三维集成电路互连线电磁积分方程方法关键技术研究

Interconnects with interposers are the fundamental and key elements to develop three dimensional integrated circuits (3D ICs) and in charge of signal exchange between chips. Based on the surface admittance operator, a novel surface integral equation method for full-wave simulation is proposed to accurately and efficiently model metallic interconnects in interposers with multilayer planar media stacked in 3D ICs. However, this method has the following drawbacks, low computational efficiency when handling conductors, low frequency instability and being incapable of dealing multilayer media. Three main researches will be made to overcome those them. First, a novel integration method for highly conductive media is proposed. In this method, valid integration regions in the source and field triangles are extracted based on the Green function decaying ratio in conductive regions. To further improve efficiency, those integration regions in the field triangles are further decomposed into several polygons and then each polygon will be integrated separately. Second, Loop-Star and Loop-Tree decomposition methods are selected to solve the instable problem in the proposed surface integral equation method in low frequency region. Therefore, we could obtain stable and accurate results in both low and high frequency regions. Third, to efficiently obtain the spatial multilayer Green function values for interposers, interpolation methods based on a lookup table are used in near and far field region. Therefore, this new integral equation method could model interconnects imbedded in interposers with multilayer media, which lay theoretical and technical foundation for further development of corresponding fast algorithms for interconnects in 3D ICs.

转接板(Interposer)中互连线是构建三维集成电路，实现芯片间信号传递的核心结构，准确获取其电路参数是进行三维集成电路有效设计的前提。本课题基于表面导纳算子，建立新型的高效表面积分方程方法，用于Interposer金属互连线全波段高效精确建模与仿真。针对该方法在金属导体中计算效率低下、低频不稳定和不能处理多层平面介质的问题，拟进行三方面的基础理论研究：①根据格林函数在高电导率导体中强衰减的特性，提取出有效积分区域，并根据格林函数变化进一步分区积分，提高计算效率；②研究Loop-Star和Loop-Tree两种方法解决其低频不稳定问题；③研究适用于Interposer结构从谱域到空域多层介质格林函数近、远场转换方法，应用插值方法高效高精度计算积分点格林函数值，建立适用于多层介质的导纳算子积分方程方法，用于Interposer互连线参数提取，为进一步开发相应的快速算法奠定理论和技术基础。

本项目围绕三维集成电路互连线电磁快速、宽频带建模的难题，基于表面等效原理，研究了多种基于差分表面导纳算子的单源表面积分方程方法，相比于传统的积分方程方法可以显著提高计算效率、减少内存消耗。具体包括：（1）针对电磁仿真计算中矩量法阻抗矩阵元素重复计算的问题，研究了矩量法中积分核的变化规律，提出了一种高效准确的自适应插值方法，实现了相同精度下计算效率提升20%；（2）针对三维集成电路中多层内埋结构仿真计算量大的问题，提出了一种基于差分表面导纳算子的单源表面积分方程方法，实现了在结构最外层边界上施加表面电流密度，未知量可减少为PMCHWT方法的12%，时间减少到48%，矢量TE模式下未知量减少50%，求解时间缩短到40%；（3）研究了嵌入多层物体内可能出现的部分接触结构的单源等效模型，该等效模型可实现未知量减小62%，计算时间缩短48%；（4）针对平面介质结构中多层介质格林函数计算精度与效率问题，基于Schelkunoff表面等效原理，研究了平面结构的公共边界表面等效电流源条件，实现了将平面复合结构按照几何特征进行非共形区域分割；基于准静态近似方法，研究了分解表面导纳算子积分方程中的等效电流方法，建立从低频到高频稳定的数学模型，实现不同三维集成电路结构的仿真分析。通过本项目的研究工作，可以为开发快速的三维集成电路奠定理论和技术基础。