Excitons in semiconductor quantum wells with a small band offset: Exact numerical solution to the envelope function

Abstract

We use an accurate method to solve the ground state and binding energy of a Wannier exciton in a semiconductor quantum well with a small valence (or conduction) band offset. By choosing fixed envelope function in the conduction (or valence) band quantum well and taking the relative part of the exciton wavefunction in the commonly assumed variational form, a one-dimensional second-order differential equation for the envelope function in the valence (or conduction) band is derived. The exciton intergap energy is then deduced from the eigenvalue of this equation. This approach includes the effect of the additional confinement on the carrier in the valence (or conduction) band quantum well by the electron-hole Coulomb interaction, and has the advantage of being numerically exact in determining the envelope function comparing to the generalized variational approach developed earlier. The application of this method to II–VI compound semiconductor quantum wells is discussed.