Quantum corrected drift-diffusion modeling and simulation of tunneling effects in nanoscale semiconductor devices

In this communication, we deal with the numerical approximation of a Quantum Drift-Diffusion model capable of describing tunneling effects through the thin oxide barrier in nanoscale semiconductor devices. We propose a novel formulation of the mathematical model, based on a spatially heterogeneous approach, and a generalization of the Gummel decoupled algorithm, widely adopted in the case of the Drift-Diffusion system. Then, we address the finite element discretization of the linearized problems obtained after decoupling, proving well-posedness and a discrete maximum principle for each of them. Finally, we validate the physical accuracy and numerical stability of the proposed algorithms on the numerical simulation of a real-life nanoscale device.