Title :
Determination of optimal polynomial regression function to decompose on-die systematic and random variations
Author :
Sato, Takashi ; Ueyama, Hiroyuki ; Nakayama, Noriaki ; Masu, Kazuya
Author_Institution :
Tokyo Inst. of Technol., Yokohama
Abstract :
A procedure that decomposes measured parametric device variation into systematic and random components is studied by considering the decomposition process as selecting the most suitable model for describing on-die spatial variation trend. In order to maximize model predictability, the log-likelihood estimate called corrected Akaike information criterion is adopted. Depending on on-die contours of underlying systematic variation, necessary and sufficient complexity of the systematic regression model is objectively and adaptively determined. The proposed procedure is applied to 90-nm threshold voltage data and found the low order polynomials describe systematic variation very well. Designing cost-effective variation monitoring circuits as well as appropriate model determination of on-die variation are hence facilitated.
Keywords :
CMOS integrated circuits; polynomials; regression analysis; Akaike information criterion; CMOS; log-likelihood estimate; model predictability; on-die systematic-random variations; optimal polynomial regression function; parametric device variation; systematic regression model; systematic-random components; threshold voltage data; variation monitoring circuits; Circuit synthesis; Data mining; Electronic design automation and methodology; Equations; Fabrication; Integrated circuit technology; Monitoring; Polynomials; Predictive models; Threshold voltage;
Conference_Titel :
Design Automation Conference, 2008. ASPDAC 2008. Asia and South Pacific
Conference_Location :
Seoul
Print_ISBN :
978-1-4244-1921-0
Electronic_ISBN :
978-1-4244-1922-7
DOI :
10.1109/ASPDAC.2008.4484006