Phonon Matrix Elements Research Articles

Efficient first-principles electronic transport approach to complex band structure materials: the case of n-type Mg3Sb2

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.

A DFT study of electron–phonon interactions for the and defects in hexagonal boron nitride: investigating the role of the transition dipole direction

Quantum emitters in two-dimensional hexagonal boron nitride (h-BN) have generated significant interest due to observations of ultra-bright emission made at room temperature. The expectation that solid-state emitters exhibit broad zero-phonon lines at elevated temperatures has been put in question by recent observations of Fourier transform (FT) limited photons emitted from h-BN flakes at room temperature. All decoupled emitters produce photons that are directed in-plane, suggesting that the dipoles are perpendicular to the h-BN plane. Motivated by the promise of an efficient and scalable source of indistinguishable photons that can operate at room temperature, we have developed an approach using density functional theory (DFT) to determine the electron-phonon coupling for defects that have in- and out-of-plane transition dipole moments. Our DFT calculations reveal that the transition dipole for the defect is parallel to the h-BN plane, and for the defect is perpendicular to the plane. We calculate both the phonon density of states and the electron–phonon matrix elements associated with the h-BN defective structures. We find no indication that an out-of-plane transition dipole by itself will result in the low electron–phonon coupling that is expected to produce FT-limited photons at room temperature. Our work provides direction to future DFT software developments and adds to the growing list of calculations relevant to researchers in the field of solid-state quantum information processing.

Electronic heat generation in semiconductors: Non-equilibrium excitation and evolution of zone-edge phonons via electron–phonon scattering in photo-excited germanium

We investigate experimentally and using first-principles theory the generation of phonons and the relaxation of carriers on picosecond timescales across the Brillouin zone of photo-excited Ge by inter-valley electron–phonon scattering. The phonons generated are typical of those generated in semiconductor devices, contributing to the accumulation of heat within the material. We simulate the time-evolution of phonon populations, based on first-principles band structure and electron–phonon and phonon–phonon matrix elements, and compare them to data from time-resolved x-ray diffuse scattering experiments, performed at the Linac Coherent Light Source x-ray free-electron laser facility, following photo-excitation by a 50 fs near-infrared optical pulse. We show that the intensity of the non-thermal x-ray diffuse scattering signal, which is observed to grow substantially near the L-point of the Brillouin zone over 3–5 ps, is due to phonons generated by scattering of carriers between the Δ and L valleys. These phonons have low group velocities, resulting in a heat bottleneck. With the inclusion of phonon decay through 3-phonon processes, the simulations also account for other non-thermal features observed in the x-ray diffuse scattering intensity, which are due to anharmonic phonon–phonon scattering of the phonons initially generated by electron–phonon scattering.

Electron–phonon coupling and superconductivity in an alkaline earth hydride CaH6 at high pressures

Recently, an alkaline earth hydride CaH6 having a sodalitelike clathrate structure has been experimentally synthesized at megabar pressures with a maximum T c of 215 K, comparable to that of a rare earth hydride LaH10. Here, based on first-principles calculations, we find that CaH6 exhibits a huge peak in the Eliashberg spectral function α 2 F around the low-frequency region of H-derived phonon modes, in contrast to LaH10 having a widely spreading spectrum of α 2 F over the whole frequencies of H-derived phonon modes. It is revealed that the huge peak of α 2 F in CaH6 is associated with an effective electron–phonon coupling (EPC) between low-frequency optical phonons and hybridized H 1s and Ca 3d states near the Fermi energy. As pressure increases, the strengthened H–H covalent bonding not only induces a hardening of optical phonon modes but also reduces the electron–phonon matrix elements related to the low-frequency optical modes, thereby leading to a lowering of the EPC constant. It is thus demonstrated that H-derived low-frequency phonon modes play an important role in the pressure-induced variation of T c in CaH6. Furthermore, unlike the presence of two distinct superconducting gaps in LaH10, CaH6 is found to exhibit a single isotropic superconducting gap.

Nonrad: Computing nonradiative capture coefficients from first principles

Point defects in semiconductor crystals provide a means for carriers to recombine nonradiatively. This recombination process impacts the performance of devices. We present the Nonrad code that implements the first-principles approach of Alkauskas et al. (2014) [8] for the evaluation of nonradiative capture coefficients based on a quantum-mechanical description of the capture process. An approach for evaluating electron-phonon coupling within the projector augmented wave formalism is presented. We also show that the common procedure of replacing Dirac delta functions with Gaussians can introduce errors into the resulting capture rate, and implement an alternative scheme to properly account for vibrational broadening. Lastly, we assess the accuracy of using an analytic approximation to the Sommerfeld parameter by comparing with direct numerical evaluation. Program summaryProgram Title: NonradCPC Library link to program files:https://doi.org/10.17632/xmfj4zxmn3.1Developer's repository link:https://doi.org/10.5281/zenodo.4274317Code Ocean capsule:https://codeocean.com/capsule/5582062Licensing provisions: MIT LicenseProgramming language: Python 3Nature of problem: Nonradiative carrier capture at point defects in semiconductors and insulators significantly impacts the performance of devices. A first-principles approach to calculating nonradiative capture rates is necessary to guide materials design and provide atomistic insight into the nonradiative capture process.Solution method: Our code, written in the Python language, implements the first-principles methodology developed by Alkauskas et al. (2014) [8]. Nonradiative capture rates are calculated using a one-dimensional approach, which maps the prohibitively large phonon problem onto a single, effective phonon mode. Harmonic phonon matrix elements may then be computed using an analytic technique or by direct numerical integration of the harmonic oscillator wavefunctions. The electron-phonon coupling is evaluated using the VASP code [Kresse and Furthmüller (1996) [27]] to linear order for the effective mode.

Inverted V-shaped evolution of superconducting temperature in SrBC under pressure* *Project supported by the National Natural Science Foundation of China (Grant Nos. 11974194 and 11974207) and K. C. Wong Magna Fund in Ningbo University.

Based on density functional first-principles calculations and anisotropic Eliashberg equations, we have investigated the electronic structure, lattice dynamics, and phonon-mediated superconductivity in newly synthesized layered compound SrBC under pressure. Different from LiBC and MgB2, our calculations surprisingly reveal that SrBC is isotropic in compressibility, due to the accumulation of substantial electrons in the interstitial region. We find that the Sr phonons strongly couple with B-2p z orbital and the interstitial states, giving rise to a two-gap superconductivity in SrBC, whose transition temperature shows an inverted V-shaped dependence on pressure. The maximal transition temperature is about 22 K at 50 GPa. On both sides of 50 GPa, the transition temperature exhibits quasi-linear variation with positive and negative slopes, respectively. Such a variation of transition temperature is infrequent among phonon-mediated superconductors. The competition between enhanced electron–phonon matrix element and hardened phonons plays an essential role in governing the behavior of the critical temperature.

Monte Carlo analysis of phosphorene nanotransistors

Experimental studies on two-dimensional (2D) materials are still in the early stages, and most of the theoretical studies performed to screen these materials are limited to the room-temperature carrier mobility in the free-standing 2D layers. With the dimensions of devices moving toward nanometer-scale lengths, the room-temperature carrier mobility—an equilibrium concept—may not be the main quantity that controls the performance of devices based on these 2D materials, since electronic transport occurs under strong off-equilibrium conditions. Here we account for these non-equilibrium conditions and, for the case of monolayer phosphorene (monolayer black phosphorus), show the results of device simulations for a short-channel n-MOSFET, using the Monte Carlo method coupled with the Poisson equation, including full bands and full electron–phonon matrix elements obtained from density functional theory. Our simulations reveal significant intrinsic limitations to the performance of phosphorene as a channel material in nanotransistors.

First-principles study of the phonon replicas in the photoluminescence spectrum of 4H -SiC

The free-exciton photoluminescence (PL) spectrum of $4H$-SiC exhibits a detailed fine structure due to the different phonons involved in the indirect gap transition. Here a first-principles calculation of these phonons, their symmetry labeling and their contribution to the photoluminescence spectrum is presented. The calculation uses phonons and electron-phonon coupling matrix elements computed via density functional perturbation theory and energy bands and optical phonon matrix elements calculated in density functional theory. The results are in excellent agreement with the experiment for the phonon energies and the polarization dependence of the spectrum. The relative intensities are also in fair agreement if we allow for some phonons within a few meV to be interchanged. There is however a remarkable discrepancy that the experimental spectrum shows a distinct behavior for phonons with energy below $\ensuremath{\sim}55$ meV and above that energy, which is absent in the theory. The experimental PL lines corresponding to phonon energies below 55 meV are about a factor 5--10 smaller in intensity. This is not found in our calculations. The calculations show a similar peak distribution as the experiment in this range but with intensities comparable to those above 55 meV. This indicates that another mechanism outside the scope of the electron-phonon mediated transitions is operative for photon energies of the PL lines closer to the indirect exciton gap than this 55 meV cutoff, which reduces the overall intensity of these lines. We propose that this may result from competition between the phonon-assisted PL and trapping of the electron in the available unoccupied hexagonal site N-donor shallow level at 53-meV binding energy. As part of this study, we also present the phonon dispersions and density of states in $4H$-SiC and the electronic band structure including quasiparticle corrections.

Electronic Transport Properties of Silicane Determined from First Principles.

Silicane, a hydrogenated monolayer of hexagonal silicon, is a candidate material for future complementary metal-oxide-semiconductor technology. We determined the phonon-limited mobility and the velocity-field characteristics for electrons and holes in silicane from first principles, relying on density functional theory. Transport calculations were performed using a full-band Monte Carlo scheme. Scattering rates were determined from interpolated electron–phonon matrix elements determined from density functional perturbation theory. We found that the main source of scattering for electrons and holes was the ZA phonons. Different cut-off wavelengths ranging from 0.58 nm to 16 nm were used to study the possible suppression of the out-of-plane acoustic (ZA) phonons. The low-field mobility of electrons (holes) was obtained as 5 (10) cm2/(Vs) with a long wavelength ZA phonon cut-off of 16 nm. We showed that higher electron (hole) mobilities of 24 (101) cm2/(Vs) can be achieved with a cut-off wavelength of 4 nm, while completely suppressing ZA phonons results in an even higher electron (hole) mobility of 53 (109) cm2/(Vs). Velocity-field characteristics showed velocity saturation at 3 × 105 V/cm, and negative differential mobility was observed at larger fields. The silicane mobility was competitive with other two-dimensional materials, such as transition-metal dichalcogenides or phosphorene, predicted using similar full-band Monte Carlo calculations. Therefore, silicon in its most extremely scaled form remains a competitive material for future nanoscale transistor technology, provided scattering with out-of-plane acoustic phonons could be suppressed.

Raman spectroscopy in black phosphorus

In this article, we review the current status of Raman spectroscopy in orthorhombic black phosphorus (BP) (for simplicity, henceforth, referred to as BP). BP is a layered semiconductor crystal that recently regained interest because it can be exfoliated down to the single layer, thus exhibiting 2‐D properties. First, we briefly review the crystalline structure and the phonon dispersion relations in BP. Then, the symmetries of the Raman‐active modes are discussed in the light of group theory, and the scattering configurations for observing the different phonon modes are presented. Polarized Raman spectroscopy results are discussed and reveal unusual angular dependence features, which can be ascribed to the linear dichroism and to the complex nature of the electron–phonon matrix elements. Edge phonon effects originated from rearrangements of the atomic terminations are also discussed. Subsequently, Raman modes that emerge from interlayer interaction and that are only visible in the few‐layer regime are presented and discussed. Finally, we outline new perspectives to BP Raman spectroscopy in directions that remain partially or totally unexplored and that can provide potentially important outcomes to problems such as defects, oxidation, doping, strain, stacking order and other BP‐like 2‐D materials. Copyright © 2017 John Wiley & Sons, Ltd.

Electron–phonon superconductivity in BaSn5

First-principles calculations of the electronic structure and phonon dispersion relation of the superconducting compound were performed. This has allowed the calculation of the electron–phonon matrix elements from which the electron–phonon coupling constant was found to be . Application of the Allen–Dynes formula with yielded a superconducting transition temperature of K. The calculated agrees well with the available experimental data and indicates that is an electron–phonon superconductor with intermediate strength electron–phonon coupling.

Stokes–anti‐Stokes contribution to double resonance Raman processes in graphene

The most relevant two‐phonon band in the Raman spectrum of graphene is the 2D band. In addition, there are numerous other combination bands with much smaller intensities in the observed spectra (e.g. or ). Their origin can be understood within the double resonance theory. However, calculations on single‐layer graphene found in the literature so far took into account only the Stokes processes for both electron–phonon interaction steps. This leads to the creation of two phonons, thus it gives the positive combination of the phonon frequencies in the Raman shift. Here we calculate the Raman spectra considering the Stokes–anti‐Stokes combinations as well: one phonon is created and another is annihilated. As a consequence features at the differences of the phonon frequencies show up. Tight binding calculations are carried out including the electron–photon and electron–phonon matrix elements explicitly. Phonon normal‐modes and frequencies are calculated at the level of density functional theory.

Verification of first-principles codes: Comparison of total energies, phonon frequencies, electron–phonon coupling and zero-point motion correction to the gap between ABINIT and QE/Yambo

With the ever-increasing sophistication of codes, the verification of the implementation of advanced theoretical formalisms becomes critical. In particular, cross comparison between different codes provides a strong hint in favor of the correctness of the implementations, and a measure of the (hopefully small) possible numerical differences. We lead a rigorous and careful study of the quantities that enter in the calculation of the zero-point motion renormalization of the direct band gap of diamond due to electron–phonon coupling, starting from the total energy, and going through the computation of phonon frequencies and electron–phonon matrix elements. We rely on two independent implementations: Quantum Espresso+Yambo and ABINIT. We provide the order of magnitude of the numerical discrepancies between the codes, that are present for the different quantities: less than 10-5Ha per atom on the total energy (−5.722Ha/at), less than 0.07cm-1 on the Γ,L,X phonon frequencies (555–1330cm-1), less than 0.5% on the square of the electron–phonon matrix elements and less than 4meV on the zero-point motion renormalization of each eigenenergies (44–264meV). Within our approximations, the DFT converged direct band gap renormalization in diamond due to the electron–phonon coupling is −0.409eV (reduction of the band gap).

Ab initiostudy of the effects of pressure and strain on electron-phonon coupling in IV and III-V semiconductors

In this work, we examine the pressure and biaxial tensile strain dependence of the intervalley electron–phonon matrix elements in the lowest conduction band of GaAs, GaP, Si and Ge within the density functional perturbation theory. We study both individual transitions and average deformation potential values which can be used as parameters in transport simulations. In the case of a hydrostatic pressure, we draw the general conclusion that the hydrostatic pressure dependence of the intervalley electron–phonon matrix elements can be safely neglected in the interpretation of most commonly studied phenomena. In contrast, the case of a biaxial strain in silicon shows that strain-dependence should be taken into account in calculations of the intervalley electron–phonon matrix elements.

Interaction of hot carriers with optical phonons in Selenium

An interaction of hot charge carriers with optical phonons in Selenium is studied theoretically from first principles. The results suggest that the electron–phonon matrix element for energetic electrons is significantly greater than that for holes. This effect is attributed to the weak coupling of lone-pair states to lattice perturbations associated with optical vibrational modes. Hence, the energy relaxation time due to the emission of optical phonons for holes is expected to be longer than that for electrons. The longer relaxation time favors the impact ionization of holes.

Superconductivity in monolayer Pb on Si(111) from first principles

Observation of superconductivity in a single layer of Pb on the (111) surface of bulk silicon has renewed interest in a longstanding question; can superconductivity persist to the ultimate atomic limit? Using first-principles techniques, we investigate the total electron–phonon coupling in monolayer Pb supported by a Si(111) substrate. Our ultra-fine sampling of the electronic structure, lattice dynamics and electron–phonon matrix elements in the nearly two-dimensional Brillouin zone yields a total electron–phonon coupling parameter which explains the experimentally observed superconducting transition temperature of 1.83 K [T. Zhang, et al., Nat. Phys. 6 (2010) 104]. The observed suppression of the superconducting transition temperature from the bulk value of 7.2 K is found to arise from the interplay of reduced electron–phonon matrix elements and a modification of the lattice dynamics resulting from the Pb–Si bonding.

EPW: A program for calculating the electron–phonon coupling using maximally localized Wannier functions

EPW ( Electron– Phonon coupling using Wannier functions) is a program written in Fortran90 for calculating the electron–phonon coupling in periodic systems using density-functional perturbation theory and maximally localized Wannier functions. EPW can calculate electron–phonon interaction self-energies, electron–phonon spectral functions, and total as well as mode-resolved electron–phonon coupling strengths. The calculation of the electron–phonon coupling requires a very accurate sampling of electron–phonon scattering processes throughout the Brillouin zone, hence reliable calculations can be prohibitively time-consuming. EPW combines the Kohn–Sham electronic eigenstates and the vibrational eigenmodes provided by the Quantum ESPRESSO package (see Giannozzi et al., 2009 [1]) with the maximally localized Wannier functions provided by the wannier90 package (see Mostofi et al., 2008 [2]) in order to generate electron–phonon matrix elements on arbitrarily dense Brillouin zone grids using a generalized Fourier interpolation. This feature of EPW leads to fast and accurate calculations of the electron–phonon coupling, and enables the study of the electron–phonon coupling in large and complex systems. Program summary Program title: EPW Catalogue identifier: AEHA_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEHA_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU Public License No. of lines in distributed program, including test data, etc.: 304 443 No. of bytes in distributed program, including test data, etc.: 1 487 466 Distribution format: tar.gz Programming language: Fortran 90 Computer: Any architecture with a Fortran 90 compiler Operating system: Any environment with a Fortran 90 compiler Has the code been vectorized or parallelized?: Yes, optimized for 1 to 64 processors RAM: Heavily system dependent, as small as a few MB Supplementary material: A copy of the “EPW/examples” directory containing the phonon binary files can be downloaded Classification: 7 External routines: MPI, Quantum-ESPRESSO package [1], BLAS, LAPACK, FFTW. (The necessary Blas, Lapack and FFTW routines are included in the Quantum-ESPRESSO package [1].) Nature of problem: The calculation of the electron–phonon coupling from first-principles requires a very accurate sampling of electron–phonon scattering processes throughout the Brillouin zone; hence reliable calculations can be prohibitively timeconsuming. Solution method: EPW makes use of a real-space formulation and combines the Kohn–Sham electronic eigenstates and the vibrational eigenmodes provided by the Quantum-ESPRESSO package with the maximally localized Wannier functions provided by the wannier90 package in order to generate electron–phonon matrix elements on arbitrarily dense Brillouin zone grids using a generalized Fourier interpolation. Running time: Single processor examples typically take 5–10 minutes.

Excitonic effects on radial breathing mode intensity of single wall carbon nanotubes

We develop exciton–photon and exciton–phonon interaction matrix elements for single wall carbon nanotubes within extended tight binding method. The exciton–photon matrix elements using the extended tight binding wave function have a large chirality dependence compared with the previous calculation by simple tight binding method. Using the exciton–photon and exciton–phonon matrix elements presented here, we calculate resonance Raman intensity for radial breathing mode as a function of diameter and chiral angle. Excitonic effect of resonance Raman intensities for the radial breathing mode is enhanced by the curvature and trigonal warping effects.

Calculational aspects of electron–phonon coupling at surfaces

We study the validity of two frequently used approximations in calculations ofelectron–phonon coupling at surfaces. The rigid-ion approximation is a standardapproximation used for the bulk metals. On the basis of density functional theorycalculations, we find that for Be this approximation is as valid for surface atoms as for bulkatoms. In addition, the slab method for calculations of a phonon induced surface statelifetime is examined. The convergence of the electron–phonon matrix element with respectto the thickness of the slab is studied for several systems. When the number of slab layersis increased, the net effect of decreasing overlap and increasing number of final statesdepends strongly on the decay length of the surface state wavefunction and the bandstructure.

Ab initio study of electron–phonon coupling and excitonic linewidth in GaAs under pressure and in GaP

Interactions between excited electrons and short-wavelength (intervalley) phonons are the major source for the broadening of the excitonic line in GaAs under pressure and in GaP. We have studied the intervalley scattering deformation potential using density functional theory for the conduction bands, and density functional perturbation theory for phonon frequencies and for the matrix elements of the electron–phonon interaction. We have calculated the electron–phonon scattering time due to intervalley scattering τ , integrating the scattering probabilities over all possible final states in the Brillouin zone without any ad hoc assumption about the behavior of the electron–phonon matrix elements nor the topology of the conduction band. We compare our theoretical results with time-resolved photoluminescence experiment in GaAs, and with spectroellipsometry measurements in GaAs under pressure and in GaP. We show that our ab initio method also allows the evaluation of effective deformation potentials.