Fröhlich Electron-Phonon Vertex from First Principles

Giant Enhancement of Hole Mobility for 4H-Silicon Carbide through Suppressing Interband Electron-Phonon Scattering

4H-silicon carbide (4H-SiC) possesses a high Baliga figure of merit, making it a promising material for power electronics. However, its applications are limited by low hole mobility. Herein, we found that the hole mobility of 4H-SiC is mainly limited by the strong interband electron-phonon scattering using mode-level first-principles calculations. Our research indicates that applying compressive strain can reverse the sign of crystal-field splitting and change the ordering of electron bands close to the valence band maximum. Therefore, the interband electron-phonon scattering is severely suppressed and the electron group velocity is significantly increased. The out-of-plane hole mobility of 4H-SiC can be greatly enhanced by ∼200% with 2% uniaxial compressive strain applied. This work provides new insights into the electron transport mechanisms in semiconductors and suggests a strategy to improve hole mobility that could be applied to other semiconductors with hexagonal crystalline geometries.

Phonon screening and dissociation of excitons at finite temperatures from first principles

The properties of excitons, or correlated electron-hole pairs, are of paramount importance to optoelectronic applications of materials. A central component of exciton physics is the electron-hole interaction, which is commonly treated as screened solely by electrons within a material. However, nuclear motion can screen this Coulomb interaction as well, with several recent studies developing model approaches for approximating the phonon screening of excitonic properties. While these model approaches tend to improve agreement with experiment, they rely on several approximations that restrict their applicability to a wide range of materials, and thus far they have neglected the effect of finite temperatures. Here, we develop a fully first-principles, parameter-free approach to compute the temperature-dependent effects of phonon screening within the ab initio [Formula: see text]-Bethe-Salpeter equation framework. We recover previously proposed models of phonon screening as well-defined limits of our general framework, and discuss their validity by comparing them against our first-principles results. We develop an efficient computational workflow and apply it to a diverse set of semiconductors, specifically AlN, CdS, GaN, MgO, and [Formula: see text]. We demonstrate under different physical scenarios how excitons may be screened by multiple polar optical or acoustic phonons, how their binding energies can exhibit strong temperature dependence, and the ultrafast timescales on which they dissociate into free electron-hole pairs.

Topological polarons in halide perovskites

Halide perovskites emerged as a revolutionary family of high-quality semiconductors for solar energy harvesting and energy-efficient lighting. There is mounting evidence that the exceptional optoelectronic properties of these materials could stem from unconventional electron-phonon couplings, and it has been suggested that the formation of polarons and self-trapped excitons could be key to understanding such properties. By performing first-principles simulations across the length scales, here we show that halide perovskites harbor a uniquely rich variety of polaronic species, including small polarons, large polarons, and charge density waves, and we explain a variety of experimental observations. We find that these emergent quasiparticles support topologically nontrivial phonon fields with quantized topological charge, making them nonmagnetic analog of the helical Bloch points found in magnetic skyrmion lattices.

Ab Initio Predictions of Spin Relaxation, Dephasing, and Diffusion in Solids

Spin relaxation, dephasing, and diffusion are at the heart of spin-based information technology. Accurate theoretical approaches to simulate spin lifetimes (τs), determining how fast the spin polarization and phase information will be lost, are important to the understanding of the underlying mechanism of these spin processes, and invaluable in searching for promising candidates of spintronic materials. Recently, we develop a first-principles real-time density-matrix (FPDM) approach to simulate spin dynamics for general solid-state systems. Through the complete first-principles descriptions of light-matter interaction and scattering processes including electron-phonon, electron-impurity, and electron-electron scatterings with self-consistent spin-orbit coupling, as well as ab initio Landé g-factor, our method can predict τs at various conditions as a function of carrier density and temperature, under electric and magnetic fields. By employing this method, we successfully reproduce experimental results of disparate materials and identify the key factors affecting spin relaxation, dephasing, and diffusion in different materials. Specifically, we predict that germanene has long τs (∼100 ns at 50 K), a giant spin lifetime anisotropy, and spin-valley locking effect under electric fields, making it advantageous for spin-valleytronic applications. Based on our theoretical derivations and ab initio simulations, we propose a new useful electronic quantity, named spin-flip angle θ↑↓, for the understanding of spin relaxation through intervalley spin-flip scattering processes. Our method can be further applied to other emerging materials and extended to simulate exciton spin dynamics and steady-state photocurrents due to photogalvanic effect.

How spin relaxes and dephases in bulk halide perovskites

Spintronics in halide perovskites has drawn significant attention in recent years, due to their highly tunable spin-orbit fields and intriguing interplay with lattice symmetry. Here, we perform first-principles calculations to determine the spin relaxation time (T1) and ensemble spin dephasing time ([Formula: see text]) in a prototype halide perovskite, CsPbBr3. To accurately capture spin dephasing in external magnetic fields we determine the Landé g-factor from first principles and take it into account in our calculations. These allow us to predict intrinsic spin lifetimes as an upper bound for experiments, identify the dominant spin relaxation pathways, and evaluate the dependence on temperature, external fields, carrier density, and impurities. We find that the Fröhlich interaction that dominates carrier relaxation contributes negligibly to spin relaxation, consistent with the spin-conserving nature of this interaction. Our theoretical approach may lead to new strategies to optimize spin and carrier transport properties.

Infrared-active phonons in one-dimensional materials and their spectroscopic signatures

Dimensionality provides a clear fingerprint on the dispersion of infrared-active, polar-optical phonons. For these phonons, the local dipoles parametrized by the Born effective charges drive the LO-TO splitting of bulk materials; this splitting actually breaks down in two-dimensional materials. Here, we develop the theory for one-dimensional (1D) systems-nanowires, nanotubes, and atomic and polymeric chains. Combining an analytical model with the implementation of density-functional perturbation theory in 1D boundary conditions, we show that the dielectric splitting in the dispersion relations collapses as x 2 log ( x ) at the zone center. The dielectric properties and the radius of the 1D materials are linked by the present work to these red shifts, opening infrared and Raman characterization avenues.

Reversal of Band-Ordering Leads to High Hole Mobility in Strained p-type Scandium Nitride

Low hole mobility of nitride semiconductors is a significant impediment to realizing their high-efficiency device applications. Scandium nitride (ScN), an emerging rocksalt indirect band gap semiconductor, suffers from low hole mobility. Utilizing the ab initio Boltzmann transport formalism including spin-orbit coupling, here we show the dominating role of ionized impurity scattering in reducing the hole mobility in ScN thin films. We suggest a route to increase the hole mobility by reversing band ordering through strain engineering. Our calculation shows that the biaxial tensile strain in ScN lifts the split-off hole band above the heavy hole and light hole bands, leading to a lower hole-effective mass and increasing mobility. Along with the impurity scattering, the Fröhlich interaction also plays a vital role in the carrier scattering mechanism due to the polar nature of ScN. Increased hole mobility in ScN will lead to higher efficiencies in thermoelectric, plasmonics, and neuromorphic computing devices.

Accurate Prediction of Hall Mobilities in Two-Dimensional Materials through Gauge-Covariant Quadrupolar Contributions

Despite considerable efforts, accurate computations of electron-phonon and carrier transport properties of low-dimensional materials from first principles have remained elusive. By building on recent advances in the description of long-range electrostatics, we develop a general approach to the calculation of electron-phonon couplings in two-dimensional materials. We show that the nonanalytic behavior of the electron-phonon matrix elements depends on the Wannier gauge, but that a missing Berry connection restores invariance to quadrupolar order. We showcase these contributions in a MoS_{2} monolayer, calculating intrinsic drift and Hall mobilities with precise Wannier interpolations. We also find that the contributions of dynamical quadrupoles to the scattering potential are essential, and that their neglect leads to errors of 23% and 76% in the room-temperature electron and hole Hall mobilities, respectively.

Possible enhancement of the superconductingTcdue to sharp Kohn-like soft phonon anomalies

Phonon softening is a ubiquitous phenomenon in condensed matter systems which is often associated with charge density wave (CDW) instabilities and anharmonicity. The interplay between phonon softening, CDW and superconductivity is a topic of intense debate. In this work, the effects of anomalous soft phonon instabilities on superconductivity are studied based on a recently developed theoretical framework that accounts for phonon damping and softening within the Migdal-Eliashberg theory. Model calculations show that the phonon softening in the form of a sharp dip in the phonon dispersion relation, either acoustic or optical (including the case of Kohn-type anomalies typically associated with CDW), can cause a manifold increase of the electron-phonon coupling constantλ. This, under certain conditions, which are consistent with the concept of optimal frequency introduced by Bergmann and Rainer, can produce a large increase of the superconducting transition temperatureTc. In summary, our results suggest the possibility of reaching high-temperature superconductivity by exploiting soft phonon anomalies restricted in momentum space.

Polaron states of the full-configuration defects in metal halide perovskites

The systematical analysis for varieties of defects with different depths and lattice relaxation strengths in metal halide perovskites (MHPs) is a challenging task. Here, we study the energy shifts of the full-configuration defects due to the polaron effect based on the all-coupling variational method in MHPs, where these polaron states are formed stemming from different defect species coupling with the longitudinal optical phonon modes via Fro¨hlich mechanism. We find that the polaron effect results in defect levels varying from tens to several hundreds of meV, which are very close to the correction of defect levels due to the defect-polaron effect, especially for these defects migration proved in the recent experiments in MHPs. These results provide the significant enlightenment not only for analyzing the radiation and non-radiation processes of carriers mediated by defects, but also for optimizing defect effect in the photovoltaic and photoelectric devices based on MHPs materials.

Simultaneous capturing phonon and electron dynamics in MXenes

Plasmonic MXenes are of particular interest, because of their unique electron and phonon structures and multiple surface plasmon effects, which are different from traditional plasmonic materials. However, to date, how electronic energy damp to lattice vibrations (phonons) in MXenes has not been unraveled. Here, we employed ultrafast broadband impulsive vibrational spectroscopy to identify the energy damping channels in MXenes (Ti₃C₂T_x and Mo₂CT_x). Distinctive from the well-known damping pathways, our results demonstrate a different energy damping channel, in which the Ti₃C₂T_x plasmonic electron energy transfers to coherent phonons by nonthermal electron mediation after Landau damping, without involving electron-electron scattering. Moreover, electrons are observed to strongly couple with A_1g mode (~60 fs, 85-100%) and weakly couple with E_g mode (1-2 ps, 0-15%). Our results provide new insight into the electron-phonon interaction in MXenes, which allows the design of materials enabling efficient manipulation of electron transport and energy conversion.

Biaxial strain improving carrier mobility for inorganic perovskite:ab initioBoltzmann transport equation

Inorganic halide perovskites have attracted interest due to their high efficiency and low cost. Considering the uncertainty of experimental measurements, it was important to predict the upper limit of carrier mobility. In this study, theab initioBoltzmann transport equation, including all electron-phonon interactions, was used to accurately predict the mobilities of CsPbI₃, CsSnI₃, CsPbBr₃, and CsSnBr₃. Using the iterative Boltzmann transport equation (IBTE), the calculated mobility for CsPbI₃isµ_e= 512/µ_h= 379 cm² V^-1 s^-1, and Sn-based perovskite exhibited high hole mobility. The longitudinal optical phonons associated with the stretching between halogen anions and divalent metal cations were revealed to be the dominant scattering source for the carriers. Furthermore, the effect of biaxial strain on mobility was investigated. We observed that biaxial compressive strain could improve the mobility of CsPbI₃and CsPbBr₃. Surprisingly, under a compressive strain of-2%, the mobilities of CsPbI₃using IBTE approach were improved toµ_e= 1176/µ_h= 936 cm² V^-1 s^-1. It was revealed that the compressive strain could decrease the effective mass of CsPbI₃and CsPbBr₃.

Electron-Phonon Interaction and Longitudinal-Transverse Phonon Splitting in Doped Semiconductors

We study the effect of doping on the electron-phonon interaction and on the phonon frequencies in doped semiconductors, taking into account the screening in the presence of free carriers at finite temperature. We study the impact of screening on the Fröhlich-like vertex and on the long-range components of the dynamical matrix, going beyond the state-of-the-art description for undoped crystals, thanks to the development of a computational method based on maximally localized Wannier functions. We apply our approach to cubic silicon carbide, where in the presence of doping the Fröhlich coupling and the longitudinal-transverse phonon splitting are strongly reduced, thereby influencing observable properties such as the electronic lifetime.

First-Principles-Based Quantum Transport Simulations of High-Performance and Low-Power MOSFETs Based on Monolayer Ga2O3

The electronic properties of monolayer (ML) Ga₂O₃ and transport properties of ML Ga₂O₃-based n-type metal-oxide-semiconductor field-effect transistors (MOSFETs) are investigated by first-principles calculations under the framework of density functional theory (DFT) coupled with the nonequilibrium Green's function (NEGF) formalism. The results show that ML Ga₂O₃ has a quasi-direct band gap of 4.92 eV, and the x- and y-directed electron mobilities are 1210 and 816 cm² V^-1 s^-1 at 300 K, respectively, under the full consideration of phonon scattering. The electron-phonon scattering mechanism shows a temperature-dependent behavior, with the acoustic modes dominating below 300 K and optical modes dominating above 300 K. At a gate length of L_g = 5 nm, the on-current of ML Ga₂O₃ n-MOSFET for high-performance (HP) application is 2890 μA/μm, which is more than those of the most reported two-dimensional (2D) materials. The delay time as well as the power delay product of ML Ga₂O₃ MOSFETs can meet the demands of the latest International Technology Roadmap for Semiconductors (ITRS) for HP and low-power (LP) applications until L_g is less than 4 and 5 nm, respectively. Through underlap structure and doping optimization strategies, ML Ga₂O₃ n-MOSFET can further fulfill the ITRS requirements for 1 nm. At last, we compare the performance of the 32-bit arithmetic logic unit (ALU) built on ML Ga₂O₃ MOSFETs with the recently reported beyond-CMOS devices. Our results indicate that ML Ga₂O₃ can serve as a promising channel material in the post-silicon era.

Diagrammatic quantum Monte Carlo toward the calculation of transport properties in disordered semiconductors

A new diagrammatic quantum Monte Carlo approach is proposed to deal with the imaginary time propagator involving both dynamic disorder (i.e., electron–phonon interactions) and static disorder of local or nonlocal nature in a unified and numerically exact way. The establishment of the whole framework relies on a general reciprocal-space expression and a generalized Wick’s theorem for the static disorder. Since the numerical cost is independent of the system size, various physical quantities, such as the thermally averaged coherence, Matsubara one-particle Green’s function, and current autocorrelation function, can be efficiently evaluated in the thermodynamic limit (infinite in the system size). The validity and performance of the proposed approach are systematically examined in a broad parameter regime. This approach, combined with proper numerical analytic continuation methods and first-principles calculations, is expected to be a versatile tool toward the calculation of various transport properties, such as mobilities in realistic semiconductors involving multiple electronic energy bands, high-frequency optical and low-frequency acoustic phonons, different forms of dynamic and static disorders, and anisotropy.

Spectroscopic signatures of nonpolarons: the case of diamond

Polarons are quasi-particles made from electrons interacting with vibrations in crystal lattices. They derive their name from the strong electron-vibration polar interactions in ionic systems, that induce spectroscopic and optical signatures of such quasi-particles. In this paper, we focus on diamond, a non-polar crystal with inversion symmetry which nevertheless shows interesting signatures stemming from electron-vibration interactions, better denoted "nonpolaron" signatures in this case. The (non)polaronic effects are produced by short-range crystal fields, while long-range quadrupoles only have a small influence. The corresponding many-body spectral function has a characteristic energy dependence, showing a plateau structure that is similar to but distinct from the satellites observed in the polar Fröhlich case. We determine the temperature-dependent spectral function of diamond by two methods: the standard Dyson-Migdal approach, which calculates electron-phonon interactions within the lowest-order expansion of the self-energy, and the cumulant expansion, which includes higher orders of electron-phonon interactions. The latter corrects the nonpolaron energies and broadening, providing a more realistic spectral function, which we examine in detail for both conduction and valence band edges.

Mobility enhancement in heavily doped semiconductors via electron cloaking

Doping is central for solid-state devices from transistors to thermoelectric energy converters. The interaction between electrons and dopants plays a pivotal role in carrier transport. Conventional theory suggests that the Coulomb field of the ionized dopants limits the charge mobility at high carrier densities, and that either the atomic details of the dopants are unimportant or the mobility can only be further degraded, while experimental results often show that dopant choice affects mobility. In practice, the selection of dopants is still mostly a trial-and-error process. Here we demonstrate, via first-principles simulation and comparison with experiments, that a large short-range perturbation created by selected dopants can in fact counteract the long-range Coulomb field, leading to electron transport that is nearly immune to the presence of dopants. Such “cloaking” of dopants leads to enhanced mobilities at high carrier concentrations close to the intrinsic electron–phonon scattering limit. We show that the ionic radius can be used to guide dopant selection in order to achieve such an electron-cloaking effect. Our finding provides guidance to the selection of dopants for solid-state conductors to achieve high mobility for electronic, photonic, and energy conversion applications.

Doping is central to solid-state devices and generally believed to hinder electron transport. Here, the authors show that certain dopants can cloak themselves from electrons and achieve higher mobility than the conventional limit.

Nonadiabatic Born Effective Charges in Metals and the Drude Weight

In insulators, Born effective charges describe the electrical polarization induced by the displacement of individual atomic sublattices. Such a physical property is at first sight irrelevant for metals and doped semiconductors, where the macroscopic polarization is ill defined. Here we show that, in clean conductors, going beyond the adiabatic approximation results in nonadiabatic Born effective charges that are well defined in the low-frequency limit. In addition, we find that the sublattice sum of the nonadiabatic Born effective charges does not vanish as it does in the insulating case, but instead is proportional to the Drude weight. We demonstrate these formal results with density functional perturbation theory calculations of Al and electron-doped SnS_{2} and SrTiO_{3}.

The carrier mobility of monolayer and bulk GaS: from first-principles calculations

Metal chalcogenides have become popular materials for next-generation electronic devices due to their wide band gap and excellent transport property. Specifically, two-dimensional metal chalcogenides also have outstanding physical properties. For...

Origin of phonon-limited mobility in two-dimensional metal dichalcogenides

Metal dichalcogenides are novel two-dimensional (2D) semiconductors after the discovery of graphene. In this article, phonon-limited mobility for six kinds of 2D semiconductors with the composition of MX₂is reviewed, in which M (Cr, Mo and W) is the transition metal, and X (S and Se) is the chalcogen element. The review is divided into three parts. In the first part, we briefly introduce the calculation method of mobility, including the empirical model and Boltzmann transport theory (BTE). The application scope, merits and limitations of these methods are summarized. In the second part, we explore empirical models to calculate the mobility of MX₂, including longitudinal acoustic phonon, optical phonon (OP) and polar optical phonon (POP) models. The contribution of multi-valley to mobility is reviewed in the calculation. The differences between static and high-frequency dielectric constants (Δϵ) are only 0.13 and 0.03 for MoS₂and WS₂. Such a low value indicates that the polarization hardly changes in the external field. So, their mobility is not determined by POP, but by deformation potential models. Different from GaAs, POP scattering plays a decisive role in its mobility. Our investigations also reveal that the scattering from POP cannot be ignored in CrSe₂, MoSe₂and WSe₂. In the third parts, we investigate the mobility of MX₂using electron-phonon coupling matrix element, which is based on BTE from the framework of a many-body quantum-field theory. Valence band splitting of MoS₂and WS₂is induced by spin-orbit coupling effect, which leads to the increase of hole mobility. In particular, we review in detail the theoretical and experimental results of MoS₂mobility in recent ten years, and its mobility is also compared with other materials to deepen the understanding.

Electronic transport descriptors for the rapid screening of thermoelectric materials

The discovery of novel materials for thermoelectric energy conversion has potential to be accelerated by data-driven screening combined with high-throughput calculations. One way to increase the efficacy of successfully choosing a candidate material is through its evaluation using transport descriptors. Using a data-driven screening, we selected 12 potential candidates in the trigonal ABX₂ family, followed by charge transport property simulations from first principles. The results suggest that carrier scattering processes in these materials are dominated by ionised impurities and polar optical phonons, contrary to the oft-assumed acoustic-phonon-dominated scattering. Using these data, we further derive ground-state transport descriptors for the carrier mobility and the thermoelectric powerfactor. In addition to low carrier mass, high dielectric constant was found to be an important factor towards high carrier mobility. A quadratic correlation between dielectric constant and transport performance was established and further validated with literature. Looking ahead, dielectric constant can potentially be exploited as an independent criterion towards improved thermoelectric performance. Combined with calculations of thermal conductivity including Peierls and inter-branch coherent contributions, we conclude that the trigonal ABX₂ family has potential as high performance thermoelectrics in the intermediate temperature range for low grade waste heat harvesting.

Phonon Screening of Excitons in Semiconductors: Halide Perovskites and Beyond

The ab initio Bethe-Salpeter equation (BSE) approach, an established method for the study of excitons in materials, is typically solved in a limit where only static screening from electrons is captured. Here, we generalize this framework to include dynamical screening from phonons at lowest order in the electron-phonon interaction. We apply this generalized BSE approach to a series of inorganic lead halide perovskites, CsPbX_{3}, with X=Cl, Br, and I. We find that inclusion of screening from phonons significantly reduces the computed exciton binding energies of these systems. By deriving a simple expression for phonon screening effects, we reveal general trends for their importance in semiconductors and insulators, based on a hydrogenic exciton model. We demonstrate that the magnitude of the phonon screening correction in isotropic materials can be reliably predicted using four material specific parameters: the reduced effective mass, static and optical dielectric constants, and frequency of the most strongly coupled longitudinal-optical phonon mode. This framework helps to elucidate the importance of phonon screening and its relation to excitonic properties in a broad class of semiconductors.

Electronic structures and anisotropic carrier mobilities of monolayer ternary metal iodides MLaI5(M=Mg, Ca, Sr, Ba)

Exploiting two-dimensional (2D) materials with natural band gaps and anisotropic quasi-one-dimensional (quasi-1D) carrier transport character is essential in high-performance nanoscale transistors and photodetectors. Herein, the stabilities, electronic structures and carrier mobilities of 2D monolayer ternary metal iodides MLaI₅(M = Mg, Ca, Sr, Ba) have been explored by utilizing first-principles calculations combined with numerical calculations. It is found that exfoliating MLaI₅monolayers are feasible owing to low cleavage energy of 0.19-0.21 J m^-2and MLaI₅monolayers are thermodynamically stable based on phonon spectra. MLaI₅monolayers are semiconductors with band gaps ranging from 2.08 eV for MgLaI₅to 2.51 eV for BaLaI₅. The carrier mobility is reasonably examined considering both acoustic deformation potential scattering and polar optical phonon scattering mechanisms. All MLaI₅monolayers demonstrate superior anisotropic and quasi-1D carrier transport character due to the striped structures. In particular, the anisotropic ratios of electron and hole mobilities along different directions reach hundreds and tens for MLaI₅monolayers, respectively. Thus, the effective electron-hole spatial separation could be actually achieved. Moreover, the absolute locations of band edges of MLaI₅monolayers have been aligned. These results would provide fundamental insights for MLaI₅monolayers applying in nano-electronic and optoelectronic devices.

When band convergence is not beneficial for thermoelectrics

Band convergence is considered a clear benefit to thermoelectric performance because it increases the charge carrier concentration for a given Fermi level, which typically enhances charge conductivity while preserving the Seebeck coefficient. However, this advantage hinges on the assumption that interband scattering of carriers is weak or insignificant. With first-principles treatment of electron-phonon scattering in the CaMg2Sb2-CaZn2Sb2 Zintl system and full Heusler Sr2SbAu, we demonstrate that the benefit of band convergence can be intrinsically negated by interband scattering depending on the manner in which bands converge. In the Zintl alloy, band convergence does not improve weighted mobility or the density-of-states effective mass. We trace the underlying reason to the fact that the bands converge at a one k-point, which induces strong interband scattering of both the deformation-potential and the polar-optical kinds. The case contrasts with band convergence at distant k-points (as in the full Heusler), which better preserves the single-band scattering behavior thereby successfully leading to improved performance. Therefore, we suggest that band convergence as thermoelectric design principle is best suited to cases in which it occurs at distant k-points.

Phonon-Limited Mobility and Electron-Phonon Coupling in Lead-Free Halide Double Perovskites

Lead-free halide double perovskites have attracted considerable attention as complements to lead-based halide perovskites in a range of optoelectronic applications. Experiments on Cs₂AgBiBr₆ indicate carrier mobilities in the range of 0.3-11 cm²/(V s) at room temperature, considerably lower than in lead-based perovskites. The origin of low mobilities is currently unclear, calling for an atomic-scale investigation. We report state-of-the-art ab initio calculations of the phonon-limited mobility of charge carriers in lead-free halide double perovskites Cs₂AgBiX₆ (X = Br, Cl). For Cs₂AgBiBr₆, we obtain room-temperature electron and hole mobilities of 17 and 14 cm²/(V s), respectively, in line with experiments. We demonstrate that the cause for the lower mobility of this compound, compared to CH₃NH₃PbI₃, resides in the heavier carrier effective masses. A mode-resolved analysis of scattering rates reveals the predominance of Fröhlich electron-phonon scattering, similar to lead-based perovskites. Our results indicate that, to increase the mobility of lead-free perovskites, it is necessary to reduce the effective masses, for example by cation engineering.

Efficient calculation of carrier scattering rates from first principles

The electronic transport behaviour of materials determines their suitability for technological applications. We develop a computationally efficient method for calculating carrier scattering rates of solid-state semiconductors and insulators from first principles inputs. The present method extends existing polar and non-polar electron-phonon coupling, ionized impurity, and piezoelectric scattering mechanisms formulated for isotropic band structures to support highly anisotropic materials. We test the formalism by calculating the electronic transport properties of 23 semiconductors, including the large 48 atom CH3NH3PbI3 hybrid perovskite, and comparing the results against experimental measurements and more detailed scattering simulations. The Spearman rank coefficient of mobility against experiment (rs = 0.93) improves significantly on results obtained using a constant relaxation time approximation (rs = 0.52). We find our approach offers similar accuracy to state-of-the art methods at approximately 1/500th the computational cost, thus enabling its use in high-throughput computational workflows for the accurate screening of carrier mobilities, lifetimes, and thermoelectric power.

Strong Electron-Phonon Interaction in 2D Vertical Homovalent III-V Singularities

Highly polar materials are usually preferred over weakly polar ones to study strong electron-phonon interactions and its fascinating properties. Here, we report on the achievement of simultaneous confinement of charge carriers and phonons at the vicinity of a 2D vertical homovalent singularity (antiphase boundary, APB) in an (In,Ga)P/SiGe/Si sample. The impact of the electron-phonon interaction on the photoluminescence processes is then clarified by combining transmission electron microscopy, X-ray diffraction, ab initio calculations, Raman spectroscopy, and photoluminescence experiments. 2D localization and layer group symmetry properties of homovalent electronic states and phonons are studied by first-principles methods, leading to the prediction of a type-II band alignment between the APB and the surrounding semiconductor matrix. A Huang-Rhys factor of 8 is finally experimentally determined for the APB emission line, underlining that a large and unusually strong electron-phonon coupling can be achieved by 2D vertical quantum confinement in an undoped III-V semiconductor. This work extends the concept of an electron-phonon interaction to 2D vertically buried III-V homovalent nano-objects and therefore provides different approaches for material designs, vertical carrier transport, heterostructure design on silicon, and device applications with weakly polar semiconductors.

Why Two-Dimensional Semiconductors Generally Have Low Electron Mobility

Atomically thin (two-dimensional, 2D) semiconductors have shown great potential as the fundamental building blocks for next-generation electronics. However, all the 2D semiconductors that have been experimentally made so far have room-temperature electron mobility lower than that of bulk silicon, which is not understood. Here, by using first-principles calculations and reformulating the transport equations to isolate and quantify contributions of different mobility-determining factors, we show that the universally low mobility of 2D semiconductors originates from the high "density of scatterings," which is intrinsic to the 2D material with a parabolic electron band. The density of scatterings characterizes the density of phonons that can interact with the electrons and can be fully determined from the electron and phonon band structures without knowledge of electron-phonon coupling strength. Our work reveals the underlying physics limiting the electron mobility of 2D semiconductors and offers a descriptor to quickly assess the mobility.

Electronic transport properties of hydrogenated and fluorinated graphene: a computational study

Hydrogenation and fluorination have been presented as two possible methods to open a bandgap in graphene, required for field-effect transistor applications. In this work, we present a detailed study of the phonon-limited mobility of electrons and holes in hydrogenated graphene (graphane) and fluorinated graphene (graphene fluoride). We pay special attention to the out-of-plane acoustic (ZA) phonons, responsible for the highest scattering rates in graphane and graphene fluoride. Considering the most adverse cut-off for long-wavelength ZA phonons, we have obtained electron (hole) mobilities of 28 (41) cm² V^-1 s^-1 for graphane and 96 (30) cm² V^-1 s^-1 for graphene fluoride. Nonetheless, for a more favorable cut-off wavelength of ∼2.6 nm, significantly higher electron (hole) mobilities of 233 (389) cm² V^-1 s^-1 for graphane and 460 (105) cm² V^-1 s^-1 for graphene fluoride are achieved. Moreover, while complete suppression of ZA phonons can increase the electron (hole) mobility in graphane up to 278 (391) cm² V^-1 s^-1, it does not affect the carrier mobilities in graphene fluoride. Velocity-field characteristics reveal that the electron velocity in graphane saturates at an electric field of ∼4 × 10⁵ V cm^-1. Comparing the mobilities with other two-dimensional (2D) semiconductors, we find that hydrogenation and fluorination are two promising avenues to realize a 2D semiconductor while providing good carrier mobilities.

Electron-Phonon beyond Fröhlich: Dynamical Quadrupoles in Polar and Covalent Solids

We include the treatment of quadrupolar fields beyond the Fröhlich interaction in the first-principles electron-phonon vertex in semiconductors. Such quadrupolar fields induce long-range interactions that have to be taken into account for accurate physical results. We apply our formalism to Si (nonpolar), GaAs, and GaP (polar) and demonstrate that electron mobilities show large errors if dynamical quadrupoles are not properly treated.

Piezoelectric Electron-Phonon Interaction from Ab Initio Dynamical Quadrupoles: Impact on Charge Transport in Wurtzite GaN

First-principles calculations of e-ph interactions are becoming a pillar of electronic structure theory. However, the current approach is incomplete. The piezoelectric (PE) e-ph interaction, a long-range scattering mechanism due to acoustic phonons in noncentrosymmetric polar materials, is not accurately described at present. Current calculations include short-range e-ph interactions (obtained by interpolation) and the dipolelike Frölich long-range coupling in polar materials, but lack important quadrupole effects for acoustic modes and PE materials. Here we derive and compute the long-range e-ph interaction due to dynamical quadrupoles, and apply this framework to investigate e-ph interactions and the carrier mobility in the PE material wurtzite GaN. We show that the quadrupole contribution is essential to obtain accurate e-ph matrix elements for acoustic modes and to compute PE scattering. Our work resolves the outstanding problem of correctly computing e-ph interactions for acoustic modes from first principles, and enables studies of e-ph coupling and charge transport in PE materials.

Electron mobility and mode analysis of scattering for β-Ga2O3from first principles

The electrical transport properties of β-Ga2O3are studied by first-principles calculations. The calculated intrinsic electron Hall mobilities agree well with experiments, with intrinsic Hall factor decreasing monotonically from 1.54 at 100 K to 1.14 at 800 K. The anisotropy of electron mobility is weak due to the almost isotropic electron effective mass, which also results in nearly isotropic Seebeck coefficient and electronic contribution to the thermal conductivity. The mode analysis of phonon scattering reveals that the optical phonon scattering is almost entirely determined by the long-range polar interactions, whereas the acoustic phonon scattering also plays an important role especially at low temperatures. The intrinsic electron mobility is significantly overestimated even above room temperature by only considering the polar optical phonon scattering, in contrast to previous predictions from fitting of phenomenological models.

Spin-phonon relaxation from a universal ab initio density-matrix approach

Designing new quantum materials with long-lived electron spin states urgently requires a general theoretical formalism and computational technique to reliably predict intrinsic spin relaxation times. We present a new, accurate and universal first-principles methodology based on Lindbladian dynamics of density matrices to calculate spin-phonon relaxation time of solids with arbitrary spin mixing and crystal symmetry. This method describes contributions of Elliott-Yafet and D'yakonov-Perel' mechanisms to spin relaxation for systems with and without inversion symmetry on an equal footing. We show that intrinsic spin and momentum relaxation times both decrease with increasing temperature; however, for the D'yakonov-Perel' mechanism, spin relaxation time varies inversely with extrinsic scattering time. We predict large anisotropy of spin lifetime in transition metal dichalcogenides. The excellent agreement with experiments for a broad range of materials underscores the predictive capability of our method for properties critical to quantum information science.

Evidence of Large Polarons in Photoemission Band Mapping of the Perovskite Semiconductor CsPbBr_{3}

Lead-halide perovskite (LHP) semiconductors are emergent optoelectronic materials with outstanding transport properties which are not yet fully understood. We find signatures of large polaron formation in the electronic structure of the inorganic LHP CsPbBr_{3} by means of angle-resolved photoelectron spectroscopy. The experimental valence band dispersion shows a hole effective mass of 0.26±0.02 m_{e}, 50% heavier than the bare mass m_{0}=0.17 m_{e} predicted by density functional theory. Calculations of the electron-phonon coupling indicate that phonon dressing of the carriers mainly occurs via distortions of the Pb-Br bond with a Fröhlich coupling parameter α=1.81. A good agreement with our experimental data is obtained within the Feynman polaron model, validating a viable theoretical method to predict the carrier effective mass of LHPs ab initio.

Ab initio electron-two-phonon scattering in GaAs from next-to-leading order perturbation theory

Electron-phonon (e-ph) interactions are usually treated in the lowest order of perturbation theory. Here we derive next-to-leading order e-ph interactions, and compute from first principles the associated electron-two-phonon (2ph) scattering rates. The derivations involve Matsubara sums of two-loop Feynman diagrams, and the numerical calculations are challenging as they involve Brillouin zone integrals over two crystal momenta and depend critically on the intermediate state lifetimes. Using Monte Carlo integration together with a self-consistent update of the intermediate state lifetimes, we compute and converge the 2ph scattering rates, and analyze their energy and temperature dependence. We apply our method to GaAs, a weakly polar semiconductor with dominant optical-mode long-range e-ph interactions. We find that the 2ph scattering rates are as large as nearly half the value of the one-phonon rates, and that including the 2ph processes is necessary to accurately predict the electron mobility in GaAs from first principles.

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

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. These new developments are unlocking exciting new opportunities, from exploring carrier transport in quantum matter to in silico designing new semiconductors with tailored transport properties. In this article, we review the most recent developments in the area of ab initio calculations of carrier mobilities of semiconductors. Our aim is threefold: to make this rapidly-growing research area accessible to a broad community of condensed-matter theorists and materials scientists; to identify key challenges that need to be addressed in order to increase the predictive power of these methods; and to identify new opportunities for increasing the impact of these computational methods on the science and technology of advanced materials. The review is organized in three parts. 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, gallium arsenide, gallium nitride, gallium oxide, and lead halide perovskites as well as low-dimensional semiconductors such as graphene, silicene, phosphorene, molybdenum disulfide, and indium selenide. We also review recent efforts toward high-throughput calculations of carrier transport. In the last part, we identify important classes of materials for which an ab initio study of carrier mobilities is warranted. We discuss the extension of the methodology to study topological quantum matter and materials for spintronics and we comment on the possibility of incorporating Berry-phase effects and many-body correlations beyond the standard Boltzmann formalism.

Theoretical prediction of intrinsic electron mobility of monolayer InSe: first-principles calculation

Recently, a novel two-dimensional (2D) semiconductor, InSe, has attracted great attention due to its potential applications in optoelectronic devices and field effect transistors. In this study, phonon-limited mobility is investigated by the first-principles calculation. At 300 K, the intrinsic electron mobilities calculated from the electron-phonon coupling (EPC) matrix element are as high as [Formula: see text] (zigzag direction) and [Formula: see text] [Formula: see text] (Armchair direction), respectively. The deformation potential theory (DPT) based on longitudinal acoustic and optical phonon scattering is also employed to investigate electron mobility. The mobility from optical phonon scattering is much higher than that from longitudinal acoustic phonon scattering. If the polarization characteristics of InSe are not considered, the electron mobility calculated from EPC matrix element is closed to that from the longitudinal acoustic phonon DPT. In this study, we have also investigated the effect of polarization properties in 2D InSe on electron mobility. At 300 K, the electron mobility for including Fröhlich interaction is reduced to [Formula: see text] and [Formula: see text] [Formula: see text]. Therefore, the electron mobility for InSe is controlled by the scattering from polar phonons. The mobility can be increased to [Formula: see text] and [Formula: see text] [Formula: see text] under 4% biaxial strain. This result is compared with the experiment, and some disagreements are explained.

Monte Carlo Study of Electronic Transport in Monolayer InSe

The absence of a band gap in graphene makes it of minor interest for field-effect transistors. Layered metal chalcogenides have shown great potential in device applications thanks to their wide bandgap and high carrier mobility. Interestingly, in the ever-growing library of two-dimensional (2D) materials, monolayer InSe appears as one of the new promising candidates, although still in the initial stage of theoretical studies. Here, we present a theoretical study of this material using density functional theory (DFT) to determine the electronic band structure as well as the phonon spectrum and electron-phonon matrix elements. The electron-phonon scattering rates are obtained using Fermi's Golden Rule and are used in a full-band Monte Carlo computer program to solve the Boltzmann transport equation (BTE) to evaluate the intrinsic low-field mobility and velocity-field characteristic. The electron-phonon matrix elements, accounting for both long- and short-range interactions, are considered to study the contributions of different scattering mechanisms. Since monolayer InSe is a polar piezoelectric material, scattering with optical phonons is dominated by the long-range interaction with longitudinal optical (LO) phonons while scattering with acoustic phonons is dominated by piezoelectric scattering with the longitudinal (LA) branch at room temperature (T = 300 K) due to a lack of a center of inversion symmetry in monolayer InSe. The low-field electron mobility, calculated considering all electron-phonon interactions, is found to be 110 cm2V-1s-1, whereas values of 188 cm2V-1s-1 and 365 cm2V-1s-1 are obtained considering the long-range and short-range interactions separately. Therefore, the calculated electron mobility of monolayer InSe seems to be competitive with other previously studied 2D materials and the piezoelectric properties of monolayer InSe make it a suitable material for a wide range of applications in next generation nanoelectronics.

Polarons from First Principles, without Supercells

We develop a formalism and a computational method to study polarons in insulators and semiconductors from first principles. Unlike in standard calculations requiring large supercells, we solve a secular equation involving phonons and electron-phonon matrix elements from density-functional perturbation theory, in a spirit similar to the Bethe-Salpeter equation for excitons. We show that our approach describes seamlessly large and small polarons, and we illustrate its capability by calculating wave functions, formation energies, and spectral decomposition of polarons in LiF and Li_{2}O_{2}.

Dimensional Crossover in the Carrier Mobility of Two-Dimensional Semiconductors: The Case of InSe

Two-dimensional (2D) semiconductors are at the center of an intense research effort aimed at developing the next generation of flexible, transparent, and energy-efficient electronics. In these applications, the carrier mobility, that is the ability of electrons and holes to move rapidly in response to an external voltage, is a critical design parameter. Here, we show that the interlayer coupling between electronic wave functions in 2D semiconductors can be used to drastically alter carrier mobility and dynamics. We demonstrate this concept by performing state-of-the-art ab initio calculations for InSe, a prototypical 2D semiconductor that is attracting considerable attention, because of its exceptionally high electron mobility. We show that the electron mobility of InSe can be increased from 100 cm² V^-1 s^-1 to 1000 cm² V^-1 s^-1 by exploiting the dimensional crossover of the electronic density of states from two dimensions to three dimensions. By generalizing our results to the broader class of layered materials, we discover that dimensionality plays a universal role in the transport properties of 2D semiconductors.

Electron-Phonon Scattering in the Presence of Soft Modes and Electron Mobility in SrTiO_{3} Perovskite from First Principles

Structural phase transitions and soft phonon modes pose a long-standing challenge to computing electron-phonon (e-ph) interactions in strongly anharmonic crystals. Here we develop a first-principles approach to compute e-ph scattering and charge transport in materials with anharmonic lattice dynamics. Our approach employs renormalized phonons to compute the temperature-dependent e-ph coupling for all phonon modes, including the soft modes associated with ferroelectricity and phase transitions. We show that the electron mobility in cubic SrTiO_{3} is controlled by scattering with longitudinal optical phonons at room temperature and with ferroelectric soft phonons below 200 K. Our calculations can accurately predict the temperature dependence of the electron mobility in SrTiO_{3} between 150-300 K, and reveal the microscopic origin of its roughly T^{-3} trend. Our approach enables first-principles calculations of e-ph interactions and charge transport in broad classes of crystals with phase transitions and strongly anharmonic phonons.

Hot electron relaxation dynamics in semiconductors: assessing the strength of the electron-phonon coupling from the theoretical and experimental viewpoints

The rapid development of the computational methods based on density functional theory, on the one hand, and of time-, energy-, and momentum-resolved spectroscopy, on the other hand, allows today an unprecedently detailed insight into the processes governing hot-electron relaxation dynamics, and, in particular, into the role of the electron-phonon coupling. Instead of focusing on the development of a particular method, theoretical or experimental, this review aims to treat the progress in the understanding of the electron-phonon coupling which can be gained from both, on the basis of recently obtained results. We start by defining several regimes of hot electron relaxation via electron-phonon coupling, with respect to the electron excitation energy. We distinguish between energy and momentum relaxation of hot electrons, and summarize, for several semiconductors of the IV and III-V groups, the orders of magnitude of different relaxation times in different regimes, on the basis of known experimental and numerical data. Momentum relaxation times of hot electrons become very short around 1 eV above the bottom of the conduction band, and such ultrafast relaxation mechanisms are measurable only in the most recent pump-probe experiments. Then, we give an overview of the recent progress in the experimental techniques allowing to obtain detailed information on the hot-electron relaxation dynamics, with the main focus on time-, energy-, and momentum-resolved photoemission experiments. The particularities of the experimental approach developed by one of us, which allows to capture time-, energy-, and momentum-resolved hot-electron distributions, as well as to measure momentum relaxation times of the order of 10 fs, are discussed. We further discuss the main advances in the calculation of the electron-phonon scattering times from first principles over the past ten years, in semiconducting materials. Ab initio techniques and efficient interpolation methods provide the possibility to calculate electron-phonon scattering times with high precision at reasonable numerical cost. We highlight the methods of analysis of the obtained numerical results, which allow to give insight into the details of the electron-phonon scattering mechanisms. Finally, we discuss the concept of hot electron ensemble which has been proposed recently to describe the hot-electron relaxation dynamics in GaAs, the applicability of this concept to other materials, and its limitations. We also mention some open problems.

Carrier Lifetimes and Polaronic Mass Enhancement in the Hybrid Halide Perovskite CH_{3}NH_{3}PbI_{3} from Multiphonon Fröhlich Coupling

We elucidate the nature of the electron-phonon interaction in the archetypal hybrid perovskite CH_{3}NH_{3}PbI_{3} using ab initio many-body calculations and an exactly solvable model. We demonstrate that electrons and holes near the band edges primarily interact with three distinct groups of longitudinal-optical vibrations, in order of importance: the stretching of the Pb-I bond, the bending of the Pb-I-Pb bonds, and the libration of the organic cations. These polar phonons induce ultrafast intraband carrier relaxation over timescales of 6-30 fs and yield polaron effective masses 28% heavier than the bare band masses. These findings allow us to rationalize previous experimental observations and provide a key to understanding carrier dynamics in halide perovskites.

Crossover from lattice to plasmonic polarons of a spin-polarised electron gas in ferromagnetic EuO

Strong many-body interactions in solids yield a host of fascinating and potentially useful physical properties. Here, from angle-resolved photoemission experiments and ab initio many-body calculations, we demonstrate how a strong coupling of conduction electrons with collective plasmon excitations of their own Fermi sea leads to the formation of plasmonic polarons in the doped ferromagnetic semiconductor EuO. We observe how these exhibit a significant tunability with charge carrier doping, leading to a polaronic liquid that is qualitatively distinct from its more conventional lattice-dominated analogue. Our study thus suggests powerful opportunities for tailoring quantum many-body interactions in solids via dilute charge carrier doping.

Large thermoelectric power factor from crystal symmetry-protected non-bonding orbital in half-Heuslers

Modern society relies on high charge mobility for efficient energy production and fast information technologies. The power factor of a material—the combination of electrical conductivity and Seebeck coefficient—measures its ability to extract electrical power from temperature differences. Recent advancements in thermoelectric materials have achieved enhanced Seebeck coefficient by manipulating the electronic band structure. However, this approach generally applies at relatively low conductivities, preventing the realization of exceptionally high-power factors. In contrast, half-Heusler semiconductors have been shown to break through that barrier in a way that could not be explained. Here, we show that symmetry-protected orbital interactions can steer electron–acoustic phonon interactions towards high mobility. This high-mobility regime enables large power factors in half-Heuslers, well above the maximum measured values. We anticipate that our understanding will spark new routes to search for better thermoelectric materials, and to discover high electron mobility semiconductors for electronic and photonic applications.

The intrinsic origin of high-power factors observed in half-Heusler alloys remains elusive, limiting the design of new thermoelectric materials. In this work, the authors reveal it is due to weakened electron–acoustic phonon coupling, originating from crystal symmetry protection of non-bonding orbitals.

Electron-phonon coupling from finite differences

The interaction between electrons and phonons underlies multiple phenomena in physics, chemistry, and materials science. Examples include superconductivity, electronic transport, and the temperature dependence of optical spectra. A first-principles description of electron-phonon coupling enables the study of the above phenomena with accuracy and material specificity, which can be used to understand experiments and to predict novel effects and functionality. In this topical review, we describe the first-principles calculation of electron-phonon coupling from finite differences. The finite differences approach provides several advantages compared to alternative methods, in particular (i) any underlying electronic structure method can be used, and (ii) terms beyond the lowest order in the electron-phonon interaction can be readily incorporated. But these advantages are associated with a large computational cost that has until recently prevented the widespread adoption of this method. We describe some recent advances, including nondiagonal supercells and thermal lines, that resolve these difficulties, and make the calculation of electron-phonon coupling from finite differences a powerful tool. We review multiple applications of the calculation of electron-phonon coupling from finite differences, including the temperature dependence of optical spectra, superconductivity, charge transport, and the role of defects in semiconductors. These examples illustrate the advantages of finite differences, with cases where semilocal density functional theory is not appropriate for the calculation of electron-phonon coupling and many-body methods such as the GW approximation are required, as well as examples in which higher-order terms in the electron-phonon interaction are essential for an accurate description of the relevant phenomena. We expect that the finite difference approach will play a central role in future studies of the electron-phonon interaction.

Electron mean-free-path filtering in Dirac material for improved thermoelectric performance

Recent advancements in thermoelectric materials have largely benefited from various approaches, including band engineering and defect optimization, among which the nanostructuring technique presents a promising way to improve the thermoelectric figure of merit (zT) by means of reducing the characteristic length of the nanostructure, which relies on the belief that phonons' mean free paths (MFPs) are typically much longer than electrons'. Pushing the nanostructure sizes down to the length scale dictated by electron MFPs, however, has hitherto been overlooked as it inevitably sacrifices electrical conduction. Here we report through ab initio simulations that Dirac material can overcome this limitation. The monotonically decreasing trend of the electron MFP allows filtering of long-MFP electrons that are detrimental to the Seebeck coefficient, leading to a dramatically enhanced power factor. Using SnTe as a material platform, we uncover this MFP filtering effect as arising from its unique nonparabolic Dirac band dispersion. Room-temperature zT can be enhanced by nearly a factor of 3 if one designs nanostructures with grain sizes of ∼10 nm. Our work broadens the scope of the nanostructuring approach for improving the thermoelectric performance, especially for materials with topologically nontrivial electronic dynamics.