Theory of potential modulation in lateral surface superlattices. III. Two-dimensional superlattices and arbitrary surfaces

We have calculated the potential energy induced in a two-dimensional electron gas by a two-dimensional array of gates on the surface of a heterostructure. Differential thermal contraction of the gates generates strain that couples to the electrons by the deformation potential and piezoelectric effect. The piezoelectric effect usually dominates, and its angular dependence breaks the symmetry of the gate or array. For example, the potential under a circular gate on a (100) surface varies as sin 2 theta, where theta is measured from the [010] axis. This nulls the lowest Fourier components of the potential from a square array of gates aligned parallel to the principal axes. The lowest surviving component has a smaller period than the gates, and is rotated with respect to them by 45 degrees. Arrays are usually aligned parallel to the {011} cleavage planes in practice, which causes a stronger potential without such cancellation. We also provide results for (110), (111), and (311) surfaces; (111) may be attractive because the piezoelectric effect is nearly isotropic. The potential due to a bias on the gates, and the limit of a one-dimensional array, are considered briefly. Our calculations are for the strain induced by metal gates but also apply to devices with stressors such as mismatched semiconductors. [S0163-1829(98)06240-7].