Optimal Wire-Sizing Formula Under the Elmore Delay Model

In this paper, we consider non-uniform wire-sizing. Given a wire segment of length L, let f(x) be the width of the wire at position x, 0 x L. We show that the optimal wire-sizing function that minimizes the Elmore delay through the wire is f(x) = ae \Gammabx , where a ? 0 and b ? 0 are constants that can be computed in O(1) time. In the case where lower bound (L ? 0) and upper bound (U ? 0) on the wire widths are given, we show that the optimal wire-sizing function f(x) is a truncated version of ae \Gammabx that can also be determined in O(1) time. Our wire-sizing formula can be iteratively applied to optimally size the wire segments in a routing tree. 1 Introduction As VLSI technology continues to scale down, interconnect delay has become the dominant factor in deep submicron designs. As a result, wire-sizing plays an important role in achieving desirable circuit performance. Recently, many wire-sizing algorithms have been reported in the literature [1, 2, 4, 5, 7]. All thes..