PHONON TRANSMISSION ALONG SAPPHIRE PLATES

Abstract

Experiments are reported in which high frequency phonons, both thermally distributed and monochromatic, are generated and detected on a sapphire single crystal substrate at temperatures between 0.3 OK and 1 O K . Inelastic processes in the system (revealed by using superconducting tunnel junctions as high pass detectors of the monochromatic phonons) and the thermal bonding of the sapphire to a copper block are investigated. Introduction. Experiments have been carried out in which monochromatic and broad band thermal phonons are generated and detected in thin films evaporated on synthetic sapphire single crystals. Copper heaters were used to generate the thermal phonons and superconducting aluminium tunnel junctions to generate the monochromatic phonons. When a junction is biased at or above the gap edge (2 A, the energy gap in aluminium) the main current carrying process is the breaking of ground state pairs which injects excitations into both films. The recombination of these excitations to Cooper pairs releases energy as phonons at the gap frequency, 2 Alh. The tunnel junctions were also used to detect both thermal and gap frequency phonons. When the junction is biased at less than 2 A the current is due solely to the tunnelling of excitations present in the films. The number of excitations increases with temperature as exp(AlkT) and thus the cc within-gap current )) (which is approximately proportional to the number of excitations) can be used as a thermometer. Monochromatic phonons of energy 2 2 A entering the junction films can break Cooper pairs, creating extra excitations and hence extra current which will be a measure of the number of phonons arriving. The number of extra excitations in the films when monochromatic phonons are incident is proportional to the lifetime of excitations to recombination. This is inversely proportional to the number of thermal excitations and therefore proportional to exp(A/kT). The signal therefore increases with decreasing temperature. The generator was fed with a constant current chopped at a frequency of 80 Hz and the detected (*) Supported during this work by a Science Research Council Grant. signal was measured using a Princeton HR 8 cr lockin )> amplifier. For most of the experiments the relevant relaxation and propagation times in the system were shorter than the chopping period, so that detected signals correspond to steady state conditions. The experiments were performed in a He3 cryostat, the sapphire being bonded to a copper block one end of which formed the bottom of the He3 pot. A minimum temperature of .29 OK was attainable. The signals obtained using copper heaters are a measure of the local temperature change and this is made up to temperature drops across all thermal resistances to the He3 bath. The monochromatic phonons (which have an equivalent temperature T = hvlk > 4 OK) are rapidly thermalized by the electrons in the copper, so only thermal resistances before the copper block will affect the signal. Because the tunnel junction is a high pass detector, any inelastic processes will show up as a loss of signal. For monochromatic phonons each junction on the crystal can be used as generator or detector. Thus with an array of n junctions, a rr transfer sensitivity )) (detected current + generator current) can be measured for each pair. These results can be most easily displayed in an nxn matrix, where the element (i, j ) is the transfer sensitivity with the ith junction as detector and the jth junction as generator. The detector sensitivity is inversely proportional to the normal resistance of the junction, so that matrix is normalised to 1 ohm detectors. Once normalized the matrix should be symmetric : this can be seen by considering the phonon flow for the case of diffuse flow, we can compare the system to a passive electrical network where two nodes have a transfer resistance (independent of direction). Considering direct flight of phonons, the reversibility of flight paths must give Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1972414