Accurate interconnect modeling for efficient transient simulation in VLSI chip design

Aggressive VLSI feature size shrinking makes integrated circuits and systems both larger and faster. CMOS integrated circuits are now operating at well more than 3 GHz of clock; nevertheless, it is projected that the VLSI chip speed will enhance in a decade by a factor of four. As the interconnect scaling poses a serious challenge to signal integrity and circuit speed, these interconnects must be represented as distributed RLC transmission lines. The huge number of interconnects within the chip makes the traditional simulators prohibitively slow. Therefore, among other techniques to speed up the simulation, efficient interconnect modeling algorithms are needed to obtain accurate models for efficient circuit simulation in VLSI chip design.; Since the Differential Quadrature (DQ) method was invented for solving partial differential equations (PDE's) in 1972, it has been recognized by mathematicians as a computationally efficient approximation technique. The DQ method can accurately compute nonlinear PDE's with ten times less grid points than required by the finite difference (FD) methods. In this research, this key feature of the DQ method is exploited to build faster mathematical modeling tools for solving inter-connect modeling problems in high-speed VLSI chip design and simulation. Passivity preservation is an important criterion for interconnect modeling. Although original DQ methods demonstrate high efficiency, their passivities are not guaranteed. We have adapted DQ methods to interconnect modeling to ensure its passivity. Using the equivalent circuit based on the DQ method to represent interconnects, a speedup of up to six times over HSPICE is demonstrated in the numerical experiments of transient simulation.; The Finite Difference Quadrature FDQ method is proposed for transmission line modeling. The FDQ method adapts coarse grid points along the transmission line to compute the finite difference between adjacent grid points by using a global approximation scheme in the form of a weighted sum of quantities beyond the local grid points. Unlike the Gaussian Quadrature method that computes numerical integrals by using global approximation framework, the FDQ method uses global, quadrature method to construct the approximation schemes to compute, however, numerical finite differences. The FDQ method has superior numerical dispersion to the FD method and needs much sparser grid points to achieve comparable accuracy. Numerical results show that FDQ method is an effective way to accurately model transmission lines for fast circuit simulation.