Random dopant model for three-dimensional drift-diffusion simulations in metal–oxide–semiconductor field-effect-transistors

We investigate the dopant model employed in drift-diffusion device simulations for the study of statistical threshold voltage variations associated with discrete random dopants. It is pointed out that the conventional dopant model, when extended to the extreme “atomistic” regime, becomes physically inconsistent with the length-scale presumed in drift-diffusion simulations. Splitting the Coulomb potential of localized dopants between the long-range and short-range parts, we propose a dopant model appropriate for three-dimensional drift-diffusion simulations.