Method for evaluating influence of convective heat transfer coefficient on hot spot temperature of integrated packaging system

Abstract

The invention provides a method for evaluating the influence of a convective heat transfer coefficient on the hot spot temperature of an integrated packaging system, and the method comprises the steps: dividing the whole system into a packaging region and a chip region according to the distribution of a heat source and a packaging position of the integrated packaging system; a key reference value is determined based on the change range of the convective heat transfer coefficient in the packaging area; establishing a temperature-heat flow mapping relation on the regional interface; constructing a rational expression of the mapping relation matrix about the convective heat transfer coefficient; and constructing an equivalent thermal boundary condition of the chip area through a rational expression, and evaluating the hot-spot temperature of the chip area in combination with a finite volume method. According to the method, the temperature-heat flow mapping relation and the rational expression are introduced, the influence of the convective heat transfer coefficient on the integrated packaging system is accurately represented, the calculation efficiency is remarkably improved on the premise of ensuring the reliable calculation precision, and the evaluation process of the hot spot temperature of the system under different convective heat transfer coefficients is optimized.

Description

Technical Field

[0001] This invention relates to the field of temperature field simulation technology for integrated packaging systems, and more specifically, to a method for evaluating the influence of convective heat transfer coefficient on hot spot temperature of integrated packaging systems. Background Technology

[0002] Integrated packaged systems, with their highly integrated architecture, demonstrate significant advantages in improving computing performance, reducing power consumption, and miniaturizing device size, thus enhancing the overall performance of products. However, with the increasing complexity of integrated packaged system functions and the continuous shrinking of process nodes, the significant increase in power density brings severe thermal management challenges. Elevated localized hotspot temperatures can cause circuit performance degradation and even reliability issues such as thermal failure. Therefore, to fully address these challenges during the design phase, efficient thermal analysis methods must be employed to accurately assess the thermal behavior of integrated packaged systems, thereby ensuring system reliability and superior performance.

[0003] Numerical methods are crucial for studying the impact of convective heat transfer coefficients on hotspot temperatures in integrated packaged systems (IPS). This allows for verification of the system's thermal completeness under varying heat dissipation conditions, ultimately guiding optimized design. However, existing solutions suffer from two main problems: First, the thermal design of IPS requires frequent adjustments to the boundary convective heat transfer coefficients to study the system's thermal behavior under different conditions. Each change necessitates a complete re-simulation of the entire system, leading to significant computational resource consumption and reduced design efficiency. Second, in IPS thermal design, designers primarily focus on hotspot temperatures within the chip region, while the thermal distribution within the package structure is not a core design metric. Therefore, effectively improving the simulation efficiency of IPS using appropriate techniques under different heat dissipation environments is key to achieving agile optimization design. Summary of the Invention

[0004] To address the shortcomings of existing technologies, the present invention aims to provide a method for evaluating the impact of convective heat transfer coefficient on the hot spot temperature of an integrated packaging system. This method is used for the simulation and optimization design of integrated packaging systems. By using the temperature-heat flux mapping relationship and rational expressions, the impact of the convective heat transfer coefficient on the integrated packaging system is accurately characterized, thereby avoiding repeated solutions to the entire system and significantly improving simulation and design efficiency.

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

[0006] A method for evaluating the impact of convective heat transfer coefficient on hot spot temperature of an integrated packaging system includes the following steps:

[0007] Based on the distribution of heat sources and packaging locations in the integrated packaging system, the overall system is divided into a packaging area and a chip area.

[0008] Based on the range of variation of the convective heat transfer coefficient in the encapsulation region, key reference values ​​are determined;

[0009] Establish the temperature-heat flux mapping relationship at the regional interface;

[0010] Construct a rational expression for the mapping matrix with respect to the convective heat transfer coefficient;

[0011] The equivalent thermal boundary conditions of the chip region are constructed using rational expressions, and the hot spot temperature of the chip region is evaluated by combining the finite volume method.

[0012] Preferably, in the step of dividing the overall system into a packaging region and a chip region based on the distribution of heat sources and packaging positions of the integrated packaging system, the packaging region is a packaging and heat dissipation structure containing convection boundaries, and the chip region is an integrated circuit chip containing heat sources.

[0013] Preferably, in the step of determining the key reference value based on the variation range of the convective heat transfer coefficient in the encapsulation region, the key reference value h k From the interpolation formula The calculations are as follows, where k takes values ​​of 1, 2, and 3, and h... min and h max These are the minimum and maximum values ​​of the convective heat transfer coefficient, respectively.

[0014] Preferably, in the step of establishing the temperature-heat flux mapping relationship at the interface of the regions, the steps for establishing the mapping relationship are as follows:

[0015] The first step is to set the heat transfer coefficient of the convection boundary as the key reference value and set the temperature of the interface between the package area and the chip area as the ambient temperature. The finite volume method is used to solve the steady-state heat conduction equation in the package area to obtain the heat flow of the center node of each surface unit on the interface, which is denoted as the reference heat flow of the interface.

[0016] The second step is to apply a uniform temperature rise excitation to each surface element of the interface in sequence, while keeping the ambient temperature on other surface elements, and record the selected temperature rise excitation magnitude and the heat flow matrix formed by the corresponding interface heat flow.

[0017] The third step is to calculate the mapping matrix based on the interface reference heat flow obtained in the first step and the temperature rise excitation magnitude and heat flow matrix recorded in the second step.

[0018] Preferably, in the step of constructing a rational expression for the mapping relationship matrix with respect to the convective heat transfer coefficient, the calculation steps for the coefficient matrix of the rational expression are as follows:

[0019] The first step is to derive an approximate rational expression for the mapping relationship matrix with respect to the convective heat transfer coefficient by combining the finite volume method and matrix theory;

[0020] The second step is to substitute the key reference values ​​of the convective heat transfer coefficient and its corresponding mapping matrix into the rational expression to obtain a system of equations about the coefficient matrix.

[0021] The third step is to solve the system of equations constructed in the second step to obtain the coefficient matrix.

[0022] Preferably, in the step of constructing the equivalent thermal boundary conditions of the chip region through rational expressions and evaluating the hot spot temperature of the chip region using the finite volume method, the calculation steps for the hot spot temperature are as follows:

[0023] The first step is to calculate the mapping matrix corresponding to the discrete values ​​of the convection heat transfer coefficient based on the actual convection heat transfer coefficient in the encapsulation area using a rational expression;

[0024] The second step is to treat the temperature-heat flux mapping matrix as the equivalent thermal boundary condition of the chip region and apply the finite volume method to solve for the temperature distribution in the chip region, thereby obtaining its hot spot temperature.

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

[0026] 1. This invention decomposes the integrated packaging system into a packaging region and a chip region. By constructing equivalent thermal boundary conditions at the interface of the chip region, thermal simulation is performed only on the chip region, thereby significantly reducing the number of unknowns to be solved and improving simulation efficiency.

[0027] 2. When the convective heat transfer coefficient of the packaging area of ​​the integrated packaging system changes, the corresponding temperature-heat flux mapping matrix can be calculated through rational expressions, avoiding repeated solutions for the packaging area and thus significantly improving simulation efficiency. 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 illustrating the method of evaluating the effect of convective heat transfer coefficient on the hot spot temperature of an integrated packaging system according to the present invention.

[0030] Figure 2 This is a schematic diagram of the region decomposition strategy proposed in this invention;

[0031] Figure 3 This is a schematic diagram of the geometry of an integrated packaging system in a specific embodiment;

[0032] Figure 4 This is a cross-sectional schematic diagram of an integrated package system without a heat sink in a specific embodiment;

[0033] Figure 5 This is a curve comparison of the influence of the convective heat transfer coefficient on the hot spot temperature of the system in a specific embodiment. Detailed Implementation

[0034] 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.

[0035] Specifically, this invention provides a method for evaluating the impact of convective heat transfer coefficient on the hot spot temperature of an integrated packaging system, such as... Figure 1 As shown, the method includes the following steps:

[0036] S1: Based on the distribution of heat sources and packaging locations in the integrated packaging system, the overall system is divided into a packaging area and a chip area;

[0037] Specifically, such as Figure 2 As shown, in step S1, the packaging area is a packaging and heat dissipation structure containing convection boundaries. The convection heat transfer coefficient of the boundary will change frequently during the thermal design process to simulate different heat dissipation environments. The chip area is an integrated circuit chip containing a heat source, and its hot spot temperature is the core indicator of the thermal design of the integrated packaging system.

[0038] S2: Determine key reference values ​​based on the range of variation of the convective heat transfer coefficient in the encapsulation region;

[0039] Specifically, in step S2, let h min and h max Let be the minimum and maximum values ​​of the convective heat transfer coefficient, respectively. Then, the three key reference values ​​are obtained by interpolation formula. The calculated values ​​are denoted as h1, h2, and h3, respectively.

[0040]

[0041] S3: Establish the temperature-heat flux mapping relationship at the interface of the region;

[0042] Specifically, in step S3, the steps for establishing the mapping relationship matrix are as follows:

[0043] Step S31: Set the heat transfer coefficients of the convection boundary to key reference values ​​h1, h2, and h3 respectively, and set the temperature of the interface between the packaged area and the chip area to the ambient temperature T. amb The steady-state heat conduction equation within the encapsulated region is solved using the finite volume method. Assuming there are M surface elements on the spatially discretized interface, the heat flux values ​​at the center nodes of each surface element on the interface are interpolated based on the temperature distribution within the fixed region obtained from the solution. These interpolated values ​​are denoted as the reference heat flux of the interface, and these M heat flux values ​​are combined into a vector denoted as Q0.

[0044] Step S32: Apply a uniform temperature rise excitation sequentially to M surface elements on the interface, while maintaining ambient temperature on the other surface elements. Record the selected temperature rise excitation magnitude and the corresponding heat flux matrix formed by the interface heat flux. Let ∆T be the magnitude of the temperature rise excitation applied to the j-th surface element. j By applying the finite volume method, a vector consisting of the heat flux values ​​at the center nodes of the M surface elements on the interface is obtained, denoted as Q. j .

[0045] Step S33: Based on the interface reference heat flux obtained in step S31 and the temperature rise excitation magnitude and heat flux matrix recorded in step S32, calculate the mapping relationship matrix. That is, calculate the equivalent thermal conductivity between the j-th surface element and the i-th surface element. , as in the formula As shown:

[0046]

[0047] By repeating the above process, an M×M dimensional mapping matrix U can be constructed. (k) .

[0048] Step S34: Based on the mapping matrix obtained in step S33, and combined with the superposition theorem, the mapping relationship between the temperatures T of all M nodes on the interface and the normal heat flux Q of all M surface elements is obtained, as shown in the formula. As shown:

[0049]

[0050] Among them, T amb It is a constant vector, where all M elements have the value T. amb .

[0051] S4: Construct a rational expression for the mapping relationship matrix with respect to the convective heat transfer coefficient;

[0052] Specifically, the steps for calculating the coefficient matrix of the rational expression are as follows:

[0053] Step S41: Combining the finite volume method and matrix theory, an approximate rational expression for the mapping relationship matrix with respect to the convective heat transfer coefficient is derived.

[0054]

[0055] Where matrices a, b, and c are the M×M dimensional coefficient matrices to be determined. This represents a matrix divided by its elements. Matrix h is a constant matrix, and each element represents the heat transfer coefficient h.

[0056] Step S42 involves obtaining the key reference values ​​h1, h2, and h3 of the convective heat transfer coefficient, along with their corresponding mapping matrix U. (1) U (2) and U (3) Substituting the rational expressions, we obtain a system of equations concerning the coefficient matrices a, b, and c.

[0057]

[0058] Step S43: Solve the system of equations constructed in S42 to obtain the coefficient matrices a, b, c, thereby obtaining the equations. The rational expression of the mapping relationship matrix with respect to the convective heat transfer coefficient.

[0059] S5: Construct the equivalent thermal boundary conditions of the chip region using rational expressions, and evaluate the hot spot temperature of the chip region using the finite volume method.

[0060] Specifically, the calculation steps for the hotspot temperature are as follows:

[0061] Step S51: Based on the actual convective heat transfer coefficient in the encapsulation region, use the formula... The rational expression shown calculates the mapping matrix corresponding to the discrete values ​​of the convective heat transfer coefficient;

[0062] Step S52: Based on the mapping relationship matrix obtained in step S51, construct the temperature-heat flow mapping relationship on the interface, regard it as the equivalent thermal boundary condition of the chip region, and apply the finite volume method to solve the temperature distribution in the chip region. Then, select the maximum value to obtain the hot spot temperature.

[0063] Based on the simulation method of the present invention described above, a specific embodiment is calculated.

[0064] The following is in conjunction with the accompanying drawings, Figure 3The implementation of the technical solution will be further described in detail using the thermal analysis of the integrated packaging system shown 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.

[0065] This embodiment is a typical integrated packaging system, and its geometry is as follows: Figure 3 As shown. Figure 4 This is a cross-sectional schematic diagram of an integrated package system excluding the heat sink. Based on a region decomposition strategy, it is divided into two types of regions: the chip region, which is the integrated circuit and includes the top chip, metal layer, intermediate chip layer, and adhesive layer; and the other structures, which are the package region. This embodiment uses a rational expression of the mapping relationship matrix with respect to the convective heat transfer coefficient to achieve efficient calculation of hotspot temperature, thereby quickly and accurately assessing the impact of the convective heat transfer coefficient on the hotspot temperature.

[0066] In this embodiment, the influence of the convective heat transfer coefficient at the convection boundary on the hot spot temperature of the integrated package system under two different power consumptions (1 W and 5 W). The convective heat transfer coefficient varies within a range of 10 W / (m²). 2 •K) to 400 W / (m 2 •K), variation interval 10 W / (m 2 ∙K). Therefore, to meet the above analysis requirements, thermal simulation is needed for 80 operating conditions.

[0067] To verify the effectiveness of the method of the present invention, thermal simulations of the above 80 working conditions were performed using the method of the present invention and the commercial software ANSYS FLUENT. Figure 5 This is a curve comparison of the influence of the convective heat transfer coefficient on the system hotspot temperature. (Through...) Figure 5 Comparing the simulation results curves, it can be found that the method of the present invention is in excellent agreement with the calculation results of the commercial software ANSYS FLUENT, fully verifying the correctness of the method of the present invention. To demonstrate the efficiency of the method of the present invention, the total time of thermal simulation for the above 80 working conditions was statistically analyzed. The method of the present invention took 4 m 6 s, while the commercial software ANSYS FLUENT took 3 h 40 s, achieving a speedup effect of 44 times.

[0068] 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 method for evaluating the influence of convective heat transfer coefficient on the hot spot temperature of an integrated packaging system, characterized in that, The method includes the following steps: Based on the distribution of heat sources and packaging locations in the integrated packaging system, the overall system is divided into a packaging area and a chip area. Based on the range of variation of the convective heat transfer coefficient in the encapsulation region, key reference values ​​are determined; Establish the temperature-heat flux mapping relationship at the regional interface; Construct a rational expression for the mapping matrix with respect to the convective heat transfer coefficient; The equivalent thermal boundary conditions of the chip region are constructed using rational expressions, and the hot spot temperature of the chip region is evaluated by combining the finite volume method.

2. The method for evaluating the influence of convective heat transfer coefficient on the hot spot temperature of an integrated packaging system according to claim 1, characterized in that, In the step of dividing the overall system into a packaging region and a chip region based on the distribution of heat sources and packaging positions of the integrated packaging system, the packaging region is a packaging and heat dissipation structure containing convection boundaries, and the chip region is an integrated circuit chip containing heat sources.

3. The method for evaluating the influence of convective heat transfer coefficient on the hot spot temperature of an integrated packaging system according to claim 1, characterized in that, In the step of determining the key reference value based on the variation range of the convective heat transfer coefficient in the encapsulation region, the key reference value h k From the interpolation formula The calculations are as follows, where k takes values ​​of 1, 2, and 3, and h... min and h max These are the minimum and maximum values ​​of the convective heat transfer coefficient, respectively.

4. The method for evaluating the influence of convective heat transfer coefficient on the hot spot temperature of an integrated packaging system according to claim 1, characterized in that, The steps for establishing the temperature-heat flux mapping relationship at the interface of the regions are as follows: The first step is to set the heat transfer coefficient of the convection boundary as the key reference value and set the temperature of the interface between the package area and the chip area as the ambient temperature. The finite volume method is used to solve the steady-state heat conduction equation in the package area to obtain the heat flow of the center node of each surface unit on the interface, which is denoted as the reference heat flow of the interface. The second step is to apply a uniform temperature rise excitation to each surface element of the interface in sequence, while keeping the ambient temperature on other surface elements, and record the selected temperature rise excitation magnitude and the heat flow matrix formed by the corresponding interface heat flow. The third step is to calculate the mapping matrix based on the interface reference heat flow obtained in the first step and the temperature rise excitation magnitude and heat flow matrix recorded in the second step.

5. The method for evaluating the influence of convective heat transfer coefficient on the hot spot temperature of an integrated packaging system according to claim 1, characterized in that, In the step of constructing the rational expression for the mapping relationship matrix with respect to the convective heat transfer coefficient, the calculation steps for the coefficient matrix of the rational expression are as follows: The first step is to derive an approximate rational expression for the mapping relationship matrix with respect to the convective heat transfer coefficient by combining the finite volume method and matrix theory; The second step is to substitute the key reference values ​​of the convective heat transfer coefficient and its corresponding mapping matrix into the rational expression to obtain a system of equations about the coefficient matrix. The third step is to solve the system of equations constructed in the second step to obtain the coefficient matrix.

6. The method for evaluating the influence of convective heat transfer coefficient on the hot spot temperature of an integrated packaging system according to claim 1, characterized in that, In the step of constructing the equivalent thermal boundary conditions of the chip region using rational expressions and then evaluating the hotspot temperature of the chip region using the finite volume method, the calculation steps for the hotspot temperature are as follows: The first step is to calculate the mapping matrix corresponding to the discrete values ​​of the convection heat transfer coefficient based on the actual convection heat transfer coefficient in the encapsulation area using a rational expression; The second step is to treat the temperature-heat flux mapping matrix as the equivalent thermal boundary condition of the chip region and apply the finite volume method to solve for the temperature distribution in the chip region, thereby obtaining its hot spot temperature.

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