Theoretical model for the Seebeck coefficient in superlattice materials with energy relaxation

We present an analytical model for the Seebeck coefficient $S$ of superlattice materials that explicitly takes into account the energy relaxation due to electron-optical phonon (e-ph) scattering. In such materials, the Seebeck coefficient is not only determined by the bulk Seebeck values of the materials but, in addition, is dependent on the energy relaxation process of charge carriers as they propagate from the less-conductive barrier region into the more-conductive well region. We calculate $S$ as a function of the well size $d$⁠, where carrier energy becomes increasingly relaxed within the well for $d>λE$⁠, where $λE$ is the energy relaxation length. We validate the model against more advanced quantum transport simulations based on the nonequilibrium Green’s function (NEGF) method and also with an experiment, and we find very good agreement. In the case in which no energy relaxation is taken into account, the results deviate substantially from the NEGF results. The model also yields accurate results with only a small deviation (up to $∼3%$⁠) when varying the optical phonon energy $ℏω$ or the e-ph coupling strength $D0$⁠, physical parameters that would determine $λE$⁠. As a first order approximation, the model is valid for nanocomposite materials, and it could prove useful in the identification of material combinations and in the estimation of ideal sizes in the design of nanoengineered thermoelectric materials with enhanced power factor performance.