第一性原理输运计算：天下武功，唯快不破

电子输运性质计算对于半导体材料至关重要，其中最广泛应用的是常数弛豫时间近似。基于密度泛函微扰理论，弛豫时间可以精确求解，但是计算速度较慢，难以应用在具有复杂能带结构的材料体系中。

来自英国华威大学工程学院的李圳博士、Patrizio Graziosi博士和Neophytos Neophytou教授，提出了密度泛函微扰理论结合形变势理论的计算策略，研究了半导体的电子–声子耦合和输运性质，实现了与完全第一性原理计算方法一致的准确度。

作者基于电子–声子矩阵元推导声学、光学和谷间形变势，并考虑极性光学支声子和电离杂质散射，基于自主开发的开源玻尔兹曼输运软件ElecTra进行计算。以n型Mg₃Sb₂为例，阐述了如何应用在具有复杂能带结构的材料。

与DFPT + Wannier方法相比，计算结果取得了极好的一致性，同时计算成本小于其10%。将同样的方法应用于Si，在准确度类似的情况下，计算成本小于其1%。除了实现快速计算外，该方法还提供了准确性和灵活性：1）通过在特定能量和波矢下选择性地计算关键矩阵元，在重要的电子散射区域提供密集网格；2）明确了各个散射过程（声学、光学、谷内和谷间），提供了能带工程中有关多谷结构的关键信息。

与最先进的完全第一性原理方法相比，作者的计算策略同时实现了高效、准确、灵活的输运计算。相关论文近期发布于npj Computational Materials 10: 9 (2024)。手机阅读原文，请点击本文底部左下角“阅读原文”，进入后亦可下载全文PDF文件。

Fig. 5 Comparison of intra-valley and inter-valley scattering in Mg3Sb2. 

Editorial Summary

Transport parameters are crucial for novel material deployment in a variety of technological applications, including solar cells, solid-state batteries, light-emitting diodes (LED), photocatalysis, thermoelectrics, and many more. One of the earliest and most common approaches is to calculate transport is solving the Boltzmann transport equation (BTE) in the constant relaxation time (CRT) approximation. DFT and DFPT have enabled calculations of electron–phonon interactions from the first principles. This procedure can be accelerated within the EPW code. However, this method is still highly resource-intensive for materials with larger unit cells (containing more atoms and basis functions) and lower symmetry (featuring larger non-equivalent k-space regions). Dr Zhen Li, Dr Patrizio Graziosi and Prof Neophytos Neophytou from School of Engineering, University of Warwick, UK, combined the DFPT + Wannier method with the deformation potential theory, offering an alternative direction to calculate transport properties which provides efficiency, robustness, and flexibility. Acoustic, optical, and inter-valley deformation potentials are calculated from e–ph matrix elements using first-principles calculations. Overall scattering rates is completed by computing polar optical-phonon and ionized impurity scattering rates. Using ElecTra, they validate the approach by performing an in-depth investigation for the promising TE material n-type Mg3Sb2, chosen for its band structure complexity, unit cell size, and degree of symmetry. Excellent agreement with the DFPT + Wannier method is achieved while utilizing no more than 10% of its computational cost. Applying the same approach to Si, a simpler material, once again that ab initio accuracy is attained, this time at less than 1% of the corresponding ab initio computational cost. This method belongs to the category of methods that compute and process matrix elements. However, it distinguishes itself through advancements in accuracy and flexibility. Firstly, accuracy is ensured by selectively computing crucial matrix elements at specific energies and wavevectors, focusing on regions responsible for electronic transitions. This allows to afford dense grids around these significant areas. Secondly, this approach provides explicit information on individual scattering processes (acoustic, optical, intra- and inter-valley), offering valuable insights and capabilities that are particularly advantageous for designing materials with optimal multi-valley electronic structures. This approach offers an alternative that combines efficiency, robustness, and flexibility beyond the commonly employed constant relaxation time approximation with the accuracy of fully first-principles calculations. This article was recently published in npj Computational Materials 10: 9 (2024).

原文Abstract及其翻译

Efficient first-principles electronic transport approach to complex band structure materials: the case ofn-type Mg₃Sb₂(具有复杂能带结构材料的高效第一性原理电子输运计算策略：以n型Mg₃Sb₂为例)

Zhen Li, Patrizio Graziosi & Neophytos Neophytou 

Abstract We present an efficient method for accurately computing electronic scattering rates and transport properties in materials with complex band structures. Using ab initio simulations, we calculate a limited number of electron–phonon matrix elements, and extract scattering rates for acoustic and optical processes based on deformation potential theory. Polar optical phonon scattering rates are determined using the Fröhlich model, and ionized impurity scattering rates are derived from the Brooks-Herring theory. Subsequently, electronic transport coefficients are computed within the Boltzmann transport theory. We exemplify our approach with n-type Mg₃Sb₂, a promising thermoelectric material with a challenging large unit cell and low symmetry. Notably, our method attains competitive accuracy, requiring less than 10% of the computational cost compared to state-of-the-art ab initio methods, dropping to 1% for simpler materials. Additionally, our approach provides explicit information on individual scattering processes, offering an alternative that combines efficiency, robustness, and flexibility beyond the commonly employed constant relaxation time approximation with the accuracy of fully first-principles calculations.

摘要

本研究提出了一种高效方法，用于精确计算具有复杂能带结构材料中的电子散射率和传输特性。采用第一性原理计算，获得了有限数量的电子–声子矩阵元，并基于形变势理论推导了声学支和光学支声子的散射率。根据Fröhlich模型确定了极性光学声子散射率，采用Brooks-Herring理论计算了电离杂质散射率。进一步的，基于玻尔兹曼输运理论计算了电子输运。以n型Mg₃Sb₂为例，我们展示了如何应用于具有较大晶胞和较低对称性的热电材料。值得注意的是，与最先进的完全第一性原理计算方法相比，我们的方法具有类似的准确度，但是计算成本降低到其10%，对于更简单的材料则降到1%。此外，与广泛采用的常数弛豫时间近似相比，我们的方法提供了关于各个散射过程的明确信息，是一种同时实现高效、准确、灵活的计算方案。