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

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 (ωL∝k1/2) of the two-dimensional longitudinal mode at intermediate wave vectors (D^-1ka^-1) to the normal dispersion (ωL∝k) in the extremely-long-wavelength limit (kD1) due to screening effects is studied as a function of the ratio of insulator thickness D and lattice constant a.