Estimation of Drain-Induced Barrier Lowering Variation Due to Random Dopant Fluctuation Effect in Nanometer MOSFETs by Gamma Distribution

Abstract

Drain-induced barrier lowering (DIBL) and its variations are regarded as significant challenges in nanometer semiconductor device and circuit analysis, design as well as fabrication. This paper investigates the statistical characteristic of DIBL due to random dopant fluctuation (RDF) effect in MOSFETs. The results exhibit that the DIBL variation is more suitably described by a gamma distribution than a Gaussian distribution, based on validation by Monte Carlo simulations. The average error and mean square error of a gamma approximation are –0.14987 and 0.42591, respectively, for the probability density function, and 0.13523 and 0.50584, respectively, for the cumulative density function, which are much smaller than the equivalent measures of a Gaussian approximation. Our study also reveals that DIBL dispersion due to RDF effect in nanometer MOSFET channels is asymmetric with a long tail, which should be described with higher moments such as skewness and kurtosis.