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 (
${0}\le \rho \le {0.85}$
) 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
${W}_{\text {fin}})$
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.