Binding energies of acceptors in GaAs-AlxGa1−xAsquantum wells

We present a variational calculation of acceptor binding energies in a GaAs-${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ quantum well. The calculation includes the coupling of the top four valence bands of both materials in the multiband effective-mass approximation. Because the quantum-well potential reduces the bulk symmetry, the bulk ${\Gamma }_8$ acceptor ground state splits into ${\Gamma }_6$ and ${\Gamma }_7$ states. The ground-state energies in both symmetries have been calculated for three barrier heights as functions of well width. These calculations for barrier heights corresponding to $x=0.3\mathrm{}$ are in excellent agreement with the available experimental data.