Diffusion thermopower due to interface roughness-induced piezoelectric scattering in lattice-mismatched semiconductor quantum wells

We calculate the diffusion thermopower for a degenerate two-dimensional electron gas in real lattice-mismatched semiconductor quantum wells (QWs) at low temperatures. We consider explicitly two scattering mechanisms: (i) the surface roughness-induced piezoelectric effect, a new important scattering source, arising due to a large fluctuating density of roughness-induced piezoelectric charges and (ii) the surface roughness. The scattering parameter p of energy dependence of the momentum relaxation time and the diffusion thermopower Sd, of each of the mechanisms separately and also when both the mechanisms are combined, are calculated as a function of electron concentration and well width. The diffusion thermopower, as a function of electron concentration, due to piezoelectric field shows a change in sign for lower concentrations. Interestingly, the diffusion thermopower, due to this mechanism, as a function of well width also shows a change in sign and it is dominant for larger well widths. The numerical calculations are presented for In0.2Ga0.8As/GaAs and AlN/GaN QWs. The piezoelectric mechanism is expected to be very important in systems with large piezoelectric constant and lattice mismatch.