Semiconductor Simulations Using a Coupled Quantum Drift-diffusion Schrödinger-poisson Model

A coupled quantum drift-diffusion Schrödinger-Poisson model for stationary resonant tunneling simulations in one space dimension is proposed. In the ballistic quantum zone with the resonant quantum barriers, the Schrödinger equation is solved. Near the contacts, where collisional effects are assumed to be important, the quantum drift-diffusion model is employed. The quantum drift-diffusion model have been derived by a quantum moment method from a collisional Wigner equation by Degond et al. The derivation yields an O(~) approximation of the Wigner function which is used as the “alimentation function” in the mixed-state formula for the electron and current densities at the interface. The coupling of the two models is realized by assuming the continuity of the electron and current densities at the interface points. Current-voltage characteristics of a one-dimensional tunneling diode are numerically computed. The results are compared to those from the three models: quantum drift-diffusion equations, Schrödinger-Poisson system, and the coupled drift-diffusion Schrödinger-Poisson equations.