An entropic quantum drift-diffusion model for electron transport in resonant tunneling diodes

We present an entropic quantum drift-diffusion model (eQDD) and show how it can be derived on a bounded domain as the diffusive approximation of the Quantum Liouville equation with a quantum BGK operator. Some links between this model and other existing models are exhibited, especially with the density gradient (DG) model and the Schrödinger–Poisson drift-diffusion model (SPDD). Then a finite difference scheme is proposed to discretize the eQDD model coupled to the Poisson equation and we show how this scheme can be slightly modified to discretize the other models. Numerical results show that the properties listed for the eQDD model are checked, as well as the model captures important features concerning the modeling of a resonant tunneling diode. To finish, some comparisons between the models stated above are realized.