Simple models of phonon-drag in 3D and quasi-2D

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Abstract
The simple 'metallic' formulae for the phonon drag thermoelectric power (Sg) of 3D free-electron systems appears to be in conflict with the model of Herring, by predicting different dependences of Sg upon electron density and temperature (T) at low T. The authors show that both approaches can be understood physically by considering the net phonon drift velocity. A simple quasi-2D expression for Sg is then obtained which predicts the underlying dependence upon T, phonon mean free path L, and electron surface density n, as LT3/n which is the observed behaviour in heterojunctions and MOSFETs. This dependence is modified by the efficiency with which momentum is transferred between the electron and phonon systems. Boltzmann transport calculations confirm these conclusions and support the simple models by reproducing the simple formulae in appropriate limits.