Scaling and spatial analysis of the dielectric response of cadmium selenide nanowires

Transverse dielectric response of hexagonal cadmium selenide (CdSe) nanowires was investigated using first-principles quantum mechanical calculations. Scaling behavior of polarizability was found to closely follow a simple dielectric cylinder model even for small nanowires with a diameter of a few nanometers. The spatial dependence of the dielectric response in the nanowires was analyzed in terms of maximally localized Wannier functions in order to elucidate the model behavior. Localized $d$ electrons at cadmium atoms were found responsible for the simple analytic scaling of the polarizability, and the dielectric response in the center of nanowire was found converged to that of bulk already for 3 nm diameter nanowires.

Figure 1

Ball and stick cross-section representation of the four CdSe nanowires with nonpolar $\left(1\overline{1}00\right)$ lateral surfaces investigated in this work. See Table 1 for the structural details. Yellow (gray) spheres represent selenium (cadmium) atoms.

Figure 2

Projected charge differences on cadmium (Cd) and selenium (Se) atoms as a function of the surface layer at the CdSe $\left(1\overline{1}00\right)$ face, calculated with respect to the bulk values. Surface relaxation results in significant charge transfer in Cd-Se unit at the topmost layer.

Figure 3

Total transverse polarizability per unit length as a function of the nanowire radius squared $\left(R_2\right)$, evaluated from first-principles calculations (black) and by employing a dielectric cylinder model. The latter values were calculated by using either the DFT-PBE bulk dielectric constant (blue) or the experimental one (green). Percentage errors are shown in the right $y$ axis.

Figure 4

Density of Wannier states (DOWS) as a function of the local polarizability (see text) for NW-I (red), NW-II (orange), NW-III (green), and NW-IV (blue) as in listed in Table 1.

Figure 5

Spatially resolved local polarizability (a.u.) as defined in texts in $\left[1\overline{1}00\right]$ direction (top) and in $\left[11\overline{2}0\right]$ direction (bottom).

Figure 6

Density of Wannier states (DOWS) as a function of the local polarizability (see text), decomposed in terms of the nanowire concentric shell (see inset), and of the applied electric field direction, for NW-I (red), NW-II (organge), NW-III (green), and NW-IV (blue) as listed in Table 1.

Figure 7

Density of Wannier states (DOWS) as a function of the local polarizability (see text) for NW-IV passivated with trimethylphosphine at 50% coverage.

Figure 8

Density of Wannier states (DOWS) as a function of the local polarizability (see text) for NW-IV passivated with trimethylphosphine at 50% coverage, decomposed in terms of the nanowire shell and the electric field direction.

Figure 9

Spatially resolved local polarizability (a.u.) in $\left[1\overline{1}00\right]$ direction (left) and $\left[11\overline{2}0\right]$ direction (right) for the largest nanowire with the surfactants.