Vibrational properties of thin films adsorbed on crystals with strong spatial dispersion

Abstract

The effect of strong spatial dispersion of the substrate crystal onto the dynamics of thin epitaxially adsorbed films is described in a simple model through the following quantities: i) phonon reflection coefficients ii) depth-dependent local densities of states (LDOS) and iii) finite-lifetime surface states called leaky waves. The correspondence of these three types of characteristics accessible in different experimental methods is established. The bulk band of the substrate crystal consists of two distinct frequency ranges separated by an edge singularity: above the singularity the substrate supports two different waves for a given frequency, whereas only one wave can exist for each frequency in the low-frequency range. The resonances in the low-frequency range are found to correspond to maxima in the LDOS, to maxima in the amplitude of a near field arising in phonon reflection and to leaky waves involving a single leakage wave packet. The antiresonances in the same frequency range are characterised by minima in LDOS and in the near field, whereas the corresponding leaky waves involve two leakage wave packets. The only leaky waves found in the high-frequency range involve two leakage wave packets and are related to resonances. The antiresonances then are characterised by an anomalous increase in the extraordinary reflected wave. The edge singularity manifests itself in an additional quasi resonance, whose features depend on the coupling between the substrate and the thin film.