Temperature-adaptive TSV layer equivalent thermal conductivity dynamic calculation method

Abstract

The invention relates to the field of integrated circuit design, and provides a temperature-adaptive TSV layer equivalent thermal conductivity dynamic calculation method. The invention aims to solve the problem of insufficient precision caused by nonlinear change of thermal conductivity of a silicon material along with temperature in equivalent thermal conductivity calculation of a TSV layer of a 3D integrated circuit, and obtains initial structure parameters of the TSV layer, including TSV array density and radius; based on the density and radius of the TSV array, determining a mixing coefficient of copper and silicon through a pre-constructed mixing coefficient lookup table, querying real-time heat conductivity of silicon and copper according to current temperature field data, calculating equivalent heat conductivity, and substituting the equivalent heat conductivity into a heat conduction equation for temperature field simulation to obtain updated temperature distribution data; and updating the heat conductivity of copper and silicon according to the simulation temperature, carrying out iteration until the relative variation of the equivalent heat conductivity is smaller than a preset threshold value, and outputting the converged equivalent heat conductivity.

Description

Technical Field

[0001] The present invention relates to the field of integrated circuit design, and provides a method for dynamically calculating the equivalent thermal conductivity of a TSV layer with temperature adaptability. Background Art

[0002] With the development of three-dimensional integrated circuit (3DIC) technology, through-silicon vias (TSVs), as key vertical interconnect structures, their heat conduction characteristics have an important impact on the overall chip thermal management. In the prior art, the equivalent thermal conductivity modeling of the TSV layer usually adopts static analysis methods, such as the equivalent volume method based on the material volume ratio or the data-driven method based on specific temperature points. However, these methods have the following problems:

[0003] Insufficient temperature dynamic adaptability: The thermal conductivity of silicon material changes significantly with temperature (for example, the thermal conductivity of silicon decreases by about 20% in the range of 300K to 400K), while the traditional model does not consider the temperature dependence of the thermal conductivity, resulting in an increase in the modeling error under high-temperature conditions;

[0004] Lack of iterative correction mechanism: The existing methods do not introduce a dynamic feedback mechanism and cannot update the thermal conductivity iteratively through the mixing coefficient to match the actual temperature distribution;

[0005] Ignoring the influence of the inter-dielectric layer (IDL): IDL structures such as micro-bumps (μbumps) cause significant temperature gradients due to their low thermal conductivity, but the existing equivalent models do not clearly distinguish the differences in the heat conduction characteristics between the TSV layer and the IDL.

[0006] For example, the TSV equivalent thermal conductivity model proposed by Zhang et al. only calculates the mixing effect of copper and silicon through the volume ratio and does not consider the non-linear effect of temperature change on the thermal conductivity of silicon; the data-driven method of Wang et al. needs to retrain the model for different stacking numbers and lacks scalability. In addition, experiments show that ignoring the IDL layer may lead to a prediction error of up to 30K in the temperature of the base chip.

[0007] Therefore, there is an urgent need for a method for calculating the equivalent thermal conductivity of the TSV layer that can dynamically correct the material thermal conductivity, adapt to temperature changes, and be compatible with multi-layer stacking, so as to improve the accuracy and efficiency of 3DIC thermal modeling. Summary of the Invention

[0008] The purpose of the present invention is to solve the problem of insufficient accuracy in calculating the equivalent thermal conductivity of the TSV layer in 3D integrated circuits due to the non-linear change of the thermal conductivity of silicon material with temperature. By dynamically iteratively correcting the copper / silicon thermal conductivity weight through the mixing coefficient, the real-time update of the temperature-adaptive equivalent thermal conductivity is realized, thereby overcoming the error accumulation defect of the traditional fixed-value ETC model under high-temperature conditions.

[0009] To achieve the above purpose, the present invention adopts the following technical solutions:

[0010] The present invention provides a method for dynamically calculating the equivalent thermal conductivity of a TSV layer with temperature adaptability, including the following steps:

[0011] Step (1): Obtain the initial structural parameters of the TSV layer, including the TSV array density and radius;

[0012] Step (2): Based on the TSV array density and radius, determine the mixing coefficient α of copper and silicon through a pre-constructed mixing coefficient look-up table, α = LUT(ρ TSV , r TSV );

[0013] Step (3): According to the current temperature field data, query the real-time thermal conductivities k si and k cu of silicon and copper, and calculate the equivalent thermal conductivity according to the following formula:

[0014] k′ TSV = αk Cu + (1 - α)k Si

[0015] where k Si represents the thermal conductivity of silicon, and k Cu represents the thermal conductivity of copper;

[0016] Step (4): Substitute the equivalent thermal conductivity into the heat conduction equation for temperature field simulation to obtain updated temperature distribution data;

[0017] Step (5): Update the thermal conductivities of copper and silicon according to the simulated temperature, and repeat steps (3)-(4) until the relative change amount of the equivalent thermal conductivity is less than a preset threshold, and output the converged equivalent thermal conductivity.

[0018] In the above solution, the mixing coefficient α has an approximately linear relationship with the TSV array density and cross-sectional area, and the look-up table is generated by two-parameter interpolation.

[0019] In the above solution, the mixing coefficient look-up table is constructed in the following manner:

[0020] Step (2-1): Set the range of structural parameters of the TSV layer, including the TSV array density ρ TSV and radius T TSV , where ρ TSV ∈[ρ min , ρ max , r TSV ∈[r min , r max );

[0021] Step (2-2): Generate an experimental data set based on a surrogate model, and the surrogate model is trained through the following steps:

[0022] a. For different combinations of ρ TSV and r TSV calculate the equivalent thermal conductivity k′ of the TSV layer through finite element simulation TSV ;

[0023] b. According to the formula inversely deduce the mixing coefficient α, where k Cu and k Si are the temperature-dependent thermal conductivities of copper and silicon respectively;

[0024] The physical meaning represented by:

[0025] When α = 1, k′ TSV = k Cu , indicating that the thermal conductivity of the TSV layer is completely dominated by copper;

[0026] When α = 0, k′ TSV = k Si , indicating that the thermal conductivity is completely dominated by silicon;

[0027] Step (2-3) establishes a mapping relationship between α and the corresponding ρ TSV and r TSV and generates a lookup table through two-parameter linear interpolation, where the interpolation formula is:

[0028] α = LUT(ρ TSV , r TSV ) = d·ρ TSV + b·r TSV + c

[0029] where d and b are linear weight coefficients, reflecting the contribution ratios of the array density and radius to the mixing coefficient, and c is a constant term used to correct the model error or minor non-linear factors;

[0030] Step (2-4) verifies the accuracy of the lookup table. If the maximum relative error exceeds 1%, increase the sampling point density of ρ TSV and r TSV and repeat steps (2-2)-(2-3) until the accuracy requirement is met.

[0031] In the above solution, the iteration termination condition in step (5) is: the relative error of the equivalent thermal conductivity between two consecutive iterations is less than 0.5%.

[0032] The present invention provides a device for dynamically calculating the equivalent thermal conductivity of a temperature-adaptive TSV layer, including:

[0033] An initial parameter acquisition module for acquiring the initial structural parameters of the TSV layer, including the TSV array density and radius;

[0034] A mixing coefficient determination module that determines the mixing coefficient α of copper and silicon based on the TSV array density and radius through a pre-constructed mixing coefficient look-up table;

[0035] A real-time thermal conductivity query module for querying the real-time thermal conductivities k of silicon and copper according to the current temperature field data si and k cu

[0036] An equivalent thermal conductivity calculation module that calculates the equivalent thermal conductivity according to the formula k’ TSV = αk Cu +(1 - α)k Si ;

[0037] A temperature field simulation module for substituting the equivalent thermal conductivity into the heat conduction equation to perform temperature field simulation and obtain updated temperature distribution data;

[0038] A thermal conductivity update module for updating the thermal conductivities of copper and silicon according to the simulated temperature, and repeating the calculation of the equivalent thermal conductivity and the temperature field simulation until the relative change amount of the equivalent thermal conductivity is less than a preset threshold, and outputting the converged equivalent thermal conductivity.

[0039] In the above solution, the mixing coefficient α has an approximately linear relationship with the TSV array density and cross-sectional area, and the look-up table is generated by two-parameter interpolation.

[0040] In the above solution, the mixing coefficient look-up table is constructed in the following manner:

[0041] Step (2-1) Set the range of the structural parameters of the TSV layer, including the TSV array density ρ TSV and radius r TSV , where ρ TSV ∈[ρ min , ρ max , r TSV ∈[r min , r max ;

[0042] Step (2-2) Generate an experimental data set based on a surrogate model, and the surrogate model is trained through the following steps:

[0043] a. For different combinations of ρ TSV and r TSV , calculate the equivalent thermal conductivity k′ of the TSV layer through finite element simulation TSV ;

[0044] b. Invert the mixing coefficient α according to the formula , where k Cu and k Siare the temperature-dependent thermal conductivities of copper and silicon, respectively;

[0045] The physical meaning represented is:

[0046] When α = 1, k' TSV = k Cu , indicating that the thermal conductivity of the TSV layer is completely dominated by copper;

[0047] When α = 0, k' TSV = k Si , indicating that the thermal conductivity is completely dominated by silicon;

[0048] Step (2-3) establishes a mapping relationship between α and the corresponding ρ TSV and r TSV to generate a lookup table through two-parameter linear interpolation, where the interpolation formula is:

[0049] α = LUT(ρ TSV , r TSV ) = d·ρ TSV + b·r TSV + c

[0050] where d and b are linear weight coefficients, reflecting the contribution ratios of the array density and radius to the mixing coefficient, and c is a constant term used to correct the model error or minor non-linear factors;

[0051] Step (2-4) verifies the accuracy of the lookup table. If the maximum relative error exceeds 1%, the sampling point density of ρ TSV and r TSV is increased and steps (2-2)-(2-3) are repeated until the accuracy requirement is met.

[0052] In the above solution, the iteration termination condition is: the relative error of the equivalent thermal conductivity between two consecutive iterations is less than 0.5%.

[0053] The present invention also provides a storage medium. When a processor executes a program in the storage medium, it implements the described dynamic calculation method for the equivalent thermal conductivity of a temperature-adaptive TSV layer.

[0054] The dynamic calculation method and device for the equivalent thermal conductivity of a temperature-adaptive TSV layer provided by the present invention achieve the following remarkable advantages in 3D integrated circuit thermal management by introducing a dynamic iteration mechanism of the mixing coefficient and a pre-built lookup table technology:

[0055] 1. Enhanced temperature adaptability

[0056] By querying the temperature-dependent thermal conductivities of silicon and copper in real time and based on the dynamic iterative correction of the mixing coefficient α, the problem of error accumulation caused by ignoring the non-linear variation of material thermal conductivity with temperature in traditional static models is overcome. This method can adapt to the changes in the temperature field and significantly improve the calculation accuracy of the equivalent thermal conductivity under high-temperature conditions and in scenarios with complex temperature gradients.

[0057] 2. Optimization of the balance between calculation efficiency and accuracy

[0058] By adopting a pre-built mixing coefficient look-up table (LUT) and two-parameter interpolation technology, the mixing coefficient can be quickly determined through structural parameters (TSV array density, radius), avoiding the repeated calculations required by traditional finite element simulations. Combining the data sets generated by the linear interpolation model and the surrogate model can significantly reduce the real-time operation complexity while ensuring the calculation accuracy, realizing efficient dynamic update of the thermal conductivity.

[0059] 3. Improvement of model scalability and compatibility

[0060] By decomposing the equivalent thermal conductivity of the TSV layer into a weighted mixture of copper / silicon thermal conductivities and combining a hierarchical modeling strategy, the differences in heat conduction characteristics between the TSV layer and other interconnect structures (such as micro-bumps, redistribution layers) can be effectively distinguished. This model supports modular modeling of non-uniform TSV distributions and can be directly extended to the thermal field simulation of multi-layer stacked chips to meet the diverse design requirements of 3DICs.

[0061] 4. Iterative convergence reliability

[0062] An iterative termination condition based on the relative change in the equivalent thermal conductivity is introduced. Through the closed-loop feedback mechanism of temperature field simulation and thermal conductivity update, the convergence stability of the mixing coefficient with temperature changes is ensured, avoiding the temperature distribution deviation caused by single calculation in traditional methods.

[0063] 5. Enhancement of process adaptability

[0064] The approximate linear relationship between the mixing coefficient and the TSV array density and radius simplifies the construction logic of the look-up table. Combining the parameter range adaptive adjustment and accuracy verification mechanism can flexibly adapt to the changes in structural parameters under different TSV manufacturing processes, improving the robustness of the model to actual process fluctuations.

[0065] In summary, the present invention solves the technical bottlenecks of poor temperature adaptability, low calculation efficiency, and insufficient scalability in traditional TSV equivalent thermal conductivity models through dynamic mixing coefficient iteration, optimized construction of the look-up table, and hierarchical modeling strategy, providing an efficient and accurate solution for the thermal reliability and thermal design optimization of 3D integrated circuits. Description of the drawings

[0066] Figure 1 : Schematic diagram of the algorithm flow of the present invention;

[0067] Figure 2 : The equivalent thermal conductivity curve of the TSV layer varying with temperature. In the figure, (a) shows the variation of the equivalent thermal conductivity with temperature under different TSV densities; (b) shows the variation of the equivalent thermal conductivity with temperature under different TSV radii.

[0068] Figure 3 : α is the mixing coefficient of the materials in the TSV layer;

[0069] Figure 4 : Thermal field verification of three 4-layer stacking cases. In the figure, (a) is for uniform distribution; (b) is for globally non-uniform and locally uniform (GNLU); (c) is for randomly reducing solder joints, TSVs, and wires based on GNLU. Detailed implementation manners

[0070] The following will give a detailed description of the embodiments of the present invention. Although the present invention will be described and explained in conjunction with some specific implementation manners, it should be noted that the present invention is not limited only to these implementation manners. On the contrary, any modifications or equivalent replacements made to the present invention shall be covered within the scope of the claims of the present invention.

[0071] In addition, for better explaining the present invention, numerous specific details are given in the following detailed implementation manners. Those skilled in the art will understand that the present invention can also be implemented without these specific details.

[0072] For the convenience of those skilled in the art to better understand the technical concept of the present invention, the related technologies of the present invention are described as follows:

[0073] The TSV layer is the most effective heat conduction path inside the chip stack. The thermal conductivities of copper and the surrounding silicon are both higher than the equivalent thermal conductivities of the solder ball layer and RDL. The thermal conductivity of silicon shows an obvious downward trend with temperature. Therefore, it is inaccurate to directly derive the equivalent thermal conductivity of the TSV layer by querying the array density and radius of the TSVs.

[0074] As Figure 2 shown, the downward trend of the equivalent thermal conductivity of the TSV layer is close to the thermal conductivity curve of silicon. As the TSV array density and radius increase, the equivalent thermal conductivity of the TSV layer also increases and maintains its original downward trend with temperature.

[0075] Due to the sensitivity of the TSV layer thermal conductivity to temperature, instead of directly calculating its equivalent thermal conductivity through the array density and size of the TSVs, it is regarded as a weighted mixture of the thermal conductivities of silicon and copper.

[0076] k′ TSV = αk Cu +(1 - α)k Si #(1)

[0077] Among them, α is the mixing coefficient. Therefore, the relationship between the equivalent thermal conductivity of the TSV layer and the mixing coefficient α at multiple temperatures was measured, and the results are as Figure 3 shown. The variation of the thermal conductivity mixing coefficient α of the two materials with temperature can be ignored. In Figure 2 , we plotted the relationship between α and the TSV array density and radius. The mixing coefficient α shows an approximately linear relationship with the TSV array density and cross-sectional area. In this way, a look-up table (LUT) based on the TSV array density and radius parameters was constructed for the thermal conductivity mixing coefficient α of the TSV layer. An iterative method was used to obtain the equivalent thermal conductivity of the TSV layer:

[0078] 1) Obtain the value of the mixing coefficient α through the look-up table (LUT);

[0079] 2) Query the initial thermal conductivities of copper and silicon at the expected operating temperature of the chip;

[0080] 3) Calculate the equivalent thermal conductivity of the TSV layer according to Equation 1;

[0081] 4) Use the macro model containing the equivalent thermal conductivity for simulation, calculate the temperature of the TSV layer, and update the thermal conductivities of copper and silicon;

[0082] 5) Update the equivalent thermal conductivity of the TSV layer. [[ID=2^{}3]]

[0083] Since the thermal conductivity of the TSV layer is better than that of the RDL and solder ball layers and its temperature gradient is smaller, in our dataset, this process converges after one iteration.

[0084] F. Summary

[0085] In summary, the present invention constructs a look-up table (LUT) for the TSV layer for each chip size and height. Modeling method:

[0086] α = LUT(h, ρ TSV , r TSV )

[0087] k′ TSV = αk cu + (1 - α)k Si

[0088] k′ TSV represents the equivalent thermal conductivity of the silicon through via, k′ RDL represents the equivalent thermal conductivity of the redistribution layer, h is the layer height, ρ TSV is the TSV array density, r TSV is the TSV radius, k Si represents the thermal conductivity of silicon, k Cn represents the thermal conductivity of copper.

[0089] In the design space exploration, once the material parameters of each layer are determined, the equivalent model of the TSV layer can be quickly established using the modeling method we proposed. In a typical design scenario, the distribution of TSVs is usually not uniform, but the layer can be subdivided into multiple uniform small blocks. We build a macro model for each small block (a macro model refers to a high-level simplification of a refined model, representing a complex refined model with a (parameterized) simple model), and the combined macro models of multiple small blocks form an equivalent layer. These models can be directly stacked for simulating chip stacking in 3D integrated circuits. Based on the above models, the TSV thermal conductivity can be quickly evaluated to optimize the thermal field.

[0090] Example 1

[0091] The present invention provides a method for dynamically calculating the equivalent thermal conductivity of a temperature-adaptive TSV layer, comprising the following steps:

[0092] Step (1): Obtain the initial structural parameters of the TSV layer, including the TSV array density and radius;

[0093] Step (2): Based on the TSV array density and radius, determine the mixing coefficient α of copper and silicon through a pre-constructed mixing coefficient look-up table, α = LUT(h, ρ TSV , r TSV );

[0094] Step (3): According to the current temperature field data, query the real-time thermal conductivities k si and k cu of silicon and copper, and calculate the equivalent thermal conductivity according to the following formula:

[0095] k' TSV = αk Cu + (1 - α)k Si

[0096] where k Si represents the thermal conductivity of silicon, and k Cu represents the thermal conductivity of copper;

[0097] Step (4): Substitute the equivalent thermal conductivity into the heat conduction equation for temperature field simulation to obtain the updated temperature distribution data;

[0098] Step (5): Update the thermal conductivities of copper and silicon according to the simulated temperature, and repeat steps (3)-(4) until the relative change amount of the equivalent thermal conductivity is less than the preset threshold, and output the converged equivalent thermal conductivity.

[0099] In the above solution, the mixing coefficient α has an approximately linear relationship with the TSV array density and cross-sectional area, and the look-up table is generated by two-parameter interpolation.

[0100] In the above solution, the mixing coefficient lookup table is constructed in the following manner:

[0101] Step (2-1) sets the range of structural parameters of the TSV layer, including the TSV array density ρ TSV and the radius r TSV , where ρ TSV ∈[ρ min , ρ max , r TSV ∈[r min , r max );

[0102] Step (2-2) generates an experimental data set based on a surrogate model, and the surrogate model is trained through the following steps:

[0103] a. For different combinations of ρ TSV and r TSV , the equivalent thermal conductivity k′ of the TSV layer is calculated by finite element simulation TSV ;

[0104] b. The mixing coefficient α is inversely deduced according to the formula , where k Cu and k Si are the temperature-dependent thermal conductivities of copper and silicon, respectively;

[0105] The physical meaning represented by:

[0106] When α = 1, k′ TSV = k Cu , indicating that the thermal conductivity of the TSV layer is completely dominated by copper;

[0107] When α = 0, k′ TSV = k Si , indicating that the thermal conductivity is completely dominated by silicon;

[0108] Step (2-3) establishes a mapping relationship between α and the corresponding ρ TSV and r TSV , and generates a lookup table through two-parameter linear interpolation, where the interpolation formula is:

[0109] α = LUT(ρ TSV , r TSV ) = d·ρ TSV + b·r TSV + c

[0110] where d and b are linear weight coefficients, reflecting the contribution ratios of the array density and the radius to the mixing coefficient, and c is a constant term used to correct model errors or minor non-linear factors;

[0111] Step (2-4) verifies the accuracy of the look-up table. If the maximum relative error exceeds 1%, increase ρ TSV and T TSV the sampling point density of and repeat steps (2-2)-(2-3) until the accuracy requirement is met.

[0112] In the above solution, the iteration termination condition in step (5) is that the relative error of the equivalent thermal conductivity between two consecutive iterations is less than 0.5%.

[0113] Embodiment 2

[0114] The present invention provides a temperature-adaptive dynamic calculation device for the equivalent thermal conductivity of a TSV layer, including:

[0115] An initial parameter acquisition module for acquiring the initial structural parameters of the TSV layer, including the TSV array density and radius;

[0116] A mixing coefficient determination module that determines the mixing coefficient α of copper and silicon through a pre-constructed mixing coefficient look-up table based on the TSV array density and radius;

[0117] A real-time thermal conductivity query module for querying the real-time thermal conductivities k si and k cu ;

[0118] An equivalent thermal conductivity calculation module that calculates the equivalent thermal conductivity according to the formula k' TSV = αk Cu +(1-α)k Si ;

[0119] A temperature field simulation module for substituting the equivalent thermal conductivity into the heat conduction equation for temperature field simulation to obtain updated temperature distribution data;

[0120] A thermal conductivity update module for updating the thermal conductivities of copper and silicon according to the simulated temperature, and repeating the calculation of the equivalent thermal conductivity and the temperature field simulation until the relative change amount of the equivalent thermal conductivity is less than a preset threshold, and outputting the converged equivalent thermal conductivity.

[0121] In the above solution, the mixing coefficient α has an approximately linear relationship with the TSV array density and cross-sectional area, and the look-up table is generated by two-parameter interpolation.

[0122] In the above solution, the mixing coefficient look-up table is constructed in the following manner:

[0123] Step (2-1) sets the range of the structural parameters of the TSV layer, including the TSV array density ρ TSV and radius r TSV , where ρ TSV ∈[ρ min, ρ max , r TSV ∈ [r min , r max );

[0124] Step (2-2) generates an experimental data set based on the surrogate model, and the surrogate model is trained through the following steps:

[0125] a. For different combinations of ρ TSV and r TSV , calculate the equivalent thermal conductivity k′ of the TSV layer through finite element simulation TSV ;

[0126] b. Invert the mixing coefficient α according to the formula , where k Cu and k Si are the temperature-dependent thermal conductivities of copper and silicon, respectively;

[0127] The physical meaning represented by:

[0128] When α = 1, k′ TSV = k Cu , indicating that the thermal conductivity of the TSV layer is completely dominated by copper;

[0129] When α = 0, k′ TSV = k Si , indicating that the thermal conductivity is completely dominated by silicon;

[0130] Step (2-3) establishes a mapping relationship between α and the corresponding ρ TSV and r TSV , generates a look-up table through two-parameter linear interpolation, and the interpolation formula is:

[0131] α = LUT(ρ TSV , r TSV ) = d·ρ TsV + b·r TSV + c

[0132] where d and b are linear weight coefficients, reflecting the contribution ratios of the array density and radius to the mixing coefficient, and c is a constant term used to correct the model error or minor non-linear factors;

[0133] Step (2-4) verifies the accuracy of the look-up table. If the maximum relative error exceeds 1%, increase the sampling point density of ρ TSV and r TSV and repeat steps (2-2)-(2-3) until the accuracy requirement is met.

[0134] In the above solution, the iteration termination condition is: the relative error of the equivalent thermal conductivity between two consecutive iterations is less than 0.5%.

[0135] Embodiment 3

[0136] The present invention also provides a storage medium. When a processor executes a program in the storage medium, the dynamic calculation method for the equivalent thermal conductivity of the temperature-adaptive TSV layer described above is implemented.

Claims

1. A dynamic calculation method for the equivalent thermal conductivity of a TSV layer with temperature adaptability, characterized in that, Including the following steps: Step (1): Obtain the initial structural parameters of the TSV layer, including the TSV array density and radius; Step (2) determines the mixing coefficient α of copper and silicon based on the TSV array density and radius through a pre-constructed mixing coefficient look-up table, α = LUT(ρ TSV , T TSV ); Step (3) queries the real-time thermal conductivities k of silicon and copper according to the current temperature field data si and k cu , and calculates the equivalent thermal conductivity according to the following formula: k′ TSV = αk Cu + (1 - α)k Si where k Si represents the thermal conductivity of silicon, and k Cu represents the thermal conductivity of copper; Step (4): Substitute the equivalent thermal conductivity into the heat conduction equation for temperature field simulation to obtain the updated temperature distribution data; Step (5): Update the thermal conductivities of copper and silicon according to the simulated temperature, and repeat steps (3)-(4) until the relative change amount of the equivalent thermal conductivity is less than the preset threshold, and output the converged equivalent thermal conductivity.

2. The method according to claim 1, wherein The mixing coefficient α has an approximately linear relationship with the TSV array density and cross-sectional area, and the look-up table is generated by two-parameter interpolation.

3. The method according to claim 1, wherein The mixing coefficient look-up table is constructed in the following manner: Step (2-1) sets the structural parameter range of the TSV layer, including the TSV array density ρ TSV and the radius r TSV , where ρ TSV ∈[ρ min , ρ max , r TSV ∈[r min , r max ); Step (2-2): Generate an experimental data set based on the surrogate model, and the surrogate model is trained through the following steps: a. For different combinations of ρ TSV and r TSV the equivalent thermal conductivity k′ of the TSV layer is calculated by finite element simulation TSV ; b. According to the formula back-calculate the mixing coefficient α, where k Cu and k Si are the temperature-dependent thermal conductivities of copper and silicon, respectively; Physical meaning represented: When α = 1, k TSV = k Cu , indicating that the thermal conductivity of the TSV layer is completely dominated by copper; When α = 0, k TSV = k Si , indicating that the thermal conductivity is completely dominated by silicon; Step (2-3) maps α to the corresponding ρ TSV and r TSV to establish a mapping relationship, and a lookup table is generated by two-parameter linear interpolation, where the interpolation formula is: α = LUT(ρ TSV , r TSV ) = d·ρ TSV + b·r TSV + c Where d and b are linear weight coefficients, reflecting the contribution ratios of the array density and radius to the mixing coefficient, and is a constant term used to correct the model error or minor non-linear factors; Step (2-4) verifies the accuracy of the look-up table. If the maximum relative error exceeds 1%, increase ρ TSV and r TSV of the sampling point density and repeat steps (2-2)-(2-3) until the accuracy requirement is met.

4. The method according to claim 1, wherein The iteration termination condition in step (5) is that the relative error of the equivalent thermal conductivity between two consecutive iterations is less than 0.5%.

5. A device for dynamically calculating the equivalent thermal conductivity of a TSV layer with temperature adaptability, characterized in that, Including: An initial parameter acquisition module, configured to obtain the initial structural parameters of the TSV layer, including the TSV array density and radius; A mixing coefficient determination module, based on the TSV array density and radius, determines the mixing coefficient α of copper and silicon through a pre-constructed mixing coefficient look-up table; A real-time thermal conductivity query module, which is used to query the real-time thermal conductivities k of silicon and copper according to the current temperature field data si and k cu ; Equivalent thermal conductivity calculation module, calculating the equivalent thermal conductivity according to the formula k′ TSV = αk Cu +(1 - α)k Si ; A temperature field simulation module, configured to substitute the equivalent thermal conductivity into the heat conduction equation for temperature field simulation to obtain the updated temperature distribution data; A thermal conductivity update module, configured to update the thermal conductivities of copper and silicon according to the simulated temperature, and repeat the calculation of the equivalent thermal conductivity and the temperature field simulation until the relative change amount of the equivalent thermal conductivity is less than the preset threshold, and output the converged equivalent thermal conductivity.

6. The device according to claim 5, wherein The mixing coefficient α has an approximately linear relationship with the TSV array density and cross-sectional area, and the look-up table is generated by two-parameter interpolation.

7. The device according to claim 5, wherein The mixing coefficient look-up table is constructed in the following manner: Step (2-1) sets the structural parameter range of the TSV layer, including the TSV array density ρ TSV and the radius r TSV , where ρ TSV ∈[ρ min , ρ max , r TSV ∈[r min , r max ) Step (2-2): Generate an experimental data set based on the surrogate model, and the surrogate model is trained through the following steps: a. For different combinations of ρ TSV and r TSV the equivalent thermal conductivity k′ of the TSV layer is calculated by finite element simulation TSV : b. Calculate the mixing coefficient α by reverse deduction according to the formula where k Cu and k Si are the temperature-dependent thermal conductivities of copper and silicon, respectively; Physical meaning represented: When α = 1, k TSV = k Cu , indicating that the thermal conductivity of the TSV layer is completely dominated by copper; When α = 0, k TSV = k Si , indicating that the thermal conductivity is completely dominated by silicon; Step (2-3) maps α to the corresponding ρ TSV and r TSV to establish a mapping relationship, and a lookup table is generated through two-parameter linear interpolation. The interpolation formula is as follows: α = LUT(ρ TSV , r TSV ) = d·ρ TSV + b·r TSV + c Where d and b are linear weight coefficients, reflecting the contribution ratios of the array density and radius to the mixing coefficient, and is a constant term used to correct the model error or minor non-linear factors; Step (2-4) verifies the accuracy of the look-up table. If the maximum relative error exceeds 1%, increase ρ TSV and r TSV of the sampling point density and repeat steps (2-2)-(2-3) until the accuracy requirement is met.

8. The device according to claim 5, characterized in that The iteration termination condition is that the relative error of the equivalent thermal conductivity between two consecutive iterations is less than 0.5%.

9. A storage medium, characterized in that, When the processor executes the program in the storage medium, it implements a method for dynamically calculating the equivalent thermal conductivity of a temperature-adaptive TSV layer as described in claim 1.

Images