One of the fundamental properties of semiconductors is their ability to support highly tunable electric currents in the presence of electric fields or carrier concentration gradients. These properties are described by transport coefficients such as electron and hole mobilities. Over the last decades, our understanding of carrier mobilities has largely been shaped by experimental investigations and empirical models. Recently, advances in electronic structure methods for real materials have made it possible to study these properties with predictive accuracy and without resorting to empirical parameters. In this article, we review the most recent developments in the area of ab initio calculations of carrier mobilities of semiconductors. In the first part, we offer a brief historical overview of approaches to the calculation of carrier mobilities, and we establish the conceptual framework underlying modern ab initio approaches. We summarize the Boltzmann theory of carrier transport and we discuss its scope of applicability, merits, and limitations in the broader context of many-body Green's function approaches. We discuss recent implementations of the Boltzmann formalism within the context of density functional theory and many-body perturbation theory calculations, placing an emphasis on the key computational challenges and suggested solutions. In the second part of the article, we review applications of these methods to materials of current interest, from three-dimensional semiconductors to layered and two-dimensional materials. In particular, we discuss in detail recent investigations of classic materials such as silicon, diamond, GaAs, GaN, Ga2O3, and lead halide perovskites as well as low-dimensional semiconductors such as graphene, silicene, phosphorene, MoS2, and InSe. We also review recent efforts toward high-throughput calculations of carrier transport. In the last part, we discuss the extension of the methodology to study spintronics and topological materials and we comment on the possibility of incorporating Berry-phase effects and many-body correlations beyond the standard Boltzmann formalism.

中文翻译：

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体半导体和二维材料中载流子迁移率和电导率的第一性原理计算

半导体的基本特性之一是它们能够在存在电场或载流子浓度梯度的情况下支持高度可调的电流。这些特性由传输系数描述，例如电子和空穴迁移率。在过去的几十年里，我们对载体移动性的理解很大程度上是由实验研究和经验模型形成的。最近，真实材料的电子结构方法的进步使得以预测精度研究这些特性成为可能，而无需求助于经验参数。在本文中，我们回顾了半导体载流子迁移率从头计算领域的最新进展。在第一部分，我们简要介绍了计算载体移动性的方法的历史概述，我们建立了现代 ab initio 方法的概念框架。我们总结了载流子传输的玻尔兹曼理论，并在多体格林函数方法的更广泛背景下讨论了其适用范围、优点和局限性。我们在密度泛函理论和多体微扰理论计算的背景下讨论了玻尔兹曼形式主义的最新实现，重点是关键的计算挑战和建议的解决方案。在文章的第二部分，我们回顾了这些方法在当前感兴趣的材料中的应用，从三维半导体到分层和二维材料。特别是，我们详细讨论了最近对经典材料的研究，例如硅、金刚石、GaAs、GaN、Ga2O3、和卤化铅钙钛矿以及低维半导体，如石墨烯、硅烯、磷烯、MoS2 和 InSe。我们还回顾了最近在高通量计算载体运输方面的努力。在最后一部分，我们讨论了研究自旋电子学和拓扑材料的方法论的扩展，我们评论了在标准玻尔兹曼形式主义之外结合浆果相效应和多体相关性的可能性。