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     

Coherent phonon excitation in bismuth

Ultrafast time-resolved reflectivity of a bismuth thin film evaporated on a silicon substrate is measured to investigate coherent phonons in bismuth. The reflectivity result is analyzed by a linear chirp approximation to obtain the time dependent frequencies of coherent phonons. Not only the optical modes are detected, which are generated by a combination of impulsive stimulated Raman scattering and displacive excitation of coherent phonon, acoustic phonon modes are also observed, which are emitted by the A_1g optical phonon.     

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.     

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     

Phonon emission spectra of thin metallic films

Thin metallic films evaporated on an Al₂O₃-single crystal and cooled to liquid helium temperatures are heated by short electric current pulses. The high frequency part of the emitted phonons is detected by calibrated superconductive tunneling junctions on the opposite surface of the substrate. The observed phonon detector signal amplitude is compared with theoretical models taking account of the boundary conditions for elastic waves in the film. It is found that the phonon spectrum emitted perpendicularly to the substrate-film boundary depends strongly on the thickness of the heater film.     

Generation of nonequilibrium phonons in semiconductors and dielectrics by a pulse-heated metallic film: Model and experiment

Characteristics of a phonon generator in the form of a pulse-heated metallic film, viz., the time dependences of the film temperature and the kinetics of phonon ejection from the film into a substrate, are considered. The time dependences of the film temperature are calculated for cadmium telluride, diamond, and silicon substrates. It is shown that the duration of film cooling substantially exceeds the heating pulse length and the film continues to generate phonons with lower frequencies at the end of heating pulse. The inference is drawn that the film cooling should be correctly taken into account in analysis of the propagation of nonequilibrium acoustic phonons, specifically for phonon processes occurring in nanostructures.     

Fourier spectroscopy of radiative transitions between Landau levels in InSb

Radiative transitions between Landau levels were analyzed by Fourier spectroscopy in n-InSb. The experiments were carried out at cyclotron resonance frequencies below and above the optical phonons. Two types of transitions between Landau levels were observed, namely between free carrier states and between impurity states. Compared with absorption data the emitted lines are shifted to smaller energies. At energies above the LO phonon the emitted lines are affected by the electron-LO phonon coupling. An analysis of the line width revealed the important influence of self-absorption.     

Coherent phonons, nanoseismology and THz radiation in InGaN/GaN heterostructures

The ultrafast optical photoexcitation of hot electrons and holes in semiconductors by femtosecond laser pulses can trigger coherent phonon oscillations. We discuss the huge coherent acoustic phonons which have been generated in InGaN/GaN heterostructures and epilayers and how they might be used in imaging of surfaces and interfaces in nanostructures. We also discuss the THz radiation emitted from these phonons.     

Ultrafast switching of hard X‐rays

A new concept for shortening hard X‐ray pulses emitted from a third‐generation synchrotron source down to few picoseconds is presented. The device, called the PicoSwitch, exploits the dynamics of coherent acoustic phonons in a photo‐excited thin film. A characterization of the structure demonstrates switching times of ≤ 5 ps and a peak reflectivity of ～10^?3. The device is tested in a real synchrotron‐based pump–probe experiment and reveals features of coherent phonon propagation in a second thin film sample, thus demonstrating the potential to significantly improve the temporal resolution at existing synchrotron facilities.     

Quasiparticle recombination and 2Δ-phonon-trapping in superconducting tunneling junctions

The experimental recombination lifetime τ_eff of quasiparticles in superconducting films in general exceeds the intrinsic recombination lifetime τ _R by phonon trapping. On the basis of geometric acoustic propagation and reabsorption of phonons emitted in quasiparticle recombination, τ_eff is calculated as a function of film thicknessd taking into account longitudinal and transverse phonon reabsorption, bulk loss processes and acoustical phonon transmission into the substrate. With increasing thicknessd three characteristic ranges are found: range 1 with film thicknessd small compared to the phonon reabsorption mean free path Λ _w range 2 withd larger than Λ _w and dominating boundary losses, and range 3, also withd larger than Λ _w but with dominating bulk losses. For very smalld the relation between τ_eff and τ _R , the intrinsic recombination lifetime, contains only the limiting angle of total reflection of phonons within the superconducting film. Therefore, τ _R can be directly obtained by τ _eff measurements and from the sound velocities of the film-substrate system. Range 2 is characterized by a linear dependence of τ _eff ond. In this range it is not possible to obtain τ _R from τ _eff measurements, however, τ _eff allows a determination of the phonon boundary transmission. Range 3 shows no thickness dependence of τ _eff ond in the limit of larged values. In this range a further method for obtaining τ _R from τ _eff values is suggested.     

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.     

On the effect of phonon decay on electronic transitions in ionic crystal semiconductors

Generally electronic processes in semiconductors are accompanied by phonon excitations. These excitations themselves influence electronic transitions. On the other hand excited phonons decay by interaction with other impurities in the crystal, which act as a heat-bath. The resulting competition between phonon exciting electronic processes and phonon decay is described by Pauli's master equation. By expansion of its solutions into phonon decay solutions the problem can be separated into different decay equations for phonons and electrons as proposed by Stumpf. Assuming linear phonon-heat-bath coupling the phonon decay equation can be solved exactly by a generating function technique. The appropriate phonon decay frequencies are calculated for a simple heat-bath model.     

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.     

The kinetics of low-temperature electron-phonon relaxation in a metallic film following instantaneous heating of the electrons

The theoretical analysis of experiments on pulsed laser irradiation of metallic films sputtered on insulating supports is usually based on semiphenomenological dynamical equations for the electron and phonon temperatures, an approach that ignores the nonuniformity and the nonthermal nature of the phonon distribution function. In this paper we discuss a microscopic model that describes the dynamics of the electron-phonon system in terms of kinetic equations for the electron and phonon distribution functions. Such a model provides a microscopic picture of the nonlinear energy relaxation of the electron-phonon system of a rapidly heated film. We find that in a relatively thick film the energy relaxation of electrons consists of three stages: the emission of nonequilibrium phonons by “hot” electrons, the thermalization of electrons and phonons due to phonon reabsorption, and finally the cooling of the thermalized electron-phonon system as a result of phonon exchange between film and substrate. In thin films, where there is no reabsorption of nonequilibrium phonons, the energy relaxation consists of only one stage, the first. The relaxation dynamics of an experimentally observable quantity, the phonon contribution to the electrical conductivity of the cooling film, is directly related to the dynamics of the electron temperature, which makes it possible to use the data of experiments on the relaxation of voltage across films to establish the electron-phonon and phonon-electron collision times and the average time of phonon escape from film to substrate. Zh. éksp. Teor. Fiz. 111, 2106–2133 (June 1997)     

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.     

Influence of phonon dimensionality on electron energy relaxation

We studied experimentally the role of phonon dimensionality on electron-phonon (e-p) interaction in thin copper wires evaporated either on suspended silicon nitride membranes or on bulk substrates, at sub-Kelvin temperatures. The power emitted from electrons to phonons was measured using sensitive normal metal-insulator-superconductor tunnel junction thermometers. Membrane thicknesses ranging from 30 to 750 nm were used to clearly see the onset of the effects of two-dimensional (2D) phonon system. We observed for the first time that a 2D phonon spectrum clearly changes the temperature dependence and strength of the e-p scattering rate, with the interaction becoming stronger at the lowest temperatures below approximately 0.5 K for the 30 nm membranes.     

An electrohydrodynamics model for non-equilibrium electron and phonon transport in metal films after ultra-short pulse laser heating

The electrons and phonons in metal films after ultra-short pulse laser heating are in highly non-equilibrium states not only between the electrons and the phonons but also within the electrons. An electrohydrodynamics model consisting of the balance equations of electron density, energy density of electrons, and energy density of phonons is derived from the coupled non-equilibrium electron and phonon Boltzmann transport equations to study the nonlinear thermal transport by considering the electron density fluctuation and the transient electric current in metal films, after ultra-short pulse laser heating. The temperature evolution is calculated by the coupled electron and phonon Boltzmann transport equations, the electrohydrodynamics model derived in this work, and the two-temperature model. Different laser pulse durations, film thicknesses, and laser fluences are considered. We find that the two-temperature model overestimates the electron temperature at the front surface of the film and underestimates the damage threshold when the nonlinear thermal transport of electrons is important. The electrohydrodynamics model proposed in this work could be a more accurate prediction tool to study the non-equilibrium electron and phonon transport process than the two-temperature model and it is much easier to be solved than the Boltzmann transport equations.     

Quantum tunneling of light particles in metals

The motion of a particle in a metallic crystal is studied for low temperatures where transitions between adjacent interstitial sites are caused by quantum tunneling. The influence of electrons and phonons on the hopping rate is taken into account by means of a functional integral method. The electronic influence may effectively be described by Ohmic damping which dominates the low temperature behavior of the defect motion. When subsequent tunneling transitions are statistically independent, the diffusion constant is found to obey a power law, D∼T^2K−1, where K depends on the defect-electron interaction. This power law is limited at low temperatures by the effects of phonon excitations. Near the transition between electron and phonon dominated behavior the diffusion constant has a minimum where the precise temperature dependence of the rate depends not only on phonon spectra but also on the processes limiting phonon lifetimes.     

Elastic and inelastic tunneling of photoelectrons from the dimensional quantization band at a p +-GaAs-(Cs,O) interface into vacuum

The photoemission of electrons from a p ⁺-GaAs surface with negative electron affinity was studied experimentally at 4.2 K. A narrow peak and its phonon replicas were observed in the distribution of emitted electrons over the energies of longitudinal motion. These replicas are caused by elastic and inelastic electron tunneling from the bottom of the dimensional quantization band in the near-surface spatial-charge region through the potential barrier of the (Cs,O) activating coverage with emission of LO phonons. The measured position of the peak corresponding to elastically tunneling electrons is close to the calculated one.     

Low-temperature anisotropy of the thermal conductivity of single-crystal nanofilms and nanowires

The effect of phonon focusing on the phonon transport in single-crystal nanofilms and nanowires is studied in the boundary scattering regime. The dependences of the thermal conductivity and the free path of phonons on the geometric parameters of nanostructures with various elastic energy anisotropies are analyzed for diffuse phonon scattering by boundaries. It is shown that the anisotropies of thermal conductivity for nanostructures made of cubic crystals with positive (LiF, GaAs, Ge, Si, diamond, YAG) and negative (CaF₂, NaCl, YIG) anisotropies of the second-order elastic moduli are qualitatively different for both nanofilms and nanowires. The single-crystal film plane orientations and the heat flow directions that ensure the maximum or minimum thermal conductivity in a film plane are determined for the crystals of both types. The thermal conductivity of nanowires with a square cross section mainly depends on a heat flow direction, and the thermal conductivity of sufficiently wide nanofilms is substantially determined by a film plane orientation.