Band gap renormalization, carrier mobility, and transport in Mg₂Si and Ca₂Si: Ab initio scattering and Boltzmann transport equation study

2025/01/27 by Vinod Kumar Solet, Solet, Vinod Kumar, Sudhir K. Pandey +1
Physics and Astronomy · Materials Science · #Semiconductor materials and interfaces #Superconductivity in MgB2 and Alloys #Iron-based superconductors research

paper · pdf · doi:10.48550/arxiv.2501.15992

Abstract

We perform first-principles electron-phonon interaction (EPI) calculations based on many-body perturbation theory to study the temperature-dependent band-gap and charge-carrier transport properties for Mg₂Si and Ca₂Si using the Boltzmann transport equation (BTE) under different relaxation-time approximations (RTAs). For a PBE band gap of 0.21 (0.56) eV in Mg₂Si (Ca₂Si), a zero-point renormalization correction of 29-33 (37-51) meV is obtained using various approaches, while the gap at 300 K is 0.15-0.154 (0.46-0.5) eV. The electron mobility (μ_e), with a detailed convergence study at 300 K, is evaluated using linearized (self-energy and momentum RTA, or SERTA and MRTA) and iterative BTE (IBTE) solutions. At 300 K, the μ_e values are 351 (100), 573 (197), and 524 (163) cm²V^-1s^-1 from SERTA, MRTA, and IBTE, respectively, for Mg₂Si (Ca₂Si). SERTA (MRTA) provides results in better agreement with IBTE at higher (lower) temperatures, while SERTA-derived μ_e closely matches experimental μ_e values for Mg₂Si. Thermoelectric (TE) transport coefficients significantly influenced by the choice of RTA, with SERTA and MRTA yielding improved agreement with experimental results compared to constant RTA (CRTA) for Mg₂Si over an electron concentration range of 10¹⁷ to 10²⁰ cm^-3. The lattice thermal conductivity (κ_ph) at 300 K due to phonon-phonon interactions is estimated to be 22.7 (7.2) W m^-1K^-1 for Mg₂Si (Ca₂Si). The highest calculated figure of merit (zT) under CRTA is 0.35 (0.38), which decreases to 0.08 (0.085) when EPI is included using MRTA. This study clearly identifies the critical role of EPI in accurate transport predictions of TE silicides. Finally, we explore strategies to enhance zT by reducing κ_ph through nanostructuring and mass-difference scattering.

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