Thermal Modeling And Optimization Of Three-dimensional Integrated Circuits Based On Finite Element And Equivalent Thermal Network Methods

Three-dimensional Integrated Circuits(3D ICs)contain a large number of Through Silicon Vias(TSV)and micro-bumps,and have complex and cross-scale package structures,so it is difficult to quickly and accurately analyze them thermally.For the constructed 3D IC thermal analysis model,the optimization of physical parameters and heat source arrangement consumes a lot of computing resources,and the optimization results are easy to fall into local optimization.In this paper,a rapid thermal analysis method for 3D IC is proposed by combining finite element and equivalent thermal network method,and a process method combining artificial neural network surrogate model and Bayesian optimization algorithm is constructed,which can efficiently optimize the physical parameters and heat source location of TSV.The proposed method can quickly and accurately obtain the temperature distribution of 3D IC,and can optimize and analyze its physical parameters,which is conducive to the calculation of thermal design parameters of 3D IC and is also expected to propose corresponding solutions to its thermal management problems.First,a high-efficiency thermal analysis method for 3D ICs containing conical TSVs is proposed.Based on finite element and equivalent thermal network methods and combining the advantages of both,the proposed method can quickly and accurately extract the equivalent thermal conductivity of TSV and micro-bumps in 3D ICs.By comparing with the experimental results of predecessors and detailed 3D finite element models,the effectiveness of the proposed method is verified.Secondly,this method is applied to the thermal analysis of the constructed 6-layer stacked 3D IC model,and compared with the detailed model,the number of meshes is reduced by 84.5%,the calculation time is shortened by 88%,and the accuracy(maximum temperature difference ≤ 1%)is obtained.In addition,the influence of different physical parameters on the equivalent thermal conductivity of conical TSV and micro-bumps was analyzed,and the best physical parameters in the thermal design of 3D ICs were selected.Finally,a surrogate model parameter optimization process combining neural network and Bayesian optimization is constructed.Based on the proposed rapid thermal analysis method,Latin hypercube sampling was used for data sampling,the heat source location information was parameterized,and the corresponding data set was generated by batch calculation by MATLAB.By selecting a suitable objective function,the temperature distribution data of 3D IC under different hot spot positions is fitted,and the neural network agent model for temperature distribution prediction of 3D IC is obtained.By comparing the optimization results and efficiency of the analysis algorithm,the Bayesian optimization algorithm is finally selected for the model used in this paper,and the global optimal value is found in only 4.07 s and 250 iterations,and the best power distribution strategy for the constructed model is obtained.The equivalent thermal conductivity calculation method proposed in this paper can be applied to the thermal analysis of 3D ICs containing conical TSV,and the influence of the heat transfer area between layers on the calculation of equivalent thermal conductivity during the dimensionality reduction process is considered,taking into account the efficiency and accuracy of the calculation.When calculating the inplane equivalent thermal conductivity,the equivalent thermal conductivity expression of the cylindrical dispersion element model with contact thermal resistance is adopted,which is more consistent with the actual model and higher accuracy is obtained.