Full Phonon Dispersion Research Articles

Effects of Al and C doping on the electronic structure and phonon renormalization inMgB2

We have studied the structural, electronic, and lattice dynamical properties of ${\text{Mg}}_{1\ensuremath{-}x}{\text{Al}}_{x}{\text{B}}_{2}$ and ${\text{MgB}}_{2(1\ensuremath{-}y)}{\text{C}}_{2y}$ alloys within the framework of density-functional theory using the self-consistent virtual-crystal approximation (VCA). The structural properties, electronic band structure, and full phonon dispersion have been analyzed for the $0\ensuremath{\le}x(\text{Al})\ensuremath{\le}1$ and $0\ensuremath{\le}y(\text{C})\ensuremath{\le}0.3$ ranges of concentrations. We found that both dopants reduce the number of holes in the $\ensuremath{\sigma}$ bands until they are completely filled at different doping concentrations. These concentrations correlate with the experimentally observed loss of superconductivity in these alloys. The largest influence of doping on the phonon dispersion is found for the branches connected to the ${E}_{2g}$ and ${B}_{1g}$ modes. For both alloys a sudden increase in the ${E}_{2g}$-mode frequency is observed in a well-defined region of Al and C concentrations which correlates with the topological changes in the $\ensuremath{\sigma}$-Fermi surfaces.

Rigid ion model of high field transport in GaN

Here we report on high field transport in GaN based on the rigid ion model of theelectron–phonon interaction within the cellular Monte Carlo (CMC) approach. Usingthe rigid pseudo-ion method for the cubic zinc-blende and hexagonal wurtzitestructures, the anisotropic deformation potentials are derived from the electronicstructure, the atomic pseudopotential and the full phonon dispersion and eigenvectorsfor both acoustic and optical modes. Several different electronic structure andlattice dynamics models are compared, as well as different models for theinterpolation of the atomic pseudopotentials required in the rigid pseudo-ionmethod. Piezoelectric as well as anisotropic polar optical phonon scattering isaccounted for as well. In terms of high field transport, the peak velocity is primarilydetermined by deformation potential scattering described through the rigid pseudo-ionmodel. The calculated velocity is compared with experimental data from pulsedI–V measurements. Good agreement is found using the rigid ion model to the measuredvelocity–field characteristics with the inclusion of dislocation and ionized impurityscattering. The crystal orientation of the electric field is investigated, where very littledifference is observed in the velocity–field characteristics. We simulate the effects ofnonequilibrium hot phonons on the energy relaxation as well, using a detailed balancebetween emission and absorption during the simulation, and an anharmonic decay of LOphonons to acoustic phonons, as reported previously. Nonequilibrium phonons are shown toresult in a significant degradation of the velocity–field characteristics for high carrierdensities, such as those encountered at the AlGaN/GaN interface due to polarizationeffects.

The anharmonic phonon decay rate in group-III nitrides

Measured lifetimes of hot phonons in group-III nitrides have been explained theoreticallyby considering three-phonon anharmonic interaction processes. The basic ingredients of thetheory include full phonon dispersion relations obtained from the application of anadiabatic bond charge model and crystal anharmonic potential within the isotropic elasticcontinuum model. The role of various decay routes, such as Klemens, Ridley, Vallée–Boganiand Barman–Srivastava channels, in determining the lifetimes of the Raman activezone-centre longitudinal optical (LO) modes in BN (zincblende structure) andA1(LO) modes in AlN, GaN and InN (wurtzite structure) has been quantified.

Impact of Phonon-Surface Roughness Scattering on Thermal Conductivity of Thin Si Nanowires

We present a novel approach for computing the surface roughness-limited thermal conductivity of silicon nanowires with diameter D<100 nm. A frequency-dependent phonon scattering rate is computed from perturbation theory and related to a description of the surface through the root-mean-square roughness height Delta and autocovariance length L. Using a full phonon dispersion relation, we find a quadratic dependence of thermal conductivity on diameter and roughness as (D/Delta)(2). Computed results show excellent agreement with experimental data for a wide diameter and temperature range (25-350 K), and successfully predict the extraordinarily low thermal conductivity of 2 W m(-1) K-1 at room temperature in rough-etched 50 nm silicon nanowires.

Hydrostatic pressure induced structural instability and dielectric property of cubic BaZrO3

Using the first-principle calculations, we investigate in detail the structure instability resulting from softening of the polar zone-center phonon mode [ferroelectric (FE) instability] and nonpolar zone-boundary mode [antiferrodistortive (AFD) instability] in cubic BaZrO3 (BZO) under hydrostatic pressure P from −20 to 90 GPa. The hydrostatic pressure enhances the AFD instability, while it suppresses and then enhances the FE instability. A sequence of FE→cubic→AFD→AFD/FE phase transitions with increasing P is predicted. A careful examination of the pressure dependence of full phonon dispersions and interatomic force constants in real space reveals the microscopic key interactions in driving the transitions. With increasing pressure P, the drastically evolving short-range forces suppress the FE instability induced by the long-range dipole-dipole forces under low pressure, and enhance both the AFD and FE instability under high pressure. We investigate the dielectric properties of cubic BZO under hydrostatic pressure. The dielectric constant as a function of pressure shows a minimum contributed from the TO1 mode with the lowest frequency. We argue that this pressure dependence of the dielectric constant mainly originates from fluctuations of the SR forces.

Theoretical investigation of zincblende AlSb and GaSb compounds

In this study, first principles calculation results of the all elastic parameters, characteristic Debye temperatures, Poisson’s ratios, ultrasound velocities and full phonon dispersion spectra of two III–V group zincblende semiconductors, AlSb and GaSb, are presented. Calculations are based on plane wave basis sets together with Vanderbilt ultrasoft pseudopotentials in the framework of Density Functional Theory (DFT) with Perdew–Wang parameterization of generalized gradient approximation. The detailed total energy calculations are performed in order to obtain elastic stiffness coefficients using volume conserving (isochoric) strains on cubic zincblende phase. The phonon dispersion spectra are calculated in linear response approach. All calculated parameters as well as phonon dispersion spectra are in excellent agreement with experimental works and available theoretical calculations.

Theory of the elastic constants of graphite and graphene

AbstractBorn's long wave method is used to study the elastic properties of graphite and graphene. Starting from an empirical force constant model derived from full inplane phonon dispersions of graphite [Mohr et al., Phys. Rev. B 76, 035439 (2007)] we calculate the tension coefficients of graphene. Extending the model by interplanar interactions, we calculate the elastic constants of graphite. The agreement of our theoretical values with inelastic x‐ray scattering results on elastic constants of graphite [Bosak et al., Phys. Rev. B 75, 153408 (2007)] is very satisfactory. (© 2008 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Raman spectrum of vanadium pentoxide from density‐functional perturbation theory

AbstractWe present ab initio calculation within the framework of the density‐functional theory (DFT) on band structure and vibrational properties of bulk V2O5. The structure of V2O5 comes from optimization of the experimental data with lattice parameters fixed. The band structure of the optimized structure has been calculated, and the result fits the experimental data very well and also gives similar results as those calculated by other methods. The phonon eigenwavenumbers of the Γ‐ point of V2O5 bulk have been calculated ab initio in density‐functional perturbation theory (DFPT). The calculated vibrational wavenumbers are in good agreement with observed infrared and Raman wavenumbers, and the predictive full phonon dispersion of bulk V2O5 has also been obtained. Further we calculated the Raman spectrum of vanadium pentoxide (V2O5) powder sample using the obtained Raman susceptibility. Calculated and measured intensities show overall good agreement. Copyright © 2008 John Wiley &amp; Sons, Ltd.

Effect of curvature on structures and vibrations of zigzag carbon nanotubes: A first-principles study

First-principles pseudopotential-based density functional theory calculations of atomic and electronic structures, full phonon dispersions and thermal properties of zigzag single wall carbon nanotubes (SWCNTs) are presented. By determining the correlation between vibrational modes of a graphene sheet and of the nanotube, we understand how rolling of the sheet results in mixing between modes and changes in vibrational spectrum of graphene. We find that the radial breathing mode softens with decreasing curvature. We estimate thermal expansion coefficient of nanotubes within a quasiharmonic approximation and identify the modes that dominate thermal expansion of some of these SWCNTs both at low and high temperatures.

Microscopic modeling of phonon dynamics and charge response inNdCuO

A description of phonon dynamics and charge response of the $n$-doped high-temperature superconductor (HTSC) $\mathrm{NdCuO}$ is presented based upon a microscopic modeling of the electronic density response. This is accomplished starting from the insulating state via the underdoped strange metallic to the more conventional metallic state by consecutive orbital selective incompressibility-compressibility transitions in terms of strict sum rules for the charge response. The approach proposed in this work for the $n$-doped HTSC's modifies the modeling recently applied to the $p$-doped compounds and expresses an electron-hole asymmetry introduced by doping. A qualitative physical picture consistent with our modeling of the electronic state in the cuprates is given in which a sufficiently broad set of orbital degrees of freedom, i.e., $\mathrm{Cu}\phantom{\rule{0.2em}{0ex}}3d∕4s$ and $\mathrm{O}\phantom{\rule{0.2em}{0ex}}2p$, is essential. Within the framework of linear response theory we calculate full phonon dispersion curves in the different phases. In particular, the strongly doping dependent anomalous high-frequency oxygen bond-stretching modes (OBSM) found experimentally in the $p$-doped HTSC's and also recently for $n$-doped ${\mathrm{Nd}}_{1.85}{\mathrm{Ce}}_{0.15}{\mathrm{CuO}}_{4}$ are investigated and compared with experimental results from inelastic neutron scattering and inelastic x-ray scattering, respectively. We calculate an anticrossing scenario for the OBSM in $n$-doped $\mathrm{NdCuO}$ which is absent in the case of $p$-doped $\mathrm{LaCuO}$ and relate it to the different crystal structure. Phonon-induced electronic charge redistributions of the anomalous OBSM due to nonlocal electron-phonon interaction effects of charge-fluctuation type giving reason to dynamic stripes are also studied. Finally, calculations of a characteristic rearrangement of the phonon density of states across the insulator-metal transition are presented and a comparison with experimental results has been accomplished.

Ab initio investigation of phonon dispersion and anomalies in palladium

In recent years, palladium has proven to be a crucial component for devices ranging from nanotube field effect transistors to advanced hydrogen storage devices. In this work, I examine the phonon dispersion of fcc Pd using first-principle calculations based on density functional perturbation theory (DFPT). While several groups in the past have studied the acoustic properties of palladium, this is the first study to reproduce the full phonon dispersion and associated anomaly in the [110]-direction with high accuracy and no adjustable parameters. I will show that the [110] anomaly is a Kohn anomaly due to electron–phonon interactions and that paramagnons play no significant role in the [110] phonon dispersion.

First-principles study of high-pressure phonon dispersions of wurtzite, zinc-blende, and rocksalt AlN

We present ab initio calculations of the phonon dispersions and density of states for wurtzite, zinc-blende, and rocksalt AlN under hydrostatic pressure using density functional perturbation theory. The calculations predict the full phonon dispersions throughout the Brillouin zone. Our results regarding zone-center modes for wurtzite and zinc-blende structures show generally good agreement with Raman measurements and previous theoretical data. For rocksalt structure, the present results are predictions. The different behavior of the lattice vibration properties under pressure in the three phases being studied here is discussed. The pressure coefficients and mode Grüneisen parameters are determined from the pressure dependence of vibration modes.

Electron–Phonon Interaction Model and Prediction of Thermal Energy Transport in SOI Transistor

An electron–phonon interaction model is proposed and applied to thermal transport in semiconductors at micro/nanoscales. The high electron energy induced by the electric field in a transistor is transferred to the phonon system through electron–phonon interaction in the high field region of the transistor. Due to this fact, a hot spot occurs, which is much smaller than the phonon mean free path in the Si-layer. The full phonon dispersion model based on the Boltzmann transport equation (BTE) with the relaxation time approximation is applied for the interactions among different phonon branches and different phonon frequencies. The Joule heating by the electron–phonon scattering is modeled through the intervalley and intravalley processes for silicon by introducing average electron energy. The simulation results are compared with those obtained by the full phonon dispersion model which treats the electron–phonon scattering as a volumetric heat source. The comparison shows that the peak temperature in the hot spot region is considerably higher and more localized than the previous results. The thermal characteristics of each phonon mode are useful to explain the above phenomena. The optical mode phonons of negligible group velocity obtain the highest energy density from electrons, and resides in the hot spot region without any contribution to heat transport, which results in a higher temperature in that region. Since the acoustic phonons with low group velocity show the higher energy density after electron–phonon scattering, they induce more localized heating near the hot spot region. The ballistic features are strongly observed when phonon–phonon scattering rates are lower than 4 × 1010 s−1.

Electron–Phonon Interaction Model and Prediction of Thermal Energy Transport in SOI Transistor

An electron-phonon interaction model is proposed and applied to thermal transport in semiconductors at micro/nanoscales. The high electron energy induced by the electric field in a transistor is transferred to the phonon system through electron-phonon interaction in the high field region of the transistor. Due to this fact, a hot spot occurs, which is much smaller than the phonon mean free path in the Si-layer. The full phonon dispersion model based on the Boltzmann transport equation (BTE) with the relaxation time approximation is applied for the interactions among different phonon branches and different phonon frequencies. The Joule heating by the electron-phonon scattering is modeled through the intervalley and intravalley processes for silicon by introducing average electron energy. The simulation results are compared with those obtained by the full phonon dispersion model which treats the electron-phonon scattering as a volumetric heat source. The comparison shows that the peak temperature in the hot spot region is considerably higher and more localized than the previous results. The thermal characteristics of each phonon mode are useful to explain the above phenomena. The optical mode phonons of negligible group velocity obtain the highest energy density from electrons, and resides in the hot spot region without any contribution to heat transport, which results in a higher temperature in that region. Since the acoustic phonons with low group velocity show the higher energy density after electron-phonon scattering, they induce more localized heating near the hot spot region. The ballistic features are strongly observed when phonon-phonon scattering rates are lower than 4 x 10(10) S(-1).

First-principles study of the relations between the elastic constants, phonon dispersion curves, and melting temperatures of bcc Ta at pressures up to1000GPa

The possibility to relate analytically elastic shear modulus to melting temperature in the framework of Lindemann melting criterion is investigated here in the particular case of the body-centered cubic phase of tantalum, which is identified as a problematic case. Equation of state, elastic constants, and full phonon dispersion curves (PDCs) are first gathered for a wide pressure range using density functional theory and its perturbation within the generalized gradient approximation. A global fair agreement is found with previous experimental studies. Anomalies in PDCs tend to disappear with compression. Various equivalent Debye temperatures ${\ensuremath{\theta}}_{\mathrm{D}}(n)$ are then deduced and compared for increasing compression. The initial Debye model for atomic vibration is found to stand well above $120\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$. Under this pressure a possibly significant difference up to 10% is found between elastic Debye temperature ${\ensuremath{\theta}}_{\mathrm{D}}(\ensuremath{-}3)$ and ${\ensuremath{\theta}}_{\mathrm{D}}(\ensuremath{-}2)$ required in Lindemann melting criterion. As for all the theoretical melting curves proposed in the past, the one found here using ${\ensuremath{\theta}}_{\mathrm{D}}(\ensuremath{-}2,V)$ completely overpasses the melting curve established by static measurements in diamond anvil cells, but agrees well with the shock melting experiment available. This fact is extensively discussed in terms of evolution of PDCs and explaining hypotheses to be tested in the future are proposed.

Phonon dispersion of graphite by inelastic x-ray scattering

We present the full in-plane phonon dispersion of graphite obtained from inelastic x-ray scattering, including the optical and acoustic branches, as well as the midfrequency range between the $K$ and $M$ points in the Brillouin zone, where the experimental data have been unavailable so far. The existence of a Kohn anomaly at the $K$ point is further supported. We fit a fifth-nearest neighbor force-constant model to the experimental data, making improved force-constant calculations of the phonon dispersion in both graphite and carbon nanotubes available.

Vibrational Properties of Single-Wall Carbon Nanotubes: A First-Principles Study

We present first-principles pseudopotential-based density functional theory (DFT) calculation of structures, full phonon dispersions and thermal properties of armchair single wall armchair carbon nanotubes (SWCNTs) in the isolated and bundle forms. Comparison between the properties of isolated and bundled nanotubes is used to estimate the intertube interaction. We determine correlation between vibrational modes of a graphene sheet and of the nanotube to understand how rolling of the sheet results in mixing between modes and changes in vibrational spectrum. The radial breathing mode hardens with increasing diameter (or decreasing curvature). We estimate thermal expansion coefficient of nanotubes within a quasiharmonic approximation and identify the modes that dominate thermal expansion of some of these SWCNTs both at low and high temperatures.

Joule heating and phonon transport in silicon MOSFETs

This work examines the generation of heat in silicon MOSFETs using self-consistent Monte Carlo device simulation with full electron bandstructure and a full phonon dispersion computed from the Adiabatic Bond Charge model. We devise an efficient algorithm for the inclusion of full phonon dispersion in order to account for anisotropy and details of heat transport with great accuracy. We compute the density-of-states (DOS) and the lattice thermal energy numerically and use them to generate maps of local temperatures in a representative small-channel MOSFET device. Our results show that most heat is dissipated in the form of optical g-type phonons in a small region in the drain, and that the heat flows in a preferred direction aligned with the flow of the electron current. We also show that the distribution of generated phonons in energy closely follows the phonon DOS.

Ab initio lattice dynamics evidence for the broken-symmetry phase of solid hydrogen

The lattice dynamics of solid hydrogen in the broken-symmetry phase (phase II) areextensively studied using density functional linear-response theory. The full phonondispersion curves in the whole Brillouin zone for the previously proposed candidatestructures are examined for the first time. It is found that the energetically preferredPca 21 structure shows exclusively dynamical stability in the pressure range ofphase II (110–150 GPa), as indicated by the absence of phonon softening.A pressure-induced soft transverse acoustic (TA) phonon mode is identifiedand the TA mode completely softens at the zone boundary of the Y point at∼151 GPa, which coincides well with the experimentally observed transition pressure(150 GPa) from phase II to phase III. Moreover, the analysis of the eigenvector ofthe TA soft mode suggested that this phonon softening will result in enlargedintramolecular bond lengths. This fact might serve to explain the experimentalobservation of a sudden decrease in Raman and IR active vibron frequencies during thephase II to phase III transition. The physical reason for the reduction of Ramanvibron frequency with pressure has been discussed. The newly proposed structure with Pa3-type local order has been explored for the first time. However, the calculated results oftotal energy, band structure, and phonon do not support the choice of structure.

Influence of pressure on the structural, dynamical, and electronic properties of theSnP2S6layered crystal

Using the density functional theory in the local density approximation the pressure dependence of the structural, dynamical, and electronic properties of the $\mathrm{Sn}{\mathrm{P}}_{2}{\mathrm{S}}_{6}$ layered semiconductor in the pressure range up to $35\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$ is investigated. The pressure dependence of the lattice parameters is well described by the Murnaghan equation of state. The nonmonotonic pressure dependence of the structural polarization is obtained. The $\mathrm{Sn}{\mathrm{P}}_{2}{\mathrm{S}}_{6}$ compound is predicted to be an indirect-gap semiconductor. At a pressure of above $10\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$, an indirect-direct bandgap crossover is observed. The pressure dependence of the long-wavelength lattice vibration frequencies is calculated and compared with experimental results from Raman spectroscopy in the pressure range $0--21.5\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$. Full phonon dispersion curves do not indicate mode softening over the entire range of the Brillouin zone. The stability of the structure under pressure is discussed.