GaAs GaAlAs Quantum Wells

GaAs-GaAlAs Quantum Well. Electrons, heavy and light holes energy levels vs. Lz. Eigenfuctions.

GaAs-GaAlAs Quantum Well

In a type I quantum well, the energy difference ΔEg between the larger band gap of the barrier and the smaller band gap of the well material causes a confinement potential both for the electrons in the conduction band and for the holes in the valence band. In a GaAs-GaAlAs quantum well, e.g., the resulting well depths are ΔVe~ 2ΔEg/3 and ΔVh~ ΔEg/3, respectively. In these semiconductors, the electrons in the conduction band behave as if they had an effective mass, m*, that is different from the free electron mass, mo, and this mass is different in the two materials, e.g., mw in the well and mb in the barrier. Because the electron effective mass differs in the two materials, the boundary condition that is used at the interface between the two materials for the derivative of the wavefunction is not continuity of the derivative dψ / dz ; instead, a common choice is continuity of (1/m*)(dψ / dz) where m* is different for the materials in the well and in the barrier.

This m-file (GaAs_GaAlAs_QW.m) plots the eigenfuctions for electrons, heavy and light holes given the Al composition (x) and the well width Lz (Å) of a GaAs-GaAlAs quantum well. It also calculates the different energy levels for electrons, heavy and light holes given the Al composition (x).

UNIVERSITY OF ESSEX
Optoelectronics Research Group
PhD Student Ernesto Momox Beristain

March 2009

Enjoy!