Thermoelectric effect in superlattices; applicability of coherent and incoherent transport models

Calculations of thermoelectric transport coefficients including quantum effects are performed on superlattices using the Buttiker approximation. The results are compared to the Boltzmann transport equation with minibands present, and to an incoherent transport model. Comparisons are performed in the linear regime for the electrical conductivity, Seebeck and Lorenz coefficients. We show that at superlattice periods smaller than the typical electron mean free path, the former model and the calculations including quantum effects are in agreement. However, for longer superlattices the incoherent model is shown to be more correct