Phonon conductivity of insulators and semiconductors

Phonon conductivity calculations for materials from groups IV, III–V, II–VI and I–VII are presented. The method uses an effective relaxation time for a phonon taking into account departure from equilibrium of all other phonons which participate in both three-phonon N- and U-processes. It is shown that an important role is played by the off-diagonal part of the three-phonon collision operator above the boundary regime. In particular it is found that the off-diagonal U-processes operator gives a negative contribution to the conductivity at high temperatures. The role of optical phonons in heat transport and in acoustic-optical phonon scattering is also studied. For materials with the mass ratio m₁/m₂ ? 1 we have used the Debye dispersion law in the ‘reduced zone’ scheme, while for materials with m₁/m₂ > 1 but <4 we have used the Debye dispersion law for the acoustic phonons and the Einstein dispersion law or the optical phonons. Inclusion of the optical phonons does not modify the temperature dependence of the conductivity but does change the magnitude significantly.     

Ternary effects on the optical interface phonons in onion-like GaN/AlxGa1 − xN quantum dots

The interface optical phonons and its ternary effects in onion-like quantum dots are studied by using dielectric continuum model and the modified random-element isodisplacement model. The dispersion relations, the electron–phonon interactions and ternary effects on the interface optical phonons are calculated in the GaN/Al_xGa_1 − xN onion-like quantum dots. The results show that aluminium concentration has important influence on the interface optical phonons and electron–phonon interactions in GaN/Al_xGa_1 − xN onion-like quantum dots. The frequencies of interface optical phonons and electron–phonon coupling strengths change linearly with increase of aluminium concentration in high frequency range, and do not change linearly with increasing aluminium concentration in low frequency range.     

Ternary mixed crystal effects on interface optical phonon and electron-phonon coupling in zinc-blende GaN/AlxGa1−xN spherical quantum dots

The theoretical investigations of the interface optical phonons, electron–phonon couplings and its ternary mixed effects in zinc-blende spherical quantum dots are obtained by using the dielectric continuum model and modified random-element isodisplacement model. The features of dispersion curves, electron–phonon coupling strengths, and its ternary mixed effects for interface optical phonons in a single zinc-blende GaN/Al_xGa_1−xN spherical quantum dot are calculated and discussed in detail. The numerical results show that there are three branches of interface optical phonons. One branch exists in low frequency region; another two branches exist in high frequency region. The interface optical phonons with small quantum number l have more important contributions to the electron–phonon interactions. It is also found that ternary mixed effects have important influences on the interface optical phonon properties in a single zinc-blende GaN/Al_xGa_1−xN quantum dot. With the increase of Al component, the interface optical phonon frequencies appear linear changes, and the electron–phonon coupling strengths appear non-linear changes in high frequency region. But in low frequency region, the frequencies appear non-linear changes, and the electron–phonon coupling strengths appear linear changes.     

Impact of anisotropy on polar optical vibration in a wurtzite cylindrical nanowire with ring geometry

The quasi-confined (QC) phonon modes, surface optical (SO) phonon modes and corresponding Fröhlich-like Hamiltonian in a wurtzite cylindrical nanowire with ring geometry are investigated in the framework of the dielectric continuum model and Loudon’s uniaxial crystal model. Numerical calculations are focused on the dispersion relations of the SO phonons and the electron–SO phonon coupling strength. Results show that there are only two branches of SO phonon modes. The dispersions of the two branches of SO phonon modes are obvious when the phonon wave-number k_z or the azimuthal quantum number m is small. Typical degenerating behavior of the SO modes is evidenced due to the anisotropic effect of wurtzite crystal. Moreover, when k_z or m are large enough, the frequencies of the two branches of SO modes converge to a definite limiting frequency in single planar heterostructure. The calculations of the electron–SO phonon coupling strength reveal that the high-frequency SO modes (SO₊) play a more important role in the coupling strength than the low-frequency ones (SO₋). Furthermore, the long-wavelength SO phonons with small m are the main factor contributing to the electron–phonon interaction.     

Dispersive effects and correction term in two-mode phonon conduction model for Ge

A complete analysis of the phonon conductivity κ, still lacking in the literature, is presented in the two-mode conduction model for Germanium. First a method is derived from which the correction term κ_c of the Callaway model is separated into its longitudinal and transverse parts and then the effects of strong phonon dispersion and the role of longitudinal and transverse phonons on κ_c are studied. For this purpose we have also proposed some new empirical expressions for the three phonon relaxation rates τ_3ph⁻¹'s which are valid in the entire temperature range. This improvised model, when applied simultaneously to the phonon conductivity data of both normal and enriched Ge, yields some new results. These are (i) κ_c neglected by the earlier workers in the two-mode phonon conduction model, gives a substantial contribution beyond the conductivity maximum and (ii) the longitudinal phonons are the major carriers of heat at high temperature.     

Parametrische Phononen-Turbulenz im Feld zweier zirkular polarisierter UHF-Wellen

The interaction of two strong circulary polarized u.h.f. pump waves with a fully ionized homogeneous plasma is considered. If the difference Ω of their frequencies is near or smaller than twice the ion plasma frequency phonons can be parametrically excited. The threshold value (E₀E₁)_s for this decay-process depends on Ω and the dissipative effects in the plasma. After exceeding the thermal level the phonons are stabilized due to the scattering by the ions. The evolution of the parametrically excited phonon turbulence and the transition into a stationary state are described by a nonlinear integro-differential equation for the spectral energy density of the phonons. This equation is solved analytically as well as numerically and it is shown, that the phonon turbulence is strongly influence by the propagation directions of the pump waves and the ratio of electron- to ion-temperature.     

Ultrasonic attenuation in insulating crystals

A theory for the dampingΓ of ultrasonic waves due to three-phonon processes is developed by using a Green's function method. The imaginary part of the self-energy of the impressed ultrasound phonons interacting with thermal phonons is calculated. In the limits ofω τ very large and very small the known results are rederived, whereω is the frequency of the ultrasonic wave andτ the thermal phonon relaxation time. The intermediate range ofω τ values is discussed in detail for the case of longitudinal phonon attenuation. It is found, that forω τ>1 a Landau-Rumer type law applies also for longitudinal phonons,Γ～ωT ⁴. But it is shown that dispersion effects and large third-order elastic anisotropy can lead to a stronger temperature dependence thanT ⁴ and a weaker dependence on frequency thanω. These results are compared with recent experiments.     

Soft modes and phonon interactions in studied by neutron scattering

The low frequency lattice dynamics and its relationship to the second order paraelectric-to-ferroelectric transition in Sn₂P₂S₆ is studied. The dispersion branches of the acoustic and lowest lying optical phonons in the a^*-c^* plane have been obtained in the ferroelectric phase, for x-polarized phonons. Close to the phase transition a considerable softening is found for the lowest optical mode (P_x), comparable to the behaviour observed in previous Raman investigations. As found previously in Sn₂P₂Se₆, a strong coupling between the TO(P_x) and TA(u_xz) phonons is observed, although, apparently, not strong enough to lead to an incommensurate phase. The soft TO(P_x) mode at the zone center is observed. The temperature dependence of its frequency and damping shows that the transition is not entirely displacive. At low temperatures an unusual apparent negative LO-TO splitting is observed which is shown to arise from the coupling of the x-polarized soft mode to the nearby z-polarized optical phonon. For comparison, the soft TO(P_x) dispersion in the a^*-b^* plane is measured in both the paraelectric and ferroelectric phases. Consistent frequency changes and LO-TO splitting are observed, revealing a significant interaction between the TA(u_yx) and LA(u_xx) acoustics branches and the TO and LO soft optic branches, respectively. In contrast, the nearby y-polarized optic branch shows almost no temperature dependence. Finally, the influence of piezoelectric effects on the limiting acoustic slopes in the ferroelectric phase is discussed. Received: 11 May 1998 / Revised and Accepted: 15 June 1998     

Finite confining effect on electron–phonon interaction in GaAs/Ga1−xAlxAs single heterostructures

The form factors of the electron–phonon interaction for GaAs/Ga_1−xAl_xAs single heterostructures have been evaluated using a finite height barrier. The calculations are performed within the extreme quantum limit approximation, assuming for the envelope electronic wavefunction a modified Fang–Howard wavefunction. Both types of long-wave phonons, longitudinal optical and interface phonons, are considered. It is found that the effect of the finite height is to reduce the strength of the electron–phonon interaction.     

声子色散对量子点中弱耦合磁极化子声子平均数的影响

利用线性组合算符和幺正变换相结合的方法,研究了声子色散对抛物量子点中弱耦合磁极化子电子周围光学声子平均数的影响。计及纵光学（ LO）声子色散,在抛物近似下导出了基态能量与量子点有效受限长度、声子色散系数、回旋共振频率以及电子－声子耦合常数之间的关系,电子周围光学声子平均数与声子色散系数以及电子－声子耦合常数的关系。数值计算结果表明在弱耦合情况下抛物量子点中磁极化子的基态能量随声子色散系数的增大而减小;电子周围光学声子平均数随声子色散系数增大而增大,随电子－声子耦合常数的增大而增大。     

声子色散对量子点中弱耦合磁极化子声子平均数的影响

利用线性组合算符和幺正变换相结合的方法,研究了声子色散对抛物量子点中弱耦合磁极化子电子周围光学声子平均数的影响．计及纵光学(LO)声子色散,在抛物近似下导出了基态能量与量子点有效受限长度、声子色散系数、回旋共振频率以及电子-声子耦合常数之间的关系,电子周围光学声子平均数与声子色散系数以及电子-声子耦合常数的关系．数值计算结果表明在弱耦合情况下抛物量子点中磁极化子的基态能量随声子色散系数的增大而减小;电子周围光学声子平均数随声子色散系数增大而增大,随电子-声子耦合常数的增大而增大．     

Estimation of the influence of ionic dielectricity on the dynamic superconducting order parameter

We consider the influence of an ω-dependent ionic dielectric constant ?(ω) on the properties of a superconductor. Assuming that the pairing interaction is proportional to ?² we have solved the Eliashberg equations for this case, both for imaginary and real frequencies. The interaction potential depends on a coupling constant λ and on a longitudinal phonon frequency Ω. The dielectric constant is assumed to be independent of wavevector q, and to depend on frequency through the expression: ?(ω) = (ω² - ω²_long)/(ω² - ω²_trans), where ω_long, ω_trans are the frequencies of optical phonons of the dielectric. We find that along the imaginary frequency axis (but not for real frequencies) the weighted phonon propagator can be modeled by an appropriate choice of a cutoff frequency and an effective coupling constant. The influence of ?(ω) on T_c, the gap δ(ω), and the renormalization function Z(ω) are studied and it is found that these quantities increase significantly with the dielectric constant.     

Neural network learning dynamics in a path integral framework

Using the local-density approximation, calculating the Hellmann-Feynman forces and applying the direct method, the phonon dispersion relations for the rutile-like structure of crystalline SnO₂ have been derived for the first time. The phonon frequencies at the point agree very well with Raman and infrared data and other phenomenological model calculations. The LO/TO splitting is estimated by calculating phonons from an elongated supercell. The computations under pressure reveal a soft mode of B_1g symmetry which leads to a ferroelastic phase transition. The pressure-dependence of the lattice constants and the Grüneisen parameters of the modes are calculated. Received 18 July 1999     

Raman scattering by optical phonons and polaritons in CuCl

We present data on forward and backward scattering in CuCl at liquid N₂ temperature. Peaks at 146 and 172 cm^-1 which appear in both forward and backward scattering spectra are attributed to other than first order scattering by optical phonons. The data on polarition scattering indicate that the atomic displacement contribution to the scattering by TO phonons is rather small. From the experimentally determined polarition dispersion curve we obtain a value of 174 ±2.5 cm^-1 for ω_T and a value of 5.3 for ?_S.     

Correlation of size and oxygen bonding at the interface of Si nanocrystal in Si–SiO2 nanocomposite: A Raman mapping study

Raman spectroscopy/mapping is used to investigate the variation of Si phonon wavenumbers, i.e., lower wavenumber (LW ~ 495–510 cm⁻¹) and higher wavenumber (HW ~ 515–519 cm⁻¹) phonons, observed in Si–SiO₂ multilayer nanocomposite (NCp) grown using pulsed laser deposition. Sensitivity of Raman spectroscopy as a local probe to surface/interface is effectively used to show that LW and HW phonons originate at surface (Si–SiO₂ interface) and core of Si nanocrystals, respectively. The consistent picture of this understanding is developed using Raman spectroscopy monitored laser heating/annealing and cooling experiment at the site of the desired wavenumber, chosen with the help of Raman mapping. Raman spectra calculations for Si₄₁ cluster with oxygen and hydrogen termination show strong mode at 512 cm⁻¹ for oxygen terminated cluster corresponding to the vibration of surface Si atoms. This supports our attribution of LW phonons to be originating at the Si–SiO₂ surface/interface. These results along with XPS show that nature of interface (oxygen bonding) in turn depends on the size of nanocrystals and LW phonons originate at the surface of smaller Si nanocrystals. The understanding developed can conclude the ongoing debate on large variation in Si phonon wavenumbers of Si–SiO₂ NCps in the literature. Copyright © 2015 John Wiley & Sons, Ltd.     

Generation and detection of very high frequency acoustic phonons in diamond

Generation and detection of very high frequency acoustic phonons in diamond is reported. We generate phonons at a frequency of 28 THz by defect-induced one-phonon absorption of CO₂ laser radiation and observe, after pulsed excitation, phonon decay products in the frequency range from 1 THz to 7 THz. For detection vibronic sideband spectroscopy is used. We find strongly frequency dependent lifetimes for frequencies above 4 THz which we attribute to spontaneous phonon decay.Dedicated to K. Dransfeld on occasion of his 60th birthday     

First principles lattice dynamical calculation of semiboride Be2B and its ternary alloys XBeB (X=Na, Mg, Al)

We present results of first principles total energy calculations of the structure, electronic and lattice dynamics for beryllium semiboride and its three ternary alloys using generalized gradient and local density approximations under the framework of density functional theory. The generalized gradient approximation is used for all compounds except MgBeB using the Perdew-Burke-Ernzehorf exchange correlation functional while local density approximations use the Perdew-Zunger ultrasoft exchange correlation functional. The calculated ground state structural parameters are in good agreement with those of experimental and previous theoretical studies. The electronic band structure calculations show that Be₂B may transform to a semiconductor after Al substitution. A linear response approach to density functional theory is used to calculate phonon dispersion curves and vibrational density of states. The phonon dispersion curves of Be₂B and AlBeB are positive indicating a dynamical stablility of the structure for these compounds. The phonon dispersion curves of NaBeB and MgBeB show the imaginary phonons throughout the Brillouin zone, which confirms dynamical instability as indicated in band structures for these alloys. We also present the partial phonon density of states for different species of Be₂B and AlBeB to bring out the details of the participation of different atoms in the total phonon density of state, particularly the role played by Al atom. The first time calculated phonon properties are clearly able to bring out the significant effect of isoelectronic substitution in Be₂B.     

Reflection coefficient of phonons between 15 and 315 GHz at a crystal—liquid-helium interface

The frequency dependence of the reflection coefficient was measured for transverse phonons scattered at a SrF₂ cleaved surface covered by bulk liquid He⁴ using a tuneable phonon spectrometer. The reflection coefficient changes monotonically from a value which is greater than 98% at 20 GHz to less than 50% around 120 GHz and is frequency independent between 120 and 315 GHz. The data were essentially temperature independent between 1.4 and 2 K.     

The Investigation of Bulk and Surface Polariton Modes in Ga1?xNxAs by Using Infrared Magneto Spectroscopy

We present and discuss infrared magnetoplasma reflectivity and surface polariton modes in Ga_1–xN_xAs. It assumed that the sample is characterized by a magnetoplasma dielectric tensor. Surface polariton dispersion for two component magnetoplasma was calculated from reflectivity spectra data. We detect transverse optic phonon of GaN sublattice in 470 cm^-1. The origin of sharp feature in p-polarization reflectivity about 300 cm^–1 as well as LO phonon frequency of GaAs sublattice is due to Brewster mode. An interesting feature of surface modes in Voigt geometry is nonreciprocalicity, which means that the frequency changes when the direction of propagation is reversed. Also, the infrared magnetoplasma reflectivity of GaNAs should be providing determination of the electrons and heavy holes effective mass and carrier's concentration.     

Influence of magnetoelastic effects on lattice vibrations in the ferromagnetic invar alloy Fe0.65Ni0.35

Neutron scattering measurements have been made of phonons in a Fe₆₅Ni₃₅ crystal at several temperatures. Marked softening of the [110] acoustic shear modes and a dip in the dispersion relation are found at low temperatures. Above the magnetic ordering temperature T_c, the frequency shift is removed completely, which suggests phonon perturbation by magnetoelastic coupling.