Lightweight reusable thermal model for corelet packaging and method of constructing the same

Abstract

The application discloses a light-weight reusable thermal model suitable for core particle packaging and a construction method thereof. The light-weight reusable thermal model comprises a core particle thermal resistance network matrix and a thermal resistance network matrix of an interposer structure, is obtained through an interface model combination between boundary information of a light-weight core particle thermal model and a finite element model of an interposer structure subdomain, is used for solving boundary heat flux, is input into the light-weight core particle thermal model and the interposer finite element model after being converted into average flux distribution, and temperature field distribution inside the core particle and the interposer is obtained. The light-weight core particle thermal model comprises reduced-order basis functions obtained through model reduction and an artificial neural network learning a mapping relationship between boundary heat flux and corresponding low-order characteristic coefficients of the core particle temperature field. The thermal resistance network matrix of the core particle only needs to be extracted once in the initial modeling stage and can be repeatedly used in subsequent simulation. Through joint solving of the core particle and the interposer contact surface heat flux, the system temperature distribution can be quickly calculated.

Description

Technical Field

[0001] This invention belongs to the field of thermal modeling and simulation technology of integrated circuit packaging systems, and in particular, it is a lightweight and reusable thermal modeling method suitable for chiplet packaging structures, belonging to the field of integrated circuit thermal management and system-level thermal simulation. Background Technology

[0002] Chip-based packaging integration technology manufactures chips with different functions using their respective optimal processes, and then integrates them into a single packaging system using advanced packaging technology. This enables modular design and flexible configuration, thereby effectively improving chip yield, reducing manufacturing costs, and shortening the R&D cycle, and has significant engineering and economic value.

[0003] However, as the density and complexity of package integration continue to increase, the spatial distance between chips is shrinking, and power consumption is rising steadily, leading to a significant increase in local power density and making thermal issues in packaged systems increasingly prominent. High temperatures can cause device performance degradation, reduced reliability, and even thermal failure. Therefore, accurate and rapid thermal simulation analysis methods have become an indispensable key link in the thermal design process of chip systems, especially in the early stages of product design, where efficient thermal modeling and simulation of integrated packaged systems are of great significance.

[0004] Traditional thermal simulation methods for modeling highly complex multi-core package structures typically require constructing fine meshes and solving large-scale sparse matrices, resulting in long computation times and high resource consumption, making it difficult to meet the efficiency and real-time requirements of system-level package thermal simulation. Furthermore, existing methods often model the system as a whole, lacking flexibility and failing to meet design requirements such as module reuse or sensitivity analysis. As relatively stable and reusable modules, cores are still solved globally using traditional finite element or finite volume methods during thermal modeling, ignoring their invariant internal structure and the dominance of thermal boundary conditions, thus causing unnecessary redundant calculations.

[0005] Therefore, there is an urgent need for a lightweight chip thermal modeling method that takes into account accuracy, efficiency and reusability, can work in conjunction with traditional thermal models, and can support rapid analysis of thermal behavior and thermal design optimization of chip packaging systems, thereby solving the problems of high computational burden, low integration efficiency and high modeling repetition in existing technologies for thermal modeling of high-complexity packaging. Summary of the Invention

[0006] In view of the deficiencies of the prior art, the present application provides a lightweight reusable thermal model suitable for core particle packaging and a construction method thereof, which combines model reduction (MOR) technology and artificial neural network (ANN) to construct a core particle thermal model, and introduces a boundary condition independent modeling strategy, so as to realize rapid response to different boundary heat flux distributions, and has good system reusability and high simulation efficiency.

[0007] A lightweight reusable thermal model suitable for core particle packaging, comprising a core particle thermal resistance network matrix and a thermal resistance network matrix of an interposer structure, which is obtained by combining an interface model of boundary information between a lightweight core particle thermal model and a finite element model of an interposer structure subdomain, and is used for solving boundary heat flux Q B , which is converted into an average flux distribution and input into the lightweight core particle thermal model and the interposer finite element model to obtain the temperature field distribution inside the core particle and the interposer.

[0008] The core particle thermal resistance network matrix R C,B,B is extracted based on its stiffness matrix. The lightweight core particle thermal model comprises a model reduction to obtain a reduced basis function and an artificial neural network that learns the mapping relationship between the boundary heat flux and the core particle temperature field corresponding to the low-order characteristic coefficients, and the low-order characteristic coefficients and the reduced basis function are recombined to obtain the complete temperature field.

[0009] A construction method of a lightweight reusable thermal model suitable for core particle packaging, specifically comprising the following steps:

[0010] S1, system structure partitioning and modeling strategy

[0011] Based on the heat flux continuity principle, a thermal model space decoupling strategy is proposed, the core particle and its carrier are divided into multiple subdomains, and each subdomain can be independently modeled and reused, which is suitable for the modeling needs of modular integrated microsystems.

[0012] S2, lightweight core particle thermal modeling method

[0013] The model reduction (MOR) technology is used to reduce the dimension of the core particle temperature data under different boundary heat flux conditions, and the reduced characteristic coefficients are input into the artificial neural network to train the artificial neural network to learn the mapping relationship between the boundary heat flux and the core particle temperature field, so as to obtain the lightweight core particle thermal model, thereby rapidly reconstructing the core particle internal temperature distribution within milliseconds, and taking into account the calculation accuracy and model robustness.

[0014] S3, interface information exchange model

[0015] An interface model for transmitting boundary information between the light-weighted core pellet thermal model and the finite element model of the interposer structure sub-domain is established, and the thermal coupling of the whole system is realized by constructing a compact thermal resistance network matrix. After the solution is completed, the boundary heat flux obtained by the solution is input into the trained light-weighted core pellet thermal model and the finite element model of the interposer structure sub-domain to quickly solve the temperature field of the whole system. Once the thermal resistance network matrix is constructed, it can be reused without re-solving each time simulation, which can greatly improve the modeling efficiency.

[0016] S3.1, based on the principle of heat flux conservation, set the Neumann boundary condition on the contact surface, so that the independent solution results of adjacent sub-domains are consistent with the overall solution:

[0017]

[0018] wherein , are the material thermal conductivities of adjacent sub-domains Ω1 and Ω2, denotes the normal temperature gradient q Ω1 of sub-domain Ω1 on the boundary, Ω2 denotes the normal heat flux passing through the boundary.

[0019] S3.2, the heat conduction control equation is discretized by finite element:

[0020]

[0021] wherein, K represents the stiffness matrix, T is the temperature matrix, B P (P), B h (h, T 环境 ), B q (q) respectively represent the loading matrix related to power density, convection boundary and heat flux density at the contact boundary, P is the internal power density source term, q is the heat flux density at the contact boundary, h and T 环境 respectively represent the boundary convection heat transfer coefficient and the environment temperature.

[0022] S3.3, after the core pellet and the interposer are discretized, the corresponding stiffness matrix and the loading term are constructed:

[0023]

[0024]

[0025] wherein, K -1 is the inverse matrix of the stiffness matrix, the subscript C represents the core pellet model index, and I represents the interposer model index.

[0026] S3.4, under the steady-state assumption, the node temperature TC,B , T I,B

[0027]

[0028]

[0029] Since the corresponding point space positions of T C,B and T I,B are consistent, they have temperature consistency. Therefore, the model of the core particle and the interposer can be solved simultaneously at the contact surface to obtain the heat flux T P,C,B (P):

[0030]

[0031]

[0032]

[0033] where S n and q n represent the area and heat flux density corresponding to point n, respectively; N n represents the number of interpolation nodes related to the area S n , which depends on the type of interpolation function selected in the finite element discretization process. In the case of linear interpolation, N n is equal to the number of vertices of the element corresponding to S n . m represents the number of points.

[0034] S3.5, obtain the heat flux matrix Q B by merging and dimension reduction:

[0035]

[0036]

[0037]

[0038] where I B is an m-size unit matrix. R C,B,B and R I,B,B represent the thermal resistance network matrices of the core particle domain and the interposer domain, respectively. The heat flux matrix Q B can be normalized to obtain the average flux distribution w m after solving, and the solution of the core particle temperature field T q can be completed by inputting the pre-trained lightweight core particle model. For a core particle model with a fixed structure, the thermal resistance network matrix R C,B,B ​The core particle thermal resistance network matrix extracted from the stiffness matrix can be repeatedly used in subsequent simulation, and only needs to be extracted once in the initial modeling stage.

[0039] S4, system-level space cooperative simulation method

[0040] The core particle thermal resistance network matrix extracted from the stiffness matrix through matrix transformation is combined with the thermal resistance network matrix of the interposer structure to complete assembly of the system model, realize global thermal coupling solving, and obtain boundary heat flux Q B After the boundary heat flux is converted and input into the lightweight core particle thermal model and the interposer finite element model, the temperature field distribution inside the core particle and the interposer can be obtained, and finally the thermal simulation analysis of the multi-core particle packaging system is realized.

[0041] The present application has the following beneficial effects:

[0042] The method can splice multiple core particle lightweight thermal models and traditional finite element thermal models like building blocks to construct a system-level thermal model, and quickly calculate the system temperature distribution by jointly solving the contact surface heat flux. Compared with the traditional finite element method, the simulation speed can be accelerated by more than 10 times while ensuring an error within 2K, and the acceleration advantage is more significant in a high degree of freedom system. BRIEF DESCRIPTION OF DRAWINGS

[0043] Figure 1 : Core particle and interposer structure division schematic diagram

[0044] Figure 2 : Lightweight core particle thermal model modeling specific flowchart of the present application

[0045] Figure 3 : Area Correspondence diagram of heat flux density

[0046] Figure 4 : Modeling structure diagram of a multi-core particle integrated microsystem

[0047] Figure 5 : Finite element thermal simulation temperature field result of a multi-core particle integrated microsystem

[0048] Figure 6 : Lightweight core particle assembly model temperature field result of a multi-core particle integrated microsystem

[0049] Figure 7 : Comparison diagram of finite element lightweight core particle assembly model thermal simulation temperature field results of a multi-core particle integrated microsystem DETAILED DESCRIPTION

[0050] ​In order to make the technical solutions of the present application more clear and complete, a light-weight reusable thermal model for core particle packaging and a construction method thereof provided by the present application are described in detail below in combination with the drawings through specific examples:

[0051] A construction method of a light-weight reusable thermal model for core particle packaging, specifically comprising the following steps:

[0052] S1, according to the structural complexity and reusability of the integrated microsystem, the core particle and the packaging structure are divided into a core particle subdomain and an interposer structure subdomain. Because the core particle usually has a small fixed size and a defined heat power distribution, the design no longer changes, and is suitable for constructing a reusable model. The interposer structure subdomain such as an interposer has a larger geometric size and frequent material parameter changes, and is the core part of thermal design optimization, so the modeling freedom should be retained.

[0053] By dividing the complete integrated microsystem into a core particle subdomain and an interposer structure subdomain, different subdomains are modeled separately, and coupling solution is realized through interface boundaries, and finally the internal temperature distribution is reconstructed.

[0054] S2, as shown in Figure 2 , singular value decomposition is performed on the temperature data of the core particle subdomain under different boundary heat flux conditions, and an artificial neural network is trained using the reduced dimension characteristic coefficients to establish a fast mapping model from the boundary heat flux q to the temperature distribution T:

[0055]

[0056] wherein q0 is the total heat flux, w m is the average flux distribution, obtained by normalizing the boundary heat flux matrix Q B . U k is the kth column of the reduced basis function, and r represents the dimension of the reduced characteristic coefficient. N() is the trained artificial neural network function. The input of the artificial neural network function N() is the heat flux density of each node of the contact surface, and the output is the reduced coefficient. The light-weight core particle thermal model can predict the internal temperature distribution within milliseconds, and can be reused in different system packaging without re-modeling.

[0057] S3, based on the physical boundary conditions of heat flux conservation and temperature continuity, an interface information exchange model is constructed at the boundary of the light-weight core particle thermal model and the finite element model of the interposer structure subdomain, heat exchange is calculated, and boundary heat flux is transmitted through a thermal resistance network:

[0058]

[0059] wherein R C,B , R I,BBoundary thermal resistance matrix of the core particle domain and the interposer structure sub-domain, respectively; B q,C (q B ) is a boundary vector composed of the heat flux of the core particle contact surface; B q,I (q B ) represents a boundary vector composed of the heat flux of the interposer model contact surface; T P,C,B (P) is a temperature component obtained by driving the core particle power. Further, the heat flux matrix Q B can be efficiently solved by the following compact expression:

[0060]

[0061]

[0062]

[0063] where I B is the unit matrix. R C,B,B and R I,B,B represent the thermal resistance network matrix of the core particle domain and the interposer structure sub-domain, respectively. The heat flux matrix Q B can be obtained by normalization after solving. m The average flux distribution w m can be obtained by normalization after solving. q The solution of the core particle temperature field T C,B,B can be completed by inputting the average flux distribution w m into the trained lightweight core particle model in step S2. The thermal resistance network matrix R C,B,B of the core particle domain can be reused in multiple simulations once extracted, thereby effectively improving the overall simulation efficiency. This mechanism realizes the transmission and joint solution of thermal information between different modeling domains.

[0064] S4, the above model is used for thermal simulation verification of a multi-core particle integrated system as shown in Figure 4 The system includes two graphics processing units (GPU) Chiplets, one control processing unit (CPU) Chiplet, and three high bandwidth memory (HBM) Chiplets. Through the above modeling strategy, the corresponding lightweight core particle thermal model is obtained by modeling different Chiplets. The lightweight core particle thermal model and the interposer structure sub-domain finite element thermal model can be flexibly combined in space. After model assembly, the thermal resistance network matrix of the lightweight core particle thermal model and the thermal resistance network matrix of the interposer structure can be combined to realize global thermal coupling solution, obtain the boundary heat flux Q B , and finally input into the lightweight core particle thermal model to obtain the Chiplet internal temperature field distribution, and finally realize the thermal simulation analysis of the multi-core particle packaging system (such as the co-packaging structure of GPU, CPU, and HBM).

[0065] Figure 5 、 Figure 6 are respectively for the multi-core particle integrated system instance shown in Figure 4 The experimental results of thermal simulation using finite element model and the present method for the multi-core particle integrated system instance shown in Figure 7 is the error between the present method and the finite element model simulation. According to the simulation results, compared with the finite element model, the simulation speed is improved by more than 10 times under the premise of maximum temperature difference error < 2K by the reuse of the lightweight core particle thermal model, which effectively supports the thermal design optimization and sensitivity analysis of the core particle packaging system level.

[0066] In summary, the present embodiment provides a lightweight core particle thermal model method with reusable structure, high efficiency and reliable precision, which can be widely applied to the thermal analysis and design tasks of future high-density and high-performance core particle packaging systems.

[0067] Note that the above are only the preferred embodiments of the present application and the technical principles applied. Those skilled in the art will understand that the present application is not limited to the specific embodiments described herein, and those skilled in the art can make various obvious changes, readjustments and substitutions without departing from the scope of the present application. Therefore, although the present application has been described in more detail through the above embodiments, the present application is not limited to the above embodiments, and can include more other equivalent embodiments without departing from the concept of the present application, and the scope of the present application is determined by the scope of the appended claims.

Claims

1. A method for constructing a lightweight reusable thermal model suitable for die package, characterized in that: Specifically comprising the following steps: S1, the core particle and the packaging structure of the integrated microsystem are divided into domains to obtain the core particle domain and the interposer structure subdomain; S2, the model reduction technology is used to reduce the dimension of the core particle temperature data under different boundary heat flux conditions, and the characteristic coefficients after dimension reduction are input into the artificial neural network to train the artificial neural network to learn the mapping relationship between the boundary heat flux and the core particle temperature field, and obtain the lightweight core particle thermal model; S3, a thermal resistance network matrix is constructed to establish an interface model for transferring boundary information between the lightweight core particle thermal model and the finite element model of the interposer structure subdomain: S3.1, based on the heat flux conservation principle, the Neumann boundary condition is set on the contact surface of the subdomain, so that the independent solving result of the adjacent subdomain is consistent with the overall solving; S3.2, the heat conduction control equation of the integrated microsystem is discretized by finite element; S3.3, after the core particle domain and the interposer structure subdomain are discretized, the corresponding stiffness matrix and load term are constructed: where K -1 is the inverse of the stiffness matrix, B P (P), B h (h, T 环境 ), and B q (q) are the loading matrices related to the power density, convection boundary, and heat flux density at the contact boundary, respectively, P is the internal power density source term, q is the heat flux density at the contact boundary, h and T 环境 are the boundary convection heat transfer coefficient and ambient temperature, respectively; the subscript C denotes the core particle model index, and I denotes the interposer model index. S3.4, under the steady-state assumption, the node temperatures T of the lightweight core pellet thermal model and the finite element model of the interposer structure subdomain at the boundary surface are simplified as: C,B , I,B ​ Since the node temperature T C,B corresponds to the point space position of T I,B , it has temperature consistency, so the lightweight core particle thermal model and the finite element model of the interposer structure sub-domain are coupled at the contact surface, and the heat flux T P,C,B (P) is solved by heat resistance network transmission. where S m and q m represent the area and heat flux density of the point n respectively; m represents the number of points; N m represents the number of interpolation nodes related to the area S m ; R C,B , R I,B represent the boundary thermal resistance matrix of the core particle domain and the interlayer structure subdomain respectively; B q,C (q B ) is the boundary vector composed of the heat flux of the core particle contact surface; B q,I (q B ) represents the boundary vector composed of the heat flux of the interlayer model contact surface; S4, thermal resistance network matrix R using core particle domains and interposer subdomains C,B,B and R I,B,B combining the lightweight core particle thermal model and the finite element model of the interposer structure subdomain to solve for the boundary heat flux Q B : where I B is an m x m identity matrix; The boundary heat flux Q B The normalized average flux distribution w m is obtained, and the trained lightweight kernel model is input to complete the solution of the kernel temperature field T q .

2. The method of claim 1, wherein the method is applied to a core package. The temperature data of the core particle domain under different boundary heat flux conditions are singular value decomposed, the characteristic coefficients after dimension reduction are used to train the artificial neural network, and a fast mapping model from the boundary heat flux q to the temperature distribution T is established: where q0is the total heat flux, w m is the average flux distribution, which is obtained by normalizing the boundary heat flux matrix Q B ; U k is the kth column of the reduced basis function, and r represents the dimension of the reduced characteristic coefficients; N() is the trained artificial neural network function; the input of the artificial neural network function N() is the average flux distribution of each node, and the output is the reduced coefficient.

3. A method of thermal simulation analysis of a multi-chip package system, characterized by: A lightweight reusable thermal model suitable for core particle packaging is constructed by the method of claim 1, the lightweight core particle thermal model and the finite element model of the interposer structure sub-domain are combined through the core particle thermal resistance network matrix and the thermal resistance network matrix of the interposer structure, the assembly of the system model is completed, the global thermal coupling is solved, and the boundary heat flux Q is obtained B After the boundary heat flux is converted and input into the lightweight core particle thermal model and the interposer finite element model, the temperature field distribution inside the core particle and the interposer is obtained, and finally the thermal simulation analysis of the multi-core particle packaging system is realized.

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