A closed-form expression for estimating minimum operating voltage (VDDmin) of CMOS logic gates

Authors:
Hiroshi Fuketa;Satoshi Iida;Tadashi Yasufuku;Makoto Takamiya;Masahiro Nomura;Hirofumi Shinohara;Takayasu Sakurai
Affiliations:
University of Tokyo, Japan;University of Tokyo, Japan;University of Tokyo, Japan;University of Tokyo, Japan;Semiconductor Technology Academic Research Center (STARC), Japan;Semiconductor Technology Academic Research Center (STARC), Japan;University of Tokyo, Japan
Venue:
Proceedings of the 48th Design Automation Conference
Year:
2011

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Abstract

In this paper, a closed-form expression for estimating a minimum operating voltage (VDDmin) of CMOS logic gates is proposed. VDDmin is defined as the minimum supply voltage at which circuits can operate correctly. VDDmin of combinational circuits can be written as a linear function of the square-root of logarithm of the number of logic gates and its slope is proportional to the standard deviation of the within-die variation in the threshold voltage difference between PMOS and NMOS transistors. The proposed expression is verified with Monte Carlo simulations using various gate chains. The verification reveals that VDDmin of inverter chains can be estimated within 11% error. The expression is also verified with silicon measurements in a 65nm CMOS process.