# Condensed Matter Seminar Series

## Quantum Drift-Diffusion Equations for Semiconductor Superlattices

### Luis Bonilla

#### University Caros III, Madrid

##### Thursday April 12, 11:30 am, Room 298, Physics Building

Abstract: We
present quantum kinetic equations for electron transport in quasi
one-dimensional periodic structures (superlattices) having one or two
populated minibands. Electron-electron collisions are modeled by the
Poisson equation and inelastic collisions by a BGK-type term that
describes relaxation to local equilibrium. We derive drift-diffusion
equations and systems in the hyperbolic limit in which
electron-electron and inelastic collisions are equally important and
dominate other terms in the kinetic equations. Numerical simulation of
the drift-diffusion equations show high-frequency self-sustained
oscillations of the current through a dc voltage biased superlattice,
which are similar to the experimentally observed behavior.

*Host: Harold Baranger*