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     

Superconducting tunnel junctions as quantitative detector of intense thermal phonon radiation

Thermal phonons are emitted from a pulse-heated constantan film into an a-cut sapphire (kept at 1.2 K) and are detected quantitatively by recording the current-voltage characteristic of the tunnel junction during the relatively strong phonon irradiation. These measurements are made with the maximum of the Planck distribution of the emitted phonons varied in the frequency range from 0.3 to 1.5 THz. These momentary diode characteristics coincide within experimental error withd c-characteristics at higher substrate temperatures. Assuming thermal equilibrium between electrons and phonons in the tin film and assuming the validity of the acoustic-mismatch model, a comparison can be made between observed phonon power and theoretically expected phonon power. Good agreement is achieved if the influence of the acoustic cut-off frequencies of the tin detector material is taken into account.Supported by Deutsche Forschungsgemeinschaft     

Tin- and lead-tunnel junctions as quantitative detector for intense thermal phonon pulses

Pulse-heated constantan films emit thermal phonon pulses into an a-cut sapphire held at a temperature of some Kelvin. The frequencies of these thermal phonons depend on the radiation temperature and can easily be shifted into the THz range. After a path of 6 mm these phonons are detected by observing the momentary current/voltage characteristics of evaporated symmetric tin- or lead-tunnel junctions during irradiation time. These characteristics correspond to characteristics taken in thermal equilibrium at higher substrate temperature which means that a momentary temperature of the electronic system can be deduced. Using a set of model assumptions concerning phonon transmission across interfaces, phonon propagation in the anisotropic sapphire, absorption in the superconducting detector film and reemission of the absorbed power into the substrate, a comparison with theoretically expected diode temperatures within the one-temperature model for the detector material can be made. Using a variety of quite different experimental conditions there is a remarkable and astonishing well agreement between experiment and theory by fitting only two parameters for each phonon polarization and metal:i) the phonon absorption coefficient in the normal state andii) a phonon cutoff-frequency for the detected phonons. From this fit an information about these important, so far unknown parameters is achieved.Supported by Deutsche Forschungsgemeinschaft     

Nonequilibrium phonons in SiGe quantum-well nanostructures upon excitation by picosecond laser pulses

The phonon pulses initiated by photoexcitation of structures containing Si_0.8Ge_0.2 double quantum wells under picosecond radiation of a MIRA 900P titanium-sapphire laser (λ = 760 nm) are studied. The propagation of nonequilibrium acoustic phonons is detected with a superconducting bolometer. The recorded bolometer response is found to differ substantially from that observed in photoexcitation of the same structure by nanosecond pulses of a nitrogen laser (λ = 337 nm). The generation of coherent acoustic phonons is suggested as an explanation.     

Dispersive anisotropic ballistic phonon propagation in [100] GaAs

We report experimental observations of the phonon focusing pattern in [100] GaAs using low temperature electron beam scanning for phonon generation. The typical dispersive effects for high-frequency phonons expected from the calculations by Tamura have clearly been observed using PbIn tunnel junctions for phonon detection. The quantitative comparison of our experimental results with the frequency dependent calculations by Tamura allowed to determine the dominant phonon frequencies contributing to the detector signal in our different experiments. Above the temperature of the -point the dominant phonon frequencies appear to be shifted considerably to lower values, which could be explained by a heating effect in the liquid-He layer adjacent to the tunnel junction detector. By comparing the observed magnitude of the detector signal with different theoretical treatments of the detector response, we have found satisfactory agreement for a model where the perturbation due to the high-frequency phonons is restricted to the base electrode of the detector reached first by the phonons following their passage through the crystal.     

Phonon focussing patterns: Calculation of response of finite area detectors to pulsed ballistic beams of dispersive and dispersionless phonons

The phonon images of crystals are described in the frame of the Boltzmann kinetic equation. Monochromatic heat pulses of the dispersive and dispersionless acoustic phonons are considered. Exact expressions for the energy and quasimomentum carried by a pulsed beam of monochromatic dispersionless acoustic phonons falling onto a detector of the finite area are derived. These formulae provide us with a convenient starting point for numerical calculations of phonon images. For the example of long wave-length acoustic phonons and a point as well as extended sources, an algorithm for numerical calculations of phonon images of anisotropic crystalline media is presented. However, it is quite general and can be easily adapted for dispersive phonons and to quasiparticles with an arbitrary dispersion low.     

Nonlocal effects in diffusive propagation of heat pulses in systems with trapping centers of nonequilibrium phonons

The propagation of heat pulses in systems with defects as trapping centers of nonequilibrium phonons is investigated theoretically. Among these defects are point defects involving two-level systems (TLSs) of different nature. It is demonstrated that, in addition to the principal signal, one more signal can be detected by the bolometer due to reemission of the nonequilibrium TLS energy at a certain ratio of relaxation times in the phonon and TLS subsystems. The temperature and concentration dependences of the time of signal arrival at the bolometer are analyzed. The results of theoretical investigations are compared with experimental data on the propagation of weakly nonequilibrium thermal phonons in solid solutions of the Y_3?x Er_xAl₅O₁₂ rare-earth yttrium aluminum garnets.     

Propagation of ballistic phonons in crystals and their detection with a detachable bolometer

Ballistic phonons were generated in single-crystalline sapphire samples by scanning the crystal surface with the electron beam in a scanning electron microscope equipped with a low-temperature stage. The phonons were detected using a superconducting thin film (granular Al) bolometer configuration which could be detached from the sample crystal (allowing repeated use). We have applied these experimental techniques for obtaining phonon images of laser-drilled holes in the sample crystals, achieving a spatial resolution of better than 10 m.     

Channeling of acoustic phonons in silicon: the polarization dependence in elastic scattering

Ballistic phonon flux in crystals at low temperatures is highly directional due to phonon focusing. In this paper, a phonon-imaging experiment is reported which shows that scattered phonons, too, can retain a highly directed flux. Basically, the combination of phonon focusing and the elastic-scattering selection rule act to channel phonons along the ballistic focusing directions. Together with Monte Carlo simulations, the experiments show that the scattered phonon flux is indeed due to elastic scattering processes, which depend on the polarizations of the scattering phonons. Isotropic scattering is inconsistent with the data. The experimental technique shows promise for quantifying the microscopic scattering processes and revealing the dynamics of a phonon hot spot.     

Imaging of crystal defects with ballistic phonons and their three-dimensional reconstruction using digital image processing

Spatial defects in single crystals were imaged with ballistic phonons by their shadow projections using low-temperature scanning electron microscopy. Digital image recording and processing was applied for a quantitative evaluation of the experimental results. We have investigated sapphire and -quartz samples with laser-drilled holes as special model cases of crystal defects. Computer algorithms have been developed to separate the shadows of the defects from the focusing pattern in the phonon images. We obtained binary images of the structures with a typical resolution of about 20 m. Cross-correlation functions of two images were found to be well suited for image alignment procedures. By this technique and from theoretically calculated phonon intensity distributions the bolometer positions within the experimental phonon images could be determined automatically. Using two phonon detectors at different locations stereoscopical imaging of the defects became possible. From the different views the three-dimensional distribution of the defects could be calculated.     

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.     

High Precision Characterisation of Semiconductor Bolometers

We describe techniques for testing and characterising semiconductor bolometers, using the bolometer model presented in Sudiwala et. al. [1]. The procedures are illustrated with results from a prototype bolometer for the high frequency instrument (HFI) in the Planck Surveyor cosmic microwave background mission. This is a bolometer using spider-web geometry and a neutron transmutation doped (NTD) germanium thermistor, designed for operation at 100 mK. Details are given of the laboratory facility used to take data at temperatures from 70 mK to 350 mK. This employs an adiabatic demagnetisation refrigerator to cool the detector and optics. The spatial and spectral properties of the optical system are controlled using feedhorns and edge filters. To characterise the bolometer, blanked and optically loaded load curves were measured over a range of temperatures, and the response to modulated radiation was measured as a function of modulation frequency, temperature and bias current. Results for the prototype bolometer show that its behaviour is well represented by an ideal thermal detector down to a temperature of approximately 100 mK. Below this, non-thermal effects such as electron-phonon decoupling or electric field dependent resistance appear to lead to departure from ideal behaviour. The performance was in good agreement with the design goals for the bolometer.     

Adiabatic electron-phonon interaction and high-temperature thermodynamics of A15 compounds

Inelastic neutron scattering was used to measure the phonon densities of states of the A15 compounds V3Si, V3Ge, and V3Co at temperatures from 10 to 1,273 K. It was found that phonons in V3Si and V3Ge, which are superconducting at low temperatures, exhibit an anomalous stiffening with increasing temperature, whereas phonons in V3Co have a normal softening behavior. First-principles calculations show that this anomalous increase in phonon frequencies at high temperatures originates with an adiabatic electron-phonon coupling mechanism. The anomaly is caused by the thermally induced broadening of sharp peaks in the electronic density of states of V3Si and V3Ge, which tends to decrease the electronic density at the Fermi level. These results show that the adiabatic electron-phonon coupling can influence the phonon thermodynamics at temperatures exceeding 1,000 K.     

Observation of the quasidiffusive propagation of phonons in Mg<Subscript>2</Subscript>SiO<Subscript>4</Subscript>:Ho<Superscript>3+</Superscript> using time-resolved photo-phonon spectroscopy

The energy flux of phonons produced due to the nonradiative laser-induced transitions of Ho³⁺ impurity ions in forsterite from the ⁵F₅ states has been measured using a superconductor bolometer at a temperature of 2 K. The dependence of the flux on the laser wavelength, the time elapsed after the action of a laser pulse, and the phonon propagation path length is analyzed. It is found that the excitation of Ho³⁺ to some states leads to the diffusive propagation of emitted phonons in the spontaneous frequency decay mode (quasidiffusive mode of propagation): the time of arrival of a phonon pulse is almost a linear function of the path length, but it is several times longer than the longest ballistic time of flight (for transverse phonons). The diffusion coefficient and the nonradiative relaxation time are determined from the best fit to the experiment.     

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-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.     

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.     

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.     

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.