Dispersion Relations Of Acoustic Phonons Research Articles

Simulating stress-tunable phonon and thermal properties in heterostructured AlN/GaN/AlN-nanofilms

The acoustic phonon and thermal properties of GaN-based heterostructured nanofilms are investigated theoretically considering the effects of quantum confinement and prestress fields. The continuum elastic model is utilized to derive the acoustic phonon dispersion relations of GaN-based nanofilms in which the prestress fields are taken into account. The numerical results demonstrate that prestress fields can alter acoustic phonon properties significantly, such as dispersion relation and phonon group velocities. The trend of variation turns to be opposite as the direction of prestress fields reverses. The change of phonon properties under various prestress fields is sensitive to the thickness of core layer in heterostructured nanofilms. Moreover, the modification of acoustic phonon properties in heterostructured nanofilms under prestress fields gives rise to the change of phonon thermal conductivities for different phonon modes. Moreover, prestress fields can modify the influence of temperature-dependent phonon thermal conductivity of GaN-based heterostructured nanofilms. The results in this work could be helpful for the thermal management and rational design of high-performance in nano/microelectronic devices.

Modeling nanostructure lattice thermal conductivity

We present an analytical model for the lattice thermal conductivity of semiconductor nanostructures, based on solving the Boltzmann transport equation in the relaxation time approximation. The improved model is then used to predict the lattice thermal conductivity of three samples of silicon nanowire (Si NW) with diameters 50, 98, and 115 nm. Derived formulas of the lattice thermal conductivity and correction term are presented, which differs from that of Callaway in that it considers the acoustic phonon dispersion relation. Combining the scattering relaxation rate for phonon–phonon, mass difference and boundary was carried out in the analysis of the experimental data and also considering the separate contributions for transverse and longitudinal phonons. The present theoretical model of lattice thermal conductivity agrees well with the available experimental data of Si NW over a wide range of temperature.

Acoustic phonon propagation in ultra-thin Si membranes under biaxial stress field

We report on stress induced changes in the dispersion relations of acoustic phonons propagating in 27 nm thick single crystalline Si membranes. The static tensile stress (up to 0.3 GPa) acting on the Si membranes was achieved using an additional strain compensating silicon nitride frame. Dispersion relations of thermally activated hypersonic phonons were measured by means of Brillouin light scattering spectroscopy. The theory of Lamb wave propagation is developed for anisotropic materials subjected to an external static stress field. The dispersion relations were calculated using the elastic continuum approximation and taking into account the acousto-elastic effect. We find an excellent agreement between the theoretical and the experimental dispersion relations.

Tailoring electron–phonon interaction in nanostructures

Efficient design of optoelectronic devices based on electron intersubband transitions depends critically on the knowledge of the intersubband relaxation times which in turn, depends on electron scattering with LO and acoustic phonons. In this article the intersubband scattering time associated with electron–acoustic-phonon interaction has been discussed in terms of phonon mode quantization and phonon confinement with describing the acoustic phonon dispersion relation in detail by introducing the cut-off frequency for each mode. It has been shown that the quantization of acoustic phonon modes lead to an enhancement in electron–phonon scattering time in AlGaAs quantum well structures. Based on the presented model, a new tailoring method has presented to adjust the electron–phonon scattering time in intersubband-transition-based structures while keeping the electronic properties unaltered. Also, we illustrated that for a quantum well with subband energy separation of ∼30meV, the intersubband scattering time with acoustic-phonon-assisted transitions could be tailored from ∼120ps to increased value of ∼400ps or reduced value of ∼45ps by inserting a 1nm-thickacoustically soft or hard layers, respectively, while keeping the same the initial energy separation.

A Revisit to Capture the Entire Behavior of Ultrasonic Wave Dispersion Characteristics of Single Walled Carbon Nanotubes Based on Nonlocal Elasticity Theory and Flügge Shell Model

In this paper, an ultrasonic wave propagation analysis in single-walled carbon nanotube (SWCNT) is re-studied using nonlocal elasticity theory, to capture the whole behaviour. The SWCNT is modeled using Flugge's shell theory, with the wall having axial, circumferential and radial degrees of freedom and also including small scale effects. Nonlocal governing equations for this system are derived and wave propagation analysis is also carried out. The revisited nonlocal elasticity calculation shows that the wavenumber tends to infinite at certain frequencies and the corresponding wave velocity tends to zero at those frequencies indicating localization and stationary behavior. This frequency is termed as escape frequency. This behavior is observed only for axial and radial waves in SWCNT. It has been shown that the circumferential waves will propagate dispersively at higher frequencies in nonlocality. The magnitudes of wave velocities of circumferential waves are smaller in nonlocal elasticity as compared to local elasticity. We also show that the explicit expressions of cut-off frequency depend on the nonlocal scaling parameter and the axial wavenumber. The effect of axial wavenumber on the ultrasonic wave behavior in SWCNTs is also discussed. The present results are compared with the corresponding results (for first mode) obtained from ab initio and 3-D elastodynamic continuum models. The acoustic phonon dispersion relation predicted by the present model is in good agreement with that obtained from literature. The results are new and can provide useful guidance for the study and design of the next generation of nanodevices that make use of the wave propagation properties of single-walled carbon nanotubes.

Acoustic phonon modulation and electron–phonon interaction in semiconductor slabs and nanowires

The acoustic phonon modulation (confinement) in semiconductor nanostructures and their interaction with electrons are reviewed. Special emphasis will be placed on free-standing and layered slabs, as well as nanowires. Analysis includes acoustic phonon dispersion relations, displacement wave functions, amplitudes, form factor, electron-phonon scattering rate, and electron mobility.

Anomalous sound propagation in a solid with a special acoustic phonon dispersion relation

We investigate a new type of solids which has a special acoustic phonon dispersion relation of ω = ak2 type. This has been partially observed in graphite. This type of solids usually has a mechanical instability under a homogeneous expansion or a homogeneous deformation and also has a thermal instability. These instabilities can be eliminated by introducing a small cut-off wave number or a suitable unharmonic inter-atomic interaction. We remove the former one by introducing the periodic boundary condition. Some general features of the peculiar "solid" are investigated theoretically and numerically. Especially we investigate the anomalous wave propagation of the dispersive acoustic phonons numerically. The computer simulation of the wave–packet dynamics shows us a stronger localisation character than that in a normal solid in the case of 1-dimensional disordered systems.

Influence of the electron-phonon iinteraction on phonon heat conduction in a molecular nanowire

A model for phonon heat conduction in a molecular nanowire is developed. The calculation takes into account modification of the acoustic phonon dispersion relation due to the electron-phonon interaction. The results obtained are compared with models based upon a simpler, Callaway formula.

Study of phonon dispersion in silicon and germanium at long wavelengths using picosecond ultrasonics

We have studied the dispersion of long wavelength longitudinal phonons in silicon and germanium using ultrasonic techniques. For long wavelengths, the acoustic phonon dispersion relation is of the form omega(k) approximately ck-gammak(3), where c is the speed of sound and gamma measures the lowest-order phonon dispersion. By sending an ultrasonic pulse of length a few hundred angstroms into a crystal and measuring the change of the pulse shape with propagation distance, we are able to determine the parameter gamma. The results are compared with lattice dynamics models.

Dispersion relations of acoustic phonons in pyrope garnet; relationship between vibrational properties and elastic constants

Coherent inelastic neutron scattering measurements have been performed on a natural garnet pyrope from the Dora Maira Massif, Italian Western Alps, [(M&.92Feo.osCao.o3)3Al2Si3012, space group Ia'Jd, Z = 8, a = 11.459 A] to determine the acoustic phonon-dispersion relations at room temperature. Phonon measurements have not previously been made on natural garnets, although the dispersion curves form a basis for developing and testing physically correct interatomic potentials for use in lattice dynamical models. Acoustic phononspropagating in the high-symmetry [100]and [110]directions were observed using the PRISMA spectrometer installed at the ISIS Neutron Spallation Source, U.K. The inelastic scans were performed around the (660), (080), (860), (10,6,0), and (0,10,0) Bragg points: Two transverse acoustic and one longitudinal acoustic phonon branches were measured. The observed acoustic phonon frequencies are in good agreement with those calculated on the basis of a semiempirical interatomic potential model. As a check, the elastic constants obtained from the slopes of the acoustic phonon branches are comparable with previous measurements obtained by Brillouin spectroscopy, although their large estimated errors reflectthe complexityof the experimentalmeasurements of phonon-dispersion curves on pyrope garnets.

Dispersion relations of acoustic phonons on a corrugated surface

We present the theory of surface acoustic phonon normal modes and of Brillouin scattering cross section for a shallow grating on the surface of an opaque material. The grating causes the appearing of a surface Brillouin zone and the folding of the surface modes. We study in detail the opening of gaps in the dispersion relations of the folded surface modes and resonances, for a momentum transfer up to the second zone boundary and for a grating profile beyond the simple sinusoidal approximation. The calculations are applied to the Si(001) surface.

Lattice Instability in β1-AgZn

Phase transition of β 1 -AgZn alloy was studied by means of neutron inelastic and diffuse scattering techniques. Acoustic phonon dispersion relation along the main crystal axes of the alloy was obtained. No [ζζζ]LA phonon anomalies related to the ζ-phase was observed, although previous sound experiment followed by elastic constant analysis predicts that possibility. The observed anomalies in phonon energy of both [ζζ0]TA 1 and [ζζ-2ζ]TA modes associated with the diffuse scattering peaks indicate that a strong lattice instability is involved in the phonon modes. It is pointed out that the lattice instability plays important roles in the structure transition from β 1 -phase to ζ-phase or to the martensitic phase in the AgZn alloy.

Inelastic neutron scattering study of acoustic phonons of black phosphorus

Dispersion relations of acoustic phonons of the orthorhombic black phosphorus have been measured at room temperature and atmospheric pressure. Very anisotropic dispersion surfaces were observed along the three principal directions. Comparison is made between the present measurements and the recent calculations of dispersion curves by Kaneta et al.

A neutron study of phonon dispersion relations in HgTe

Dispersion relations for acoustic phonons in mercury telluride in three high symmetry directions [111], [110] and [001] are presented. The eleven-parameter rigid-ion model is fitted to the experimental data.