Compact model extraction from quantum corrected statistical Monte Carlo simulation of random dopant induced drain current variability

An efficient method to accurately capture quantum confinement effects within Monte Carlo (MC) simulation while simultaneously resolving `ab initio' ionized impurity scattering via the density gradient (DG) formalism is presented. The model is applied to study the impact of transport variability due to scattering from random discrete dopants on the on-current variability in realistic nano CMOS transistors. Such simulations result in an increase in drain current variability when compared with similarly quantum corrected drift diffusion (DD) simulation. Following this, an efficient three-stage hierarchical strategy is presented that propagates the increased on-current variability captured in 3D quantum corrected `ab initio' MC into efficient 3D DD simulations that are in turn used to obtain target ID-VG characteristics for the extraction of statistical compact models.