A Coupled Schrِdinger Drift-Diffusion Model for Quantum Semiconductor Device Simulations

In this paper, we derive a coupled Schrödinger drift–diffusion self-consistent stationary model for quantum semiconductor device simulations. The device is decomposed into a quantum zone (where quantum effects are expected to be large) and a classical zone (where they are supposed negligible). The Schrödinger equation is solved for scattering states in the quantum zone while a drift–diffusion model is used in the classical zone. The two models are coupled through interface conditions which are derived from those of N. Ben Abdallah (1998, J. Stat. Phys.90, 627) through a diffusion approximation. Numerical tests in the case of a resonant tunneling diode illustrate the validity of the method.