First-principles calculations of charge carrier mobility and conductivity in bulk semiconductors and two-dimensional materials (1908.01733v1)

Abstract: 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. 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. Here, 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, we discuss 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.

• The paper demonstrates that first-principles methods accurately predict charge carrier mobility and conductivity in both bulk semiconductors and 2D materials.
• The paper outlines advancements in ab initio techniques, including DFT, MBPT, and Wannier interpolation, to overcome the limitations of empirical models.
• The paper identifies future research avenues in spintronics, Berry phase effects, and correlated electron systems to further enhance semiconductor modeling.

Overview of First-Principles Calculations of Charge Carrier Mobility and Conductivity in Semiconductors

This paper provides a comprehensive review of recent developments in first-principles methodologies for calculating charge carrier mobilities and conductivities in semiconductors. Historically, experimental investigations and empirical models have largely shaped our understanding of these properties. However, recent advances in electronic structure methods now allow for more predictive modeling without resorting to empirical parameters. This work identifies key challenges in the field and explores opportunities to expand the impact of these methods on materials science and semiconductor technology.

The review is structured into three main sections: a historical overview of computational approaches, applications on materials of interest, and future directions in the field.

Conceptual Framework and Computational Approaches

The paper begins by establishing the conceptual foundation for modern ab initio approaches. The discussion includes the Boltzmann transport equation (BTE) for carrier transport, its utility, and its limitations in relation to more complex many-body Green's function approaches. The implementation of the BTE is detailed, particularly within the framework of density functional theory (DFT) and many-body perturbation theory (MBPT), focusing on computational challenges such as the need for dense Brillouin zone sampling.

Applications to Bulk and Low-Dimensional Materials

The second part of the paper applies these methodologies to a wide-ranging set of materials, from traditional three-dimensional semiconductors like silicon and gallium arsenide, to emerging two-dimensional materials such as graphene, silicene, and phosphorene.

1. Bulk Semiconductors: For bulk materials, applications include silicon, where accurate electron mobility calculations show good agreement with experimental values, and the importance of using techniques like Wannier interpolation to achieve dense sampling is highlighted. Similarly, advancements are noted in modeling gallium arsenide (GaAs), wherein recent studies incorporate iterative solutions of the BTE rather than simplifying assumptions typically employed.
2. Two-Dimensional Materials: The review importantly shifts focus to layered materials and 2D semiconductors, recognizing the semiconductor industry's evolving interest in these materials for novel electronic and optoelectronic applications. Materials such as graphene and MoS2 have shown promise due to their unique electronic properties and high carrier mobilities.

Challenges and Opportunities

The review concludes by identifying several avenues for future research, including:

• Spintronics and Topological Materials: There's a growing interest in using ab initio methods to explore spin transport and the impact of spin-orbit coupling (SOC). Understanding spin decoherence mechanisms could be pivotal for spintronics applications.
• Berry Phase Effects: Berry phase and its associated curvature can influence carrier dynamics, particularly in non-centrosymmetric materials. Calculating these effects could be critical for designing devices harnessing topological insulators or valleytronics.
• Correlated Electron Systems: The authors suggest exploring methodologies beyond conventional DFT, such as dynamical mean field theory (DMFT), to better probe systems where electron correlation plays a significant role.

Summary

Overall, the paper underscores the progress made in computational technologies for semiconductor carrier transport and outlines key foundational and applicative insights for researchers. There's an emphasis on balancing method accuracy with computational feasibility and acknowledging the importance of advanced computing in pushing the field forward. This review is a resource for experts looking to understand current capabilities and future potential in the field of semiconductor mobility modeling.