First-principles predictions of Hall and drift mobilities in semiconductors

Carrier mobility is one of the defining properties of semiconductors. Significant progress on parameter-free calculations of carrier mobilities in real materials has been made during the past decade; however, the role of various approximations remains unclear and a unified methodology is lacking. Here, we present and analyse a comprehensive and efficient approach to compute the intrinsic, phonon-limited drift and Hall carrier mobilities of semiconductors, within the framework of the first-principles Boltzmann transport equation.
The methodology exploits a novel approach for estimating quadrupole tensors and including them in the electron-phonon interactions, and capitalises on a rigorous and efficient procedure for numerical convergence. The accuracy reached in this work allows to assess common approximations, including the role of exchange and correlation functionals, spin-orbit coupling, pseudopotentials, Wannier interpolation, Brillouin-zone sampling, dipole and quadrupole corrections, and the relaxation-time approximation. A detailed analysis is showcased on ten prototypical semiconductors, namely diamond, silicon, GaAs, 3C-SiC, AlP, GaP, c-BN, AlAs, AlSb, and SrO. By comparing this extensive dataset with available experimental data, we explore the intrinsic nature of phonon-limited carrier transport and magnetotransport phenomena in these compounds. We find that the most accurate calculations predict Hall mobilities up to a factor of two larger than experimental data; this could point to promising experimental improvements in the samples quality, or to the limitations of density-function theory in predicting the carrier effective masses and overscreening the electron-phonon matrix elements. By setting tight standards for reliability and reproducibility, the present work aims to facilitate validation and verification of data and software towards predictive calculations of transport phenomena in semiconductors.

载流子迁移率（carrier mobility）是半导体的关键固有特性之一。近十年来，真实材料中载流子迁移率的无参数计算研究已取得长足进展，但各类近似方法的作用机制仍未明晰，且尚未形成统一的计算方法论。本文提出并系统分析了一种基于第一性原理玻尔兹曼输运方程（first-principles Boltzmann transport equation）的高效全面方法，用于计算半导体的本征声子限制漂移与霍尔载流子迁移率（Hall carrier mobilities）。
该方法创新性地构建了四极矩张量（quadrupole tensors）的估算方案，并将其纳入电子-声子相互作用（electron-phonon interactions）框架，同时采用了一套严谨高效的数值收敛（numerical convergence）处理流程。本研究达成的计算精度，可用于评估多种常用近似方法的影响，包括交换关联泛函（exchange and correlation functionals）、自旋轨道耦合（spin-orbit coupling）、赝势（pseudopotentials）、Wannier插值（Wannier interpolation）、布里渊区采样（Brillouin-zone sampling）、偶极与四极修正（dipole and quadrupole corrections）以及弛豫时间近似（relaxation-time approximation）。我们以十种典型半导体为范例开展详细分析，分别为金刚石、硅、砷化镓、3C型碳化硅、磷化铝、磷化镓、立方氮化硼、砷化铝、锑化铝与氧化锶。通过将该大规模数据集与现有实验数据对比，我们探究了上述化合物中声子限制载流子输运与磁输运现象的本征特性。研究发现，精度最高的计算结果显示霍尔迁移率较实验数据最高高出一倍；这一现象或提示存在两方面的潜在原因：一是样品质量的实验优化尚有空间，二是密度泛函理论（density-functional theory）在预测载流子有效质量以及过度屏蔽电子-声子矩阵元方面存在固有局限。本研究为计算结果的可靠性与可复现性设定了严格标准，旨在推动半导体输运现象预测计算相关数据与软件的验证与确认工作。