Acceptor spectra of AlxGa1−xAs-GaAs quantum wells in external fields: Electric, magnetic, and uniaxial stress

Abstract

We have used the variational method to calculate the acceptor binding energies in GaAs-${\mathrm{Al}}_{\mathrm{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As quantum wells with and without the application of electric, magnetic, and uniaxial stress fields. The calculation includes the coupling of the top four valence bands of both materials in the multiband effective-mass approximation. To ensure the convergence of the calculation, a large number of basis functions which are made up of the s-like, p-like, or d-like spatial states multiplied by j=(3/2) spinors are used for the expansion of the acceptor wave function. Because the quantum well and external field potentials reduce the point-group symmetry from $T_d$ to $D_{2d}$, the bulk ${\Gamma }_8$ acceptor ground state splits into ${\Gamma }_6$ and ${\Gamma }_7$ states. The ${\Gamma }_6$ state is predominantly derived from the heavy-hole subband and the ${\Gamma }_7$ state is predominantly derived from the light-hole subband. The magnetic field further splits the ${\Gamma }_6$ and ${\Gamma }_7$ states. We have calculated the energies of the ${\Gamma }_6$ state and the ${\Gamma }_7$ state for both center doped and edge doped quantum wells as well as the ${\Gamma }_6$ and ${\Gamma }_7$ valence-subband edges for various barrier heights as functions of well width. In recent studies the photoluminescence resulting from the acceptor levels to conduction-band transition in molecular-beam-epitaxy-grown GaAs-${\mathrm{Al}}_{\mathrm{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As superlattices have been measured. Our theoretical results are in excellent agreement with these experimental data.