Ballistic phonon transport through a Fibonacci array of acoustic nanocavities in a narrow constriction

We investigate the ballistic phonon transport through a Fibonacci array of acoustic nanocavities in a narrow constriction of a semiconductor nanowire at low temperatures. It is found that the transmission spectrum of such a system consists of quasiband gaps and narrow resonances caused by the coupling of phonon waves. Both phonon transmission and thermal conductance exhibit the similarity due to the Fibonacci sequence structure. The similarity is sensitive to the number n and parameters of nanocavities. The results are compared with those in a periodic acoustic nanocavities.     

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.     

Quantitative investigation of thermal phonon pulses in sapphire,silicon, and quartz

Using pulse-heated constantan films as a thermal phonon radiator and superconducting tin bolometer as a phonon detector, we present for the first time a full quantitative comparison between observed bolometer signals and adequate rigorous model calculations for transmission experiments ina-cut sapphire, [111]-cut silicon, as well asX-cut quartz andZ-cut quartz. Details of the observed phonon signals are explained and understood. From these experiments, we are also able to extract information about the phonon absorption coefficient in the normal state of the polycrystalline tin bolometer for longitudinal and transverse polarized phonons in quantitative agreement with an earlier experiment ina-cut sapphire which was performed with a superconducting tunnel junction as a detector. The observed transmission signals can be explained for sapphire and silicon by ballistic propagation with additional small angle scattering, but for quartz strong frequency downconversion occurs for phonons with frequencies above half a Terahertz.In a succeding paper (Part II) the parameter deduced from the transmission experiment are applied to the analysis of the observed phonon signals in reflection experiments in the same crystals under the same conditions.Supported by Deutsche Forschungsgemeinschaft     

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.     

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.     

Measurement of a phonon hot spot in photoexcited Si

High frequency phonons are produced by the thermalization of photoexcited electronhole pairs in a semiconductor. Inelastic and elastic scattering processes determine the frequency down-conversion and diffusion of this thermal energy. Simple estimates of the anharmonic and isotope scattering processes suggest that the acoustic phonons will undergo a quasi-diffusive propagation process. In particular, non-equilibrium phonons high-resolution phonon-imaging experiments presented here show well defined ballistic pulses and sharp phonon-focusing caustics. We explain this discrepancy in terms of a phonon hot spot which acts to efficiently down-convert the high-frequency phonons very near the excitation spot. We present the first measurements of the size of a phonon hot spot, which depends upon excitation power.     

Terahertz absorption by electrons and confined acoustic phonons in free-standing quantum wells

The acoustic phonon confinement in a free-standing quantum well (FSQW) results in an acoustic phonon energy quantization. Typical quantization energies are in the terahertz frequency range. Free electrons may absorb electromagnetic waves in this frequency range if they emit or absorb acoustic phonons. Therefore, the terahertz absorption reveals the characteristic features of the acoustic phonon spectrum in free-standing structures. We have calculated the absorption coefficient of an electromagnetic wave by free electrons in a FSQW in the terahertz frequency range. We took into account a time dependent electric field, an exact form of the acoustic phonon spectrum and eigenmodes, and electron interactions with confined acoustic phonons through the deformation potential. We demonstrate numerical results for GaAs FSQW of width 100 Å at low lattice temperatures in the frequency range 0.1-1 THz. The absorption coefficient exhibits several structures at frequencies corresponding to the lowest acoustic phonon modes. These features occur due to absorption of photons by electrons, which is accompanied by the emission of corresponding acoustic phonons.     

Geometrical factors in the dispersion of ballistic heat pulses

The dispersion of ballistic heat pulses in dielectric crystals can partly be ascribed to geometrical factors that include the sample thickness, the contact areas of the source and detector and their relative positioning, and the acoustic anisotropy of the transmission medium. These factors are involved in determining the spread in the path lengths and group velocities of the phonons that are transmitted. In this paper we derive a simple expression, valid when the source and detector dimensions are small compared with the thickness of the slab-shaped sample, which relates the temporal width of a ballistic heat pulse to the average in-plane component of the slowness vector s of the transmitted phonons. A comparison is made between the predictions of this expression, Monte Carlo simulations and published experimental ballistic heat pulse data on paratellurite.     

Effect of magnon-phonon interaction on phonon damping of two-dimensional Heisenberg ferromagnetic system at finite temperature

A magnon-phonon interaction model is developed on the basis of a two-dimensional square Heisenberg ferromagnetic system. By using Matsubara Green function theory we studied the transverse and longitudinal acoustic phonon dampings and calculated the transverse and longitudinal acoustic phonon damping curves on the main symmetric point and line in the first Brillouin zone. It is found that on the line Δ there is no damping for transverse acoustic phonon and on the line Z there is no damping for longitudinal acoustic phonon. In the first Brillouin zone the damping of transverse acoustic phonons is at least one order larger than that of longitudinal acoustic phonons. The influences of various parameters on transverse and longitudinal acoustic phonon dampings are discussed and the lifetime and the density of state of transverse and longitudinal acoustic phonons are explored as well according to the relation of the phonon damping and its lifetime and the relation of the phonon damping and its density of state.     

The influence of surfaces and interfaces on coherent phonons in semiconductors

Experiments have shown that ultrafast optical excitation of semiconductors can produce oscillating changes in the optical properties of the material. The frequency of the oscillations in transmission or reflection usually matches one of the phonon modes, typically theq = 0 optical mode. These oscillations are known as coherent phonons. We discuss the role of surfaces and interfaces on the coherent phonon signal. We show that: (1) the coherent phonon signal can be used as a probe of the surface depletion field and (2) multiple interfaces as in a superlattice, can drastically alter the coherent phonon spectrum: screening of the modes in the superlattices is reduced and acoustic modes can now be excited.     

Subterahertz phonon dynamics in acoustic nanocavities

We report a direct determination of the dynamic behavior of confined acoustic phonons in nanocavities by picosecond acoustics. We provide the broadband, high resolution transmission amplitude curve in the subterahertz range, and we give evidence of resonant transmission peaks in three successive stop bands, in quantitative agreement with acoustic simulations. We furthermore demonstrate transit times in the nanosecond range at the cavity peaks reflecting the strong confinement of resonant phonons within the cavity layer. On the other hand, picosecond transit times are measured in the stop band, shorter than in any of the constituting materials, a tunneling effect well known both in photonic crystals and in macroscopic phononic systems.     

Effects of contact shape on ballistic phonon transport in semiconductor nanowires

We study the effects of contact shape on ballistic phonon transport in semiconductor nanowires at low temperatures using an approximative scalar model of continuum elasticity. Five different contacts connected to two semiconductor nanowires with different transverse widths are discussed. Numerical results show that the contact shape acts as an ‘acoustic impedance adaptor’, playing a crucial role on the ballistic phonon transmission and thermal conductance. The phonon coupling in the contacts with certain length facilitates ballistic phonon transmission compared to the abrupt interface, in which the phonon scattering is the strongest. It is found that the more the contact is abrupt, the smaller the thermal conductance is. The catenoidal contact rather than the abrupt interface is also the competitive candidate to obtain bigger thermal conductance. These results indicate that choosing an appropriate contact shape is one of the most critical factors to accurately measure the thermal conductance with a very high precision and reliability in different temperature ranges at low temperatures.     

Folded acoustic phonons in Si/Ge superlattices with Ge quantum dots

The spectra of Raman scattering by folded acoustic phonons in Si/Ge superlattices with pseudomorphic layers of Ge quantum dots (QDs) grown by low-temperature (T = 250°C) molecular beam epitaxy are studied. New features of the folded phonon lines related to the resonant enhancement and unusual intensity ratio of the doublet lines that cannot be explained by the existing theory have been observed. The observed modes are shown to be related to the vibrations localized to the QDs and induced by the folded phonons of the Si spacer layers. The calculations performed in the model of a one-dimensional chain of atoms have allowed the nature of the localization of acoustic phonons attributable to a modification of the phonon spectrum of a thin QD layer to be explained. The observed intensity ratio of the folded phonon doublet lines is caused by asymmetry of the relief of the QD layers.     

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.     

Acoustic phonons transport in a quantum waveguide embedded double defects

By using scattering matrix method, we investigate the acoustic phonons transport in a quantum waveguide embedded double defects at low temperatures. When acoustic phonons propagate through the waveguide, the total transmission coefficient versus the reduced phonon frequency exhibits a series of resonant peaks and dips, and acoustic waves interfere with each other in the waveguide to form standing wave with particular wavelengths. In the waveguide with void defects, acoustic phonons whose frequencies approach zero can transport without scattering. The acoustic phonons propagating in the waveguide with clamped material defects, the phonons frequencies must be larger than a threshold frequency. It is also found that the thermal conductance versus temperature is qualitatively different for different types of defects. At low temperatures, when the double defects are void, the universal quantum thermal conductance and a thermal conductance plateau can be clearly observed. However, when the double defects consist of clamped material, the quantized thermal conductance disappears but a threshold temperature where mode 0 can be excited emerges. The results can provide some references in controlling thermal conductance artificially and the design of phonon devices.     

Acoustic phonons transport in a quantum waveguide embedded double defects

By using scattering matrix method, we investigate the acoustic phonons transport in a quantum waveguide embedded double defects at low temperatures. When acoustic phonons propagate through the waveguide, the total transmission coefficient versus the reduced phonon frequency exhibits a series of resonant peaks and dips, and acoustic waves interfere with each other in the waveguide to form standing wave with particular wavelengths. In the waveguide with void defects, acoustic phonons whose frequencies approach zero can transport without scattering. The acoustic phonons propagating in the waveguide with clamped material defects, the phonons frequencies must be larger than a threshold frequency. It is also found that the thermal conductance versus temperature is qualitatively different for different types of defects. At low temperatures, when the double defects are void, the universal quantum thermal conductance and a thermal conductance plateau can be clearly observed. However, when the double defects consist of clamped material, the quantized thermal conductance disappears but a threshold temperature where mode 0 can be excited emerges. The results can provide some references in controlling thermal conductance artificially and the design of phonon devices.     

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.     

多通道石墨纳米带中弹性声学声子输运和热导特性

采用非平衡格林函数方法, 在保持总的能量输出通道中石墨链数不变的条件下, 研究并比较了并列的石墨纳米带通道中弹性声学声子输运和热导特性. 结果表明, 能量输出通道的增加能降低每个能量输出通道的热导; 与能量输入热库最近的能量输出通道热导最大, 最远的能量输出通道热导最小; 中间能量输出通道的热导性质与并列的各输出通道的结构参数密切相关, 最近和最远的能量输出通道的热导性质仅与各自能量输出通道的结构参数有关; 粗糙边缘结构能有效调节各通道的热导; 总的热导性质与能量输出通道石墨链数、能量输出通道数以及边缘结构粗糙程度密切相关.     

Phonon anharmonicities in graphite and graphene

We determine from first principles the finite-temperature properties-linewidths, line shifts, and lifetimes-of the key vibrational modes that dominate inelastic losses in graphitic materials. In graphite, the phonon linewidth of the Raman-active E(2g) mode is found to decrease with temperature; such anomalous behavior is driven entirely by electron-phonon interactions, and does not appear in the nearly degenerate infrared-active E(1u) mode. In graphene, the phonon anharmonic lifetimes and decay channels of the A(1)' mode at K dominate over E(2g) at Gamma and couple strongly with acoustic phonons, highlighting how ballistic transport in carbon-based interconnects requires careful engineering of phonon decays and thermalization.     

Contribution of the electron-phonon interaction to the broadening of cyclotron resonance line of a two-dimensional electron gas in multiple quantum well structures

Summary The theory of cyclotron resonance (CR) lineshape of a two-dimensional electron gas (2 DEG) due to the electron-phonon interaction in multiple-quantum-well structures (MQWS) is investigated. The contribution of the deformation potential acoustic and piezoelectric phonon scattering to the broadening of the cyclotron resonance spectra (CRSB) of such a system is calculated fro GaAs/AlAs. The piezoelectric phonon scattering contribution to the linewidth is smaller as compared to the deformation potential acoustic phonon scattering but is significantly comparable. The magnetic-field dependence of CRSB due to the deformation potential acoustic and piezoelectric phonons isB ^1/2 andB ^1/4, respectively, and the frequency shift Δ _N,p =0 for both interactions in the elastic-scattering approximation. Observed numerical values of the CRSB indicate that at low temperatures acoustic and piezoelectric phonons are dominant scatterers and interact strongly with 2 DEG in MQWS where the impurity scattering is suppressed due to the modulation doping. To speed up publication, the author of this paper has agreed to not receive the proofs for correction.