Earlier results had indicated, under some conditions, a discrepancy between the observed spectral distribution of phonons produced by the heat-pulse method and the distribution predicted by the acoustic-mismatch model. Through additional measurements of the film temperature we show that the discrepancy can be resolved in terms of diffusive scattering at foreign and isotopic impurities in the bulk of the substrate.We have previously reported" the spectral, spatial, and temporal distribution of phonons which cross from a Joule-heated metallic thin film into a singlecrystal insulating substrate. Experimental observations were made through a vibronic interaction between the phonons and probe ions in the substrate.It was demonstrated, for a substrate of SrF2 containing 0.1-mole '/0-Eu + probe ions, that there is little change in the relative spectral distribution of the net phonon flux crossing the interface as the magnitude of the Joule heating of a Constantan metal film is varied over the range of 25 to 5000 W/mm'. This result differs from earlier results at lower power' and is in contradiction with the standard acousticmismatch (AM) model4 and its extensions, 5 which predict an ever increasing fraction of high-frequency phonons with increased heating. Since much of the -earlier and current work on the so-called "heat-pulse" method has been interpreted in terms of the AM model it is important that the discrepancy between the experimental results of Ref. 1 and the model predictions be resolved. It was also demonstrated in Ref. 2 that phonons entering the SrF2 substrate are diffusively scattered with a probability that increases with increasing phonon frequency, v. As a result, high-frequency phonons (v & 0.6 THz) spend long periods of time ( &. 10~s ec) very close to the film-substrate interface. These observations have led to the development of a model treatment of the spectral distribution of phonons emitted by a metallic film heater into a diffusive medium. Using parameters which correspond to the experimental conditions, ' it was shown that the calculated spectral distributions are similar to those observed. Yet, the data of Ref. 1 and 2 are insufficient to prove unambiguously the necessity of the model, since the results may be explained as well by a frequency-dependent transmission of ballistic phonons through the interface; i.e. , as a surface matching effect. However, as a necessary consequence of strong scattering of the highfrequency phonons in the bulk of the substrate, the model treatment predicts, in addition, that the instan-taneous "temperature", and therefore the instantaneous electrical resistance, of the metal film should increase with time as it is electrically driven, and decay slowly thereafter. ' The physical cause of this effect is the piling up of high-frequency phonons near the interface in the substrate. These phonons are readily scattered back into the heater film thereby reducing the film's net emission of energy. Only the lowerfrequency phonons propagate in the substrate with relative eas...
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