used to constrain the model to satisfy all boundary conditions. The top and bottom boundary losses are defined as follows: (12) (13) in, N top This represents the number of sampling points at the top boundary. T top The temperature at the top boundary of the model. N bottom This represents the number of sampling points at the bottom boundary. T 0 represents the bottom boundary temperature of the model. The side boundaries are thermally insulating, with an ideal temperature gradient of 0. The side boundary loss is defined as: (14) in, N side The number of sampling points at the side boundary. r 0= r 3. Due to the model's axisymmetry, with the central axis as the boundary of symmetry, the ideal temperature gradient is 0. The central axis loss is defined as: (15) in, N center This represents the number of sampling points along the central axis. In addition, to conform to physical laws, temperature continuity needs to be ensured at different material interfaces. The temperature continuity losses at the copper-oxide interface and the oxide-silicon interface are defined as follows: (16) (17) in, N int1 and N int2 These represent the number of sampling points at the copper-oxide interface and the oxide-silicon interface, respectively. T left and T right These are the predicted temperatures on the left and right sides of the interface, respectively.

[0041] Based on the above analysis, the boundary loss function can be defined as: (18) The three loss functions constrain the model from three dimensions: physical laws, data fitting, and boundary constraints. The final total loss is the weighted sum of the three: (19) in, , and These are the weights for the physical loss function, data loss function, and boundary loss function, respectively, and they are dynamically adjusted during training according to the following formula: (20) in, It represents the weight at the current progress level. and These are the initial and final weights. t is the current training iteration number. It represents the total number of training iterations. , and The initial and final weights are set as follows: =1, =5, =10, =5, =1, = 10. In the early stages of training, It is the largest, to quickly fit the actual temperature. and Gradually strengthen the model to conform to physical laws and actual structures. In the early stages of training, prioritize fitting data to form a basic structure, and in the later stages, gradually strengthen the physical laws and boundary conditions, balancing the optimization focus at different stages to improve the final accuracy.

[0042] Training data for the TSV temperature field were obtained through COMSOL simulation. Forty-three data points were uniformly selected as the training set and 34 data points as the test set within the TSV finite element model space. A two-stage training strategy was employed, and the training flowchart is shown below. Figure 5 As shown, a genetic algorithm is first used for global optimization, with a population size of 15, 3 elite individuals retained, a crossover rate of 85%, a mutation rate of 15%, and 32 generations. Then, the Adam optimizer is used for fine-tuning, with an initial learning rate of 0.0001 and a maximum number of iterations of 2000. Learning rate scheduling and gradient pruning techniques are combined to ensure training stability.

[0043] To evaluate the performance of the constructed PINN model, the coefficient of determination R², root mean square error (RMSE), and mean absolute error (MAE) were used as evaluation metrics: (twenty one) (twenty two) (twenty three) in, n It represents the total number of test samples. y i These are simulated values. It is the average value of the simulation values. These are the predictions from the PINN model.

[0044] The selection of structural parameters and training data quality for the PINN model has a decisive impact on prediction accuracy and computational efficiency. This application conducted systematic sensitivity analysis experiments and ultimately determined the optimal configuration for PINN: four hidden layers, 32 neurons per layer, with input dimensions including three-dimensional features of spatial coordinates and thermal conductivity, and training data based on "Finer" level mesh generation in COMSOL software. This optimized configuration provides a reliable modeling foundation for three-dimensional integrated circuit thermal management, significantly enhancing the model's engineering practical value.

[0045] The constructed model performs well in R tests on the test set. 2 The accuracy reached 99.92%, with an RMSE of 0.2917 and a MAE of 0.2235, demonstrating the effectiveness of the proposed method. Compared with traditional machine learning methods, this application shows significant advantages in several key performance indicators. Table 1 shows the comparative experimental results, detailing a systematic comparison of the proposed method with Support Vector Machine (SVM), Artificial Neural Network (ANN), Deep Neural Network (DNN), Convolutional Neural Network (CNN), and Residual Network (ResNet) in terms of prediction accuracy, data utilization efficiency, and computational performance. Regarding prediction accuracy, the R... 2 The accuracy rate reached 99.92%, significantly higher than other machine learning methods, demonstrating its accuracy in temperature field prediction.

[0046] In terms of data utilization efficiency, this application only requires 43 sets of training data to achieve optimal performance. The PINN model has the least data requirement, which is of great significance in practical engineering applications, especially in scenarios where data acquisition costs are high.

[0047] In terms of computational efficiency, the PINN model established in this application requires only 10 microseconds for a single prediction, which is nearly 6000 times faster than finite element simulation. Although the training time is slightly longer than SVM and ANN, it is significantly shorter than CNN and ResNet, achieving an optimal balance between accuracy and efficiency.

[0048] Table 1 Comparative Experimental Results

[0049] Furthermore, the method presented in this application possesses physical consistency and excellent extrapolation capabilities, ensuring that the prediction results strictly adhere to the physical laws of heat conduction—a feature not found in purely data-driven methods. In summary, this application, through the deep integration of physical information and data-driven approaches, achieves a significant improvement in accuracy and extrapolation performance while maintaining high computational efficiency, providing strong technical support for the thermal reliability design of three-dimensional integrated circuits.

[0050] The TSV thermal modeling method based on the aforementioned physical information neural network achieves high-precision and high-efficiency prediction of the TSV temperature field by constructing a PINN model and combining a multi-stage training strategy with systematic sensitivity analysis experiments. Furthermore, this method requires only a small amount of training data to achieve accuracy superior to traditional machine learning methods, and possesses excellent extrapolation capabilities. The prediction results strictly adhere to physical laws, providing a novel technical means for the thermal reliability design of 3D integrated circuits, significantly improving design efficiency and model reliability.

[0051] It should be understood that the terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," and "counterclockwise" in the above description indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing the embodiments of this disclosure and simplifying the description, and are not intended to indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the embodiments of this disclosure.

[0052] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of embodiments of this disclosure, "a plurality of" means two or more, unless otherwise explicitly specified.

[0053] In the embodiments of this disclosure, unless otherwise expressly specified and limited, the terms "installation," "connection," "linking," "fixing," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components. Those skilled in the art can understand the specific meaning of the above terms in this disclosure according to the specific circumstances.

[0054] In embodiments of this disclosure, unless otherwise expressly specified and limited, "above" or "below" the second feature can include direct contact between the first and second features, or contact between the first and second features through another feature between them. Furthermore, "above," "over," and "on top" of the second feature includes the first feature being directly above or diagonally above the second feature, or simply indicates that the first feature is at a higher horizontal level than the second feature. "Below," "below," and "under" the second feature includes the first feature being directly below or diagonally below the second feature, or simply indicates that the first feature is at a lower horizontal level than the second feature.

[0055] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this disclosure. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. In addition, those skilled in the art can combine and integrate the different embodiments or examples described in this specification.

[0056] Other embodiments of this disclosure will readily occur to those skilled in the art upon consideration of the specification and practice of the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of this disclosure that follow the general principles of this disclosure and include common knowledge or customary techniques in the art not disclosed herein. The specification and examples are to be considered exemplary only, and the true scope and spirit of this disclosure are indicated by the appended claims.

Claims

1. A TSV thermal modeling method based on physical information neural network, characterized in that, The method comprises the following steps: constructing a PINN model fusing physical information of TSV; constructing a total loss function; wherein the total loss function comprises a physical loss function, a data loss function and a boundary loss function; adopting a two-stage training strategy of global optimization by genetic algorithm and gradient descent to collaboratively optimize network parameters of the PINN model, so as to obtain an optimized PINN model; performing sensitivity analysis on the optimized PINN model to determine an optimal configuration of the PINN model; based on the optimal configuration of the PINN model, realizing high-precision prediction of a TSV temperature field of a three-dimensional integrated circuit.

2. The method of claim 1, wherein, The method further comprises the following steps: establishing a TSV three-dimensional finite element model, and setting physical parameters of copper, silicon dioxide and silicon, wherein the physical parameters of copper, silicon dioxide and silicon at least include thermal conductivity, density and specific heat capacity of each material; setting boundary conditions; wherein a top boundary is set as a fixed temperature constraint to simulate a chip heating state; a bottom boundary is set as a fixed temperature constraint to simulate a heat dissipation base; and side boundaries are set as thermal insulation conditions to eliminate external environmental interference; performing steady-state heat conduction simulation to obtain temperature field distribution data of the TSV structure in the whole space; uniformly sampling in the space of the TSV three-dimensional finite element model, selecting preset coordinate points and corresponding temperatures as a training set, and selecting coordinate points and corresponding temperatures different from the training set as a test set.

3. The TSV thermal modeling method based on physical information neural network according to claim 2, wherein, In the step of constructing the total loss function, the following steps are included: calculating residual error based on a steady-state heat conduction equation without internal heat source in a cylindrical coordinate system, performing normalization processing on the residual error, and combining the physical constraint sampling point number to obtain the physical loss function; constructing the data loss function based on error between model predicted temperature and simulation data temperature; constructing the boundary loss function based on boundary condition constraints of the TSV structure; wherein, performing weighted sum on the physical loss function, the data loss function and the boundary loss function to obtain the total loss function.

4. The TSV thermal modeling method based on physical information neural network according to claim 3, wherein, The expression of the total loss function is as follows: wherein, is a weight for the physical loss function, is a weight for the data loss function, is a weight for the boundary loss function; The expression of the physical loss function is as follows: wherein, N is the number of physical constraint sampling points, is the result of the normalized residual of the i th physical constraint sampling point; The data loss function is as follows: wherein, M is the total number of data points, is the normalized result of the predicted temperature for the j th data point, is the normalized result of the simulated temperature for the j th data point; The boundary loss function is defined as follows: wherein, is a top boundary loss, is a bottom boundary loss, is a side boundary thermal insulation loss, is a center axis symmetry loss, is a copper-oxide layer interface temperature continuity loss, is an oxide layer-silicon interface temperature continuity loss.

5. The method of claim 4, wherein, the top boundary loss is based on the fixed temperature constraint; the bottom boundary loss is based on the fixed temperature constraint; the side boundary loss is based on the thermal insulation condition; the central axis loss is based on the symmetry boundary condition; and the material interface temperature continuity loss ensures continuous distribution of temperature at different material interfaces, and the material interface temperature continuity loss includes copper-oxide layer interface temperature continuity loss and oxide layer-silicon interface temperature continuity loss.

6. The method of claim 5, wherein, In the step of adopting the two-stage training strategy of global optimization by genetic algorithm and gradient descent to collaboratively optimize network parameters of the PINN model, so as to obtain the optimized PINN model, the following steps are included: adopting a smooth transition function to process the thermal conductivity mutation problem at the material interface, so as to ensure continuous distribution of the thermal conductivity at the material interface of multiple layers; designing a dynamic weight adjustment mechanism to automatically adjust weight proportions of the physical loss, the data loss and the boundary loss during the training process according to iteration progress; adopting the genetic algorithm to perform global optimization, and setting population size, crossover rate and mutation rate to screen out a globally optimal initial weight combination; adopting the Adam optimizer to perform fine tuning, and setting an initial learning rate, combining learning rate scheduling and gradient clipping technology; A learning rate scheduling strategy is introduced, and when the loss function does not decrease within a preset number of iterations, the learning rate is halved to avoid skipping the optimal solution. The gradient clipping technique is used to limit the gradient norm to obtain the optimized PINN model.

7. The method of claim 6, wherein, In the step of sensitivity analysis of the optimized PINN model to determine the optimal configuration of the PINN model, including: Sensitivity analysis of the configuration parameters of the optimized PINN model to analyze the influence of the number of hidden layers, the number of neurons, the input dimension and the quality of training data on the performance of the model; Determine the number of hidden layers, the number of neurons, the input dimension and the quality of training data to obtain the optimal configuration of the PINN model.

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