Dielectric image potential of charges in 2D quantum structures

A classical analysis is made of the image potential energy of a point charge in a semiconducting or an insulating 2D quantum well. Expressed as a function of the thickness, d, of the well, this energy takes a pseudoparabolic form: E(i)= (a/d)+ (bz(2)/d(3))+... and the parameters a and b are positive when the permittivity of the well is larger than that of its symmetrical surroundings; the charge is then self-trapped in the well. For systems such as SiO2/Si/SiO2 where the difference in the dielectric constants is significant this image potential energy, which varies as d(-1) (first order), is of the same order of magnitude as the confinement energy (which varies as d(-2)) when d is in the 4 nm range. The combination of the two positive energies explains the dependence on d(-gamma) (with gamma =1.2-1.8) observed in some photoemission experiments and this dependence may be extended to other structures such as wires and dots. When an external electric field is applied, the same analysis permits us to estimate the lowering of the Schottky barrier on the external (SiO2) side as a function of the thickness, d, of the (Si) well.