Fermi-level pinning can determine polarity in semiconductor nanorods

First-principles calculations of polar semiconductor nanorods reveal that their dipole moments are strongly influenced by Fermi-level pinning. The Fermi level for an isolated nanorod is found to coincide with a significant density of electronic surface states at the end surfaces, which are either mid-gap states or band-edge states. These states pin the Fermi level, and therefore fix the potential difference across the rod. We provide evidence that this effect can have a determining influence on the polarity of nanorods, with consequences for the way a rod responds to changes in its surface chemistry, the scaling of its dipole moment with its size, and the dependence of polarity on its composition.

Figure 1

Structurally relaxed, fully hydrogen terminated GaAs nanorod (left) and the LDOS (right) for each slab, consisting of four planes of atoms (two As and two Ga). The filled curves indicate the occupied (valence) states at each slab. The band-edge states at opposite ends of the rod are seen to coincide in energy.

Figure 2

The difference in laterally integrated electron density profiles between H/H and H/P. The standard deviation of the Gaussian used to smooth the data parallel to the nanorod axis is 0.32 nm. There has been a shift of 6.70 electrons from left to right. We show that the majority of this redistribution is attributable to changes in surface state occupancy.

Figure 3

Local densities of states for the slab of atoms on the Ga-rich (top) and As-rich (bottom) ends of nanorods H/H and H/P. The potential difference between the two ends $\Delta V\sim 1.8$ eV for H/H and $1.5$ eV for H/P.

Figure 4

The magnitude of the dipole moment increases linearly with nanorod length for nanorods of cross-sectional area $A=3.56{\text{nm}}^2$.

Figure 5

The magnitude of the dipole moment increases with nanorod cross sectional areas for nanorods of length $L=12.8\text{nm}$. Curves are fitted to the data, with functional forms $\sigma \left(A\right)=c_1/(\sqrt{A}+c_2-\sqrt{A+c_2^2})$ and $d_z=c_{3}A/(\sqrt{A}+c_2-\sqrt{A+c_2^2})$, derived from Eq. (3). Over this range $\sqrt{A}\ll c_2$, placing these rods firmly in the “thin” regime.

Figure 6

Slab-wise local densities of states for rods of four different cross-sectional areas, sampled at three positions on the rod: (top) the slab on the Ga-rich end, (middle) the slab in the middle of the rod, and (bottom) the slab on the As-rich end. For ease of comparison, we have shifted the energy of the highest occupied state for each rod to zero. The Fermi level can be imagined to remain adjacent to the band edges for all rods, and the band-gap is larger for thinner rods due to quantum confinement.

Figure 7

Laterally averaged and Gaussian-smoothed charge distributions along the lengths of nanorods of AlN, GaN, and GaAs. The ordinate has been magnified in the lower panel.

Figure 8

Local densities of states of the cation-rich (top three data sets) and anion-rich (bottom three data sets) polar surfaces of AlN, GaN, and GaAs. For ease of comparison, we have shifted the energy of the highest occupied state of each rod to zero.