Fundamental relationship between the Herring and Cantrell-Butcher formulasfor the phonon-drag thermopower of two-dimensional electron and hole gases- art. no. 165304

We show that Herring's formula for the phonon-drag thermopower S-g is equiv alent to the standard Cantrell-Butcher (CB) formula for a two-dimensional e lectron (or hole) gas. The CB approach provides a rigorous theoretical fram ework which is remarkably successful in explaining the measured S-g in two- dimensional systems. Herring's approach, although phenomenological, shows p articular interest because it leads to an elegant and simple formula for S- g in terms of the phonon-limited mobility. The equivalence of the two formu las justifies the use of Herring's expression for the estimation of the pho non-limited mobility directly from the phonon-drag thermopower data and vic e versa. Consequently, we exploit both the accuracy of the CB formula and t he simplicity of Herring's formula. Our analysis leads to the derivation of an optimum average for the inelastic carrier relaxation rate tau (-1)(ac) associated with the acoustic-phonon scattering. This average is free of the conventional approximations made in the literature and explains with remar kable accuracy mobility data in both n- and p-type AlxGa1-xAs/GaAs heterost ructures.