  Relaxing the assumption of "infinite and homogenous background" the
dielectric response function of one-dimensional (1D) semiconducting nanowires
embedded in a dielectric environment is calculated. It is shown that high-k
(higher than semiconductor dielectric constant) dielectric environment reduces
the screening by the free carriers inside the nanostructure whereas, low
dielectric environment increases the Coulombic interaction between free
carriers and enhances the strength of screening function. In long wavelength
limit, dielectric screening and collective excitation of electron gas are found
to be solely determined by the environment instead of the semiconductor.
Behavior of static dielectric function is particularly addressed at a specific
wavevector q=2k_F; a wavevector ubiquitously appears in charge transport in
nanostructures
