Fitting standard cell performance to generalized Lambda distributions

Abstract

It is well known that random fluctuations in integrated circuit manufacturing introduce variations in circuit performance. While a lot of effort has been spent on circuit variability, fitting performance parameter distributions has not been extensively examined. Our work analyzes whether the Generalized Lambda Distribution suits approximating circuit performance characteristics. We focus on statistical standard cell characterization as an important step towards statistical gate-level and system-level analyses. Our results show that the Generalized Lambda Distribution is not applicable to raw leakage power data. However, timing data and dynamic power consumption may be approximated well. The high characterization effort has to be overcome to achieve industrial application

A general approach for multivariate statistical MOSFET compact modeling preserving correlations

“…When considering an m-dimensional random variable X, we may focus on an arbitrary component X i or on the interdependency between the components X i and X j . Validity of probability distributions due to moments α i,3 and α i,4 ; adapted from [12] and [13] The distribution of a single random component X i is described by its probability density function (PDF) f Xi (x i ), its cumulative distribution function (CDF) F Xi (x i ), or its quantile function…”

“…Therefore we present a more general method for multivariate modeling using rank correlations [10], [11]. We approximate marginal distributions using the Generalized Lambda Distribution (GLD) [12] which has been applied to distributions of standard cell performance characteristics [13].…”

“…Fig.1. Validity of probability distributions due to moments α i,3 and α i,4 ; adapted from[12] and[13] …”