A Novel Expression of Spatial Correlation by a Random Curved Surface Model and Its Application to LSI Design

Shin-ichi OHKAWA  Hiroo MASUDA  Yasuaki INOUE  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E91-A   No.4   pp.1062-1070
Publication Date: 2008/04/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e91-a.4.1062
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Selected Papers from the 20th Workshop on Circuits and Systems in Karuizawa)
LSI design,  device variation,  random curved surface,  Gaussian,  systematic part,  

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We have proposed a random curved surface model as a new mathematical concept which enables the expression of spatial correlation. The model gives us an appropriate methodology to deal with the systematic components of device variation in an LSI chip. The key idea of the model is the fitting of a polynomial to an array of Gaussian random numbers. The curved surface is expressed by a new extension from the Legendre polynomials to form two-dimensional formulas. The formulas were proven to be suitable to express the spatial correlation with reasonable computational complexity. In this paper, we show that this approach is useful in analyzing characteristics of device variation of actual chips by using experimental data.