Analytical-BEM coupling method for fast 3-D interconnect resistance extraction

Abstract

Deep submicron process technology is widely being used and interconnect structures are becoming more and more complex. This means that the resistance calculation based on two-dimensional models can no longer provide sufficiently accurate results. This paper presents a three-dimensional resistance calculation method called the combined analytical formula and boundary element method (ABEM). The method cuts selected interconnecting lines then it calculates the resistances of straight sections using an analytical formula and the resistances of the other sections using the boundary element method (BEM). The resistances of the different sub-regions are combined to calculate the resistance of the entire region. Experiments on actual layouts show that compared with the commercial software Raphael based on finite difference method, the proposed method is 2 3 orders of magnitude faster. The ABEM method uses much less memory (about 0.1% 1%), and is more accurate than Raphael with default mesh partitions. The results illustrate that the proposed method is efficient and accurate.

Keywords

Very large scale integration, Interconnecting resistance, 3-D extraction, Analytical formula, BEM