三维集成电路通过高密度金属互连线实现芯片在三维空间上互连,其电路参数的快速提取是保证信号完整性良好设计的关键技术之一.文中基于体积分混合势积分方程(mixed potential integral equation,MPIE)方法,结合多层平面介质格林函数与...三维集成电路通过高密度金属互连线实现芯片在三维空间上互连,其电路参数的快速提取是保证信号完整性良好设计的关键技术之一.文中基于体积分混合势积分方程(mixed potential integral equation,MPIE)方法,结合多层平面介质格林函数与预纠正快速傅里叶变换(pre-corrected fast fourier transformation,pFFT)方法,通过对互连线内趋肤电流准确建模,实现对互连线结构S参数的快速准确提取.通过对典型互连线结构的仿真表明,本文求解器得到的结果与商业软件HFSS结果在网格剖分考虑趋肤效应时,其精度相当,计算效率可提高50%以上.所以本文方法在三维集成电路互连线参数快速提取方面具有一定的应用前景.展开更多
The flow behavior in porous media with threshold pressure gradient(TPG) is more complex than Darcy flow and the equations of motion, and outer boundary and inner boundary with TPG are also different from Darcy flow fo...The flow behavior in porous media with threshold pressure gradient(TPG) is more complex than Darcy flow and the equations of motion, and outer boundary and inner boundary with TPG are also different from Darcy flow for unsteady flow of a producing well in a reservoir. An analytic method to solve this kind of problem is in a need of reestablishment. The classical method of Green's function and Newman product principle in a new way are used to solve the unsteady state flow problems of various shapes of well and reservoir while considering the TPG. Four Green's functions of point, line, band and circle while considering the TPG are achieved. Then, two well models of vertical well and horizontal well are built and simultaneously the function to calculate the moving boundary of each well model is provided. The results show that when considering TPG the pressure field is much different, which has a sudden pressure change, with a moving boundary in it. And the moving boundary of each well model increases with time but slows down rapidly, especially when the TGP is large.展开更多
文摘三维集成电路通过高密度金属互连线实现芯片在三维空间上互连,其电路参数的快速提取是保证信号完整性良好设计的关键技术之一.文中基于体积分混合势积分方程(mixed potential integral equation,MPIE)方法,结合多层平面介质格林函数与预纠正快速傅里叶变换(pre-corrected fast fourier transformation,pFFT)方法,通过对互连线内趋肤电流准确建模,实现对互连线结构S参数的快速准确提取.通过对典型互连线结构的仿真表明,本文求解器得到的结果与商业软件HFSS结果在网格剖分考虑趋肤效应时,其精度相当,计算效率可提高50%以上.所以本文方法在三维集成电路互连线参数快速提取方面具有一定的应用前景.
基金Project(51304220) supported by the National Natural Science Foundation of ChinaProject(3144033) supported by the Beijing Natural Science Foundation,ChinaProject(20130007120014) supported by the Specialized Research Fund for the Doctoral Program of Higher Education of China
文摘The flow behavior in porous media with threshold pressure gradient(TPG) is more complex than Darcy flow and the equations of motion, and outer boundary and inner boundary with TPG are also different from Darcy flow for unsteady flow of a producing well in a reservoir. An analytic method to solve this kind of problem is in a need of reestablishment. The classical method of Green's function and Newman product principle in a new way are used to solve the unsteady state flow problems of various shapes of well and reservoir while considering the TPG. Four Green's functions of point, line, band and circle while considering the TPG are achieved. Then, two well models of vertical well and horizontal well are built and simultaneously the function to calculate the moving boundary of each well model is provided. The results show that when considering TPG the pressure field is much different, which has a sudden pressure change, with a moving boundary in it. And the moving boundary of each well model increases with time but slows down rapidly, especially when the TGP is large.
