電子輸運(yùn)性質(zhì)計(jì)算對(duì)于半導(dǎo)體材料至關(guān)重要，其中最廣泛應(yīng)用的是常數(shù)弛豫時(shí)間近似?；诿芏确汉_理論，弛豫時(shí)間可以精確求解，但是計(jì)算速度較慢，難以應(yīng)用在具有復(fù)雜能帶結(jié)構(gòu)的材料體系中。

來(lái)自英國(guó)華威大學(xué)工程學(xué)院的李圳博士、Patrizio Graziosi博士和Neophytos Neophytou教授，提出了密度泛函微擾理論結(jié)合形變勢(shì)理論的計(jì)算策略，研究了半導(dǎo)體的電子–聲子耦合和輸運(yùn)性質(zhì)，實(shí)現(xiàn)了與完全第一性原理計(jì)算方法一致的準(zhǔn)確度。

作者基于電子–聲子矩陣元推導(dǎo)聲學(xué)、光學(xué)和谷間形變勢(shì)，并考慮極性光學(xué)支聲子和電離雜質(zhì)散射，基于自主開(kāi)發(fā)的開(kāi)源玻爾茲曼輸運(yùn)軟件ElecTra進(jìn)行計(jì)算。以n型Mg₃Sb₂為例，闡述了如何應(yīng)用在具有復(fù)雜能帶結(jié)構(gòu)的材料。

與DFPT + Wannier方法相比，計(jì)算結(jié)果取得了極好的一致性，同時(shí)計(jì)算成本小于其10%。將同樣的方法應(yīng)用于Si，在準(zhǔn)確度類(lèi)似的情況下，計(jì)算成本小于其1%。除了實(shí)現(xiàn)快速計(jì)算外，該方法還提供了準(zhǔn)確性和靈活性：1）通過(guò)在特定能量和波矢下選擇性地計(jì)算關(guān)鍵矩陣元，在重要的電子散射區(qū)域提供密集網(wǎng)格；2）明確了各個(gè)散射過(guò)程（聲學(xué)、光學(xué)、谷內(nèi)和谷間），提供了能帶工程中有關(guān)多谷結(jié)構(gòu)的關(guān)鍵信息。

與最先進(jìn)的完全第一性原理方法相比，作者的計(jì)算策略同時(shí)實(shí)現(xiàn)了高效、準(zhǔn)確、靈活的輸運(yùn)計(jì)算。相關(guān)論文近期發(fā)布于npj?Computational Materials?10:?9?(2024)。手機(jī)閱讀原文，請(qǐng)點(diǎn)擊本文底部左下角“閱讀原文”，進(jìn)入后亦可下載全文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及其翻譯

Efficient first-principles electronic transport approach to complex band structure materials: the case ofn-type Mg₃Sb₂(具有復(fù)雜能帶結(jié)構(gòu)材料的高效第一性原理電子輸運(yùn)計(jì)算策略：以n型Mg₃Sb₂為例)

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 Fr?hlich 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

本研究提出了一種高效方法，用于精確計(jì)算具有復(fù)雜能帶結(jié)構(gòu)材料中的電子散射率和傳輸特性。采用第一性原理計(jì)算，獲得了有限數(shù)量的電子–聲子矩陣元，并基于形變勢(shì)理論推導(dǎo)了聲學(xué)支和光學(xué)支聲子的散射率。根據(jù)Fr?hlich模型確定了極性光學(xué)聲子散射率，采用Brooks-Herring理論計(jì)算了電離雜質(zhì)散射率。進(jìn)一步的，基于玻爾茲曼輸運(yùn)理論計(jì)算了電子輸運(yùn)。以n型Mg₃Sb₂為例，我們展示了如何應(yīng)用于具有較大晶胞和較低對(duì)稱(chēng)性的熱電材料。值得注意的是，與最先進(jìn)的完全第一性原理計(jì)算方法相比，我們的方法具有類(lèi)似的準(zhǔn)確度，但是計(jì)算成本降低到其10%，對(duì)于更簡(jiǎn)單的材料則降到1%。此外，與廣泛采用的常數(shù)弛豫時(shí)間近似相比，我們的方法提供了關(guān)于各個(gè)散射過(guò)程的明確信息，是一種同時(shí)實(shí)現(xiàn)高效、準(zhǔn)確、靈活的計(jì)算方案。