Intelligent equivalent modeling and simulation optimization method based on machine learning and multi-physics field coupling

Abstract

The invention discloses an intelligent equivalent modeling and simulation optimization method based on machine learning and multi-physics field coupling, and the method employs a 2.5 D chip stress simulation method combining a customized material with equivalent parameters output by a Python script, and can remarkably reduce the calculation time and memory resource consumption on the premise of guaranteeing high precision. Based on DNN trained by large-scale historical data, an equivalent model can be dynamically adjusted in the simulation process, and more optimized stress analysis is achieved; according to the method, the research and development period can be greatly shortened, the design reliability is improved, and the method has very high practical value and commercial value; through construction of an equivalent model and application of an automatic script, a designer can more efficiently carry out stress analysis and optimization of the 2.5 D chip, and a brand new solution is provided for design of an integrated circuit.

Description

Technical Field

[0001] The present invention relates to an intelligent equivalent modeling and simulation optimization method, and in particular to an intelligent equivalent modeling and simulation optimization method based on machine learning and multi-physical field coupling. Background Art

[0002] With the rapid development of integrated circuit technology, 2.5D chips, as a new IC architecture, have been widely used in fields such as high-performance computing, communications, and artificial intelligence. By integrating multiple functional modules on a single substrate, 2.5D chips offer higher integration, enhanced performance, and lower power consumption, making them an indispensable key technology in modern electronic devices. However, with increasing design complexity, especially when designing multi-level packaging (such as TSVs (Through Silicon Vias), bump connections, and dies), simulation computing faces unprecedented challenges. Typically, to accurately simulate chip stress distribution and thermal effects under different operating conditions, engineers must rely on complex physical simulation models, most commonly using tools such as COMSOL and ANSYS. In these simulation software, designers must precisely model every structural layer and every detailed component, performing multi-physics coupled calculations. These simulation methods can highly accurately predict chip operating conditions, such as thermal expansion, stress distribution, and material properties, ensuring the reliability and stability of the final design.

[0003] However, with the increasing complexity of chip structures, especially the introduction of tiny structures like TSVs and bump connections, traditional physical modeling methods have become incredibly large and complex, requiring significant computing resources to simulate. While simulation software such as COMSOL and ANSYS can provide highly accurate results, the computational time required to simulate large, complex modules is often very long and requires extremely high-performance computer systems. A typical workstation or server cannot effectively run such large models, and simulations can take days or even weeks, far exceeding the requirements of typical product development cycles. Furthermore, engineers often face insufficient computing resources when performing these simulations. The intricate structures of each module in 2.5D chips—such as thousands of TSVs, bump connections, and complex electrical layouts—require simulation models with extremely high geometric detail, making traditional simulation methods not only time-consuming but also requiring enormous amounts of storage resources. Consequently, simulating these complex modules is computationally demanding, forcing many companies and laboratories to rely on limited computing resources for approximate simulations, which can compromise the accuracy of design results.

[0004] The drawback of existing technologies is that, despite the high computational accuracy of existing simulation tools, traditional simulation methods face significant bottlenecks in computational time and resource consumption when faced with complex 2.5D chip structures. As chip designs become increasingly complex, existing simulation methods are unable to meet the demands for efficient and accurate simulation, significantly limiting the optimization speed and production efficiency of 2.5D chip designs.

[0005] Therefore, in order to overcome these limitations of huge computing resource consumption, slow simulation speed, and difficulty in ensuring simulation accuracy, it is urgent to develop new chip design and simulation methods that can simplify traditional simulation models, reduce computing resource consumption, and accelerate the iterative process of 2.5D chip design while ensuring sufficient simulation accuracy. Summary of the Invention

[0006] Purpose of the invention: The purpose of the present invention is to provide an intelligent equivalent modeling and simulation optimization method based on machine learning and multi-physical field coupling, which simplifies traditional simulation models, improves simulation efficiency and maintains high accuracy; by performing equivalent simplification on complex chip structures, it effectively reduces the consumption of computing resources and significantly improves the simulation speed, while ensuring sufficient simulation accuracy. Without relying on ultra-high-performance computing resources, it can quickly perform 2.5D chip stress simulation, greatly improving the efficiency and accuracy of design optimization, and meeting the needs of rapid iteration and efficient verification in modern integrated circuit design.

[0007] Technical solution: The present invention discloses an intelligent equivalent modeling and simulation optimization method based on machine learning and multi-physical field coupling. The method performs equivalent simplification on complex chip structures and completes simulation operations by sequentially performing the steps of data preparation and model training, equivalent model generation and parameter initialization, real-time monitoring and multi-physical field adaptive adjustment, sensitivity analysis and local refined reconstruction, simulation execution and result verification, feedback optimization and iterative adjustment.

[0008] The method specifically comprises the following steps:

[0009] (1) Data preparation and model training: Input data acquisition, collect the original design parameters of the target chip; and perform neural network training, building a deep neural network (DNN) based on the PyTorch framework;

[0010] (2) Equivalent model generation and parameter initialization: Dynamic equivalent model construction is performed, the TSV through-hole layer is equivalent to a locally refined equivalent cuboid, and the pad layer is homogenized to its equivalent Young's modulus; initial equivalent parameters are generated through the neural network DNN, the parameters are imported into the simulation environment, and the generated equivalent parameters are automatically imported into the ANSYS or COMSOL simulation software to establish the initial equivalent model;

[0011] (3) Real-time monitoring and multi-physics field adaptive adjustment: Deploy temperature sensors and stress sensors on the chip to collect thermal and stress field data in real time; and set a threshold trigger mechanism;

[0012] (4) Sensitivity analysis and local refined reconstruction: Calculate thermal gradients and stress concentration areas through finite element simulation and output sensitivity distribution maps; use unstructured refined meshes for highly sensitive areas with an area of 13%-16% and a mesh cell size of 2-4 μm; retain simplified meshes for the remaining areas with a cell size of 8-12 μm;

[0013] (5) Simulation execution and result verification: set the simulation time step and total duration, obtain the results and conduct comparative verification;

[0014] (6) Feedback optimization and iterative adjustment: If the simulation result error exceeds the limit, the error feedback mechanism is triggered and the DNN weights are optimized through backpropagation, the equivalent parameters are regenerated and steps 2 to 5 are repeated.

[0015] Among them, in step (1), the parameters are TSV through-hole size, material properties, thermal distribution history data and stress distribution data; TSV through-hole size is the geometric parameters of through-hole diameter (such as 5μm) and depth (such as 50μm); material properties are copper filling thermal conductivity (380W / (m·K), silicon substrate Young's modulus (170GPa), Poisson's ratio of each material, and density information; thermal distribution history data is the temperature gradient range (50℃-150℃) of the chip under different working conditions and temperature change curve data of each region; stress distribution data is the maximum stress value (1.2Pa), the location of the stress concentration area and the stress size distribution data; electrical load data is current density and voltage drop.

[0016] In step (1), the neural network training is to build a deep neural network (DNN) based on the PyTorch framework. The input layer is set to 10-dimensional features, namely the diameter and depth of the TSV through hole, the thermal conductivity, Young's modulus, Poisson's ratio, density of the material, the temperature gradient and average temperature in the thermal field, and the maximum stress value and stress concentration factor in the stress field; the output layer is set to the equivalent thermal conductivity and equivalent Young's modulus parameters; the hidden layer is set to 3 layers, with the number of neurons being 128, 64, and 32 respectively, and the ReLU activation function is used. 10,000 sets of historical simulation data are used for training. During the training process, the stochastic gradient descent method is used to optimize the model parameters. The learning rate is set to 0.001, and the training error is controlled to be less than 3%.

[0017] Wherein, in step (2), the TSV through-hole layer is equivalent to a locally refined equivalent cuboid, the length and width of the equivalent cuboid are determined according to the distribution spacing of the TSV through-holes on the chip plane. Assuming that the average spacing is d1, the length and width are both set to d1; the height is equal to the depth of the TSV through-hole (50μm), and at the same time, equivalent heat conduction and stress transfer characteristics are set inside the cuboid, and the accuracy error is controlled to ≤2%;

[0018] The equivalent Young's modulus of the pad layer is homogenized. The equivalent Young's modulus is calculated by comprehensive analysis of the pad layer materials, with an error of ≤1.5%. The specific calculation method is to use the weighted average method based on the ratio of different materials in the pad layer to calculate the equivalent Young's modulus. The formula is: Among them E eq is the equivalent Young's modulus, w i is the volume fraction of the i-th material, E i is the Young’s modulus of the i-th material.

[0019] Importing parameters into the simulation environment involves automatically importing the generated equivalent thermal conductivity, equivalent Young's modulus, equivalent Poisson's ratio, equivalent density, and other parameters into ANSYS or COMSOL simulation software through the simulation software's interface or data import function. These parameters correspond one-to-one with the corresponding material property settings in the simulation software, ensuring that the established initial equivalent model accurately reflects the post-equilibrium material properties while also reducing the mesh count by 50% (from 5 million elements in the original model to 2.5 million elements).

[0020] In step (3), the deployment area is a TSV-dense area or a bump connection. A temperature sensor (accuracy ±0.5°C) and a stress sensor (accuracy ±0.1Pa) are integrated using microelectromechanical system (MEMS) technology. A dedicated data acquisition circuit is used to collect thermal field data in real time at a sampling frequency of 10 Hz and stress field data in real time at a sampling frequency of 5 Hz.

[0021] Among them, the threshold trigger mechanism is thermal field adjustment and stress field adjustment; the thermal field adjustment is: when the temperature change rate of a certain area exceeds the threshold (such as >5℃ / s), according to the relationship formula between thermal expansion coefficient and temperature change: α new =α old (1+βΔT), where αnew is the updated thermal expansion coefficient, αold is the original thermal expansion coefficient, β is the adjustment factor (±5%), and ΔT is the temperature change. The thermal expansion coefficient of the region is automatically updated according to this formula and synchronized to the simulation model in real time through the script programming interface provided by the simulation software.

[0022] The stress field is adjusted as follows: when the local stress gradient exceeds the safety threshold (such as >0.8MPa / μm), according to the formula Dynamically modified Young's modulus, where E new is the modified Young's modulus, E old is the original Young's modulus, γ is the adjustment coefficient (value ±3%), and △σ is the stress gradient; at the same time, the mesh optimization function of the simulation software is used to refine the local mesh size from 10 μm to 2 μm to improve the accuracy of stress calculation.

[0023] In step (4), the sensitivity assessment is specifically as follows: using a finite element simulation algorithm to calculate the thermal gradient (the highest gradient area is marked as >20°C / mm) and the stress concentration area (stress >1.0Pa); generating a sensitivity distribution map by analyzing the degree of influence of different areas on the overall performance; in the specific calculation process, the heat conduction equation and the stress balance equation are used for solution, such as the heat conduction equation: Where ρ is the material density, c is the specific heat capacity, T is the temperature, t is the time, k is the thermal conductivity, and Q is the heat source; the stress balance equation is: Where σ is the stress tensor and f is the body force;

[0024] The dynamic model reconstruction is specifically as follows: an unstructured refined grid (cell size 3 μm) is used in the highly sensitive area (accounting for approximately 13%-16% of the area) to improve the simulation accuracy of this area; a simplified grid (cell size 10 μm) is retained in the remaining areas to control the amount of calculation; after each 5 iterative simulations, the sensitivity is re-evaluated according to the above-mentioned sensitivity evaluation method, and the grid strategy is adjusted according to the new evaluation results to ensure that the error in the key area is ≤1%.

[0025] Among them, in step (5), the comparative verification is: comparing the temperature field (root mean square error RMSE ≤ 3 ° C) and stress field (maximum error ≤ 5%) of the equivalent model and the traditional model; using the root mean square error formula Calculate the root mean square error of the temperature field, where n is the number of sampling points, T i eq is the temperature value of the equivalent model, T i trad is the temperature value of the traditional model; the formula is used The maximum error of the calculated stress field, where σ i eq is the stress value of the equivalent model, σ i trad is the stress value of the traditional model.

[0026] Among them, in step (6), the error feedback mechanism is: if the simulation result error exceeds the limit, that is, the temperature error is greater than 5% or the stress error is greater than 8%, the back propagation algorithm is triggered to optimize the DNN weight; the loss function is calculated based on the error, and the mean square error loss function is where y ipred is the model prediction value, y i true is the true value; by calculating the gradient of the loss function with respect to the DNN weight, the weight is updated using the gradient descent method, the equivalent parameters are regenerated and steps 2-5 are repeated; and an automated control program is set up to automate the entire process of parameter adjustment, model update and simulation restart.

[0027] Automated script control involves writing automated control programs in Python scripts to automate parameter adjustments, model updates, and simulation restarts. Within the scripts, the simulation software's command-line interface or API is used to create corresponding functions for parameter modification, model import, and simulation startup. Furthermore, scheduled tasks or event triggering mechanisms are set up to ensure the automation of the entire process, reducing manual intervention by 90%.

[0028] Principle of the Invention: The intelligent equivalent modeling and simulation optimization method based on machine learning and multi-physics field coupling of the present invention effectively reduces computing resource consumption and significantly improves simulation speed by equivalently simplifying complex chip structures, while ensuring sufficient simulation accuracy. Without relying on ultra-high-performance computing resources, it can quickly perform 2.5D chip stress simulation, greatly improving the efficiency and accuracy of design optimization, meeting the needs of rapid iteration and efficient verification in modern integrated circuit design, and solving the problems of huge computing resource consumption, slow simulation speed, and difficulty in ensuring accuracy in the existing technology. Specifically, it includes the following contents:

[0029] (1) Automatic adjustment mechanism of dynamic equivalent model based on multi-physics field coupling:

[0030] In traditional 2.5D chip simulation, complex multi-physics field coupling (such as heat, stress, current, etc.) often requires detailed modeling of every detail at all levels. To address this problem, the present invention proposes a method based on a dynamic equivalent model automatic adjustment mechanism. This mechanism can dynamically adjust the equivalent models of each module during the simulation process, so that it can be automatically optimized as the simulation progresses (such as temperature, stress state, electrical load, etc.). According to the preset multi-physics field coupling rules (such as temperature change threshold, stress distribution gradient), the thermal expansion coefficient and Young's modulus parameters of the equivalent model are dynamically updated to achieve adaptive optimization during the simulation process without manual intervention. This innovation solves the limitation that traditional static models cannot accurately capture dynamic changes, and greatly improves the simulation accuracy and efficiency.

[0031] (2) Equivalent modeling method combining adaptive geometric simplification and intelligent weight allocation

[0032] In a complex 2.5D chip, components and connection structures at different levels have different degrees of influence on the simulation results. Traditional methods usually adopt a fixed simplified model or a one-size-fits-all approach, which may lead to a loss of accuracy in some key components. To this end, the present invention proposes an equivalent modeling method that combines adaptive geometric simplification with intelligent weight distribution. This method uses deep learning and artificial intelligence algorithms to intelligently and automatically adjust the geometric simplification degree and weight distribution of different parts according to the simulation results. Through a pre-trained neural network model, the geometric simplification weights are dynamically allocated according to the simulation target priority. Specifically, based on preliminary simulation results and comparative analysis, the system can determine which modules' geometric simplification does not affect the simulation accuracy and which modules require higher-precision modeling. In this way, the strategy of dynamically adjusting the simplified model enables the simulation efficiency and accuracy to be optimized, and adapts to different design requirements and hardware environments, greatly improving the flexibility of the simulation.

[0033] (3) A multi-scale equivalent model generation method based on adjustable complexity

[0034] In 2.5D chip design, due to the complexity of the multi-layer structure, excessive modeling of details often leads to a huge computational burden. The present invention proposes a multi-scale equivalent model generation method based on adjustable complexity, which can automatically determine the degree of detail of the simplified model according to the specific design requirements of the chip, and select the appropriate modeling complexity according to different simulation objectives (such as thermal analysis, electrical performance analysis, mechanical stress analysis, etc.). Specifically, the multi-scale model is not only simplified in terms of spatial scale, but also adjusted in terms of time scale. During simulation, it can dynamically decide whether to use a low-complexity or high-complexity equivalent model for simulation based on the scope of action of each module. This method ensures that designers can perform simulations efficiently at different analysis stages and minimizes the waste of computing resources.

[0035] (4) Real-time optimization equivalent model adjustment system based on integrated feedback mechanism

[0036] Traditional simulations usually require detailed modeling in the early stages of design and gradual adjustments during the simulation process. In order to improve design efficiency, the present invention proposes a real-time optimization equivalent model adjustment system based on an integrated feedback mechanism. The system combines feedback signals from multiple simulation fields (such as heat, stress, electrical load, etc.) and optimizes the parameters of the equivalent model based on the data obtained in real time during the simulation process. Specifically, the system dynamically adjusts the equivalent model of each module through a sensor network and real-time data stream, so that the simulation can automatically adapt to the physical behavior under different working conditions. The real-time feedback mechanism not only improves the adaptability of the model, but also reduces the time and cost of traditional manual adjustment and repeated testing, thereby accelerating the process of design verification and optimization.

[0037] (5) Equivalent model refinement reconstruction technology based on local structure optimization

[0038] In the design of complex multi-layer chip structures, the details of the local structure often have an important impact on the final performance. To address this problem, the present invention proposes a fine-grained reconstruction technology of an equivalent model based on local structure optimization. This technology analyzes the local structural areas that show a significant impact in the simulation, fine-tunes the equivalent models of these areas, and fine-reconstructs the local equivalent models based on predefined sensitivity indicators (such as thermal gradient threshold, stress concentration coefficient), while maintaining high computational efficiency and ensuring simulation accuracy. Specifically, for specific parts such as thermally sensitive areas and stress-concentrated areas, the present invention will refine the construction of their equivalent models to ensure that the simulation accuracy of these key components is not affected, while simplified models are used for other less sensitive areas. Through this local fine-grained reconstruction, the present invention can ensure high-precision simulation while saving computing resources, and is particularly suitable for situations where strict requirements are placed on specific areas in the design.

[0039] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages: (1) The intelligent equivalent modeling and simulation optimization method based on machine learning and multi-physical field coupling of the present invention significantly reduces computing time and resource consumption, and the completion time of the simulation process is shortened by more than 30% compared with the traditional method; (2) Maintaining high simulation accuracy, the weight setting is intelligently adjusted by the trained model to ensure the effective weighting of different physical parameters, thereby ensuring the accuracy of the simulation results. While ensuring the simulation accuracy, the computing time is reduced by more than 30%, and the simulation efficiency is significantly improved. (3) The flexibility and applicability of simulation calculations are improved. By flexibly adjusting the weights of various physical parameters and optimizing the calculation methods in the simulation process as needed, the automated calculation process greatly simplifies the simulation operation and improves the work efficiency of engineers. In addition, it can adapt to different design requirements and provide effective simulation support for different types of chip modules; (4) Economic benefits are improved. While improving the efficiency of design verification, the overall cost of the project can be reduced, avoiding high hardware investment. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 Schematic diagram of the 2.5D chip structure, including: metal cover (1), thermal adhesive (2), structural adhesive (3), test chip (4), high-speed memory chip (5), fine-pitch metal bumps (6), silicon transfer chip (7), metal bumps (8), fine-pitch underfill (9), plastic encapsulation compound (10), underfill (11), ABF substrate (12), and solder balls (13).

[0041] Figure 2 This is a schematic diagram of the equivalent model structure of a 2.5D chip, including the construction method of the equivalent simplified TSV through-hole and redistribution layer, and the fine structure of the bump under the TSV;

[0042] Figure 3 This is a schematic diagram of the equivalent model structure of a 2.5D chip, including the construction method of the equivalent simplified TSV through-hole and redistribution layer, and the fine structure of the bump above the TSV;

[0043] Figure 4 This is a schematic diagram of the stress distribution simulation results after the model is equivalent in ANSYS;

[0044] Figure 5 The flowchart of the Python script operation includes the process of how to calculate the equivalent model based on different physical parameters, and each step and their relationship are marked. DETAILED DESCRIPTION

[0045] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0046] Example 1

[0047] The present invention's intelligent equivalent modeling and simulation optimization method based on machine learning and multi-physics field coupling:

[0048] Application of 2.5D chip custom material equivalent model method A high-performance computing chip adopts a 2.5D packaging structure, including RDL (Redistribution Layer) and high-density TSV (Through Silicon Via). Due to the complexity of these structures, traditional stress simulation requires fine-grained modeling in a multi-physics (thermal, mechanical, electrical) coupled environment. The calculation time often exceeds 48 hours and requires 500GB of memory resources. The intelligent equivalent modeling and simulation optimization method of the present invention can significantly shorten the simulation time and reduce the computing resource requirements, and specifically includes the following steps:

[0049] (1) Data preparation and model training: Input data acquisition, collect the original design parameters of the target chip; and perform neural network training, building a deep neural network (DNN) based on the PyTorch framework;

[0050] Build a 2.5D chip geometry model:

[0051] Geometric Dimension Acquisition: Using specialized data acquisition tools, we collected the target chip's original design parameters from chip design documents, pre-experimental data, and relevant process parameter databases. This included obtaining the layout and dimensions of the chip's RDL layer and TSV vias. The RDL layer is 5μm thick, while the TSV vias are approximately 50μm in diameter and 100μm in height.

[0052] Model import: Import the above geometry into finite element simulation software (such as ANSYS, COMSOL, etc.) and perform preliminary meshing to prepare for subsequent equivalent model simplification.

[0053] (2) Equivalent model generation and parameter initialization: construct a dynamic equivalent model, equate the TSV through-hole layer to a locally refined equivalent cuboid, and homogenize the equivalent Young's modulus of the Pad layer; generate initial equivalent parameters through the neural network DNN, import the parameters into the simulation environment, and automatically import the generated equivalent parameters into ANSYS or COMSOL simulation software to establish the initial equivalent model; define the name and type of the custom material

[0054] In the simulation software, create a custom material library entry for an "equivalent RDL material" and an "equivalent TSV material."

[0055] Among them, "equivalent RDL material" represents the equivalent characteristics of the RDL layer after homogenization treatment; "equivalent TSV material" represents the volume equivalent characteristics of the TSV area.

[0056] Key physical parameters

[0057] To accommodate multi-physics coupling analysis, the following key parameters need to be defined in the custom material:

[0058] 1. Coefficient of thermal expansion (CTE)

[0059] 2. Young's modulus (E)

[0060] 3. Poisson's ratio (ν)

[0061] 4. Thermal conductivity (k)

[0062] 5. Density (ρ)

[0063] 6. (Optional) Electrical conductivity (σ) or other material constants relevant to the design.

[0064] Python script automatically outputs custom material parameters

[0065] According to the method of the present invention, 10,000 sets of historical data related to the RDL layer (rewiring layer) and TSV through-holes (including geometric dimensions, material ratios, stress test results, etc.) were collected in advance, and a DNN (deep neural network) was trained based on this. In actual use, the Python script will automatically call the trained model according to the current design file (such as RDL layer thickness, TSV density, operating temperature range, etc.) and output the physical parameters of "equivalent RDL material" and "equivalent TSV material". These parameters will be directly imported into the finite element simulation software in the form of data files or APIs and filled in the custom material library.

[0066] Assume that the RDL layer material ratio in the current design is 80% copper and 20% dielectric material, and the TSV through-hole filler is 100% copper; based on the previously trained deep neural network (DNN) model, combined with the material mixing rule and a large amount of historical data, the Python script outputs the equivalent RDL material and equivalent TSV material physical parameters as follows: Equivalent RDL material: CTE = (17±1)×10^-6 / K, E = 110±5GPa, ν = 0.3±0.02, k = 350±10W / m·K Equivalent TSV material: CTE = (16.5±0.5)×10^-6 / K, E = 105±5GPa, ν = 0.31±0.02, k = 390±10W / m·K. The above specific values may change with different design schemes and are subject to the results automatically calculated by the Python script.

[0067] (3) Real-time monitoring and multi-physics field adaptive adjustment: Deploy temperature sensors and stress sensors on the chip to collect thermal and stress field data in real time; and set a threshold trigger mechanism;

[0068] Preliminary meshing

[0069] 1. According to the chip geometry, set a denser grid for the RDL layer, TSV through-holes and other key areas, and use a coarser grid for the periphery or areas that have little impact on stress.

[0070] 2. The initial grid size can reach about 2 million units.

[0071] Local area adaptive grid reconstruction

[0072] 1. In the simulation software, turn on the dynamic grid adjustment function;

[0073] 2. Calculate thermal gradients (highest gradient areas are marked as >20°C / mm) and stress concentration areas (stress >1.0Pa). Generate a sensitivity distribution map by analyzing the impact of different areas on overall performance. When the Python script detects that the stress gradient or temperature gradient in a certain area exceeds a threshold, it triggers a local mesh reconstruction to ensure calculation accuracy in high-stress or high-temperature areas.

[0074] 3. Implementation effect: The number of grids was reduced from 5 million to 2 million, while maintaining sufficient fineness in key areas; memory usage was reduced from 500GB to 220GB.

[0075] (4) Sensitivity analysis and local refinement and reconstruction: Calculate thermal gradients and stress concentration areas through finite element simulation and output sensitivity distribution maps; use unstructured refinement grids for highly sensitive areas, and retain simplified grids for other areas;

[0076] Simulation initial settings

[0077] 1. In the simulation software, assign the custom materials "equivalent RDL material" and "equivalent TSV material" to the corresponding geometric areas;

[0078] 2. Apply boundary conditions: such as thermal cycling and external fixed constraints during chip manufacturing between -40°C and 125°C.

[0079] Dynamic simulation iteration

[0080] 1. As the simulation iterates, the Python script checks the stress and temperature distribution at regular intervals (or when a threshold is met).

[0081] 2. If stress non-uniformity or temperature increment is found to exceed the preset range, the DNN model is re-calculated to calculate the corrected equivalent material parameters and update the custom material;

[0082] 3. Record and count key variables (such as the number of grid reconstructions, the number of parameter updates, the change in the stress peak position, etc.).

[0083] 4. In this embodiment, the parameter update is triggered 12 times and the local grid is reconstructed 3 times in the entire simulation.

[0084] (5) Simulation execution and result verification: set the simulation time step and total duration, obtain the results and conduct comparative verification;

[0085] Computing performance

[0086] 1. After adopting the method of the present invention, the total simulation time is shortened to 28 hours (the original method is 48 hours);

[0087] 2. Memory requirements are reduced from 500GB to 220GB, significantly saving computing resources;

[0088] 3. Python script automation reduces manual intervention, human errors and adjustment time.

[0089] Simulation accuracy

[0090] 1. Comparing the simulated stress distribution with actual test data (such as X-ray detection or slice experiment), the results show that:

[0091] 1. Stress error is less than 5%;

[0092] 2. The actual deformation of the chip is basically consistent with the simulation results;

[0093] 2. Under the same test conditions, the simulation results are consistent with those of traditional fine modeling, with only slight differences (<5%) in local areas, which verifies the reliability of the present invention.

[0094] (6) Feedback optimization and iterative adjustment: If the simulation result error exceeds the limit, the error feedback mechanism is triggered and the DNN weights are optimized through backpropagation, the equivalent parameters are regenerated and steps 2 to 5 are repeated.

[0095] Final result:

[0096] Simulation time: reduced from 48 hours to 30 hours (if dynamic updates are not used), and can be further shortened to 28 hours if dynamic updates and mesh reconstruction are used;

[0097] Calculation accuracy: maintained within ±5%;

[0098] Memory usage: reduced from 500GB to 220GB;

[0099] Material parameters: With the support of DNN, they can be automatically generated according to different packaging processes and layouts.

[0100] Example 2

[0101] The intelligent equivalent modeling and simulation optimization method based on machine learning and multi-physics field coupling of the present invention comprises the following steps:

[0102] (1) Data preparation and model training

[0103] Input data collection: Use professional data collection tools to collect various original design parameters of the target chip from chip design documents, early experimental data records and related process parameter databases. Specifically covering:

[0104] TSV through-hole size: Accurately obtain its diameter (e.g., 5μm) and depth (e.g., 50μm) geometric parameters;

[0105] Material properties: Detailed information on the thermal conductivity of copper filling (380 W / (m·K)), Young's modulus of the silicon substrate (170 GPa), Poisson's ratio, and density of each material is recorded.

[0106] Thermal distribution historical data: Collect the temperature gradient range (50°C-150°C) of the chip under different working conditions and the temperature change curve data of each area.

[0107] Stress distribution data: obtain the maximum stress value (1.2Pa), the location of the stress concentration area, and the stress distribution data.

[0108] Electrical load data: including current density, voltage drop and data related to electrical performance.

[0109] Neural Network Training: A deep neural network (DNN) was built based on the PyTorch framework. The input layer was set to 10-dimensional features: the diameter and depth of the TSV via; the thermal conductivity, Young's modulus, Poisson's ratio, and density of the material; the temperature gradient and average temperature in the thermal field; and the maximum stress and stress concentration factor in the stress field. The output layer was set to the equivalent thermal conductivity and equivalent Young's modulus parameters. Training was performed using 10,000 sets of historical simulation data. Stochastic gradient descent was used to optimize the model parameters during training. The learning rate was set to 0.001, and the training error was kept within 3%.

[0110] (2) Equivalent model generation and parameter initialization

[0111] Dynamic equivalent model construction:

[0112] The TSV layer is equated to a locally refined equivalent cuboid. The length and width of this cuboid are determined by the spacing of the TSV vias on the chip plane. Assuming the average spacing is d1, both the length and width are set to d1; the height is equal to the depth of the TSV via (50μm). Equivalent heat conduction and stress transfer properties are also set within the cuboid to ensure similar thermal and stress performance to actual TSV vias, with an accuracy error of ≤2%.

[0113] The equivalent Young's modulus of the pad layer is homogenized. By comprehensively analyzing the pad layer materials, an equivalent Young's modulus value is calculated with an error of ≤1.5%. The specific calculation method is to use the weighted average method based on the ratio of different materials in the pad layer to calculate the equivalent Young's modulus. The formula is: Among them E eq is the equivalent Young's modulus, w i is the volume fraction of the i-th material, E i is the Young’s modulus of the i-th material.

[0114] Parameter import into the simulation environment: Generated parameters such as equivalent thermal conductivity, equivalent Young's modulus, equivalent Poisson's ratio, and equivalent density are automatically imported into ANSYS or COMSOL simulation software through the simulation software's interface or data import function. These parameters correspond one-to-one with the corresponding material property settings in the simulation software, ensuring that the established initial equivalent model accurately reflects the post-equilibrium material properties while also ensuring a 50% reduction in mesh size (for example, from 5 million elements in the original model to 2.5 million elements).

[0115] (3) Real-time monitoring and adaptive adjustment of multi-physics fields

[0116] Sensor deployment: Microelectromechanical systems (MEMS) technology is used to integrate temperature sensors (accuracy ±0.5°C) and stress sensors (accuracy ±0.1Pa) in key chip areas (such as TSV-dense areas and bump connections). A dedicated data acquisition circuit collects thermal field data in real time at a sampling frequency of 10Hz and stress field data at a sampling frequency of 5Hz.

[0117] Threshold trigger mechanism:

[0118] Thermal field adjustment: When the temperature change rate of a certain area exceeds the threshold (such as >5℃ / s), according to the relationship between thermal expansion coefficient and temperature change: a new =a old (1 + βΔT), where αnew is the updated thermal expansion coefficient, αold is the original thermal expansion coefficient, β is the adjustment factor (±5%), and ΔT is the temperature change. This formula automatically updates the thermal expansion coefficient for the region and synchronizes it with the simulation model in real time through the scripting interface provided by the simulation software.

[0119] Stress field adjustment: When the local stress gradient exceeds the safety threshold (such as >0.8MPa / μm), according to the formula Dynamically modified Young's modulus, where E new is the modified Young's modulus, E old is the original Young's modulus, γ is the adjustment coefficient (value ±3%), and △σ is the stress gradient. At the same time, the mesh optimization function of the simulation software is used to refine the local mesh size from 10μm to 2μm to improve the accuracy of stress calculation.

[0120] (4) Sensitivity analysis and local refined reconstruction

[0121] Sensitivity assessment: Using finite element simulation algorithms, calculate thermal gradients (highest gradient areas are marked as >20°C / mm) and stress concentration areas (stress >1.0Pa). By analyzing the impact of different areas on overall performance, a sensitivity distribution map is generated. In the specific calculation process, the heat conduction equation and stress balance equation are used for solution, such as the heat conduction equation: Where ρ is the material density, c is the specific heat capacity, T is the temperature, t is the time, k is the thermal conductivity, and Q is the heat source; the stress balance equation is: where σ is the stress tensor and f is the body force.

[0122] Dynamic model reconstruction:

[0123] An unstructured refined mesh (3 μm cell size) was used in the highly sensitive area (approximately 13% to 16% of the area) to improve simulation accuracy in this area. A simplified mesh (10 μm cell size) was retained in the remaining areas to reduce computational complexity.

[0124] After completing every five iterative simulations, the sensitivity is re-evaluated according to the above sensitivity evaluation method, and the grid strategy is adjusted according to the new evaluation results to ensure that the error in the key area is ≤1%.

[0125] (5) Simulation execution and result verification

[0126] Simulation parameter settings: In the simulation software, set the simulation time step to 0.1s and the total duration to 3600s (simulating a 1-hour workload). At the same time, expand the number of parallel computing nodes from 32 to 64 cores. Adjust the simulation software's parallel computing parameters, such as setting the task allocation strategy and memory sharing method, to accelerate the calculation.

[0127] Results comparison and verification:

[0128] Accuracy verification: Compare the temperature field (RMSE≤3℃) and stress field (maximum error≤5%) of the equivalent model with the traditional model. Calculate the root mean square error of the temperature field, where n is the number of sampling points, T i eq is the temperature value of the equivalent model, T i trad is the temperature value of the traditional model; the formula is used The maximum error of the calculated stress field, where σ i eq is the stress value of the equivalent model, σ i trad is the stress value of the traditional model.

[0129] Resource consumption statistics: The simulation software's built-in resource monitoring tool was used to record memory usage (reduced from the original 500GB to 250GB) and computation time (reduced from 48 hours to 28 hours).

[0130] (6) Feedback optimization and iterative adjustment

[0131] Error feedback mechanism: If the simulation result error exceeds the limit (such as temperature error > 5% or stress error > 8%), the back propagation algorithm is triggered to optimize the DNN weights. The specific process is: according to the error calculation loss function, the mean square error loss function where y i pred is the model prediction value, y i true is the true value. By calculating the gradient of the loss function with respect to the DNN weights, the weights are updated using the gradient descent method, the equivalent parameters are regenerated, and steps 2-5 are repeated.

[0132] Automated script control: Automated control programs are written using Python scripts to fully automate parameter adjustments, model updates, and simulation restarts. Within the scripts, corresponding functions are written using the simulation software's command-line interface or API to implement parameter modification, model import, and simulation startup. Furthermore, scheduled tasks or event triggering mechanisms are set up to ensure the automation of the entire process, reducing manual intervention by 90%.

[0133] Example 3

[0134] An automotive electronic chip uses a 2.5D packaging structure and integrates multiple functional modules, including a power driver module, a signal processing module, and a communication module. Unlike the high-performance computing chip in Example 2, automotive electronic chips operate in a complex environment and have extremely high requirements for reliability and stability.

[0135] (1) Data preparation and model training

[0136] Data collection: Use professional tools to collect various data. The power drive module involves large currents, and its current density (such as 500-1000A / cm 2 ), power loss (3-5W); the signal processing module focuses on signal transmission quality, collecting parameters such as signal frequency (50-100MHz) and transmission line characteristic impedance (45-55Ω); and the communication module obtains communication protocol-related parameters (such as the CAN bus baud rate of 500kbps). Simultaneously, it collects conventional parameters such as the chip's TSV via size (8μm diameter, 60μm depth), material properties (such as copper-filled thermal conductivity of 370W / (m·K) and silicon substrate Young's modulus of 165GPa), thermal distribution history data (operating temperature range -40°C-125°C, temperature gradient range 30-130°C), and stress distribution data (maximum stress value 1.3Pa).

[0137] Neural network training: A deep neural network (DNN) was built based on the PyTorch framework. The input layer was set to 13-dimensional features. In addition to the 10-dimensional features in Example 2, power loss, signal frequency, and transmission line characteristic impedance were added. The output layer was still set to equivalent thermal conductivity and equivalent Young's modulus parameters. Training was performed using 12,000 sets of historical simulation data. Stochastic gradient descent was used to optimize model parameters during training. The learning rate was set to 0.0008, and the training error was kept within 2.5%.

[0138] (2) Equivalent model generation and parameter initialization

[0139] A dynamic equivalent model was constructed: The TSV layer was equated to a locally refined equivalent cuboid. The length and width were determined based on the TSV spacing on the chip plane (assuming an average spacing of d2, both length and width were set to d2). The height was equal to the TSV depth (60μm). Equivalent thermal conduction and stress transfer characteristics were set within the cuboid, with an accuracy error of ≤2%. The equivalent Young's modulus of the pad layer was homogenized and calculated using a weighted average method based on the different material ratios, with an error of ≤1.5%.

[0140] Parameter import into the simulation environment: Generated parameters such as equivalent thermal conductivity, equivalent Young's modulus, equivalent Poisson's ratio, and equivalent density are automatically imported into ANSYS or COMSOL simulation software through the simulation software's interface or data import function. This ensures that the established initial equivalent model accurately reflects the material properties after equivalentization, while also reducing the mesh count by 40% (from 4 million elements in the original model to 2.4 million elements).

[0141] (3) Real-time monitoring and adaptive adjustment of multi-physics fields

[0142] Sensor Deployment: MEMS technology is used to integrate temperature sensors (accuracy ±0.5°C) and stress sensors (accuracy ±0.1Pa) in key heat-generating areas of the power driver module, key signal transmission nodes of the signal processing module, and TSV-dense areas. A dedicated data acquisition circuit collects real-time thermal field data at an 8Hz sampling frequency and stress field data at a 4Hz sampling frequency.

[0143] Threshold trigger mechanism: In terms of thermal field adjustment, when the temperature change rate of a certain area exceeds the threshold (such as >4℃ / s), the thermal expansion coefficient of the area is automatically updated according to the relationship between the thermal expansion coefficient and temperature change: αnew=αold(1+βΔT) (β value ±5%), and synchronized to the simulation model in real time through the script programming interface of the simulation software. In terms of stress field adjustment, when the local stress gradient exceeds the safety threshold (such as >0.7MPa / μm), according to the formula (γ is ±3%). The Young's modulus is dynamically modified, and the mesh optimization function of the simulation software is used to refine the local mesh size from 10 μm to 2 μm.

[0144] (4) Sensitivity analysis and local refined reconstruction

[0145] Sensitivity assessment: Using finite element simulation algorithms, we calculated thermal gradients (highest gradient areas are marked as >18°C / mm) and stress concentration areas (stress >1.1 Pa). By analyzing the impact of different areas on overall performance, we generated a sensitivity distribution map and solved it using the heat conduction equation and stress equilibrium equation.

[0146] Dynamic model reconstruction: A refined unstructured mesh (3μm cell size) was used for highly sensitive areas (approximately 14%-17% of the area), while a simplified mesh (10μm cell size) was retained for the remaining areas. After every five simulation iterations, the sensitivity was reassessed and the mesh strategy was adjusted based on the new assessment results to ensure an error of ≤1% in critical areas.

[0147] (5) Simulation execution and result verification

[0148] Simulation parameter settings: In the simulation software, set the simulation time step to 0.08 seconds and the total duration to 4000 seconds (to simulate the chip workload during vehicle driving). Also, increase the number of parallel computing nodes from 24 to 48 cores and adjust the simulation software's parallel computing parameters.

[0149] Comparative verification results: The temperature field (RMSE ≤ 3.5°C) and stress field (maximum error ≤ 5.5%) of the equivalent model were compared with those of the traditional model. The RMS error formula for the temperature field was used to calculate the RMS error, and the corresponding formula for the maximum error in the stress field was used to calculate the maximum error. The simulation software's built-in resource monitoring tool was used to record memory usage (reduced from 400GB to 200GB) and computation time (reduced from 40 hours to 24 hours).

[0150] (6) Feedback optimization and iterative adjustment

[0151] Error feedback mechanism: If the simulation result error exceeds the limit (e.g., temperature error > 5.5% or stress error > 9%), the backpropagation algorithm is triggered to optimize the DNN weights. The loss function is calculated based on the error, and the weights are updated using gradient descent. Equivalent parameters are regenerated and steps 2-5 are repeated.

[0152] Automated script control: Automated control programs are written using Python scripts to automate parameter adjustments, model updates, and simulation restarts. Leveraging the simulation software's command-line interface or API, corresponding functions are written to implement relevant operations. Scheduled tasks or event triggers are set to automate the entire process, reducing manual intervention by 85%.

[0153] Example 4

[0154] Simulation verification under different environmental conditions

[0155] A 2.5D chip used in aerospace applications operates in a high vacuum and strong radiation environment. This chip is used for satellite data processing, which places extremely high demands on chip performance and reliability, and the environmental conditions differ significantly from those in conventional applications.

[0156] (1) Data preparation and model training

[0157] Data collection: In addition to conventional chip design parameters, data related to the radiation environment must also be collected. Such as radiation dose rate (0.1-1Gy / h), particle flux ( Particles / cm 2 ·s), etc. It also obtains TSV through-hole dimensions (6μm diameter, 55μm depth), material properties (thermal conductivity and Young's modulus of special radiation-resistant materials, such as copper-based radiation-resistant materials with a thermal conductivity of 360W / (m·K) and a Young's modulus of 168GPa), thermal distribution history data (due to slow heat dissipation in high vacuum, the temperature gradient ranges from 20-120°C), and stress distribution data (maximum stress value is 1.25Pa).

[0158] Neural Network Training: A deep neural network (DNN) was built using the PyTorch framework. The input layer was set to 12-dimensional features. In addition to the 10-dimensional features in Example 2, radiation dose rate and particle flux were added. The output layer was set to equivalent thermal conductivity and equivalent Young's modulus parameters. Training was performed using 11,000 sets of historical simulation data. Stochastic gradient descent was used to optimize model parameters during training. The learning rate was set to 0.0009, and the training error was kept within 2.8%.

[0159] (2) Equivalent model generation and parameter initialization

[0160] Dynamic equivalent model construction: The TSV layer is equated to a locally refined equivalent cuboid. The length and width are determined based on the distribution spacing on the chip plane (assuming the average spacing is d3, both length and width are set to d3). The height is equal to the TSV depth (55μm). Equivalent thermal conduction and stress transfer characteristics are set, with an accuracy error of ≤2%. The equivalent Young's modulus of the pad layer is homogenized and calculated with an error of ≤1.5%.

[0161] Import parameters into the simulation environment: The generated equivalent parameters are imported into ANSYS or COMSOL simulation software through the simulation software interface to ensure that the initial equivalent model can accurately reflect the material properties and reduce the number of meshes by 45% (from 4.5 million elements in the original model to 2.475 million elements).

[0162] (3) Real-time monitoring and adaptive adjustment of multi-physics fields

[0163] Sensor Deployment: Special radiation-resistant sensor technology is used to integrate temperature sensors (accuracy ±0.6°C) and stress sensors (accuracy ±0.12Pa) in areas of the chip susceptible to radiation and in key functional modules. A dedicated data acquisition circuit collects thermal field data in real time at a sampling frequency of 6Hz and stress field data at a sampling frequency of 3Hz.

[0164] Threshold trigger mechanism: During thermal field adjustment, when the temperature change rate in a certain area exceeds a threshold (e.g., >3.5°C / s), the thermal expansion coefficient is updated based on the relationship between thermal expansion coefficient and temperature change and synchronized with the simulation model. Regarding stress field adjustment, when the local stress gradient exceeds a safety threshold (e.g., >0.75MPa / μm), the Young's modulus is dynamically modified according to the corresponding formula, and the local mesh size is refined from 10μm to 2μm.

[0165] (4) Sensitivity analysis and local refined reconstruction

[0166] Sensitivity assessment: Using the finite element simulation algorithm, the thermal gradient (the highest gradient area is marked as >15°C / mm) and the stress concentration area (stress >1.05Pa) are calculated, and the sensitivity distribution map is generated and solved using the heat conduction equation and the stress balance equation.

[0167] Dynamic model reconstruction: An unstructured, refined mesh (3μm cell size) was used for highly sensitive areas (approximately 12%-15% of the area), while a simplified mesh (10μm cell size) was retained for the remaining areas. After every four simulation iterations, the sensitivity was reassessed and the mesh strategy was adjusted to ensure that the error in critical areas was ≤1.2%.

[0168] (5) Simulation execution and result verification

[0169] Simulation parameter settings: In the simulation software, set the simulation time step to 0.06 seconds and the total duration to 3500 seconds (to simulate the chip's operation during a period of satellite in-orbit). Adjust the number of parallel computing nodes from 30 to 50 cores, and optimize the simulation software's parallel computing parameters.

[0170] Comparative verification results: The temperature field (RMSE ≤ 4°C) and stress field (maximum error ≤ 6%) of the equivalent model were compared with those of the traditional model. The simulation software resource monitoring tool was used to record memory usage (reduced from the original 420GB to 210GB) and computation time (reduced from 38 hours to 22 hours).

[0171] (6) Feedback optimization and iterative adjustment

[0172] Error feedback mechanism: If the simulation result error exceeds the limit (such as temperature error > 6% or stress error > 9.5%), the back propagation algorithm is triggered to optimize the DNN weights, regenerate equivalent parameters and repeat steps 2-5.

[0173] Automated script control: Automated control programs are written using Python scripts to automate parameter adjustments, model updates, and simulation restarts. Functions can be written using the simulation software's command-line interface or API to set up scheduled tasks or event triggers, reducing manual intervention by 80%.

[0174] like Figure 1 Figure 2 shows a schematic diagram of a 2.5D chip structure, including metal cap 1, thermal adhesive 2, structural adhesive 3, test chip 4, high-speed memory chip 5, fine-pitch metal bumps 6, silicon interposer chip 7, metal bumps 8, fine-pitch underfill 9, molding compound 10, underfill 11, ABF substrate 12, and solder balls 13. The structure is complex, with potentially thousands of metal bumps and solder balls. The materials and connection methods of each component influence thermal conduction, electrical properties, and mechanical stress, and these components are coupled to each other. Traditional physical simulations rely on simplified assumptions, making accurate calculations difficult. As module complexity increases, the computational effort increases exponentially, significantly increasing computation time and severely restricting design iteration and optimization efficiency.

[0175] like Figure 2 Figure 2 shows a schematic diagram of the equivalent model structure of a 2.5D chip, including the equivalent simplified construction method for TSV vias and the redistribution layer, and the refined structure of the bump below the TSV. The TSV via layer is equivalent to a locally refined equivalent rectangular parallelepiped, whose length and width are determined by the distribution spacing of the TSV vias on the chip plane, and whose height is equal to the TSV via depth. This equivalent replacement simplifies the complex structure and reduces the amount of calculation. At the same time, equivalent heat conduction and stress transfer characteristics are set within the rectangular parallelepiped to ensure simulation accuracy in key areas. The redistribution layer pad adopts a homogenized equivalent Young's modulus processing, and the equivalent value is calculated based on different material proportions. The refined structure of the bump below the TSV retains key details for accurate stress transfer simulation. This equivalent design significantly improves simulation efficiency without losing key information.

[0176] like Figure 3 The figure shows the schematic diagram of the equivalent model structure of the 2.5D chip, including the equivalent simplified construction method of the TSV through hole and the redistribution layer and the fine structure of the bump above the TSV. Figure 4 Similarly, TSV vias and redistribution layers are simplified in the same way. The fine bump structure above the TSV is used in simulation to simulate the connection and stress transfer with the upper chip or package structure. By rationally simplifying and preserving details, the equivalent model balances computational efficiency and simulation accuracy, providing effective simulation models for diverse design requirements.

[0177] like Figure 4 Figure 2 shows the results of stress distribution simulation in ANSYS after model equivalence. Different colors represent different stress values, with stress increasing gradually from blue to red. By observing the stress distribution contour map, stress concentration areas can be clearly seen, such as near TSV vias and at the chip edges. This is because these areas have large structural variations, which are prone to stress concentration due to thermal expansion and external loads. The equivalent model of the present invention can accurately simulate stress distribution, providing a basis for optimizing chip structural design. By adjusting structural parameters, stress concentration can be reduced and chip reliability can be improved.

[0178] like Figure 5 The figure below shows a Python script operation flow chart, which illustrates how to calculate equivalent models based on different physical parameters. Each step and its interrelationship are highlighted. The process begins by reading design parameters, invoking a trained DNN model to calculate equivalent material parameters, and then importing these parameters into the simulation software. Real-time monitoring data is then used to determine whether the threshold adjustment mechanism has been triggered. If so, the parameters are recalculated, the model is updated, and finally the simulation results are output. The entire process is automated, reducing manual intervention, improving simulation efficiency and accuracy, and ensuring efficient calculation and simulation of equivalent models based on different physical parameters.

[0179] Therefore, through the above embodiments, it can be proved that the 2.5D chip stress simulation method of the present invention, which combines custom materials with equivalent parameters output by Python scripts, can significantly reduce the calculation time (reduced by about 30% to 40%) and memory resource consumption (reduced by about 50% or more) while ensuring high precision (error less than 5%). And the DNN trained based on large-scale historical data can dynamically adjust the equivalent model during the simulation process to achieve more optimized stress analysis. This method can significantly shorten the R&D cycle and improve design reliability for the packaging design of multi-layer RDL and high-density TSV, and has high practical value and commercial value. Through the construction of equivalent models and the application of automated scripts, designers can more efficiently perform stress analysis and optimization of 2.5D chips, providing a new solution for the design of integrated circuits.

Claims

1. An intelligent equivalent modeling and simulation optimization method based on machine learning and multi-physics field coupling, characterized in that: The method performs equivalent simplification on complex chip structures and completes simulation operations by sequentially performing the steps of data preparation and model training, equivalent model generation and parameter initialization, real-time monitoring and multi-physics field adaptive adjustment, sensitivity analysis and local refined reconstruction, simulation execution and result verification, feedback optimization and iterative adjustment.

2. The intelligent equivalent modeling and simulation optimization method according to claim 1, characterized in that: The method specifically comprises the following steps: (1) Data preparation and model training: Input data acquisition, collect the original design parameters of the target chip; and perform neural network training, building a deep neural network (DNN) based on the PyTorch framework; (2) Equivalent model generation and parameter initialization: Dynamic equivalent model construction is performed, the TSV through-hole layer is equivalent to a locally refined equivalent cuboid, and the pad layer is homogenized to its equivalent Young's modulus; initial equivalent parameters are generated through the neural network DNN, the parameters are imported into the simulation environment, and the generated equivalent parameters are automatically imported into the ANSYS or COMSOL simulation software to establish the initial equivalent model; (3) Real-time monitoring and multi-physics field adaptive adjustment: Deploy temperature sensors and stress sensors on the chip to collect thermal and stress field data in real time; and set a threshold trigger mechanism; (4) Sensitivity analysis and local refined reconstruction: Calculate thermal gradients and stress concentration areas through finite element simulation and output sensitivity distribution maps; use unstructured refined meshes for highly sensitive areas with an area of 13%-16% and a mesh cell size of 2-4 μm; retain simplified meshes for the remaining areas with a cell size of 8-12 μm; (5) Simulation execution and result verification: set the simulation time step and total duration, obtain the results and conduct comparative verification; (6) Feedback optimization and iterative adjustment: If the simulation result error exceeds the limit, the error feedback mechanism is triggered and the DNN weights are optimized through backpropagation, the equivalent parameters are regenerated and steps 2 to 5 are repeated.

3. The intelligent equivalent modeling and simulation optimization method according to claim 2, characterized in that: In step (1), the parameters are TSV hole size, material properties, thermal distribution history data and stress distribution data; TSV hole size is the hole diameter and depth geometric parameters; material properties are copper filling thermal conductivity, silicon substrate Young's modulus, Poisson's ratio of each material, and density information; thermal distribution history data is the temperature gradient range of the chip under different working conditions and the temperature change curve data of each region; stress distribution data is the maximum stress value, the location of the stress concentration area and the stress magnitude distribution data; The electrical load data are current density and voltage drop.

4. The intelligent equivalent modeling and simulation optimization method according to claim 2, characterized in that: In step (1), the neural network training is to build a deep neural network DNN based on the PyTorch framework, and the input layer is set to 10-dimensional features, namely the diameter and depth of the TSV through hole, the thermal conductivity, Young's modulus, Poisson's ratio, density of the material, the temperature gradient and average temperature in the thermal field, and the maximum stress value and stress concentration coefficient in the stress field; the output layer is set to the equivalent thermal conductivity and equivalent Young's modulus parameters; the hidden layer is set to 3 layers, the number of neurons is 128, 64, and 32 respectively, and the ReLU activation function is used; 10,000 sets of historical simulation data are used for training, and the stochastic gradient descent method is used to optimize the model parameters during the training process. The learning rate is set to 0.001, and the training error is controlled to be less than 3%.

5. The intelligent equivalent modeling and simulation optimization method according to claim 2, characterized in that: In step (2), the TSV through-hole layer is equivalent to a locally refined equivalent cuboid, the length and width of the equivalent cuboid are determined according to the distribution spacing of the TSV through-holes on the chip plane, and the height is equal to the depth of the TSV through-holes. At the same time, equivalent heat conduction and stress transfer characteristics are set inside the cuboid, with an accuracy error of ≤2%; The equivalent Young's modulus of the pad layer is homogenized. The equivalent Young's modulus is calculated by comprehensive analysis of the pad layer materials, with an error of ≤1.5%. The specific calculation method is to use the weighted average method based on the ratio of different materials in the pad layer to calculate the equivalent Young's modulus. The formula is: Among them E eq is the equivalent Young's modulus, w i is the volume fraction of the i-th material, E i is the Young’s modulus of the i-th material.

6. The intelligent equivalent modeling and simulation optimization method according to claim 2, characterized in that: In step (3), the deployment area is a TSV dense area or a bump connection; the threshold trigger mechanism is thermal field adjustment and stress field adjustment.

7. The intelligent equivalent modeling and simulation optimization method according to claim 6, characterized in that: The thermal field adjustment is as follows: when the temperature change rate of a certain area exceeds the threshold, according to the relationship formula between the thermal expansion coefficient and the temperature change: new =a old (1+βΔT), where αnew is the updated thermal expansion coefficient, αold is the original thermal expansion coefficient, β is the adjustment factor (±5%), and ΔT is the temperature change. The thermal expansion coefficient of the region is automatically updated according to this formula and synchronized to the simulation model in real time through the script programming interface provided by the simulation software. The stress field is adjusted as follows: when the local stress gradient exceeds the safety threshold, according to the formula Dynamically modified Young's modulus, where E new is the modified Young's modulus, E old is the original Young's modulus, γ is the adjustment coefficient, which is ±3%, and △σ is the stress gradient. At the same time, the mesh optimization function of the simulation software is used to refine the local mesh size from 10 μm to 2 μm to improve the accuracy of stress calculation.

8. The intelligent equivalent modeling and simulation optimization method according to claim 2, characterized in that: In step (4), the sensitivity assessment specifically includes: using a finite element simulation algorithm to calculate thermal gradients and stress concentration areas; generating a sensitivity distribution map by analyzing the degree of influence of different areas on overall performance; In the specific calculation process, the heat conduction equation and stress balance equation are used to solve, such as the heat conduction equation: Where ρ is the material density, c is the specific heat capacity, T is the temperature, t is the time, k is the thermal conductivity, and Q is the heat source; the stress balance equation is: Where σ is the stress tensor and f is the body force; The dynamic model reconstruction specifically includes: using unstructured refined grids for high-sensitivity areas to improve the simulation accuracy of the areas; The simplified mesh is retained in the remaining areas to control the amount of calculation. After every five iterative simulations, the sensitivity is re-evaluated according to the above sensitivity evaluation method, and the mesh strategy is adjusted according to the new evaluation results to ensure that the error in the key area is ≤1%.

9. The intelligent equivalent modeling and simulation optimization method according to claim 2, characterized in that: In step (5), the comparative verification is as follows: comparing the temperature field and stress field of the equivalent model with the traditional model; using the root mean square error formula Calculate the root mean square error of the temperature field, where n is the number of sampling points, T i eq is the temperature value of the equivalent model, T i trad is the temperature value of the traditional model; the formula is used The maximum error of the calculated stress field, where σ i eq is the stress value of the equivalent model, σ i trad is the stress value of the traditional model.

10. The intelligent equivalent modeling and simulation optimization method according to claim 2, characterized in that: In step (6), the error feedback mechanism is: if the simulation result error exceeds the limit, that is, the temperature error is greater than 5% or the stress error is greater than 8%, the back propagation algorithm is triggered to optimize the DNN weight; the loss function is calculated based on the error, and the mean square error loss function is where y i pred is the model prediction value, y i true is the true value; by calculating the gradient of the loss function with respect to the DNN weight, the weight is updated using the gradient descent method, the equivalent parameters are regenerated and steps 2-5 are repeated; and an automated control program is set up to automate the entire process of parameter adjustment, model update and simulation restart.

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