A comparison using a deltafunction model of envelope function approximations for quantum wells
Abstract
This paper compares four versions of the effectivemass approximation to the exact atomic wave function, as determined from a onedimensional model potential, in predicting the energies of the bound states in a single quantum well such as those formed in compound semiconductor heterostructures. The model potential consists of deltafunction barriers between atoms with a ``well'' in the strength of these delta functions. The model yields simple, closedform solutions for the bound state energy. The corresponding effectivemass model that uses the calculated dispersion relations and continuity of the wave function derivatives at the well boundaries predicts bound state energies indistinguishable from those predicted by the exact solution. The parabolicband model overestimates the lowest energy level of a 0.4eVdeep, 50Åwide well by about 15%. Continuity of 1/m* times the wave functions underestimates the energies by about the same amount.
 Publication:

Journal of Applied Physics
 Pub Date:
 June 1988
 DOI:
 10.1063/1.340357
 Bibcode:
 1988JAP....63.5393C
 Keywords:

 Delta Function;
 Gallium Arsenides;
 Quantum Wells;
 Wave Functions;
 Electron Mass;
 Free Electrons;
 Plane Waves;
 Schroedinger Equation;
 SolidState Physics