ElecTra code: Full-band electronic transport properties of materials

Abstract

This paper introduces ElecTra, an open-source code which solves the linearized Boltzmann transport equation in the relaxation time approximation for charge carriers in a full-band electronic structure of arbitrary complexity, including their energy, momentum, and band-index dependence. ElecTra stands for ‘ELECtronic TRAnsport’ and computes the electronic and thermoelectric transport coefficients electrical conductivity, Seebeck coefficient, electronic thermal conductivity, and mobility, for semiconductor materials, for both unipolar and bipolar (small bandgap) materials. The code uses computed full-bands and relevant scattering parameters as inputs and considers single crystal materials in 3D and 2D. The present version of the code (v1) considers: i) elastic scattering with acoustic phonons and inelastic scattering with non-polar optical phonons in the deformation potential approximation, ii) inelastic scattering with polar phonons, iii) scattering with ionized dopants, and iv) alloy scattering. The user is given the option of intra- and inter-band scattering considerations. The simulation output also includes relevant relaxation times and mean-free-paths. The transport quantities are computed as a function of Fermi level position, doping density, and temperature. ElecTra can interface with any DFT code which saves the electronic structure in the ‘.bxsf’ format. In this paper ElecTra is validated against ideal electronic transport situations of known analytical solutions, existing codes employing the constant relaxation time approximation, as well as experimentally well-assessed materials such as Si, Ge, SiGe, and GaAs. Program summaryProgram title: ElecTra – Electronic Transport simulation labCPC Library link to program files:https://doi.org/10.17632/ycgx2fjzb6.1Licensing provisions: GPLv3Programming Language: MATLAB®Nature of the problem: computing the electronic and thermoelectric charge transport coefficients of materials with arbitrary complex full-band electronic structures, considering the carrier energy-, momentum-, and band-dependence of the scattering rates.Solution method: Semiclassical Linearized Boltzmann transport equation, with electronic structures (DFT or analytical) as input, formed into constant-energy surfaces, with scattering rates evaluated using Fermi's Golden Rule.Additional comments including restrictions and unusual features:•Programming interface: any DFT code which saves data in the ‘.bxsf’ format.•RAM: a case study for a half-Heusler bandstructure on a 51×51×51k-mesh, 2 Gb per processor is needed•Running time: for the example above, depending on the number and complexity of the scattering mechanisms and the number of simulated Fermi levels and temperatures considered, the time needed varies from ∼ 1 hour on a desktop PC or laptop (light simulations), to 5-10 hours on an HPC with 30-45 cores (heavy simulations). Using the constant relaxation time and constant mean-free-path approximations on a desktop PC or laptop, the running time is of the order of minutes.