Hierarchical Simulation of Statistical Variability: From 3-D MC With “ ab initio” Ionized Impurity Scattering to Statistical Compact Models

Quantum corrections based on density gradient formalism, recently introduced in the 3-D Monte Carlo (MC) module of the Glasgow "atomistic" simulator, are used to simultaneously capture quantum confinement effects as well as "ab initio" ionized impurity scattering. This has allowed us to consistently 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 increased drain current variability when compared with the drift diffusion (DD) simulation. For the first time, a method that is used to accurately transfer the increased on-current variability obtained from the "ab initio" MC simulations to the DD simulations is subsequently presented. The MC-corrected DD simulations are used to produce the target I-V characteristics from which the statistical compact models are extracted for use in preliminary design kits at the early stage of new technology development.