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.     

Focusing of dispersive phonons in GaAs

The ballistic propagation of highly dispersive phonons in GaAs in analyzed with both a bond-charge model (BCM) and a shell model, and compared to imaging experiments. When scattering is neglected, both models predict dispersive focusing pattern which depend strongly on the selected group velocities. In contrast, velocity-selected phonon images obtained with a PbBi tunnel-junction detector on a 0.7-mm thick crystal, display well-defined caustic lines whose angular positions do not shift at longer delay times. When isotope scattering is considered in the calculation, however, the shell model reproduces the experimental focusing structures remarkably well.For highly dispersive phonons, the bond-charge and shell models predict markedly different phonon-focusing patterns. In particular, a concentration of heat flux along [100] is predicted by BCM forv=1.7–2.0 THz slow-transverse (ST) phonons., but this effect is absent in the shell model. Both models predict new focusing structures in the fasttransverse (FT) mode at high frequencies. Our calculations which include isotope scattering indicate that to observe these new structures considerable technical advances are required in the phonon-imaging experiments.     

Phonon scattering at siliconcrystal surfaces

Our observations of the reflection or backscattering of high-frequency phonons (v =280 GHz to 1 THz) at silicon-solid interfaces disagree significantly with predictions from the acoustic mismatch model. Interfaces composed of materials theoretically wellmatched, show high scattering experimentally. In contrast, interfaces theoretically poorly matched, show less phonon scattering than expected. Generally, this is best expressed by the fact that the interface scattering ranges from roughly 30–60% for different phonon modes with little dependence on the material covering the silicon crystal and different techniques of interface preparations. Thus, our experiments indicate that the well-known Kapitza anomaly of the phonon scattering at solid-liquid helium interfaces is not a special case; the same anomaly appears to be present at all tested interfaces. Our experiments are compared with detailed calculations which either assume pure specular or pure diffusive scattering. In these calculations the influence of the crystal anisotropy for the phonon propagation (phonon focussing) is included. This comparison shows, especially for the free silicon surface, that phonons are completely diffuse scattered. Hence, the acoustic mismatched model relying on specular reflection cannot be applied to the real silicon interface. The frequency dependence of phonon scattering at a free silicon interface indicates the existence of at least two different diffusive scattering mechanisms. Within our experimental limits in these two scattering processes the phonons are elastically scattered.     

多空穴错位分布对石墨纳米带中热输运的影响

利用非平衡格林函数方法研究了石墨纳米带中三空穴错位分布对热输运性质的影响.研究结果发现:三空穴竖直并排结构对低频声子的散射较小,导致低温区域三空穴竖直并排时热导最大,而在高频区域,三空穴竖直并排结构对高频声子的散射较大,导致较高温度区域三空穴竖直并排时热导最小;三空穴的相对错位分布仅能较大幅度地调节面内声学模高频声子的透射概率,而三空穴的相对错位分布能较大幅度地调节垂直振动膜高频声子和低频声子的透射概率,导致三空穴的相对错位分布不仅能大幅调节面内声学模和垂直振动模的高温热导,也能大幅调节垂直振动模的低温热导.研究结果阐明了空穴位置不同的石墨纳米带的热导特性,为设计基于石墨纳米带的热输运量子器件提供了有效的理论依据.     

Calculation of the dark current in a quantum well infrared photodetector

Dark currents in a biased quantum well fabricated using Al_0.27Ga_0.73As/GaAs heterojunctions are calculated at two different temperatures including thermionic field emission currents arising from the electron scattering with phonons and plasmons. In the electron–phonon scattering process several modes due to heterojunctions such as the confined, half-space and interface longitudinal optic phonons are taken into account. It is found that the confined phonon scattering process results in maximum currents compared to those obtained in the half-space and interface scattering modes. However, the magnitude of the currents that resulted from the electron–plasmon scattering process is found to be higher than that found from the electron scattering with confined phonons. Comparison of the calculated dark currents with experiments shows that the thermionic emission currents due to phonon and plasmon assisted processes are essential to get better agreement with experiments than the previously employed bulk phonon scattering process.     

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.     

Nonequilibrium Green's function approach to phonon transport in defective carbon nanotubes

We have developed a new theoretical formalism for phonon transport in nanostructures using the nonequilibrium phonon Green's function technique and have applied it to thermal conduction in defective carbon nanotubes. The universal quantization of low-temperature thermal conductance in carbon nanotubes can be observed even in the presence of local structural defects such as vacancies and Stone-Wales defects, since the long wavelength acoustic phonons are not scattered by local defects. At room temperature, however, thermal conductance is critically affected by defect scattering since incident phonons are scattered by localized phonons around the defects. We find a remarkable change from quantum to classical features for the thermal transport through defective carbon nanotubes with increasing temperature.     

Transverse electron focusing as a way of studying phonon kinetics. Turbulence of phonon flow

Novel techniques have been created for studying phonon kinetics. A supersonic conduction electron flux is used to produce a phonon flux. Transverse electron focusing (TEF) is applied for checking the electron gas affected by phonons. A turbulent regime of phonon flow-phonon flux step broadening-reveals itself as step broadening of non-equilibrium electron flux.     

Lattice dynamics of InSb from phonon imaging

The ballistic heat flux radiating from a point source of heat in a cold crystal displays a complex pattern of caustics due to phonon focusing. The caustics correspond to folds in the elastic-wave surface of the crystal. The pattern of caustics is independent of phonon frequency unless the phonon wavelength is comparable to the lattice spacing; i.e., for values of wavevectork approaching /a. We have measured both the shift in the caustic pattern (angular dispersion) and the increasing time-of-flight (velocity dispersion) for ballistic phonons in InSb with wavevectors up to 40% of the Brillouin-zone boundary. Comparison with existing lattice-dynamics models favors the Bond Charge Model (BCM). The phonon-imaging method gives information about theshapes of the wave surfaces which is complementary to the dispersion curves measured only along symmetry directions by neutron scattering.     

Mode dependent scattering of phonons by domain walls in ferroelectric KDP

Thermal conductivity and ballistic phonon imaging measurements in KH₂PO₄ (KDP) at low temperature (T<3K) indicate that scattering from domain walls has a large effect on phonon transport. kDP has a ferroelectric phase transition from tetragonal to orthorhombic structure atT _c =122 K. BelowT _c domains of opposite electric polarization and crystal orientation form unless the sample is colled in an electric field. Thermal conductivity measured along the [100] (tetragonal) axis drops 30% when domain walls are present, which is independent of sample size and temperature. We attribute this decrease to phonon polarization-dependent scattering at the domain boundaries. This is verified by measurements of ballistic transport, using phonon imaging techniques, which reveal the phonon polarization and mode dependence of the scattering. The scattering is successfully modelled using continuum acoustics with simple acoustic mismatch at the domainwall. The interface scattering is found to be mode dependent: Caustic structures in the phonon images due to slow transverse phonons are most affected by the domain wall scattering, which channels these phonons along parallel planes by multiple reflections without mode conversion. Mode conversion scattering, though possible for a number of phonons, has little effect on the overall phonon transmission.     

Resonant Raman scattering in nanostructures with InGaAs/AlAs quantum dots

Raman scattering by optical phonons in In_xGa_{1 ? x} As/AlAs nanostructures with quantum dots has been studied experimentally for compositions corresponding to x = 0.3?1 under out-resonance conditions. Features due to scattering by GaAs-and InAs-like optical phonons in quantum dots have been detected, and the phonon frequencies have been determined as a function of the dot composition. With increasing excitation energy, a red shift is observed in the frequency of the GaAs-like phonon in quantum dots, which testifies to Raman scattering selective by the size of quantum dots. Under resonant conditions, multiphonon light scattering by optical and interface phonons is observed up to the third order, including overtones of the first-order phonons of InGaAs and AlAs materials and their combinations.     

表面低配位原子对声子的散射机制

由于纳米结构具有极高的表体比,声子-表面散射机制对声子的热输运性质起到关键作用.提出了表面低配位原子对声子的散射机制,并且结合量子微扰理论与键序理论推导出该机制的散射率.由于散射率正比于材料的表体比,这种散射机制对声子输运的重要性随着纳米结构尺寸的减小而增大.散射率正比于声子频率的4次方,所以这种散射机制对高频声子的作用远远强于对低频声子的作用.基于声子玻尔兹曼输运方程,计算了硅纳米薄膜和硅纳米线的热导率,发现本文模型比传统的声子-边界散射模型更接近实验值.此发现不仅有助于理解声子-表面散射的物理机制,也有助于应用声子表面工程调控纳米结构的热输运性质.     

The creation of supra-thermal densities of high-energy phonons in He II

We report the new phenomenon that high-energy phonons can be created from low-energy phonons. This arises because the dynamics of phonons in propagating pulses are quite different to those in isotropic phonon distributions. A pulse of low-energy phonons rapidly thermalises by three-phonon processes. On a much longer time scale four-phonon processes occur within this phonon cloud which create high-energy (10 K) phonons that cannot spontaneously decay. These phonons have a lower velocity and so are lost from the back of phonon cloud; their deficit is restored continuously by four-phonon processes. These now isolated high-energy phonons are very stable and propagate ballistically behind the low-energy phonons, so giving the two pulses which are detected in experiments. For long pulses the high-energy phonons may also decay within the cloud, however the available low-energy phonons for scattering are confined to a narrow-angle cone, so the decay probability is very low because the four phonon process requires large angle scattering. A supra-thermal density of these high-energy phonons is predicted.     

Imaging nonequilibrium atomic vibrations with x-ray diffuse scattering

We use picosecond x-ray diffuse scattering to image the nonequilibrium vibrations in the lattice following ultrafast laser excitation. We present images of nonequilibrium phonons in InP and InSb throughout the Brillouin zone which remain out of equilibrium up to nanoseconds. The results are analyzed using a Born model that helps identify the phonon branches contributing to the observed features in the time-resolved diffuse scattering. In InP this analysis shows a delayed increase in the transverse-acoustic (TA) phonon population along high-symmetry directions accompanied by a decrease in the longitudinal-acoustic phonons. In InSb the increase in TA phonon population is less directional.     

Phonon-pulses propagation and phonon focusing in hexagonal-crystal rods in the boundary-scattering regime

The influence of the sample surface on the propagation of ballistic phonons in cylindrical samples of hexagonal crystals is studied. Our approach is based on the solution of the Boltzmann-Peierls equation with an external phonon source. The phonon irradiation of a detector face is calculated for⁴He and Zn crystals. It is shown how the strong phonon focusing, occurring in the slow modes of these solids, affects on the shape of energy flux falling upon the detector area. For an appropriately chosen lengthto-radius sample ratio, phonons reflected from the sample surface dominate in the detected signal.     

Phonon focusing and electron–phonon drag in semiconductor crystals with degenerate charge-carrier statistics

We study the effect of anisotropy in elastic properties on the electron–phonon drag and thermoelectric phenomena in gapless semiconductors with degenerate charge-carrier statistics. It is shown that phonon focusing leads to a number of new effects in the drag thermopower at low temperatures, when diffusive phonon scattering from the boundaries is the predominant relaxation mechanism. We analyze the effect of phonon focusing on the dependences of the thermoelectromotive force (thermopower) in HgSe:Fe crystals on geometric parameters and the heat-flow directions relative to the crystal axes in the Knudsen regime of the phonon gas flow. The crystallographic directions that ensure the maximum and minimum values of the thermopower are determined and the role of quasi-longitudinal and quasi-transverse phonons in the drag thermopower in HgSe:Fe crystals at low temperatures is analyzed. It is shown that the main contribution to the drag thermopower comes from slow quasi-transverse phonons in the directions of focusing in long samples.     

Electron-phonon scattering in asymmetric semiconductor quantum-well structures

We calculate scattering rates of intrasubband and intersubband electronic transitions in asymmetric single quantum wells (QW's) and step QW's due to interface phonons, confined bulk-like LO phonons, and half-space LO phonons. The relative importance of the different phonon modes is analyzed. The results show that the electron-phonon scattering rates have intimate relation to the QW parameters.     

声子角动量与手性声子

在经典的物理学理论中,声子广泛地被认为是线极化的、不具有角动量的.最近的理论研究发现,在具有自旋声子相互作用的磁性体系(时间反演对称性破缺)中,声子可以携带非零的角动量,在零温时声子除了具有零点能以外还带有零点角动量;非零的声子角动量将会修正通过爱因斯坦-德哈斯效应测量的回磁比.在非磁性材料中,总的声子角动量为零,但是在空间反演对称性破缺的六角晶格体系中,其倒格子空间的高对称点上声子具有角动量,并具有确定的手性;三重旋转对称操作给予声子量子化的赝角动量,赝角动量的守恒将决定电子谷间散射的选择定则;此外还理论预测了谷声子霍尔效应.     

Theory of Raman light scattering by nanocrystal acoustic vibrations

A theory of Raman scattering of light by acoustic phonons in spherical nanocrystals of zinc-blende and wurtzite semiconductors has been developed with the inclusion of the complex structure of the valence band. The deformation-potential approximation was used to describe the exciton-phonon interaction. It is shown that this approximation allows only Raman scattering processes involving spheroidal acoustic phonons with a total angular momentum F=0 or 2. The effect of phonon quantum confinement on linewidth in Raman scattering spectra and scattered polarization is analyzed. An expression for the shape of the spectral line corresponding to nonresonant scattering from F=0 phonons was obtained. Fiz. Tverd. Tela (St. Petersburg) 41, 1473–1483 (August 1999)