A numerical method for transient thermal simulation of a core pellet integration system

Abstract

The application provides a numerical method for transient thermal simulation of a core particle integrated system, and the method comprises the following steps: according to the function and structural characteristics of the core particle integrated system, the whole system is divided into several modules; the time-domain heat conduction control equation in each module is converted to the Laguerre domain; the heat transfer characteristics of each module are extracted based on the Laguerre domain heat conduction equation, and the corresponding Laguerre macro model is established; the Laguerre macro model is used as an equivalent boundary condition, and the finite volume method is used to solve the transient thermal response of each module in the order stepping mode. Under the premise of ensuring the calculation accuracy, the Laguerre macro model simultaneously reduces the calculation complexity of the spatial domain and the time domain, significantly improves the simulation efficiency, and reduces the consumption of calculation resources.

Description

Technical Field

[0001] This invention relates to the field of numerical simulation and computation technology, and more specifically, to a numerical method for transient thermal simulation of core-particle integrated systems. Background Technology

[0002] With the rapid development of heterogeneous integration technology, chip-based integration technology has become an important path for building high-performance computing systems. Chips with different process nodes and functions can achieve high-bandwidth, low-latency interconnect integration through silicon interposers. Compared with traditional monolithic designs, it has significant advantages in system integration, interconnect efficiency, and overall energy efficiency. However, to meet the ever-increasing computing performance demands, multiple chips are usually compactly arranged within a limited package space, leading to a sharp increase in system power density and a significant rise in local hotspot temperatures, which in turn poses a potential threat to system reliability. Therefore, in the design process of chip-integrated systems, efficient and accurate analysis and prediction of transient thermal behavior has become a key link in ensuring system performance and reliability.

[0003] Numerical methods are currently the commonly used approach for transient thermal simulation of core-particle integrated systems. However, due to the complex structure and high integration of core-particle integrated systems, transient thermal analysis of the complete system usually requires solving a large set of discrete equations. This leads to the common problems of low computational efficiency, long simulation time, and huge consumption of computational resources in practical applications, making it difficult to meet the needs of rapid design iteration. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention aims to provide a numerical method for transient thermal simulation of core-particle integrated systems. This method constructs Laguerre macromodels of each functional module in the system, transforming their internal heat transfer characteristics into equivalent thermal boundary conditions between modules. This simultaneously reduces the computational complexity of the original problem in both the time and spatial domains, significantly improving the efficiency of transient thermal simulation.

[0005] The specific technical solution of this invention is as follows:

[0006] A numerical method for transient thermal simulation of chip-integrated systems includes the following steps:

[0007] Based on the functional and structural characteristics of the core-particle integrated system, the overall system is decomposed into several modules;

[0008] Transform the time-domain heat conduction control equations within each module to the Laguerre domain;

[0009] The heat transfer characteristics of each module are extracted based on the Laguerre domain heat conduction equation, and the corresponding Laguerre macro model is established.

[0010] Using the Laguerre macro model as the equivalent boundary condition, the transient thermal response of each module is solved by the finite volume method in an order-step manner.

[0011] Preferably, the step of decomposing the overall system into several modules based on the functional and structural characteristics of the core-particle integrated system specifically includes: decomposing the core-particle integrated system into several modules, wherein the modules are reusable and composable, and support independent modeling and assembly.

[0012] Preferably, in the step of transforming the time-domain heat conduction control equations within each module to the Laguerre domain, the domain transformation step of the control equations includes:

[0013] The first step is to expand the time-domain temperature field variables using weighted Laguerre polynomials, and express them as a weighted summation of weighted Laguerre polynomials.

[0014] The second step is to substitute the expansion from the first step into the time-domain heat conduction control equation, and then multiply both sides of the equation by a weighted Laguerre polynomial for test integration.

[0015] The third step is to use the orthogonality of Laguerre polynomials to eliminate the time variable in the control equation, thereby obtaining the corresponding Laguerre domain heat conduction control equation.

[0016] Preferably, in the step of extracting the heat transfer characteristics of each module based on the Laguerre domain heat conduction equation and establishing the corresponding Laguerre macromodel, the step of establishing the Laguerre macromodel includes:

[0017] The first step is to use the finite volume method to spatially discretize the heat conduction control equations of the Laguerre domain in each module and establish the corresponding matrix equations.

[0018] The second step is to set the Laguerre domain temperature at the module interface to zero, solve the Laguerre domain temperature distribution of the module based on the matrix equation obtained in the first step, and further calculate the Laguerre domain heat flux density at the interface, which is denoted as the reference Laguerre domain heat flux density at the interface.

[0019] The third step is to apply a uniform Laguerre domain temperature rise excitation to each surface element of the interface in sequence, while keeping the Laguerre domain temperature at zero on other surface elements. Based on the matrix equation obtained in the first step, solve for the Laguerre domain heat flux density on the interface, and record the Laguerre domain heat flux density matrix formed by the selected Laguerre domain temperature rise excitation magnitude and the corresponding interface Laguerre domain heat flux density.

[0020] The fourth step is to establish a Laguerre macromodel based on the interface reference Laguerre domain heat flux density obtained in the second step and the Laguerre domain temperature rise excitation magnitude and Laguerre domain heat flux density matrix recorded in the third step.

[0021] Preferably, in the step of using the Laguerre macro model as the equivalent boundary condition and employing the finite volume method to solve the transient thermal response of each module in an order-step manner, the order-step solution step for the transient thermal response of each module includes:

[0022] The first step is to select the core module according to the thermal simulation requirements, and use the Laguerre macromodel of other modules as the equivalent boundary conditions on the interface of the core module. The finite volume method is used to solve the Laguerre domain temperature distribution of the core module.

[0023] The second step is to calculate the Laguerre domain temperature distribution on the interface based on the Laguerre domain temperature distribution of the core module obtained in the first step, and apply it as the first type of boundary condition to the interface of other modules to solve the Laguerre domain temperature distribution of other modules.

[0024] The third step involves reconstructing the transient temperature response of each module based on the Laguerre domain temperature distributions of the core module and other modules obtained in the first and second steps, thereby obtaining the transient temperature distribution of the entire system in the time domain.

[0025] Compared with the prior art, the present invention has the following beneficial effects:

[0026] 1. The heat conduction control equation is transformed from the time domain to the Laguerre domain, and the traditional time-step solution method is replaced with an efficient order-step solution process, which effectively reduces the amount of computation in the time domain and further improves the overall efficiency of transient thermal simulation.

[0027] 2. The core-particle integrated system is divided into several modules, and the equivalent thermal boundary conditions of the module interface are constructed using the Laguerre macro model. This decomposes the large-scale problem that originally required global solution into local sub-problems within each module, thereby significantly reducing computational complexity in the spatial domain and improving the solution efficiency of transient thermal simulation. Attached Figure Description

[0028] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings:

[0029] Figure 1 This is a flowchart of the numerical method for transient thermal simulation of chip-integrated systems according to the present invention;

[0030] Figure 2 This is a schematic diagram showing the module breakdown of the core-particle integrated system of the present invention;

[0031] Figure 3 This is a schematic cross-sectional view of a typical chip integration system in a specific embodiment;

[0032] Figure 4 This is a schematic diagram of the chip layer layout in a specific embodiment;

[0033] Figure 5 This is a chip power consumption distribution diagram of a specific embodiment;

[0034] Figure 6 This is a transient temperature response curve at a core observation point in a specific embodiment. Detailed Implementation

[0035] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present invention. These all fall within the protection scope of the present invention.

[0036] Specifically, this invention provides a numerical method for transient thermal simulation of core-particle integrated systems, such as... Figure 1 As shown, the method includes the following steps:

[0037] S1: Based on the functional and structural characteristics of the core-particle integrated system, the overall system is decomposed into several modules;

[0038] Specifically, such as Figure 2 As shown, the core-particle integrated system is decomposed into several modules. These modules are reusable and combinable, and support independent modeling and assembly, laying the foundation for modular thermal simulation.

[0039] S2: Transform the time-domain heat conduction control equations in each module to the Laguerre domain;

[0040] Specifically, in step S2, the domain transformation of the governing equations is performed as follows:

[0041] Step S21, the governing equation for the transient heat conduction problem within the invariant region is:

[0042]

[0043] Where ρ is the mass density, and c p Here, T is heat capacity, κ is thermal conductivity, and Q is the heat source. The time-domain temperature field variable... Expanding using weighted Laguerre polynomials, it can be expressed as:

[0044]

[0045] in, It is a weighted Laguerre polynomial. is the Laguerre temperature coefficient, s is the time scaling factor, and p is the order of the weighted Laguerre polynomial. For ease of expression, let's denote it as... .

[0046] Step S22, expand the formula in step S21 Substituting into the time-domain heat conduction control equation In the middle, multiply both sides of the equation by a q-order weighted Laguerre polynomial. exist Perform test scoring

[0047] .

[0048] Step S23: Eliminate the time variable in the governing equation using the orthogonality of Laguerre polynomials. Thus, the corresponding Laguerre domain heat conduction governing equations are obtained:

[0049]

[0050] in

[0051] .

[0052] S3: Extract the heat transfer characteristics of each module based on the Laguerre domain heat conduction equation and establish the corresponding Laguerre macro model;

[0053] Specifically, in step S3, the steps for establishing the Laguerre macro model are as follows:

[0054] Step S31: Use the finite volume method to determine the governing equations of heat conduction in the Laguerre domain within each module. Discretize the space and establish the corresponding matrix equation:

[0055]

[0056] Where K is the system matrix and is independent of the order q, T q f represents the temperature coefficient vector in the Laguerre domain. q b represents the contribution from known excitations within the module (e.g., volume heat sources, boundary heat sources, and the temperature coefficient of the previous order (q−1)). q This is related to the unknown excitation at the interface and is used to characterize the thermal effects from other modules.

[0057] According to different types of incentives, the formula It can be decomposed into:

[0058]

[0059] and

[0060]

[0061] Where, formula In It can be solved independently, while the formula Solving this problem requires considering the influence of other modules. To characterize this influence, we further establish a Laguerre macro model.

[0062] Step S32: Set the Laguerre domain temperature at the module interface to zero, based on the matrix equation obtained in step S31. The Laguerre domain temperature distribution of the solution module is solved, and the Laguerre domain heat flux density at the interface is further calculated, denoted as the reference Laguerre domain heat flux density Q0 at the interface.

[0063] Step S33: Apply a uniform Laguerre domain temperature rise excitation sequentially to M surface elements at the interface, while keeping the Laguerre domain temperature zero on the other surface elements, according to the matrix equation obtained in the first step. Solve for the Laguerre heat flux density at the interface, and record the Laguerre heat flux density matrix formed by the selected Laguerre temperature rise excitation magnitude and the corresponding interface Laguerre heat flux density. The magnitude of the temperature rise excitation applied to the j-th (j = 1,2, …, M) surface element is denoted as ∆T. j The vector formed by the heat flux values ​​of the M surface elements on the interface is denoted as Q. j .

[0064] Step S34: Based on the interface reference Laguerre domain heat flux density Q0 obtained in step S32 and the Laguerre domain temperature rise excitation magnitude and Laguerre domain heat flux density matrix recorded in step S33, calculate the equivalent thermal conductivity G between the j-th surface element and the i-th (i = 1,2,…,M) surface element. ij

[0065] .

[0066] Based on the superposition theorem, a mapping relationship is constructed between the Laguerre domain temperature T and the Laguerre domain heat flux Q at the interface, i.e., the Laguerre macromodel:

[0067]

[0068] in, It is by The determined interface heat flux in the Laguerre domain, G, is determined by... The calculated M×M thermal conductivity matrix.

[0069] S4: Using the Laguerre macro model as the equivalent boundary condition, the transient thermal response of each module is solved by the finite volume method in an order-step manner.

[0070] Specifically, in step S4, the order step solution steps for the transient thermal response of each module are as follows:

[0071] Step S41: Select the core module according to the thermal simulation requirements, and use the Laguerre macromodel of the other modules. As equivalent boundary conditions at the interface of the core module, the Laguerre domain temperature distribution of the core module is solved using the finite volume method. ;

[0072] Step S42, based on the Laguerre domain temperature distribution of the core module obtained in step S41. The Laguerre domain temperature at the center of the volume element adjacent to the interface is selected and denoted as . According to the finite volume method, the heat flow on the j-th surface element at the interface is determined by... The calculation yielded:

[0073]

[0074] in, s j It is the area of ​​the surface units on the interface, κ j It is thermal conductivity, l j It is the distance from the center of a surface element to the center of its adjacent volume element. (Combined formula) and We obtain:

[0075]

[0076] in, It is an M×M diagonal matrix whose elements are composed of... Decision. Further, by solving the formula... The Laguerre domain temperature distribution T at the interface is obtained and applied as a first-type boundary condition to the interfaces of other modules. The equation is then solved. The Laguerre domain temperature distribution of other modules was obtained. .

[0077] Step S43: By repeating steps S41 and S42, the Laguerre temperature coefficients of the core module and other modules are obtained sequentially in an order-step manner until the results converge. It is assumed that the first N Laguerre temperature coefficients are obtained at this point. Further, according to the formula... and Reconstruct the time-domain temperature response of the core module and other modules.

[0078]

[0079]

[0080] A specific embodiment is calculated based on the numerical method of the present invention described above.

[0081] The following is in conjunction with the accompanying drawings, Figure 3 The implementation of the technical solution is further described in detail using the transient thermal simulation of a typical chip-integrated system as an example. Obviously, the described embodiments are only some, not all, of the embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without inventive effort are within the scope of protection of this invention.

[0082] This embodiment is a typical chip-integrated system, and its cross-sectional schematic diagram is shown below. Figure 3 As shown. Its chip layer chip layout is as follows. Figure 4 As shown, the corresponding power consumption distribution is as follows: Figure 5 As shown. In this embodiment, the overall system is decomposed into three modules. Module 1 includes a heat sink, a heat conductor, and a thermal interface material; Module 2 includes a chip layer, micro solder balls, and a redistribution layer; Module 3 includes an interposer layer, C4 filler material, a packaging substrate, a ball grid array, and a printed circuit board. Module 2 is selected as the core module.

[0083] In this embodiment, convective boundary conditions are applied to the surface of the heat sink and the bottom surface of the printed circuit board, with convective heat transfer coefficients of 400 W / (m²·K) and 10 W / (m²·K), respectively. The ambient temperature is 300 K. Other outer surface boundaries are set as adiabatic boundaries.

[0084] To verify the effectiveness of the method of this invention, a time step of 0.01 s was selected, and 5000 time steps were performed. Transient thermal simulations were conducted using both the method of this invention and the commercial software FLUENT. The center of the core particle was set as the observation point, and its transient temperature response is as follows. Figure 6 As shown, the results show that the method of this invention is in excellent agreement with the calculation results of FLUENT, fully verifying the effectiveness of the method. To demonstrate the high efficiency of the method, the overall time of transient thermal simulation was statistically analyzed. The method of this invention took 2 m 49 s, while FLUENT took 6 h 40 m 50 s, achieving a speedup of 142 times.

[0085] Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. Unless otherwise specified, the embodiments and features described in this application can be arbitrarily combined with each other.

Claims

1. A numerical method for transient thermal simulation of core-particle integrated systems, characterized in that, The method includes the following steps: Based on the functional and structural characteristics of the core-particle integrated system, the overall system is decomposed into several modules; Transform the time-domain heat conduction control equations within each module to the Laguerre domain; Based on the Laguerre domain heat conduction equation, the heat transfer characteristics of each module are extracted, and the corresponding Laguerre macromodel is established. The steps for establishing the Laguerre macromodel include: The first step is to use the finite volume method to spatially discretize the heat conduction control equations of the Laguerre domain in each module and establish the corresponding matrix equations. The second step is to set the Laguerre domain temperature at the module interface to zero, solve the Laguerre domain temperature distribution of the module based on the matrix equation obtained in the first step, and further calculate the Laguerre domain heat flux density at the interface, which is denoted as the reference Laguerre domain heat flux density at the interface. The third step is to apply a uniform Laguerre domain temperature rise excitation to each surface element of the interface in sequence, while keeping the Laguerre domain temperature at zero on other surface elements. Based on the matrix equation obtained in the first step, solve for the Laguerre domain heat flux density on the interface, and record the Laguerre domain heat flux density matrix formed by the selected Laguerre domain temperature rise excitation magnitude and the corresponding interface Laguerre domain heat flux density. The fourth step is to establish a Laguerre macromodel based on the interface reference Laguerre domain heat flux density obtained in the second step and the Laguerre domain temperature rise excitation magnitude and Laguerre domain heat flux density matrix recorded in the third step. Using the Laguerre macro model as equivalent boundary conditions, the transient thermal response of each module is solved using the finite volume method in an order-step manner. The order-step solution steps for the transient thermal response of each module include: The first step is to select the core module according to the thermal simulation requirements, and use the Laguerre macromodel of other modules as the equivalent boundary conditions on the interface of the core module. The finite volume method is used to solve the Laguerre domain temperature distribution of the core module. The second step is to calculate the Laguerre domain temperature distribution on the interface based on the Laguerre domain temperature distribution of the core module obtained in the first step, and apply it as the first type of boundary condition to the interface of other modules to solve the Laguerre domain temperature distribution of other modules. The third step involves reconstructing the transient temperature response of each module based on the Laguerre domain temperature distributions of the core module and other modules obtained in the first and second steps, thereby obtaining the transient temperature distribution of the entire system in the time domain.

2. The numerical method for transient thermal simulation of chip-integrated systems according to claim 1, characterized in that, The step of decomposing the overall system into several modules based on the functional and structural characteristics of the core-particle integrated system specifically includes: decomposing the core-particle integrated system into several modules, wherein the modules are reusable and composable, and support independent modeling and assembly.

3. The numerical method for transient thermal simulation of chip-integrated systems according to claim 1, characterized in that, The step of transforming the time-domain heat conduction control equations within each module to the Laguerre domain includes the following domain transformation steps: The first step is to expand the time-domain temperature field variables using weighted Laguerre polynomials, and express them as a weighted summation of weighted Laguerre polynomials. The second step is to substitute the expansion from the first step into the time-domain heat conduction control equation, and then multiply both sides of the equation by a weighted Laguerre polynomial for test integration. The third step is to use the orthogonality of Laguerre polynomials to eliminate the time variable in the control equation, thereby obtaining the corresponding Laguerre domain heat conduction control equation.

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