Removal of accidental degeneracies in semiconductor quantum wires

We obtain the energy levels of carriers in rectangular GaAs/${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Al}}_{\mathit{x}}$As quantum-wire heterostructures with finite barriers using finite-element analysis. The energy spectra obtained are dramatically different from those determined analytically with use of the infinite-barrier approximation. The infinite-barrier approximation also introduces extra degeneracies in the energy spectra as a consequence of the separability of the potential. These accidental degeneracies are removed when the barrier height corresponding to the band offset of the surrounding medium is used in calculating the energy levels. Group-theory considerations of the square are used to explain the removal of these accidental degeneracies.