Electronic states in GaAs-AlAs lateral-surface superlattices produced by deposition of AlAs and GaAs fractional layers on (001) vicinal GaAs substrates

The electronic energy subbands and minigaps in lateral-surface superlattices (LSSL’s) produced by deposition of AlAs and GaAs fractional layers on (001) vicinal GaAs substrates were predicated by variational calculations. A coordinate transformation was introduced in the calculation that transforms the LSSL’s with periodically structured interfaces to quantum wells with planar interfaces so that the boundary conditions of the electronic wave functions on the LSSL interfaces can be satisfied exactly. The calculations showed that our theory gives lower subband energies than those predicated by other variational calculations. The dependence of the energy minigaps between the first and second subbands on the LSSL structural parameters, such as the average widths of the LSSL’s and the periods of their interface structures, was investigated. In the calculation, the barrier between GaAs and AlAs was assumed to be finite (=1.06 eV) and infinite. The infinitely high potential-barrier approximation (IHPBA) overestimates the energy minigap by 50% when the average width of the LSSL is 100 Å, and it reduces to 25% when the width is 200 Å. IHPBA does not work well when the average widths of the LSSL’s are less than 200 Å.