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 p
seudoparabolic 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, w
hich 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 n
m range. The combination of the two positive energies explains the dep
endence on d(-gamma) (with gamma =1.2-1.8) observed in some photoemiss
ion experiments and this dependence may be extended to other structure
s 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.