Eigenstates in irregular quantum wells: application to porous silicon

We discuss the effects of geometrical irregularities on the properties of quantum states in irregular wells. This may apply to small crystallites, quantum dots or wires. We show that geometrical irregularity may play an essential role in the electro-optical properties of porous silicon. The fundamental state is found to be essentially confined in the inner free volume of the irregular structure. The consequence is a screening of the fundamental wave-function from the surface. This leads to an enhancement of the quantum confinement effect hence an increase of the effective band gap and modifications in the density of states in the near band gap region. The screening also lowers the coupling with surface states, a fact which may contribute to explaining the large luminescence yield found in this material. We show that geometrical irregularities may have a surprising passivation effect for the fundamental state. In the same way the acoustic phonons have a qualitative tendency to be localized near the surface, so that the electron - phonon coupling could be also decreased, for the fundamental energy state, by the existence of geometrical irregularity.