Investigation of the Kapitza Anomaly by Frequency-Resolved Phonon Transport in Silicon Wafers

The threshold at 85 GHz for anomalously large transmission of phonons into LHe has been investigated with Si-wafers for various surface treatments and coverages by phonon spectroscopy. With this multiple boundary scattering geometry we observe an increased sensitivity to spectral features. Connected with the threshold there is a phase shift of the signal compatible with a loss of the slower diffuse portion of the phonon signal to the covering liquid helium. This phase shift depends nonlinearly on modulation frequency between 5 kHz and 200 kHz (modulation of the generator to sort out the monochromatic phonons) and in a characteristic manner on the surface treatment. The finite phase shift at 5 kHz is indicative of very long lived 85 GHz phonons up into the 100 µs is range inspite of the multiple Si-LHe-interface scattering involved. Minor differences in polishing quality show up clearly in the phase shift at low modulation frequencies.