Newk⋅ptheory for GaAs/Ga1−xA1xAs-type quantum wells

A new k⋅p theory for the description of GaAs/${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Al}}_{\mathrm{x}}$As-type quantum wells is presented. The theory combines a unified description of electron and hole states with only five adjustable parameters for each material constituting the quantum well. Unlike earlier k⋅p work it fully accounts for the coupling between the lowest electron, the light-hole, the heavy-hole, and the spin-orbit split-off hole bands and the coupling to all other bands is taken into account perturbatively. The theory thereby also applies to quantum wells where the spin-orbit splitting is comparable to the hole-confinement potential energies. The full inclusion of the ${\mathrm{k}}_{?}$ dependence of confinement energies and electron-hole transition strengths allows for accurate predictions of excitation spectra of quantum wells. In this respect the results of our simple k⋅p theory stand comparison to the results of the more complicated tight-binding theory of Chang and Schulman. Our theory can thus explain the recently observed Δn≠0 transitions. As a final application we have calculated gain spectra of quantum-well lasers.