  We analyze the results of scanning near-field infrared spectroscopy performed
on thin films of a-SiO2 on Si substrate. The measured near-field signal
exhibits surface-phonon resonances whose strength has a strong thickness
dependence in the range from 2 to 300 {nm}. These observations are compared
with calculations in which the tip of the near-field infrared spectrometer is
modeled either as a point dipole or an elongated spheroid. The latter model
accounts for the antenna effect of the tip and gives a better agreement with
the experiment. Possible applications of the near-field technique for depth
profiling of layered nanostructures are discussed.
