Intra-Die Spatial Correlation Extraction with Maximum Likelihood Estimation Method for Multiple Test Chips

Qiang FU  Wai-Shing LUK  Jun TAO  Xuan ZENG  Wei CAI  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E92-A   No.12   pp.3007-3015
Publication Date: 2009/12/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E92.A.3007
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: 
intra-die variations,  spatial correlation,  maximum likelihood estimation,  

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Summary: 
In this paper, a novel intra-die spatial correlation extraction method referred to as MLEMTC (Maximum Likelihood Estimation for Multiple Test Chips) is presented. In the MLEMTC method, a joint likelihood function is formulated by multiplying the set of individual likelihood functions for all test chips. This joint likelihood function is then maximized to extract a unique group of parameter values of a single spatial correlation function, which can be used for statistical circuit analysis and design. Moreover, to deal with the purely random component and measurement error contained in measurement data, the spatial correlation function combined with the correlation of white noise is used in the extraction, which significantly improves the accuracy of the extraction results. Furthermore, an LU decomposition based technique is developed to calculate the log-determinant of the positive definite matrix within the likelihood function, which solves the numerical stability problem encountered in the direct calculation. Experimental results have shown that the proposed method is efficient and practical.