Cross-plane Seebeck coefficient and Lorenz number in superlattices

Low dimensional and nanostructured materials have shown great potential to achieve much higher thermoelectric figure of merits than their bulk counterparts. Here, we study the thermoelectric properties of superlattices in the cross-plane direction using the Boltzmann transport equation and taking into account multiple minibands. Poisson equation is solved self-consistently to include the effect of charge transfer and band bending in the potential profile. The model is verified with the experimental data of cross-plane Seebeck coefficient for a superlattice structure with different doping concentrations. The simulations show that thermoelectric properties of superlattices are quite different from those of bulk materials because the electronic band structure is modified by the periodic potential. The Lorenz numbers of superlattices are surprisingly large at low carrier concentrations and deviate far away from the Wiedemann-Franz law for bulk materials. Under some conditions, the Lorenz number could be reduced by 50% compared to the bulk value. Most significantly, the Seebeck coefficient and the Lorenz number of superlattices do not change monotonically with doping concentration. An oscillatory behavior is observed. The effects of temperature and well and barrier thicknesses on the cross-plane Seebeck coefficient and Lorenz number are also investigated.