Time-domain orthogonal finite-element reduction-recovery (OrFE-RR) method for electromagnetics-based analysis of very large scale integrated circuit and package problems.

摘要

The scaling of supply voltages and the increased level of integration have made the analysis and design of microelectronic systems increasingly challenging. To sustain the scaling and integration of digital, analog, mixed-signal and RF circuitry for years to come, an electromagnetic solution is indispensable to overcome the fundamental limits of a circuit-based analysis. There are two major challenges associated with electromagnetics-based analysis of integrated circuits and package problems. One is the exponentially increased problem size, which requires more than billions of unknowns to describe on-die and combined die-package problems accurately. The other is the multiscaled nature of the problem. A computer-aided design tool needs to span scale ranges of at least 10000:1 to analyze a combined die-package system.;In this work, we develop a time-domain orthogonal finite-element reduction-recovery method (OrFE-RR) to address the aforementioned challenges. In this method, a set of orthogonal prism vector basis functions is first constructed. A reduction-recovery algorithm is then developed to rigorously reduce an arbitrary 3-D multilayer circuit to a single-interface problem with negligible computational cost. The reduced single-interface problem features a diagonal system matrix, and hence can be readily solved. The solutions elsewhere are then recovered in linear complexity. The overall complexity in both storage and CPU time is linear. Moreover, an efficient parallelization scheme having linear speedup is developed to fully utilize the computational resources provided by many computer nodes as well as many cores on a single chip. In addition, we develop a fast model based simulation method to build an O(M) model, in linear time, to represent the original O(N) system, with M N. The overall computational cost of the OrFE-RR method is thus further reduced. Last but not least, a direct domain decomposition based solution of linear complexity is developed to tackle the challenge of simulating multiscaled structures present in on-chip integrated circuit and package problems.;Numerous numerical experiments, including real-world on-chip circuits and package problems provided by industry, have been conducted to demonstrate the accuracy, efficiency, capability and scalability of the algorithms developed in this work.