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

Abstract

Line edge roughness (LER) is a critical variability source in scaled FinFETs. LER produces line width roughness (LWR) that causes threshold voltage ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${V}_{T}$ </tex-math></inline-formula> ) variability. Various lithography techniques demonstrate characteristic LER-LWR relationship. For translating LER/LWR to the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${V}_{T}$ </tex-math></inline-formula> distribution, an analytical model for uncorrelated fin edges (correlation coefficient, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\rho ={0}$ </tex-math></inline-formula> ) has been presented in the literature. However, a range of correlation coefficients ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${0}\le \rho \le {0.85}$ </tex-math></inline-formula> ) between two fin edges is experimentally observed for various lithography techniques. In this paper, we present an analytical model to predict <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\rho $ </tex-math></inline-formula> dependent <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${V}_{T}$ </tex-math></inline-formula> distribution for partially correlated fin edges in FinFETs. First, an analytical model of mean ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula> ) and standard deviation ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\sigma $ </tex-math></inline-formula> ) for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\rho $ </tex-math></inline-formula> 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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${V}_{T}$ </tex-math></inline-formula> distribution from the fin distribution. The model is validated against well-calibrated TCAD simulations for a wide range of geometrical (channel length <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${L}_{G}$ </tex-math></inline-formula> and nominal fin width <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${W}_{\text {fin}})$ </tex-math></inline-formula> and LER variability (correlation length <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Lambda $ </tex-math></inline-formula> and correlation coefficient <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\rho $ </tex-math></inline-formula> ) parameters to show excellent match. The model is 1000 times faster compared with TCAD simulations.