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 (${\omega }_L\propto k^{\frac{1}{2}}$) of the two-dimensional longitudinal mode at intermediate wave vectors ($D^{-1\mathrm{}}\ll k\ll a^{-1\mathrm{}}$) to the normal dispersion (${\omega }_L\propto k$) in the extremely-long-wavelength limit ($\mathrm{kD}\ll 1$) due to screening effects is studied as a function of the ratio of insulator thickness $D$ and lattice constant $a$.