Three-step order reduction method for force-heat coupling simulation of heterogeneous integrated structure

Abstract

The invention discloses a three-step order reduction method for force-heat coupling simulation of a heterogeneous integrated structure. The method aims at systematically solving the calculation bottlenecks of the complex multilayer packaging structure in three core links of geometric modeling, physical parameter definition and numerical solution. According to the method, a structured order reduction process is innovatively provided, wherein the structured order reduction process comprises picture layer-by-layer geometric modeling, intra-layer heterogeneous material equivalence and feature projection order reduction. According to the method, through systematic three-step order reduction, the complexity of the heterogeneous integrated structure in the aspects of geometry, physics and numerical solution is effectively decoupled, the simulation efficiency is improved by several orders of magnitude, and the method is particularly suitable for system-level reliability evaluation which needs to carry out batch verification on multiple design parameters and multiple working conditions.

Description

Technical Field

[0001] This invention belongs to the technical fields of computer-aided engineering (CAE), multiphysics coupled simulation, and reduced-order modeling (ROM). Specifically, it relates to a three-step method for force-thermal coupled simulation of heterogeneous integrated structures. Background Technology

[0002] Modern semiconductor packaging technology is evolving towards high-density, heterogeneous integration, leading to a dramatic increase in the variety of structural materials, geometric complexity, and the number of interfaces. Traditional finite element methods (FEM) face three major computational bottlenecks when dealing with these highly complex structures:

[0003] Geometric modeling is inefficient: the conversion process from design files to high-fidelity 3D finite element models is highly dependent on manual operation, involves a large number of microscopic details and multi-layer stacking, is time-consuming and prone to errors.

[0004] The complexity of defining physical parameters: Heterogeneous integrated structures involve various materials such as silicon, copper, and polymer substrates. Their mechanical and thermal properties (such as elastic modulus, coefficient of thermal expansion, and thermal conductivity) typically exhibit a strong nonlinear dependence on temperature and are anisotropic. Traditional methods not only require manually defining these curves for each material, but also, for high-density micro-interconnect structures, tens of thousands of complex contact conditions or coupling units must be defined. This immense complexity of the physical model is the core reason for the low efficiency and high error rate of pre-simulation preparation.

[0005] Numerical solutions involve enormous computational costs: Practical applications often require the calculation of multiple parameters or industrial controls, and the final finite element model typically has millions or even tens of millions of degrees of freedom (DOF). Solving transient or nonlinear coupled equations is extremely costly in terms of computational resources and time, which seriously hinders large-scale parameter optimization and multi-condition analysis.

[0006] Existing dimensionality reduction methods (such as intrinsic orthogonal decomposition (POD)) mainly focus on the third stage, namely dimensionality reduction in the solution stage. However, they lack systematic solutions for bottlenecks such as early modeling and material parameter definition, which limits the efficiency improvement of the entire simulation process. Summary of the Invention

[0007] This invention proposes a three-step order reduction method for efficient prediction of the force-thermal response of three-dimensional heterogeneous integrated structures: image-by-image layer-by-layer geometric modeling, intra-layer heterogeneous material equivalence, and feature projection order reduction. By decoupling and order reduction, the complexity of heterogeneous integrated structures in geometric modeling, physical parameter definition, and numerical calculation is addressed, thereby improving the efficiency of finite element simulation and achieving systematic optimization of the simulation process.

[0008] To solve the above-mentioned technical problems, the specific technical solution of the present invention is as follows:

[0009] A three-step method for order reduction in force-thermal coupling simulation of heterogeneous integrated structures includes the following steps:

[0010] Step 1: Obtain the two-dimensional graphic file of the heterogeneous integrated structure, and then convert the geometric information in the two-dimensional graphic file into a three-dimensional finite element geometric model. During the conversion process, identify the different materials represented by different colors or gray levels in the graphic file layer by layer, and assign a material identifier to each pixel unit generated by discretization of the two-dimensional image.

[0011] Step 2: Establish a material database containing all material properties in the heterogeneous integrated structure; traverse all pixel units of the three-dimensional finite element geometric model through the secondary development interface of computer software and external programming scripts to realize the lookup and batch assignment of material identifiers to the material database; simplify the equivalent boundary conditions of the heterogeneous interface with high-density micro-features.

[0012] Step 3: Run high-fidelity simulations under different working conditions on the three-dimensional finite element geometric model after the simplification process in Step 2 to obtain a set of simulation snapshots of its force-thermal response field; apply the intrinsic orthogonal decomposition method to the snapshot set to extract the low-dimensional modal basis vectors of the system; use radial basis functions or Gaussian process regression to establish a nonlinear mapping model ROM from design parameters to modal coefficients to achieve real-time and rapid prediction of the force-thermal response field under new design parameters or working conditions.

[0013] Furthermore, the material identifier is obtained in the following way: First, using predefined mesh coarsening rules, the two-dimensional image is stacked and discretized. Then, the element material identifiers provided by the FEM model are used to identify different materials represented by different colors or grayscale values ​​in the graphic file layer by layer. Finally, a three-dimensional finite element mesh with clear material identifiers is output.

[0014] Furthermore, the material properties in the material database include elastic modulus, Poisson's ratio, coefficient of thermal expansion, thermal conductivity, density, and specific heat capacity.

[0015] Furthermore, the simplification of the equivalent boundary conditions includes calculating equivalent material parameters using homogenization methods, Voigt-Reuss average models, Eshelby inclusion models, or equivalent thermal resistance models.

[0016] Furthermore, the low-dimensional modal basis vectors are obtained in the following way:

[0017] Furthermore, by performing singular value decomposition on the snapshot set matrix, the high-dimensional physical field data is projected into a low-dimensional space, and the system's eigenvalues ​​and their corresponding eigenvectors are extracted. Then, the eigenvalues ​​are sorted according to their magnitude, and the top k dominant eigenvectors whose cumulative energy contribution reaches a predetermined threshold are selected as low-dimensional modal basis vectors.

[0018] Furthermore, the nonlinear mapping model ROM is based on the reduced-order assumption that the solution under any operating condition can be formed by a linear combination of a finite number of modal basis vectors, thus transforming the reconstruction of the physical field into solving for the modal coefficients.

[0019] Furthermore, the input parameters of the new design parameters or operating conditions, including but not limited to the perturbation of parameters such as chip heat dissipation power, ambient temperature, and key materials.

[0020] Furthermore, the nonlinear mapping model ROM, during prediction, achieves the following prediction accuracy for its force-thermal response field: ,in Calculated value for ROM Calculate the true value for the finite element method.

[0021] The main advantage of this invention lies in its systematic multi-step order reduction strategy:

[0022] 1. Significantly improves modeling efficiency (first step of the process): The automated modeling process reduces the time-consuming manual modeling process to just a few minutes of parametric and automated generation.

[0023] 2. Solved the problem of complex physical parameter definition (the core advantage of the second step of order reduction): By mapping material parameters based on element identifiers and simplifying equivalent boundary conditions, the manual setting of tens of thousands of parameters and complex contacts is avoided, which significantly reduces the physical complexity of the model and lays an efficient foundation for subsequent numerical solutions.

[0024] 3. Real-time prediction capability is achieved (third step of order reduction effect): The constructed reduced-order model (ROM) can reduce the solution time of several hours required for high-fidelity finite element simulation to the real-time prediction of seconds or even milliseconds, which greatly accelerates design optimization and reliability analysis. Attached Figure Description

[0025] Figure 1 This is an overview diagram of the technical route of the present invention.

[0026] Figure 2 This is an image of a layer in the substrate GERBER file of an embodiment of the present invention.

[0027] Figure 3 This is a diagram illustrating the effect of partial material identifiers in an embodiment of the present invention.

[0028] Figure 4 This is a diagram showing the effect of material parameter mapping in one layer according to an embodiment of the present invention.

[0029] Figure 5 This is a diagram showing the thermal strain of the substrate at 140˚C in an embodiment of the present invention.

[0030] Figure 6 This is a diagram showing the thermal stress results of the substrate at 140˚C in an embodiment of the present invention.

[0031] Figure 7 The figure shows the thermal strain simulation results of the complete packaging structure at 140℃ in the embodiment of the present invention.

[0032] Figure 8 This is an error analysis diagram of the order reduction prediction and direct simulation results in an embodiment of the present invention. Detailed Implementation

[0033] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the scope of protection of the invention.

[0034] This invention proposes a three-step order reduction method for force-thermal simulation of heterogeneous integrated structures. The following detailed implementation process is illustrated with a specific example, "Order Reduction Simulation Method Based on a Typical High-Density BGA Package Structure with Wiring Width Less Than 20 Micrometers." This process mainly includes three stages: geometric modeling order reduction, parameter order reduction, and numerical calculation order reduction. Figure 1 As shown, the specific process is as follows:

[0035] Step 1: First step of reduction: Image-based layer-by-layer geometric modeling; reducing the complex CAD / CAE geometric modeling process to image recognition and fast mesh generation, realizing automatic and fast conversion from two-dimensional graphic files to three-dimensional finite element models.

[0036] In this stage, image recognition methods are used to export the GERBER and other design files of the encapsulation structure into common image files such as JPG. Figure 2 As shown. The geometric information in the two-dimensional graphic file is then converted into a three-dimensional finite element geometric model. This process involves identifying different materials represented by different colors or grayscale levels in the graphic file layer by layer, assigning a material identifier to each pixel unit generated from the discretization of the two-dimensional image. Specifically, as... Figure 3 As shown, the method first utilizes predefined mesh coarsening rules to stack and discretize the two-dimensional images, ultimately outputting a three-dimensional finite element mesh with explicit material identifiers (Element ID Tags inherent in the FEM model). This method reduces the geometric complexity to a parameterizable image recognition problem, preparing for the second step of order reduction.

[0037] Step 2: Second step of order reduction: Intra-layer heterogeneous material equivalence. This stage is key to simplifying the simulation process. By automatically mapping material parameters based on element identifiers and replacing complex micro-contacts with equivalent materials or equivalent thermal resistance, the physical complexity of the model is reduced to an acceptable level, solving the most time-consuming and error-prone problem of defining physical parameters in traditional CAE.

[0038] Automatic mapping of material parameters: First, a material database containing all heterogeneous materials required for finite element simulation is established. The materials include, but are not limited to, solder resist layer, insulating dielectric layer, copper, and core board layer. The material properties include, but are not limited to, elastic modulus, Poisson's ratio, coefficient of thermal expansion (CTE), thermal conductivity, density, and specific heat capacity, as shown in Table 1.

[0039] Table 1: Partial Material Properties of Various Materials in Packaging Substrates

[0040] Material Name Elastic modulus E (GPa) Poisson's ratio v Coefficient of thermal expansion (ppm / ℃) solder mask 3 0.25 60 Insulating dielectric layer 13 0.25 20 copper 120 0.33 17 Core layer X / Y: 29, Z: 6 X / Y: 0.25, Z: 0.25 X / Y: 5, Z: 12

[0041] Using the secondary development interface (API) of the finite element method (FE) software, a corresponding programming script was developed. The script iterates through all pixel elements of the finite element model generated in the first step of order reduction, performing lookup and batch assignment of identifiers to the parameter database. Based on the pre-assigned material identifier for each pixel element, such as a 0 / 1 binary matrix, the script automatically retrieves and assigns all corresponding physical parameters to that pixel element from the material database, such as elastic modulus, Poisson's ratio, coefficient of thermal expansion, and thermal conductivity. Figure 4 As shown, complex contact and multibody modeling is simplified to a single, non-uniform (anisotropic) material layer, significantly reducing the model's degrees of freedom and the computational cost of contact iteration. Simultaneously, this mechanism reduces the task of defining parameters for tens of thousands of pixel units to the automatic identification and assignment of a finite number of material identifiers, ensuring high accuracy and efficiency in material parameter definition. This automated mapping from element identifiers to material parameters completely eliminates the repetitive work and errors of manually setting complex parameter sets, while also reducing a large number of boundary conditions and lowering the computational load of the simulation.

[0042] Then, equivalent boundary conditions are simplified. For high-density microstructures (such as micro-bump arrays) in heterogeneous integrated structures, traditionally, detailed modeling of each micro-bump and its contact interface is required. This invention uses an equivalent homogeneous layer method, which avoids defining thousands of micro-contact elements in the FEM model, reducing the complex contact problem to a simple constitutive relation or boundary condition definition. Specifically, based on the concept of representative volume element (RVE), for micro-bump arrays or weld point arrays, whose size is much smaller than the overall structure, a homogenization method is used. Mechanically, the equivalent elastic modulus and Poisson's ratio can be calculated using the Voigt-Reuss average model or the Eshelby inclusion model. Thermally, an equivalent thermal resistance model is used to replace the complex voids and contact interfaces, reducing the definition of tens of thousands of contact pairs to a simple interface condition.

[0043] Step 3: Third step of order reduction: Feature projection order reduction. This stage aims to achieve order reduction in the numerical solution layer. A strategy combining POD-RBF is adopted to reduce the high-dimensional simulation results to a low-dimensional modal space, so as to realize real-time and fast prediction of simulation results.

[0044] Simulation snapshot set acquisition: On the simplified finite element model, run a small number of high-fidelity simulations under different operating conditions (such as changes in ambient temperature and changes in chip power consumption) to obtain a snapshot set containing temperature field and displacement field.

[0045] POD Eigenmode Extraction: Orthogonal Eigenmode Decomposition (POD) is applied to the snapshot set. Specifically, Singular Value Decomposition (SVD) is performed on the snapshot matrix to project the high-dimensional physical field data into a low-dimensional space. In this step, SVD, as the core algorithm of POD, is used to extract the eigenvalues ​​of the system and their corresponding eigenvectors (i.e., eigenmodes). Subsequently, the eigenvalues ​​are sorted according to their magnitude, and the top k dominant eigenvectors with a cumulative energy contribution reaching a predetermined threshold (e.g., 99.9%) are selected as low-dimensional modal basis vectors, thereby achieving a dimensionality reduction representation of the main dynamic characteristics of the system.

[0046] RBF / GPR Mapping Construction: This step is based on the order reduction assumption that "the solution under any operating condition can be formed by a linear combination of a finite number of modal basis vectors," transforming the reconstruction of the physical field into solving for the modal coefficients. Using radial basis functions (RBF) or Gaussian regression (GPR), a nonlinear mapping model (ROM) is established from design parameters to modal coefficients (weighted coefficients used to adjust the contribution ratio of each order mode). When new design parameters are input (such as chip heat dissipation power, ambient temperature, and parameter perturbations of key materials), the ROM can skip tedious numerical iterations and quickly calculate the corresponding modal coefficients through mapping, thereby rapidly reconstructing the complete force-thermal response field through linear combination.

[0047] In this embodiment, the thermal stress of the substrate was calculated using a reduction-order method. Figure 5 ) and thermal strain results ( Figure 6 ), and the thermal strain distribution of the complete packaging structure ( Figure 7 Comparative verification shows that its force-thermal response field prediction accuracy meets the requirements. ,in Calculated value for ROM This process calculates the true values ​​for the finite element method. It reduces the solution time from hours to seconds. Figure 8 As shown, the global error is less than 1%, achieving high-precision and rapid prediction.

[0048] It is understood that the present invention has been described through some embodiments, and those skilled in the art will recognize that various changes or equivalent substitutions can be made to these features and embodiments without departing from the spirit and scope of the invention. Furthermore, under the teachings of the present invention, these features and embodiments can be modified to adapt to specific situations and materials without departing from the spirit and scope of the invention. Therefore, the present invention is not limited to the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the protection scope of the present invention.

Claims

1. A three-step method for order reduction in force-thermal coupling simulation of heterogeneous integrated structures, characterized in that, Includes the following steps: Step 1: Obtain the two-dimensional graphic file of the heterogeneous integrated structure, and then convert the geometric information in the two-dimensional graphic file into a three-dimensional finite element geometric model. During the conversion process, identify the different materials represented by different colors or gray levels in the graphic file layer by layer, and assign a material identifier to each pixel unit generated by discretization of the two-dimensional image. Step 2: Establish a material database containing all material properties in the heterogeneous integrated structure; traverse all pixel units of the three-dimensional finite element geometric model through the secondary development interface of computer software and external programming scripts to realize the lookup and batch assignment of material identifiers to the material database; simplify the equivalent boundary conditions of the heterogeneous interface with high-density micro-features. Step 3: Run high-fidelity simulations under different working conditions on the three-dimensional finite element geometric model after the simplification process in Step 2 to obtain a set of simulation snapshots of its force-thermal response field; apply the intrinsic orthogonal decomposition method to the snapshot set to extract the low-dimensional modal basis vectors of the system; use radial basis functions or Gaussian process regression to establish a nonlinear mapping model ROM from design parameters to modal coefficients to achieve real-time and rapid prediction of the force-thermal response field under new design parameters or working conditions.

2. The three-step order reduction method for force-thermal coupling simulation of heterogeneous integrated structures according to claim 1, characterized in that, The material identifiers are obtained in the following way: First, using predefined mesh coarsening rules, the two-dimensional images are stacked and discretized. Then, the element material identifiers provided by the FEM model are used to identify different materials represented by different colors or grayscale values ​​in the graphic file layer by layer. Finally, a three-dimensional finite element mesh with clear material identifiers is output.

3. The three-step order reduction method for force-thermal coupling simulation of heterogeneous integrated structures according to claim 2, characterized in that, The material properties in the material database include elastic modulus, Poisson's ratio, coefficient of thermal expansion, thermal conductivity, density, and specific heat capacity.

4. The three-step order reduction method for force-thermal coupling simulation of heterogeneous integrated structures according to claim 3, characterized in that, The simplification of equivalent boundary conditions includes calculating equivalent material parameters using homogenization methods, Voigt-Reuss average models, Eshelby inclusion models, or equivalent thermal resistance models.

5. The three-step order reduction method for force-thermal coupling simulation of heterogeneous integrated structures according to claim 4, characterized in that, The low-dimensional modal basis vectors are obtained in the following way: By performing singular value decomposition on the snapshot set matrix, the high-dimensional physical field data is projected into a low-dimensional space, and the system's eigenvalues ​​and their corresponding eigenvectors are extracted. Then, the eigenvalues ​​are sorted according to their magnitude, and the top k dominant eigenvectors whose cumulative energy contribution reaches a predetermined threshold are selected as low-dimensional modal basis vectors.

6. The three-step order reduction method for force-thermal coupling simulation of heterogeneous integrated structures according to claim 5, characterized in that, The nonlinear mapping model ROM is based on the reduced-order assumption that the solution under any operating condition is a linear combination of a finite number of modal basis vectors, and transforms the reconstruction of the physical field into solving for the modal coefficients.

7. The three-step order reduction method for force-thermal coupling simulation of heterogeneous integrated structures according to claim 6, characterized in that, The new design parameters or operating conditions input parameters, including but not limited to chip heat dissipation power, ambient temperature, and parameter disturbances of key materials.

8. The three-step order reduction method for force-thermal coupling simulation of heterogeneous integrated structures according to claim 7, characterized in that, The nonlinear mapping model ROM, during prediction, achieves the following prediction accuracy for its force-thermal response field: ,in Calculated value for ROM Calculate the true value for the finite element method.

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