An Analytical Model to Estimate V-T Distribution of Partially Correlated Fin Edges in FinFETs Due to Fin-Edge Roughness

Line edge roughness (LER) is a critical variability source in scaled FinFETs. LER produces line width roughness (LWR) that causes threshold voltage (V-T) variability. Various lithography techniques demonstrate characteristic LER-LWR relationship. For translating LER/LWR to the V-T distribution, an analytical model for uncorrelated fin edges (correlation coefficient, (rho = 0) has been presented in the literature. However, a range of correlation coefficients (0 <= rho <= 0.85) between two fin edges is experimentally observed for various lithography techniques. In this paper, we present an analytical model to predict rho dependent V-T distribution for partially correlated fin edges in FinFETs. First, an analytical model of mean (mu) and standard deviation (sigma) for rho dependent minimum, maximum, and average fin width is presented. This is used to construct an equivalent simplified trapezoidal fin distribution. Second, percolation theory-based model is used to compute V-T distribution from the fin distribution. The model is validated against well-calibrated TCAD simulations for a wide range of geometrical (channel length L-G and nominal fin width W-fin) and LER variability (correlation length Lambda and correlation coefficient rho) parameters to show excellent match. The model is 1000 times faster compared with TCAD simulations