The general purpose semiconductor device simulator Minimos-NT is extended to a "atomistic" quantum-corrected drift-diffusion simulator to study parameter fluctuations due to random discrete dopants. It has been confirmed that discrete dopants cannot straightforwardly be included in classical drift-diffusion simulators, because of unpysically large and grid dependent charge localization. This unphysical behavior can be eliminated by splitting the Coulomb potential into a long-range and a short-range part, explicitly including the long-range part only. The issue can also be solved by first-order quantum-correction to the classical drift-diffusion model via the density gradient model.
Unfortunately, the density gradient model leads to worsened numerical robustness especially when discrete dopants are included. Thus several advanced discretization schemes of the quantum-correction equation are implemented, but their numerical benefit could not be confirmed. With the focus on sub-nanometer MOS devices the density gradient model has the advantage of additionally including basic quantum mechanical effects such as confinement due to energy quantization. With the density gradient model we are able to fit a CV-curve to the solution of the Schrödinger Poisson solver VSP2 using Cauchy boundary conditions for the quantum-correction potential at the oxide interface. In a simulation study focused on a 22nm NMOS transistor 100 macroscopically identical samples are simulated showing random discrete dopant induced threshold voltage lowering and fluctuation.