Improved modeling of excitons in type-II semiconductor heterostructures by use of a three-dimensional variational function

Binding energies and oscillator strengths of excitons in staggered-lineup heterostructures such as type-II quantum wells are calculated by a variational method, using a single parameter. This method involves the effective attractive potential imposed by the confined carrier to its unconfined companion. Contrary to previous comparable works, a three-dimensional trial function of the variable r (r=‖${\mathbf{r}}_{\mathit{e}}$-${\mathbf{r}}_{\mathit{h}}$‖) is used, instead of a two-dimensional function of the in-plane projection ρ. Due to the large spatial extension along z of the wave function of the unconfined carrier, the latter approximation commonly used up to date, is too drastic, even though it works reasonably well for type-I systems. This is demonstrated by comparison of both hypotheses for GaAs-AlAs systems: when using the 3D function, binding energies are increased by up to 52%, while electron-hole overlap integrals can be enhanced by one order of magnitude.