Structural properties and energetics of intrinsic and Si-doped GaAs nanowires: First-principles pseudopotential calculations

We investigate by first-principles pseudopotential calculations the structural properties and the energetics of undoped and Si-doped unpassivated GaAs nanowires (NWs). On the basis of total energy calculations for the undoped NWs as a function of diameter we find that, in contrast to the bulk phase, wurtzite (WZ) NWs are more stable than zincblende (ZB) NWs for diameters up to about 50 Angstrom. We also investigate the preferential position of Si dopants in GaAs WZ NWs: we find that donors segregate to the surface, while acceptors prefer inner positions. On the basis of the formation energy study, the stability ranges for Si donor and acceptor sites are similar to the bulk ZB case, with a slight increase in the stability range for donor sites. However, in contrast to acceptors, donors preferentially segregate to surface dangling-bond sites at large NW diameters, and act as deep impurities, rather than shallow donors, thus hindering $n$-type conductivity. This could contribute to explain the preferential $p$-type behavior which was observed in recent experiments on Si-doped NWs grown by molecular-beam epitaxy, in addition to other possible effects, including, e.g., the kinetics of Si incorporation.

Figure 1

(Color online) Ball and stick three-dimensional and top views of ZB and WZ structures along [0001] and [111] directions, respectively; $a,b,c$ indicate the nonequivalent anion-cation double layers. In the top views, the natural cleavage (110) and (112) planes for ZB and $\left(10\overline{1}0\right)$ and $\left(11\overline{2}0\right)$ planes for WZ are indicated.

Figure 2

(Color online) Ball and stick models of WZ-H(54,54) and WZ-H(42,42) NWs characterized by $\left(10\overline{1}0\right)$ and $\left(11\overline{2}0\right)$ facets, respectively. Top views are shown and for the sake of simplicity the atomic positions are unrelaxed.

Figure 3

(Color online) Ball and stick models of the WZ-H(54,54) NW characterized by $\left(10\overline{1}0\right)$ facets: unrelaxed (left) and relaxed (right) top and side views.

Figure 4

(Color online) Cohesive energy [Eq. (1)] as a function of diameter for undoped GaAs nanowires with ZB and WZ structures. Large circles and triangles are from full SCF calculations; small symbols and interpolating lines are drawn according to Eq. (2). The bulk limits are also indicated. For the sake of simplicity, in these ball and stick models the atomic positions are unrelaxed.

Figure 5

(Color online) Surface formation energy as a function of the diameter of undoped GaAs WZ NWs characterized by $\left(10\overline{1}0\right)$ and $\left(11\overline{2}0\right)$ facets, compared with the corresponding infinite surfaces. Among the NWs with $\left(11\overline{2}0\right)$ facets, only WZ-H(42,42) is reported here.

Figure 6

(Color online) Si donor (left panel) and acceptor (right panel) relative formation energy in some NWs characterized by $\left(10\overline{1}0\right)$ facets. Results for centerlike, surface threefold, and subsurface fourfold coordinated positions (${\text{S}}_1$ and ${\text{S}}_2$, respectively) are shown. A distinction is made for ${\text{S}}_1$: corner $\left(S_{1c}\right)$ or middle of facets $\left(S_{1f}\right)$ positions. Single $\left(c=c_0\right)$ and double size $\left(c=2c_0\right)$ structures along the NWs growth direction are compared.

Figure 7

(Color online) Si donor (left panel) and acceptor (right panel) relative formation energy in a slab with the $\left(10\overline{1}0\right)$ exposed surface in different positions with respect to the surface: first, second, third, and fifth layer. The value for the substitution in bulk is also reported for comparison. Comparison with the unrelaxed case (lower part) is also shown.

Figure 8

(Color online) Formation energy relative to Si chemical potential, $\Delta \Omega ={\Omega }_f+{\mu }_{\text{Si}}-{\mu }_{\text{Si}}^{bulk}$, of Si donors/acceptors as a function of the difference $\Delta \mu$ of Ga and As chemical potentials in bulk ZB, bulk WZ, and in WZ-H(54,54) MW. The solid lines correspond to the fourfold coordinated site ($S_2$ site in the case of the surface and NW); the dashed lines correspond to the threefold coordinated ${\text{S}}_1$ surface site (see text) which acts as a trap for carriers. The physically accessible range of $\Delta \mu$ is indicated by the dotted lines.