THEORY OF POTENTIAL MODULATION IN LATERAL SURFACE SUPERLATTICES

We have calculated analytically the potential generated in a two-dimensional electron gas by a lateral superlattice on a GaAs/AlxGa1-xAs heterostructure, formed by an array of parallel metal striped gates on the surface. The shape of the electrostatic potential produced by a bias on the gates depends on the boundary condition on the exposed surface of GaAs in the gaps between the gates. The usual assumption of a pinned GaAs surface gives a potential containing only odd harmonics. This is not in agreement with a recent experimental measurement of the potential from commensurability oscillations in the magnetoresistance. An alternative model where the surface charge is frozen in the gaps gives an asymmetry between the gates and the gaps which is closer to experiment. A quite different origin of the potential is a result of elastic strain resulting from differential contraction between the metal gates and the GaAs as the sample is cooled, coupling through the deformation potential. This gives a good fit to experiment and shows that the strain from mismatched gates cannot be neglected in electronic transport phenomena that are sensitive to weak potentials.