A novel expression of spatial correlation by a random curved surface model and its application to LSI design

Ohkawa Shin-ichi, Hiroo Masuda, Yasuaki Inoue

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    1 Citation (Scopus)


    We have proposed a random curved surface model as a new mathematical concept which enables the expression of spatial corre-lation. 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.

    Original languageEnglish
    Pages (from-to)1062-1070
    Number of pages9
    JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
    Issue number4
    Publication statusPublished - 2008



    • Device variation
    • Gaussian
    • LSI design
    • Random curved surface
    • Systematic part

    ASJC Scopus subject areas

    • Electrical and Electronic Engineering
    • Computer Graphics and Computer-Aided Design
    • Applied Mathematics
    • Signal Processing

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