基于区域分解和模型降阶混合的三维高速集成电路多尺度建模和分析方法研究

The 3D integrated technologies, like through silicon vias, have been widely used in circuit and chip designs. However,their suitable high frequency 3D simulation methods still need continuous improvement. Mainly due to thick patches, irregular vias, vertical current and kinds of multi-scale problems, popular 2D methods can't be simply used for signal integrity analysis of 3D high-speed very large-scale integrated circuits (VLSIC). The proposed project,solves large-variable spatial dyadic Green's function by homotopy deformation methods,generalized wide-band complex image methods and multi-dimensional fast interpolation schemes, builds hybrids of the method of moments and the partial element equivalent circuits by hybrids of novel non-overlapping domain decomposition methods of integral equations and novel model order reduction methods, develops novel partial basic solution vector methods of integral equations and combinations with other fast algorithms, and implements an integrated simulation for a 3D high-speed VLSIC. The proposed project divides the monolithic 3D integrated circuit apart, and selects the best combination of solutions according to sub-domains. The solutions from this research can lay some foundations for full-wave analysis of 3D high-speed VLSIC. The proposed project goes into depth on domain decomposition methods and model order reduction methods, and it is essential to both theory aspect and practical aspect for 3D integrated circuit analyses by integral equations.

以硅通孔为代表的三维集成技术在电路和芯片设计中应用广泛，但是相应的三维高速集成电路辅助设计方法还有待完善。由于贴片厚度、不规则通孔、垂直电流、多尺度等因素的影响，现有的积分方程二维数值方法还不能用于精确分析三维大规模高速集成电路信号完整性等问题。本项目通过发展同伦变换、宽频带复镜像和多维快速插值等技术精确求解大宗量空域并矢Green函数，利用新颖的积分方程非重叠型区域分解和模型降阶的混合构建三维集成电路的矩量法和部分元等效电路的混合建模和分析，再借由积分方程的部分基础解向量以及区域分解与其它快速算法混合的研究，实现大规模三维高速集成电路的整体仿真。本项目将三维集成电路分解并根据各个子区特点实现多种迭代方法的最佳组合，解决三维电路中遇到的多尺度等问题，为全波分析超大规模三维高速集成电路奠定基础。它深入探讨区域分解和模型降阶技术，对积分方程法分析三维电路具有一定理论意义和应用价值。

针对三维集成电路建模和分析中大量存在的大规模多尺度问题，开展了基于区域分解和模型降阶混合的三维高速集成电路多尺度建模和分析方法研究，重点研究了格林函数快速求解、积分方程、区域分解和快速求解技术等几个基础性内容和方法。首先，针对矩阵填充的瓶颈之一格林函数的计算问题，课题组研究了多类格林函数闭式解计算方法，以期利用新出现的压缩感知等技术加速表面波和复镜像提取，减少计算时间，增加精度。其次，针对电路问题中经常出现的低频、宽频等问题，课题组研究了电流电荷积分方程和宽频带特征基函数，通过采用新型基函数以及各种内插和外推技术，以期实现各类电路问题的稳定和高效求解。最后，针对大规模的电路问题，课题组从算法优化和硬件加速两个方面研究了区域分解和模型降阶技术。通过三个方面的研究和探索，课题组取得了一些成果，也积累了不少经验，形成了三维集成电路建模和全波分析的办法。