Scattering cross section of metal catalyst atoms in silicon nanowires

A common technique to fabricate silicon nanowires is to use metal particles (e.g., Au, Ag, Cu, Al) to catalyze the growth reaction. As a consequence, the fabricated nanowires contain small concentrations of these metals as impurities. In this work we investigate the effect of the metallic impurities on the electronic transport properties of silicon nanowires. The computational method is based on ab initio density functional theory together with nonequilibrium Green’s functions. From the computed transmission functions we extract a scattering cross section to characterize the scattering strength of the different metal atoms. We find that Au, Ag, and Cu impurities have very similar scattering cross sections, while Al differs from the rest. Impurities located in the center of the wires scatter significantly more than impurities close to or at the surface. The results for nanowires are compared with bulk Si scattering calculations and good agreement is found. This agreement shows that the scattering results for the ultrathin nanowires (which are computationally feasible) are not dominated by finite size or surface effects, and indicate that the results can be extended to larger and experimentally more relevant wires.

Figure 1

(Color online) Cross sections of a $D=12\text{Å}$ $⟨110⟩$ SiNW (a), a $D=17\text{Å}$ $⟨110⟩$ SiNW (b), and a $D=16\text{Å}$ $⟨111⟩$ SiNW (c). Bulk $4\times 3$ (110) direction (d) and $4\times 4$ (111) direction (e).

Figure 2

Schematic 2D drawing of the bulk scattering method. $k_{\perp }$ denote the transport direction, and the transmission is $k$ point sampled over $k_{\parallel }$.

Figure 3

(Color online) Transmission function through SiNWs containing a single substitutional Au impurity (solid lines), and corresponding pristine wires (dashed lines). (a) and (b) show hole and electron transport in a $D=12\text{Å}$ $⟨110⟩$ wire, (c) and (d) correspond to the $D=17\text{Å}$ $⟨110⟩$ wire, while (e) and (f) correspond to the $D=16\text{Å}$ $⟨111⟩$ wire.

Figure 4

(Color online) Scattering cross sections of $⟨110⟩$ wires (a) and (b) and of the $⟨111⟩$ wire (c) and (d). Bulk results are show with thick lines. The SiNW results are obtained from the transmission shown in Fig. 3.

Figure 5

(Color online) Transmission through $D=16\text{Å}$ $⟨111⟩$ SiNWs (a)-(b) with the Au atom in different positions: Substitutional in the center of the wire (solid), substitutional at the surface (dashed), interstitial in the center (small dotted), surface adatom (dash dotted). The pristine wire transmission is indicated by larger dots. Panels (c) and (d) show transmission through the $D=12\text{Å}$ $⟨110⟩$ SiNW with the Au in a substitutional and interstitial position in the center of the wire.

Figure 6

(Color online) Scattering cross section calculated with the bulk method. Filled and empty circles correspond to a substitutional Au position with transport in the $⟨110⟩$ and $⟨111⟩$ directions, respectively. Likewise, solid and dashed lines correspond to an interstitial Au position for transport in the $⟨110⟩$ and $⟨111⟩$ directions, respectively.

Figure 7

(Color online) Scattering cross section, $\sigma$, for substitutional positions in the center of the wires. (a) and (b) correspond to the $D=12\text{Å}$ $⟨110⟩$ wire, (c) and (d) to the $D=17\text{Å}$ $⟨110⟩$ wire, (e) and (f) to the $D=16\text{Å}$ $⟨111⟩$ wire.

Figure 8

(Color online) Scattering cross section, ${\sigma }^{\prime }$, given by Eq. (5) for the same data as shown in Figs. 4a, 4b.