I. G. Kuleyev

Relaxation times and mean free paths of phonons in the boundary scattering regime for silicon single crystals

The phonon focusing in cubic dielectric crystals and its influence on the heat transfer in the boundary phonon scattering regime at low temperatures have been investigated. The mean free paths of phonons of different polarizations in samples of infinite and finite lengths with circular and square cross sections have been calculated in the anisotropic continuum model. For samples of infinite length with circular and square cross sections in the case of the equality of the cross-sectional areas, the angular dependences of the mean free paths normalized by the Casimir length almost completely coincide. It has been shown that the anisotropy of the mean free paths decreases significantly upon changing over from infinite samples to samples of finite length. For silicon crystals, the anisotropy of the phonon mean free paths has been analyzed for each of the branches of the phonon spectrum. It has been found that the mean free paths for phonons of each vibrational mode reach maximum values in the directions of focusing, and, in these directions, they exceed the mean free paths for phonons of the other vibrational modes.

Anharmonic processes of scattering and absorption of slow quasi-transverse modes in cubic crystals with positive and negative anisotropies of second-order elastic moduli.

The quasi-transverse ultrasound absorption during anharmonic processes of the scattering in cubic crystals with positive (Ge, Si, diamond and InSb) and negative (KCl and NaCl) anisotropies of the second-order elastic moduli is studied. Mechanisms underlying the relaxation of the slow quasi-transverse mode by two slow (the SSS mechanism) or two fast (the SFF) modes are discussed in the long-wavelength approximation. Angular dependences of the ultrasound absorption for the SSS, SFF and Landau-Rumer relaxation mechanisms are analyzed in terms of the anisotropic continuum model. The full absorption of the slow quasi-transverse mode is determined. It is shown that the SSS and SFF relaxation mechanisms are due to the cubic anisotropy of the crystals, leading to the interaction between noncollinear phonons. Two most important cases-the wavevectors of phonons are in the cube face plane or the diagonal planes-are considered. In crystals with a considerable anisotropy of the elastic energy (Ge, Si, InSb, KCl and NaCl) the total contribution of the SSS and SFF relaxation mechanisms to the full absorption is either several times or one to two orders of magnitude larger than the contribution from the Landau-Rumer mechanism depending on the direction. Much of the dominance of the former relaxation mechanisms over the Landau-Rumer mechanism is explained by second-order elastic moduli.

Low-temperature anisotropy of the thermal conductivity of single-crystal nanofilms and nanowires

The effect of phonon focusing on the phonon transport in single-crystal nanofilms and nanowires is studied in the boundary scattering regime. The dependences of the thermal conductivity and the free path of phonons on the geometric parameters of nanostructures with various elastic energy anisotropies are analyzed for diffuse phonon scattering by boundaries. It is shown that the anisotropies of thermal conductivity for nanostructures made of cubic crystals with positive (LiF, GaAs, Ge, Si, diamond, YAG) and negative (CaF2, NaCl, YIG) anisotropies of the second-order elastic moduli are qualitatively different for both nanofilms and nanowires. The single-crystal film plane orientations and the heat flow directions that ensure the maximum or minimum thermal conductivity in a film plane are determined for the crystals of both types. The thermal conductivity of nanowires with a square cross section mainly depends on a heat flow direction, and the thermal conductivity of sufficiently wide nanofilms is substantially determined by a film plane orientation.

Effect of dispersion on the phonon focusing and anisotropy of thermal conductivity of silicon single crystals in the boundary scattering regime

The effect of dispersion on the focusing of thermal phonons and on the thermal conductivity of silicon single crystals in the boundary scattering regime has been investigated. Analysis of the spectra of acoustic modes obtained for silicon single crystals from inelastic neutron scattering data has demonstrated that, upon transition from long-wavelength phonons to short-wavelength phonons, the directions of their focusing change. With an increase in temperature, this leads to a change in the anisotropy of thermal conductivity of phonons with different polarizations and, consequently, to a change in the anisotropy of the total thermal conductivity. Analysis of the temperature dependence of the thermal conductivity has revealed that the presence of extended flattened sections in the spectrum of short-wavelength transverse phonons indicates anomalously low values of the group velocity and, accordingly, a significant decrease in the contribution from these phonons to the thermal conductivity with increasing temperature. The contribution from longitudinal phonons to the thermal conductivity also significantly increases even at temperatures higher than 110 K and becomes dominant.

Phonon focusing and temperature dependences of thermal conductivity of silicon nanofilms

The effect of phonon focusing on the anisotropy and temperature dependences of the thermal conductivities of silicon nanofilms is analyzed using the three-mode Callaway model. The orientations of the film planes and the directions of the heat flux for maximal or minimal heat removal from silicon chip elements at low temperatures, as well as at room temperature, are determined. It is shown that in the case of diffuse reflection of phonons from the boundaries, the plane with the {100} orientation exhibits the lowest scattering ability (and the highest thermal conductivity), while the plane with the {111} orientation is characterized by the highest scattering ability (and the lowest thermal conductivity). The thermal conductivity of wide films is determined to a considerable extent by the orientation of the film plane, while for nanowires with a square cross section, the thermal conductivity is mainly determined by the direction of the heat flux. The effect of elastic energy anisotropy on the dependences of the thermal conductivity on the geometrical parameters of films is analyzed. The temperatures of transition from boundary scattering to bulk relaxation mechanisms are determined.

Effect of dispersion and damping of thermal phonon states on the longitudinal ultrasonic absorption in germanium crystals

A method has been proposed for approximating a phonon spectrum of cubic crystals, which has been obtained from data on inelastic neutron scattering for symmetric directions, over the entire Brillouin zone in the form appropriate for studying relaxation characteristics of phonon systems. The effect of dispersion and damping of thermal phonon states on the longitudinal ultrasonic absorption in anharmonic processes of scattering with the participation of three longitudinal phonons has been investigated for germanium crystals. It has been shown that the inclusion of the dispersion leads to a decrease in the anisotropy of ultrasonic absorption in the LLL relaxation mechanism and makes it possible to fit the results obtained from calculations of the ultrasonic absorption coefficients to the experimental data in the low-temperature range. The temperature dependence and anisotropy of the relaxation rate of longitudinal thermal phonons in germanium crystals have been determined from experimental data on ultrasonic absorption. The performed analysis has refined values of the relaxation parameters obtained from the interpretation of the data on thermal conductivity of germanium crystals with different isotopic compositions in the isotropic-medium model.

Anisotropy of longitudinal ultrasonic absorption in anharmonic processes of scattering in Ge, Si, InSb, MgO, and KCl cubic crystals: The role of damping of phonon states

The relaxation of longitudinal phonons and absorption of ultrasound in cubic crystals with positive (Ge, Si, InSb, MgO) and negative (KCl) anisotropies of the second-order elastic moduli have been investigated. The scattering processes occurring with the participation of three longitudinal phonons (the LLL mechanism) and the processes of scattering of a longitudinal phonon by two transverse thermal phonons (the LTT mechanism) have been considered in terms of the anisotropic-continuum model. The influence of damping of phonon states on the anisotropy of longitudinal ultrasonic absorption has been examined. The specific features of phonon scattering and the influence of anisotropy of the harmonic and anharmonic energies of the cubic crystals on the ultrasonic absorption have been analyzed. In contrast to the previously performed calculations, the influence of cubic anisotropy of the harmonic and anharmonic energies of the phonon system on the relaxation processes has been exactly taken into account in the present study. The results of the calculations have been compared with experimental data.

Interaction of collinear and noncollinear phonons in anharmonic scattering processes and their role in ultrasound absorption of fast quasi-transverse modes in cubic crystals

The absorption of fast quasi-transverse modes during anharmonic scattering processes in cubic crystals with positive (Ge, Si, diamond and InSb) or negative (KCl and CaF(2)) anisotropies of the second-order elastic moduli is studied. Mechanisms underlying the relaxation of the fast quasi-transverse mode by two fast (the FFF mechanism) or two slow (the FSS) modes are discussed in the long-wavelength approximation. Angular dependences of the ultrasound absorption for the FFF, FSS and Landau-Rumer relaxation mechanisms are analyzed in terms of the anisotropic continuum model. The full absorption of the fast quasi-transverse mode is determined. The problem of the scattering of collinear and noncollinear phonons in cubic crystals and their role in the ultrasound absorption of the fast quasi-transverse modes is considered. It is shown that the FFF and FSS relaxation mechanisms are due to the cubic anisotropy of the crystals, leading to the interaction between noncollinear phonons. In crystals with a considerable anisotropy of the elastic energy (InSb and KCl), the total contribution of the FFF and FSS relaxation mechanisms to the full absorption is one to two orders of magnitude larger than the contribution from the Landau-Rumer mechanism, depending on the direction. Much of the dominance of the former relaxation mechanisms over the Landau-Rumer mechanism is explained by second-order elastic moduli. The role of the Landau-Rumer mechanism in ultrasound absorption may be considerable in cubic crystals with a smaller anisotropy of the elastic energy. It is demonstrated that when anharmonic scattering processes play the dominant role, the inclusion of one of the relaxation mechanisms (the Landau-Rumer mechanism or the FFF or FSS mechanisms of relaxation) is insufficient for the quantitative description of the anisotropy of the full absorption of the fast quasi-transverse modes in cubic crystals.

Phonon Flux Enhancement Factors in Crystals with Different Elastic Energy Anisotropy Types

Phonon pulse propagation in cubic crystals with different elastic energy anisotropy types is considered. A closed analytical expression is derived for the phonon flux enhancement factor. The features of its dependences on the isoenergetic surface curvature types are analyzed for all acoustic modes and anisotropy parameter values and signs.

Influence of phonon focusing on the Knudsen flow of phonon gas in single-crystal nanofilms of spintronic materials

Influence of the anisotropy of elastic energy on the phonon transport has been investigated in single- crystal nanofilms of Fe, Cu, MgO, InSb, and GaAs materials used for spintronic instruments and devices in the Knudsen flow regime of phonon gas. The dependences of the lattice thermal conductivity and lengths of free paths of phonons for all acoustic modes on the geometric parameters of the films have been considered for low temperatures with the dominance of the diffuse scattering of phonons at the boundaries. Physical aspects of the propagation of phonon modes in the films have been analyzed. It has been shown that the anisotropy of phonon transport in single-crystal films is due to the features of the propagation of phonon modes in elastically anisotropic films with a different relationship of the geometric parameters. The directions of heat flow and orientations of the film planes that yield the maximum and minimum thermal conductivity of phonons in film planes have been determined.