Ab initio Calculations of the Thermoelectric Phonon Drag Effect in Semiconductor Nanostructures

Abstract

With the advance of materials fabrication techniques and increase of computational power during the past two decades, the research aiming to enhance the efficiency of thermoelectric devices, with the search of new materials and manipulation of materials properties at the nanoscale, has attracted significant interest. In general, the efficiency of thermoelectric materials, measured by the figure of merit ZT, directly depends on the Seebeck coefficient of the material. In the present work, we have studied, by combining the density functional theory calculations of the electron-phonon [1], [2] and phonon-phonon [3] interactions, the enhancement of the Seebeck coefficient due to electron-phonon coupling, known as the “phonon-drag” effect [4]. To account for this effect, we have solved the linearized Boltzmann equation for electronic transport in presence of non-equilibrium phonon populations introduced by a temperature gradient [5]. In order to understand the phonon drag effect at the nanoscale, we have studied the effect of direction-dependent nano-structuring effect on the Seebeck coefficient of silicon. We will present our recent results related to phonon and/or impurity limited carrier mobility, as well as the variation of the Seebeck coefficient of bulk and nanostructured silicon with temperature and carrier concentrations. Our results for $n$-doped silicon not only show a good agreement with the experimental data in both bulk samples [6] and nanostructures [7] but also pave the way to further understand the contribution of phonon-drag in other semiconductor nanostructures [8], which still remain largely unexplored.