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.     

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     

Propagation of heat pulses in single-crystalline sapphire

We have studied heat-pulse propagation in single-crystalline sapphire using granular aluminum films for the heater and for the superconducting bolometer. The specimen surface carrying the bolometer was in direct contact with the liquid helium bath kept in the temperature range between 2.04 and 2.08 K. By varying the power during the heat pulse in the range between l mW and 2.8 W, we have observed the transition from purely ballistic pulse propagation at low power to diffusive propagation at higher power of the heat pulse. In the diffusive regime the phonon mean-free pathl has been experimentally determined and, using the Stefan-Boltzmann law, the variation ofl with the dominant phonon frequency has been found.     

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.     

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.     

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 linewidths in YNi<Subscript>2</Subscript>B<Subscript>2</Subscript>C

Phonons in a metal interact with conduction electrons which give rise to a finite linewidth. In the normal state, this leads to a Lorentzian shape of the phonon line. Density functional theory is able to predict the phonon linewidths as a function of wave vector for each branch of the phonon dispersion. An experimental verification of such predictions is feasible only for compounds with very strong electron-phonon coupling. YN₂B₂C was chosen as a test example because it is a conventional superconductor with a fairly high T _c (15.2 K). Inelastic neutron scattering experiments did largely confirm the theoretical predictions. Moreover, they revealed a strong temperature dependence of the linewidths of some phonons with particularly strong electron-phonon coupling which can as yet only qualitatively be accounted for by theory. For such phonons, marked changes of the phonon frequencies and linewidths were observed from room temperature down to 15 K. Further changes were observed on entering into the superconducting state. These changes can, however, not be described simply by a change of the phonon linewidth.      

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.     

Sources of loss processes in phonon generation and detection experiments with superconducting tunneling junctions

Observing the phonon yield, i.e. the ratio of the experimental phonon signal amplitude and the corresponding calculated value, phonon losses within the generation-detection system can be localized and determined quantitatively. With tin junctions on pure silicon substrates immersed in liquid helium the phonon yield is 3–5%. Under vacuum conditions the yield rises to 10–12% indicating strong phonon transmission to the helium bath. The experimental lifetime for 280 GHz phonons in the silicon substrate is longer than 65 µs indicating negligible volume losses and losses at the free substrate surface. It is further shown, that volume losses inside the phonon generator and detector are small compared to the total loss of about 90%. By phonon reverberation measurements we find evidence that the main sources for phonon losses are localized at the boundaries of the tunneling junctions to the substrate. This is supported by an increase of the phonon yield with improved polishing from about 9% (mechanical), 10% (chemical) to 12% (sputter etching). A SIMS analysis indicates the presence of carbonhydrates and probably of water in the boundaries. This layer of extraneous molecules together with the nonideal surface structure of the substrate and the evaporated films weakens the mechanical bonding between the tunnel junctions and the substrate and is possibly causing strong phonon splitting by anharmonic forces.     

Phonon transmission from incoherent radiators into quartz,sapphire, diamond,silicon and germanium within anisotropic continuum acoustics

The phonon excitation in monocrystals by phonon transmission from an adjacent incoherent phonon radiator is treated within continuum acoustics for several crystal cuts of sapphire, quartz, diamond, silicon and germanium. Whereas the theoretical treatment is made as general as possible, in numerical computation the radiator material is assumed to be mechanical isotropic, the monocrystal however anisotropic. For a diffuse phonon field with equilibrium distribution between the different polarizations in the radiator, the -space phonon intensity in the crystal substrate is calculated and presented graphically for the most important cases. Numerical values of halfspace emissivities as well as of the differential emissivities normal to the crystal faces are given for a large variety of material combinations.Supported by Bundesministerium für Forschung und Technologie     

Phonon structure in the tunneling characteristics of tin-lead sandwiches

A series of tunneling experiments have been performed on bilayers of tin and lead. Tunneling into the tin side of the proximity effect sandwhich the phonon structure of tin is readily observed in d²V/dI² vs V at 4.2 K where tin is a normal metal. The structure is very similar to that observed in tin alone below its transition temperature. In addition there appears some structure from the lead phonons which is strongly dependent on the thickness of the tin film.     

Role of phonons in superconductivity

Though the phonon mediated electron-electron interaction has been widely accepted as the cause of superconductivity, yet some doubts have been raised on the basis of the fact that many properties of superconductors are explained by employing a single Einstein frequency without taking a proper account of phonons in the superconductor. In order to check the role of phonons in superconductivity, we involve the whole of the phonon spectra for obtaining superconducting state parameters of seven superconductors, namely Mg, Zn, Be, Cd, A1, T1 and Pb in anisotropic as well as in isotropic phonon models. It has been observed that the electronphonon coupling strength and the transition temperatureT _c exhibit strong directional dependence and are sensitive to the phonons, reaffirming that the phonon mechanism is responsible for superconductivity. The computed values of isotope effect exponent and the interaction strengthN ₀ V also show similar trend, supporting the phonon mechanism.The authors express their sincere gratitude to Prof. C.M. Kachhava for many useful suggestions. They are also highly thankful to Dr. S. C. Jain for his kind cooperation. K. S. S. and R.S. are also thankful to the Principal of the M. S. J. College, Bharatpur for providing the necessary departmental facilities and to the U.G.C., New Delhi, for providing them with the financial assistance for this work.     

气相外延GaN的拉曼散射

测量了在蓝宝石衬底上气相外延生长GaN的拉曼散射谱.除观察到已被确认的两个E2,一个A1(TO)和一个E1(TO)声于振动以外,在734±3cm-1处观察到一个散射峰且从实验上确认其为GaN的纵向光学声子模E1(LO).而且发现其强度与外延层晶体质量密切相关.A1(TO)和高频E2散射峰相对强度变化显示不同生长条件引起的外延层质量的变化.     

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.     

Phonon focusing in quartz and sapphire imaged by electron beam scanning

Anisotropic phonon propagation and phonon focusing in single-crystalline -quartz and sapphire has been investigated using electron beam scanning for imaging the ballistic phonon propagation. The samples were circular disks of 20 mm diameter and 2.0 mm thickness. The phonons generated at the upper flat sample surface by the electron beam were detected with a small-size (43 m×41m) bolometer at the center of the opposite surface. The experiments were performed using a scanning electron microscope with a low-termperature stage. During electron irradiation of the upper sample surface the bottom of the sample was in direct contact with the liquid-He bath. For -quartz, also time-resolved imaging of the phonon intensity has been performed in addition to imaging of the time-integrated bolometer signal. Our results agree remarkably well with calculations by Rösch and Weis.Supported by a grant of the Deutsche Forschungsgemeinschaft     

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.     

Ab initio calculations of phonon spectra in ATiO3 perovskite crystals (A = Ca,Sr, Ba,Ra, Cd,Zn, Mg,Ge, Sn,Pb)

First-principles calculations of phonon spectra based on the density functional theory are carried out for calcium, strontium, barium, radium, cadmium, zinc, magnesium, germanium, tin, and lead titanates with a perovskite structure. By analyzing unstable modes in the phonon spectrum, the possible types of lattice distortion are determined and the energies of the corresponding phases are calculated. From analyzing the phonon spectra, force constants, and eigenvectors of TO phonons, a conclusion is drawn concerning the nature of ferroelectric phenomena in the crystals studied. It is shown that the main factors determining the possible appearance of off-center atoms in the A position are the geometric size and electronic configuration of these atoms.     

Reflection,transmission, and conversion of acoustic surface waves incident normally onto a quartz wedge with planeY,X-cut

The reflection, transmission, and conversion of an acoustic surface wave (SAW), incident normally onto the edge of a quartz wedge withY,X-cut planes are investigated as functions of the wedge angle. A maximum amplitude reflection coefficient of 80% was measured at 100° wedge angle.     

Creation of bulk elementary excitations in superfluid helium-II by helium atomic beams at low temperatures

The experimental results of creating bulk elementary excitations (BEEs) in isotopically pure liquid helium-II by helium atomic beams at low temperatures ～ 60 mK are presented. In the present experiment, BEE signals generated by ⁴He-atomic beams incident on the liquid free surface were detected by a bolometer positioned in the liquid helium-II. Some detected signals were very weak and depended on the heater power. Some examples of BEE detected signals are shown. Also, group velocities of the detected BEEs are evaluated and the threshold velocities of the helium atoms are discussed. The present experimental results demonstrate BEE creation, such as the third non-dispersive Zakharenko waves (supra-thermal phonons), with energies ～17 K (the Cooper pairing phenomenon doubles the supra-thermal phonon energy E _k ～ 2 × 17 K～34 K in order to fulfil the energy conservation law) in the positive roton branch of the BEE energy spectra by helium atomic beams with suitable energies ～ 35 K, which perturb the liquid surface at incidence points similar to heaters.