Effect of phonon focussing on thermal conductivity of silicon

Thermal conductivity of a cubic crystal in the boundary scattering regime is calculated, taking into account the difference between the phonon phase and group velocities. Numerical estimates in the case of silicon indicate appreciable anisotropy in conductivity as a result of phonon focussing, its maximum value being about 90% larger than the minimum. The contributions of the individual polarization branches are found to be more strongly dependent on direction than the total conductivity. It is further observed that the angle between the phonon phase and group velocities can be sometimes as large as 10°, 24° and 18° in the case of the longitudinal and the two transverse acoustic branches, respectively.     

Temperature dependent phonon confinement in silicon nanostructures

Temperature dependent variation in Raman line-shape from silicon (Si) nanostructures (NSs) is studied here. Asymmetry and red-shift in room temperature Raman spectrum is attributed to phonon confinement effect. Raman spectra recorded at higher temperatures show increase in FWHM and decrease in asymmetry ratio with respect to its room temperature counterpart. Theoretical Raman line-shape analyses of temperature dependence of phonon confinement is done by incorporating the temperature dependence of phonon dispersion relation. Experimental and theoretical temperature dependent Raman spectra are in good agreement.     

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.     

Remote polar phonon scattering in silicon inversion layers

A new scattering mechanism for free carriers in inversion layers is proposed. It is shown that polar optical phonons of the insulator couple effectively to the inversion layer electrons in the adjacent semiconductor. For the Si-SiO₂ interface this scattering by remote polar phonons influences substantially the field dependent mobility of the silicon inversion layer carriers.     

The one phonon Raman spectrum in microcrystalline silicon

The red shift and the broadening of the Raman signal from microcrystalline silicon films is described in terms of a relaxation in the q-vector selection rule for the excitation of the Raman active optical phonons. The relationship between width and shift calculated from the known dispersion relation in c-Si is in good agreement with available data. An increase in the decay rate of the optical phonons predicted on the basis of the same model is confirmed experimentally.     

A microscopic model for the phonon dispersion in silicon

In this paper the quasi-ion picture recently developed^1,2,6 is applied to the lattice dynamics of covalent materials using Si as an example. The phonon dispersion of Si is investigated along the main symmetry directions by modelling the electronic charge density of the quasi-ions. It is demonstrated that the phonon frequencies can be calculated reasonably well by describing this density in terms of a small set of Gauss-functions.     

Scattering of thermal phonon pulses by isotopes in silicon

The pure ballistic propagation of acoustic phonons in crystals at low temperatures can be described within anisotropic continuum acoustics. One needs only the elastic constants and mass densities to calculate the time-dependent spectral phonon irradition of the bolometer for a given radiator pulse power and detector/radiator geometry. We extend this treatment by including single isotope-scattering events for the phonons in a (111)-cut silicon disk on their flight from the radiator to the detector. Using the earlier experimentally determined polarization and frequency dependent phonon absorption in the bolometer metal, the instantaneous temperature of the bolometer can be calculated from this irradiation. This allows a direct comparison with measured bolometer temperatures using exactly the same transmission or reflection arrangement as in calculation. A very satisfying agreement is observed in the expected range of single phonon scattering.     

Density of phonon states in amorphous germanium and silicon

The density of phonon states in amorphous germanium and silicon is calculated by statistically averaging the crystalline phonon density of states according to the radial distribution function. A simple rigid ion model is used to calculate the density of phonon states at various lattice spacings. The appropriate model parameters are obtained from the pressure dependent elastic constants and the Raman frequency. The calculated results compare favorably to experimental data obtained by infrared and Raman scattering and the results of other theoretical calculations.     

Observation of coherent phonon states in porous silicon films

The dynamics of differential transmission and reflectance spectra of porous silicon films was studied using the femtosecond excitation technique (τ≈50 fs, ?ω_pump=2.34 eV) with supercontinuum probing (?ω_probe=1.6–3.2 eV) and controlled time delay with a step of Δt=7 fs between the pump and probe pulses. A short-lived region of photoinduced bleaching was observed in the differential transmission spectra at wavelengths shorter than the pump wavelength. The excitation of coherent phonon states with a spectrum corresponding to nanocrystalline silicon with an admixture of a disordered phase was observed. The relaxation of electronic excitation was found to slow down in the spectral region where the amplitude of excited coherent vibrations was maximal.     

Improved model of optical phonon confinement in silicon nanocrystals

We develop a model for calculating the Raman scattering spectra from phonons confined in for silicon nanocrystals, which is based on the familiar approach taking into account the uncertainty in the quasi-momentum of phonons localized in the nanocrystals. The model is considerably improved by taking into account dispersion of phonons not only in the magnitude of the quasi-momentum, but also in its direction. A significant refinement of the model is also due to the fact that phonon dispersion is calculated using the widely approved Keating model instead of being approximated by empirical expressions as was done in earlier approaches. The calculations based on this model make it possible to determine the sizes of silicon nanocrystals more precisely from analysis of the experimental Raman spectra.     

Size effect on phonon transport in two-dimensional silicon film

Phonon transport in two-dimensional silicon film is investigated and frequency dependent Boltzmann transport equation is solved numerically using discrete ordinate method. The transient effects of phonon transport in the film are incorporated in the analysis. The influence of film size on phonon transport is examined through equivalent equilibrium temperature in the film. It is found that increasing film thickness enhances phonon scattering and dispersion in the film while increasing equivalent equilibrium temperature. The rate of equivalent equilibrium temperature increase is high in the early heating period ( \(\hbox {t} \le 50\,\hbox {ps}\) ) and the rate of temperature increase becomes gradual in the film as the heating period progresses.     

Interplay between phonon confinement effect and anharmonicity in silicon nanowires

Getting light out of silicon is a difficult task since the bulk silicon has an indirect energy electronic band gap structure. It is expected that this problem can be circumvented by silicon nanostructuring, since the quantum confinement effect may cause the increase of the silicon band gap and shift the photoluminescence into the visible energy range. The increase in resulting structural disorder also causes the phonon confinement effect, which can be analyzed with a Raman spectroscopy. The large phonon softening and broadening, observed in silicon nanowires, are compared with calculated spectra obtained by taking into account the anharmonicity, which is incorporated through the three and four phonon decay processes into Raman scattering cross-section. This analysis clearly shows that the strong shift and broadening of the Raman peak are dominated by the anharmonic effects originating from the laser heating, while confinement plays a secondary role.     

Variable charges at govalent bonds and phonon dispersion in silicon

A model of variable charges at covalent bonds is proposed to describe the effective atomic interaction in a crystal lattice. It is shown that, in the region of elastic deformations, it is sufficient to take account only of the linear term in the expansion of the charge with respect to the relative deformation of the bond. Expressions are obtained for the dynamic matrix on the basis of the pseudopotential model and the model of variable charges at the bonds. The results of calculating the phonon spectrum of silicon are in good agreement with experimental data and reflect the characteristic features of the spectrum.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 95–98, July, 1988.     

On the phonon self-energy

It is reported that a specific phonon-phonon interaction process described by the sixth-order Hamiltonian can contribute to the real part of the phonon self-energy of an order which involves a quadratic dependence of the resulting frequency shift on temperature, in the high temperature limit. The possible connection between the occurrence of such a process and experimental mental results in α-quartz is discussed.     

Piezo-spectroscopic determination of the ratio of electron—To phonon to hole—To phonon interaction in silicon

An investigation of the stress-dependence of the normalized wavelength-modulated absorption spectra of the TO-phonon assisted indirect transition in silicon at 77 K has yielded a value of 1.4 for the ratio of the electron-phonon to hole-phonon scattering matrix elements for the TO-phonon.     

Size effects on phonon localization and Raman enhancement in silicon nanotips

Silicon nanotip arrays exhibit a wide variety of interesting optical and electronic properties associated with their dimensionality. We here investigate the effect of size‐induced changes on phonon localization and explain the enhanced Raman response. The occurrence of normally forbidden transitions in the photoluminescence spectra provides evidence for the predicted localization effect. Spatially resolved Raman spectroscopy reveals a continuous change of the silicon Raman peak position and peak width along the nanotip that is attributed to a smooth change between bulk properties at the base to size‐induced phonon confinement in the apex of the nanotip. This approach allows to exclude heating effects that normally overwhelm the phonon confinement signature. The Raman spectra are in excellent agreement with the spatial correlation model and the extracted correlation length is comparable to the tip dimensions. The observed phonon confinement coincides with an enhancement of the Raman scattering efficiency at the tip apex and results in a 40‐fold increase of the sample's Raman intensity compared with bulk silicon. These results provide a step toward the integration of Si based optoelectronic devices. Copyright © 2012 John Wiley & Sons, Ltd.     

带孔硅纳米薄膜热整流及声子散射特性研究

本文基于非平衡的分子动力学模拟方法计算了带有三角形孔的硅纳米薄膜的界面热阻特性,结果表明300-1100 K范围内随着热流方向的改变,在含有三角形孔的硅纳米薄膜中存在热整流效应,热整流系数达28％.同时借助于声子波包动力学模拟方法,获得了不同频率下的纵波声子在三角形孔处的散射特性,结果表明纵波声子在散射过程中产生了横波声子,并且从三角形底部向顶部入射的声子能量透射系数比反向时平均低22％.不对称结构引起的声子透射率的差异是引起热整流效应的主要因素.