  Low field response function calculations have been performed on a
two-dimensional electron gas with well-defined electron-surface roughness
scattering. The Lindhard model was employed to compute the response function.
In particular, detailed investigations were made on the system searching for an
interplay between surface roughness with well-defined correlation function,
(characterizes by asperity height and correlation length) spatial confinement
and the dielectric function. We analyze to what extent the normal behavior and
functionality of dielectric function of two-dimensional devices are modified by
random scattering events caused by the contribution from the surface roughness.
Results of the current work indicate that contribution of the surface roughness
on scattering and absorption process could not be considered as an
underestimating effect. We find, however, that functionality of the dielectric
function seems to be quite independent of the particular roughness features.
