Virial theorem, scaling properties and magneticfield effects on Coulombbound states in semiconductor quantum wells
Abstract
We have used the variational and fractionaldimensional space approaches, in the effectivemass approximation, in order to investigate the effects of applied magnetic fields on Coulombbound states, i.e. donor and exciton states, confined in GaAs(Ga, Al)As quantum wells. In the variational procedure, we have used a simple hydrogeniclike envelope wavefunction whereas the anisotropic Coulombbound state+quantum well+magneticfield system is modelled through an effective isotropic medium in the fractionaldimensional scheme. The magnetic fields are applied along the heterostructure growth direction, and calculations were performed for the binding energies, virialtheorem values and scaling properties. A virialtheorem value equal to 2 and a hyperbolic scaling for binding energies of Coulombbound states versus quantumconfined Bohr radii are obtained if one assumes a groundstate envelope wavefunction as a Ddimensional hydrogenic wavefunction, in contrast with results using the variational approach. Moreover, theoretical results within the variational approach lead to excitonenergy diamagnetic shifts in good agreement with available experimental measurements.
 Publication:

Semiconductor Science Technology
 Pub Date:
 June 2004
 DOI:
 10.1088/02681242/19/6/007
 Bibcode:
 2004SeScT..19..699R