一种考虑漏电流功耗的快速校正线性模型的瞬态热分析方法

An Efficient Leakage-Aware Faster Corrected Linearized Model Method for 3D-IC Transient Thermal Simulation

随着集成电路特征尺寸不断缩小,三维集成电路越来越受重视。然而,由于三维集成电路采用多层堆叠,导致芯片内部能量密度极高、散热困难。因此,精确的三维集成电路热分析是控制三维集成电路温度的重要前提。此外,实验结果表明稳态和瞬态热分析的温度差异可高达60 K,因此,在某些温度敏感的关键场景中,快速、准确的瞬态热分析是必不可少的。基于已有文献提出的漏电功耗校正线性模型稳态热分析方法,本文进一步提出了快速校正线性模型方法应用于瞬态热分析问题中。该方法采用后向欧拉法对时间进行离散,并通过减少每个时刻点中迭代方程雅可比矩阵的更新以提高计算效率。实验结果表明:本文提出的方法在最高温差不超过0.521 K的精度下,相比已有的方法有约1.3~3.1倍的加速效果。

For modern 3-D integrated circuits(ICs),transient thermal simulation,characterizing the real-time temperature distribution,becomes significant for the ever-increasing power density in 3D integrations.In[12],a Corrected Linearized Model(CLM)method for leakage-aware steady thermal simulation was proposed and achieved great speedup over HotSpot and Newton method without accuracy loss.In this paper,we further propose a Faster Corrected Linearized Model(FCLM)method for transient thermal analysis based on the steady CLM method,which is discretized along time steps by the backward Euler method.A two-loop iterative formula is carefully derived along the time steps and iterations inside the time steps.Considering the fact that updating the Jacobian matrices dominates the total CPU time,the proposed FCLM method simply calculates the Jacobian matrix only once at the first time step.The experimental results show that FCLM method could achieve 1.3-3.1x speedup over the basic transient CLM method with maximal temperature error no more than 0.521 K.Meanwhile,the temperature gaps between the steady-state and the transient may be larger than 60 K.Therefore,for applications with highly accurate thermal requirements,transient thermal analysis should be considered seriously.