A New Delay Distribution Model with a Half Triangular Distribution for Statistical Static Timing Analysis

Shuji TSUKIYAMA  Masahiro FUKUI  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E96-A   No.12   pp.2542-2552
Publication Date: 2013/12/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E96.A.2542
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on VLSI Design and CAD Algorithms)
Category: Device and Circuit Modeling and Analysis
Keyword: 
distribution model,  half triangular distribution,  long-term degradations,  statistical maximum,  mixture model,  non-Gaussian distr ibution,  statistical static timing analysis,  

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Summary: 
The long-term degradation due to aging such as NBTI (Negative Bias Temperature Instability) is a hot issue in the current circuit design using nanometer process technologies, since it causes a delay fault in the field. In order to resolve the problem, we must estimate delay variation caused by long-term degradation in design stage, but over estimation must be avoided so as to make timing design easier. If we can treat such a variation statistically, and if we treat it together with delay variations due to process variability, then we can reduce over margin in timing design. Moreover, such a statistical static timing analyzer treating process variability and long-term degradation together will help us to select an appropriate set of paths for which field testing are conducted to detect delay faults. In this paper, we propose a new delay model with a half triangular distribution, which is introduced for handling a random factor with unknown distribution such as long term degradation. Then, we show an algorithm for finding the statistical maximum, which is one of key operations in statistical static timing analysis. We also show a few experimental results demonstrating the effect of the proposed model and algorithm.