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-$\kappa$ (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 $q=2k_F$, 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-$\kappa$ dielectrics.

Figure 1

Dielectric function of a nanowire (a) with nanowire radius ($R$) and (b) as a function of carrier density ($n$) for three different dielectric environments of ${\epsilon }_e=1$ (upper branch), ${\epsilon }_e={\epsilon }_s=13$ (middle), and ${\epsilon }_e=100$ (lower branch).

Figure 2

(a) Dielectric function of a nanowire with temperature ($T$) and (b) plasma frequency of an 1DEG with wave vector ($q$) for three different dielectric environments.

Figure 3

Screened Coulomb scattering rate with (solid) and without (dashed) incorporating the dielectric mismatch in static screening at (a) low temperature, and at (b) room temperature as a function of dielectric constant of the environment. Here we assumed an impurity density $n_{\text{imp}}=2.5\times {10}^5/\text{cm}$.