Dependence of mobility and Lorenz number on electronic structure and scattering in wurtzite ZnO

Abstract

The Lorenz number relates electronic thermal conductivity to the electrical conductivity for thermoelectric materials. One of the most effective approaches to enhance thermoelectric efficiency is to lower the lattice thermal conductivity, which is unmeasurable directly, while the total thermal conductivity, including the electronic thermal conductivity and lattice thermal conductivity, is measurable. Nevertheless, the electronic thermal conductivity can be inferred from the electrical conductivity using the Lorenz number. Therefore, an accurate Lorenz number becomes the key. In literature, the Lorenz number is empirically related to the Seebeck coefficient, ignoring the electronic structure and scattering mechanism. Here, we show that the mobility and Lorenz number strongly depend on the electronic structure and scattering for the wurtzite ZnO. The electronic transport properties only depend on the band edge near the Fermi level when the bandgap is larger than 1 eV; otherwise, the bipolar effect affects the results. A low effective mass causes large mobility. The MBJ and LMBJ functionals can predict accurate band structures. The influences of the polar optical phonon, ionized impurity, and piezoelectric scatterings on mobility are in the decreasing order, while the acoustic phonon scattering can be ignored. All four scatterings are indispensable in determining the Lorenz number. These findings can be extended to other thermoelectric materials beyond oxides.