Boundary-scattering induced Seebeck coefficient enhancement in thin films within relaxation time approximation

We investigate the Seebeck coefficient based on the Boltzmann transport equation of electrons within the relaxation time approximation. Using boundary conditions along the film thickness of a thermoelectric material, we observe the enhancement of Seebeck coefficient due to electrons elastically scattering on the boundaries when the film thickness is reduced, which agrees with experimental observations and theoretical predictions. Using this simple approximation, the Seebeck coefficient of thin films increases up to 16% in comparison to the bulk value. The main factor that affects the increase of the Seebeck coefficient comes from the chemical potential which controls carrier concentrations. We also analyze the linear and non-linear temperature dependence of the Seebeck coefficient at various chemical potentials based on an explicit expression for the Seebeck coefficient in the bulk limit.