VIBRATIONAL PROPERTIES OF THIN-FILMS ADSORBED ON CRYSTALS WITH STRONGSPATIAL-DISPERSION

The effect of strong spatial dispersion of the substrate crystal onto the dynamics of thin epitaxially adsorbed films is described in a simp le model through the following quantities: i) phonon reflection coeffi cients ii) depth-dependent local densities of states (LDOS) and iii) f inite-life-time surface states called leaky waves. The correspondence of these three types of characteristics accessible in different experi mental methods is established. The bulk band of the substrate crystal consists of two distinct frequency ranges separated by an edge singula rity: above the singularity the substrate supports two different waves for a given frequency, whereas only one wave can exist for each frequ ency in the low-frequency range. The resonances in the low-frequency r ange are found to correspond to maxima in the LDOS, to maxima in the a mplitude of a near field arising in phonon reflection and to leaky wav es involving a single leakage wave packet. The antiresonances in the s ame frequency range are characterised by minima in LDOS and in the nea r field, whereas the corresponding leaky waves involve two leakage wav e packets. The only leaky waves found in the high-frequency range invo lve two leakage wave packets and are related to resonances. The antire sonances then are characterised by an anomalous increase in the extrao rdinary reflected wave. The edge singularity manifests itself in an ad ditional quasi resonance, whose features depend on the coupling betwee n the substrate and the thin film.