Dielectric-environment mediated renormalization of many-body effects in a one-dimensional electron gas

Relaxing the assumption of an “infinite and homogenous background,” the dielectric response function of one-dimensional semiconducting nanowires embedded in a dielectric environment is calculated. It is shown that a high-κ (higher than semiconductor dielectric constant) dielectric environment reduces the screening by the free carriers inside the nanostructure, whereas a low dielectric constant environment increases the Coulombic interaction between free carriers and enhances the strength of the screening function. In the long-wavelength limit, dielectric screening and collective excitations of electron gas are found to be strongly influenced by the environment. The behavior of the static dielectric function is particularly addressed at a specific wave vector q = 2kF , a wave vector that ubiquitously appears in charge transport in nanostructures. It is shown that the exclusion of the dielectric mismatch effect in free-carrier screening results in an erroneous charged impurity scattering rate, particularly for nanowires embedded in low-κ dielectrics.