A STOCHASTIC ALGORITHM FOR 3D MAXWELL SOLUTION WITHIN OPTICAL ON-CHIP IC INTERCONNECTS: MATERIALLY HOMOGENEOUS, SCALAR WAVE-EQUATION BENCHMARKS

摘要

Understanding and predicting the multi-GHz behavior of IC interconnects is crucial towards meeting objectives of the semiconductor-design industry in the present decade. Essentially, we need solve Maxwell's equations. There are two ways in which this can be done: (ⅰ) one-step, direct solution of the underlying field equations; ( ⅱ) two-step, lumped-element parasitic extraction followed by solution of the resulting circuit equations. We will presume that "one-step" Maxwell solution has been selected above. It is direct and efficient solution of Maxwell's equations―for future application in optical on-chip IC-interconnect CAD―that we consider our primary motivating factor. Traditional numerical methods for solving electromagnetic problems, unfortunately, require a numerical discretization mesh, consuming large amounts of computer memory. In particular, mesh size and resultant difficulty of solution become somewhat unmanageable in massively coupled, geometrically complicated 3D problems. The stochastic algorithm that we present here requires no such mesh; in essence, it executes a Monte Carlo integration over a meshless problem domain. We have previously reported new Impulse-Response (IR) moment-extraction algorithms for RC and RLC IC-interconnect circuit networks. These algorithms implemented diagrammatic expansion of a Laplace-transform perturbation series, inspired by the work of Feynman in theoretical physics. The proven advantages of diagrammatic expansion are contained within this approach: no numerical mesh, efficient in massively coupled, high-dimensionality problems; "dial-in" accuracy; fully parallel for computational speed up.