El Ayyadi, Asma Semiconductor simulations using a coupled quantum drift-diffusion Schrödinger-Poisson model. (English) Zbl 1099.82022 SIAM J. Appl. Math. 66, No. 2, 554-572 (2005). In order to analyze quantum effects in tunneling diodes, it has been proposed [J. Comput. Phys. 181, 222–259 (2002; Zbl 1008.82033)] to use the stationary mixed-state Schrödinger equation in the channel region and the stationary drift-diffusion equations in the diffusion zones near the contacts. Here one proposes an alternative which consists of using a diffusion approximation of the Wigner equation with a Bhatganar-Gross-Krook (BGK) collision operator. More exactly, the quantum drift-diffusion model is used in the diffusion region and the mixed-state Schrödinger equation is used in the ballistic region. The derivation of the quantum drift-diffusion model is outlined, the equations are displayed, they are solved by using numerical discretization, and some numerical results are given for a one-dimensional resonant tunneling diode. The results so obtained are compared with those previously obtained in the literature by using other models. Reviewer: Guy Jumarie (Montréal) Cited in 9 Documents MSC: 82D37 Statistical mechanics of semiconductors 76X05 Ionized gas flow in electromagnetic fields; plasmic flow 76Y05 Quantum hydrodynamics and relativistic hydrodynamics 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs Keywords:Schrödinger-Poisson system; quantum drift-diffusion model; quantum microscopic-macroscopic coupling; finite differences; resonant tunneling diode; hysteresis Citations:Zbl 1008.82033 PDFBibTeX XMLCite \textit{A. El Ayyadi}, SIAM J. Appl. Math. 66, No. 2, 554--572 (2005; Zbl 1099.82022) Full Text: DOI