Use of the Method of Images in Studying the Energy Spectra of the Surface States of Electrons or Holes in Three-layer Semiconductor–Dielectric–Conductor Structures

Abstract

For the potentials obtained by the method of images, we have found the surface states of an electron or a hole in three layer semiconductor-dielectric-conductor structures. For the arbitrarily thin layer of a dielectric, we deduced the exact formulas for the energy spectra En by the method of effective mass (En ~ 1/n2) and with regard for the discreteness of the crystal lattice of a semiconductor (En ~ √A + 1/n2). The surface states of an electron or a hole can be formed also in the two-layer semiconductor-dielectric structures in the cases where the permittivity of a dielectric is greater than that of a semiconductor. The obtained earlier exact solutions are applicable in this case as well. Other versions of the application of the method of images are discussed.