ab initio Electronic Transport Model with Explicit Solution to the Linearized Boltzmann Transport Equation

Abstract

Accurate models of carrier transport are essential for describing the electronic properties of semiconductor materials. To the best of our knowledge, the current models following the framework of the Boltzmann transport equation (BTE) either rely heavily on experimental data (i.e., semi-empirical), or utilize simplifying assumptions, such as the constant relaxation time approximation (BTE-cRTA). While these models offer valuable physical insights and accurate calculations of transport properties in some cases, they often lack sufficient accuracy -- particularly in capturing the correct trends with temperature and carrier concentration. We present here a general transport model for calculating low-field electrical drift mobility and Seebeck coefficient of n-type semiconductors, by explicitly considering all relevant physical phenomena (i.e. elastic and inelastic scattering mechanisms). We first rewrite expressions for the rates of elastic scattering mechanisms, in terms of ab initio properties, such as the band structure, density of states, and polar optical phonon frequency. We then solve the linear BTE to obtain the perturbation to the electron distribution -- resulting from the dominant scattering mechanisms -- and use this to calculate the overall mobility and Seebeck coefficient. Using our model, we accurately calculate electrical transport properties of the compound n-type semiconductors, GaAs and InN, over various ranges of temperature and carrier concentration. Our fully predictive model provides high accuracy when compared to experimental measurements on both GaAs and InN, and vastly outperforms both semi-empirical models and the BTE-cRTA. Therefore, we assert that this approach represents a first step towards a fully ab initio carrier transport model that is valid in all compound semiconductors.

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