A Semiclassical coupled model for the transient simulation of semiconductor devices

Philippe Béchouche (1) , Laurent Gosse (2)

1 UGR - Universidad de Granada = University of Granada
2 IAC - Istituto per le Applicazioni del Calcolo "Mauro Picone"

We consider the approximation of a microelectronic device corresponding to a $n^+-n-n^+$ diode consisting in a channel flanked on both sides by two highly doped regions. This is modelled through a system of equations: ballistic for the channel and drift-diffusion elsewhere. The overall coupling stems from the Poisson equation for the self-consistent potential. We propose an original numerical method for its processing, being realizable, explicit in time and nonnegativity preserving on the density. In particular, the boundary conditions at the junctions express the continuity of the current and don't destabilize the general scheme. At last, efficiency is shown by presenting results on test-cases of some practical interest.

Mots clés: Drift-diffusion equation; Schr{ö}dinger-Poisson equation; WKB ansatz; open quantum system; Robin boundary condition.; Robin boundary condition

Domaines: Analyse numérique [math.NA]; Electronique

Philippe Béchouche, Laurent Gosse. A Semiclassical coupled model for the transient simulation of semiconductor devices. SIAM Journal on Scientific Computing, 2007, 29 (1), pp.376-396. ⟨10.1137/060655262⟩. ⟨hal-00426854⟩