Anisotropy of the mean free paths of phonons in single-crystal films of germanium,silicon, and diamond at low temperatures

The physical aspects of the influence of the elastic energy anisotropy of crystals on the anisotropy of the mean free paths of phonons in single-crystal films of germanium, silicon, and diamond in the diffuse scattering of phonons at the boundaries of the samples have been considered. It has been shown that, for sufficiently wide films of germanium, silicon, and diamond with the {100} and {111} orientations and the lengths of less than or equal to their width, the phonon mean free paths are isotropic (independent of the direction of the temperature gradient in the plane of the film). The anisotropy of the phonon mean free paths depends primarily on the orientation of the film plane and is determined by the focusing and defocusing of phonon modes. For single-crystal films of germanium, silicon, and diamond with the {100} and {111} orientations and lengths much larger than their width, the phonon mean free paths are anisotropic.     

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.     

Characterization of single-crystalline GaAs by imaging with ballistic phonons

Ballistic phonon propagation in single-crystalline [001]-oriented gallium arsenide has been studied using low-temperature scanning electron microscopy for imaging. Deviations in the phonon focusing pattern due to dispersion effects were found by comparing the phonon images to theoretical calculations of the long-wavelength limit. The phonon propagation behavior in, samples cut from differently prepared wafers has been investigated. For highly impure crystals we found a pronounced increase of the diffusive signal component at the expense of the ballistic one. Samples with varying dislocation densities also showed a sensitive dependence, of the ballistic phonon propagation on these crystal defects. For focusing calculations considering elastic scattering processes the diffusivity of the phonons could be determined as a function of the mean scattering length. We have found phonon mean free paths of 0.35 mm to 0.80 mm for the various GaAs crystals.     

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.     

Phonon focusing and temperature dependences of the thermal conductivity of silicon nanowires

The influence of phonon focusing on the anisotropy and temperature dependences of the thermal conductivity of silicon nanowires (NWs) has been studied using the three-mode Callaway theory. The calculated temperature dependences of the thermal conductivity of silicon NWs with diameters above 50 nm agree well with experimental data in the 20–300 K range. The temperatures of transitions from the boundary-scattering to volume-relaxation mechanisms are determined. Variation of the thermal conductivity anisotropy depending on temperature is analyzed. The free paths of phonons with various polarizations in the boundary scattering regime in silicon NWs significantly differ and depend to a considerable degree on the phonon focusing. The free paths reach maxima in the directions of phonon focusing and exceed values for other oscillatory modes. However, in the isotropic medium model, the phonon free paths for various polarizations coincide and are fully determined by the geometric parameters of NWs.     

Nonequilibrium acoustic phonons in ZnTe at liquid-helium temperatures: Effect of impurities and structural defects on the phonon mean free path

ZnTe crystallites isolated from a druse of coarse-grained polycrystalline ZnTe, prepared by chemical vapor synthesis at a temperature of ～650°C, were studied using x-ray diffractometry, luminescence, and the heat pulse technique. The crystallites are stacked in {110}-oriented macroscopic layers with a common twin system. The {111} twin planes separated at a distance of 50–100 μm are perpendicular to the (110) growth layers. Acoustic phonon propagation was studied using the heat pulse technique. A comparison of the responses to the arrival of differently polarized phonons in a given sample with the responses obtained on high-purity coarse-grained ZnTe with randomly distributed twin systems with a separation of 5–10 μm and on twin-free single-crystal ZnTe suggests that twins radically affect the scattering of acoustic phonons. The mean free paths of LA, FTA, and STA phonons were determined by comparing the experimental responses with Monte Carlo calculations.     

Acoustic waves and phonon focus in Li crystal: the first principle study

The acoustic waves in Li are investigated by solving the Christoffel equations.Theoretical calculations of the three dimensional slowness surfaces give insights into themixing of longitudinal and transverse modes and show the origin of the phonon caustics.The results are explained in terms of phonon focusing due to the anisotropy of crystals.The propagation of elastic waves in Li is affected by the elastic anisotropy of thelattice.     

Electron transmission measurements of electron mean free path in supported thin films from 1–5 keV

Measurements are made of the transmission of medium energy electrons through in vacuo deposited films in order to determine the inelastic electron mean free path as a function of energy. Films of Al, Ge and Au are deposited in small increments on 20–30 Å carbon substrates supported by “holey” carbon films. The no-loss electron current is measured for each thickness as a continuous function of incident energy in the range of 1–5 keV. Although this preliminary experiment does not result in a precise separation of elastic and inelastic scattering effects, the attenuation lengths estimated are in reasonable agreement with measured and calculated in-elastic mean free paths. Elastic scattering cross sections appear to be smaller than estimated by simple theory.     

Effect of defect scattering on anisotropic phonon density in metal films

The effect of defect phonon scattering on the spatial dependence of the distribution of phonons generated by Joule heating in metal films is studied. This interaction process is shown to significantly modify the dependence on the direction of propagation of the phonon energy density spectrum.     

Slowness surfaces, ray velocity surfaces and phonon focussing in highT c superconductor crystals

This paper reports the results of the study of anisotropy in elastic wave propagation in single crystal superconducting BSCCO. The inverse and group velocities of elastic waves propagating in different directions have been computed and the corresponding slowness and ray velocity surfaces plotted, taking elastic constant data from literature. In addition, the phenomenon of phonon focussing has been investigated in this material by computing the phonon enhancement factor along different directions in spherical polar coordinates. The abnormally high values in phonon enhancement factor exhibited in certain directions for the phonon modes are interpreted as due to caustics occurring in the geometrical acoustics approximation adopted in the computational analysis. The results in LSCO and YBCO are found to be similar to those in BSCCO.     

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.     

Temperature dependence of the thermal conductivity for tellurium dioxide

The thermal conductivity of tellurium dioxide is reported as a function of temperature. At 77K, the thermal conductivity is 0.09 W/cm-K and it decreases approximately as the inverse of the temperature to a value of 0.02 W/cm-K at 300K. The anisotropy between the a- and c-axes is less than 20% over the entire experimental temperature range, with the a-axis more conductive than the c-axis. By making some simplifying assumptions, the phonon mean free paths and relaxation times are deduced.     

Propagation of nonequilibrium acoustic phonons in high-purity coarse-grained ZnTe

Propagation of nonequilibrium acoustic phonons in coarse-grained ZnTe obtained through vacuum sublimation was studied using the heat pulse method under both optical and metallic-heater phonon generation. The phonon mean free paths in the samples studied were shown to be 14 µm and to be dominated by scattering from twin boundaries.     

氢化非晶硅薄膜的热导率研究

采用铂电极为加热电阻,研究了厚度为300—370nm等离子体化学气相沉积(PECVD)工艺制备的氢化非晶硅(a-Si：H)薄膜的热导率随衬底温度的变化规律.用光谱式椭偏仪拟合测量薄膜的厚度,得到了沉积速率随衬底温度变化规律,傅里叶红外(FTIR)表征了在KBr晶片衬底上制备的a-Si：H薄膜的红外光谱特性,SiH原子团键合模的震动对热量的吸收降低了薄膜热导率.从动力学角度分析了薄膜热导率随平均温度升高而增大的原因,并比较了声子传播和自由电子移动在a-Si：H薄膜热导率变化上的作用差异. 关键词： 非晶硅 热导率 薄膜 热能     

Topological singularities and phonon focusing

The focusing directions of phonon images generated by the anisotropic propagation of ballistic phonons are interpreted as singularities of the Gauss map of the energy surface. While a linear dispersion produces only folds and cusps, a nonlinear dispersion relation generically induces singular events for critical values of the frequency. These events are classified by means of catastrophe theory and the local topology on the energy surfaces is elucidated. On reflection planes or symmetry axes new types of singularities occur. The consequences of Morse singularities in the dispersion relation for the focusing directions are discussed.     

Phonon emission induced dynamic fracture phenomena

We use molecular dynamics simulations to calculate the phonon energy emitted during rapid crack propagation in brittle crystals. We show that this energy is different for different crack planes and propagation directions and that it is responsible for various phenomena at several length scales: energetically preferred crack systems and crack deflection at the atomic scale, reduced maximum crack speed with volume at the micrometer scale, and the inability of a crack to attain the theoretical limiting speed at the macroscale. We propose to include the contribution of this energy in the Freund equation of motion of a dynamically propagating crack.     

Reduction of phonon mean free path: From low-temperature physics to room temperature applications in thermoelectricity

It has been proposed for a long time now that the reduction of the thermal conductivity by reducing the phonon mean free path is one of the best way to improve the current performance of thermoelectrics. By measuring the thermal conductance and thermal conductivity of nanowires and thin films, we show different ways of increasing the phonon scattering from low-temperature up to room-temperature experiments. It is shown that playing with the geometry (constriction, periodic structures, nano-inclusions), from the ballistic to the diffusive limit, the phonon thermal transport can be severely altered in single crystalline semiconducting structures; the phonon mean free path is in consequence reduced. The diverse implications on thermoelectric properties will be eventually discussed.     

Phonon focusing of elastically scattered phonons in GaAs

The propagation of high-frequency phonons through crystals at low temperatures is characterized by both ballistic and diffusive processes. Ballistic propagation of heat pulses is highly anisotropic due to phonon focusing, while diffusive propagation is expected to be nearly isotropic in cubic crystals. By using phonon imaging techniques, we have attempted to identify the heat flux from ballistic and scattered phonons in GaAs. Comparison of this data to Monte Carlo calculations which incorporate elastic scattering shows that the flux from phonons scattered a few times in the bulk retains a significant degree of anisotropy. In particular, a sharp feature discovered by Stock, Ulbrich, and Fieseler and attributed to ballistic propagation of phonons with frequencies up to 1.5 THz is now identified with the scattering of sub-THz phonons. Our analysis provides insights into the evolution of heat propagation from the ballistic to diffusive regimes.     

Transmission of high-frequency phonons through thin glass films

By means of phonon spectroscopy we measured the transmission of high-frequency phonons through thin glass films in the frequency range from 100 to 300 GHz. The films were prepared by thermal oxydation of silicon single crystals. Our data obtained from films with different thicknesses suggest that the observed phonon attenuation is due to scattering processes at the silicon-glass interface and not to a bulk effect in the glass film. The phonon mean free path at 300 GHz turns out to be larger than 4microm. We find evidence for the absence of inelastic scattering processes.     

Anisotropy of electron-phonon interactions in alkali metals

Electron-phonon scattering in the solid alkalis is distinguished from that in most other metals by a combination of three circumstances: The phonon spectra and structure factors are very anisotropic, the Fermi surface in the reduced zone is simply connected and virtually spherical and important large momentum transfers (0.7<(q/2k _F)<1.0) fall within the first large peaks of the phonon structure factors. Anisotropy of microscopic contributions to the macroscopic coefficients is controlled by and is quite sensitive to values of electron-ion matrix elements at large momentum transfer, and can be explored by a realistic yet relatively simple theoretical calculation. A brief summary is presented of such calculations, for the all alkalies, of mean free paths, thermoelectric powers, and electron-phonon mass enhancements. The results show marked anisotropy only for lithium, are consonant with experimental low field Hall coefficients and in addition indicate strong anisotropy in the mass enhancement for lithium.