Stability and image-potential-induced screening of electron vibrational excitations in a three-layer structure

Abstract

The relative static stability of square and triangular electron lattices (two-dimensional Wigner crystals), the instability against vibrational excitations, and the effect of image-potential-induced screening on the dispersion of the frequency spectra are studied in the inversion layer of a metal-insulator-semiconductor structure. In harmonic approximation the two-dimensional Wigner crystal turns out to be stable against transverse vibrations for a triangular lattice but unstable for a square lattice in the [10] direction in disagreement with previous calculations. In triangular lattices, the transition of the anomalous dispersion (${\ensuremath{\omega}}_{L}\ensuremath{\propto}{k}^{\frac{1}{2}}$) of the two-dimensional longitudinal mode at intermediate wave vectors (${D}^{\ensuremath{-}1}\ensuremath{\ll}k\ensuremath{\ll}{a}^{\ensuremath{-}1}$) to the normal dispersion (${\ensuremath{\omega}}_{L}\ensuremath{\propto}k$) in the extremely-long-wavelength limit ($\mathrm{kD}\ensuremath{\ll}1$) due to screening effects is studied as a function of the ratio of insulator thickness $D$ and lattice constant $a$.