First-principles study of GaAs nanowires

In this paper we present a detailed analysis of the atomic and electronic structures of GaAs nanowires using first-principles pseudopotential calculations. We consider six different types of nanowires with different diameters all grown along [111] direction, and we reveal interesting trends between cohesive energy and nanowire type with varying diameters. Generally, the average cohesive energy of nanowires with wurtzite stacking is higher than those with zinc-blende stacking for small diameters. We found that most of the bare nanowires considered here are semiconducting and continue to be semiconducting upon the passivation of surface dangling bonds with hydrogen atoms. However, the surface states associated with the surface atoms having two dangling bonds in zinc-blende stacking occur in the band gap and can decrease the band gap to change the nanowire from semiconducting to metallic state. These nanowires become semiconducting upon hydrogen passivation. Even if the band gap of some nanowires decreases with increasing diameter and hence reveals the quantum confinement effect, generally the band-gap variation is rather complex, and depends on the type and geometry, diameter, type of relaxation, and also whether the dangling bonds of surface atoms are saturated with hydrogen.

Figure 1

(Color online) Ideal and relaxed atomic structures of bare GaAs nanowires considered in this paper. Numerals given in parenthesis indicate the crystallographic directions perpendicular to the surfaces. Numerals given to the bottom left of the structures stand for the number of atom pairs per unit cell $N$. $wz$ and $zb$ stand for structures having wurtzite and zinc-blende stackings.

Figure 2

(Color online) Cohesive energy per Ga-As atom pair versus number of Ga-As atom pairs in the unit cell of different type of relaxed nanowires. Horizontal axes presented inside the figure are derived by fitting the diameter versus number of atom data of $wz$ and $zb$ nanowires to quadratic polynomials. Since $wz$ and $zb$ structures have different number of atomic planes in the unit cell, the fitting was done separately.

Figure 3

(Color online) Band structure and charge-density isosurface plots of GaAs nanowires having $wz1$ structure. Energy band gap between the valence and conduction bands is shaded. Numerals given on top of the bands stand for the number of GaAs atom pairs $N$ in the unit cell. Charge density isosurfaces of specific states at $\Gamma$ point are shown on the right-hand side of the bands they belong to. Isosurface charge densities correspond to three valence-band and three conduction-band edge states, ordered in the same manner as bands themselves are. Here we also give the band structure of infinite slab of bulk wurtzite structure consisting 11 atomic layers with the same planar $\left(10\overline{1}0\right)$ surfaces as $wz1$ nanowires does. Zero of energy is set at the Fermi level $E_F$.

Figure 4

(Color online) Same as in Fig. 3 but for $wz2$ structure. Isosurface charge densities correspond to three valence-band and three conduction-band edge states, ordered in the same manner as bands themselves are.

Figure 5

(Color online) Band structure and charge-density isosurface plots of GaAs nanowires having $wz3$ structure. Energy band gap between the valence and conduction bands of bare nanowire is (yellow) light shaded. Numerals given on top of the bands stand for the number of GaAs atom pairs $N$ in the unit cell. Charge density isosurfaces of specific states at $\Gamma$ point are shown on the right side of the bands they belong to. Isosurface charge densities correspond to three valence-band and three conduction-band edge states, ordered in the same manner as bands themselves are. Here we also give the band structure of infinite slab of bulk wurtzite structure consisting 11 atomic layers with the same planar $\left(10\overline{1}0\right)$ surfaces as $wz3$ nanowires does. Zero of energy is set at the Fermi level $E_F$. The widening of the band gap upon the termination of dangling bonds by hydrogen is shown by (green) dark-shaded regions delineated by black curves at the valence- and conduction-band edges.

Figure 6

(Color online) Interatomic distance distribution of the core and shell parts of bare and hydrogen saturated $wz3–96$ structures. The ball and stick model illustrates the structure of $wz3–96$ nanowire while the shaded regions defines the core and shell parts of the nanowires. (a) Interatomic distance distribution of interior atoms of bare nanowire. (b) Interatomic distance distribution of exterior atoms of bare nanowires. (c) Interatomic distance distribution of hydrogen passivated exterior atoms. (d) Local density of states on surface atoms (green/light) and on the remaining atoms (blue/dark) of bare nanowire. (e) Same as (d) after passivation of surface atoms with hydrogen.

Figure 7

(Color online) Band structure and charge-density isosurface plots for $A$ wires.

Figure 8

(Color online) Band structure and charge-density isosurface plots of GaAs nanowires having $zb1$ structure. Energy band gap between the valence and conduction bands of bare nanowire is (yellow) light shaded. Numerals given on top of the bands stand for the number of GaAs atom pairs $N$ in the unit cell. Charge density isosurfaces of specific states at $\Gamma$ point are shown on the right-hand side of the bands they belong to. Isosurface charge densities correspond to three valence-band and three conduction-band edge states, ordered in the same manner as bands themselves are. Here we also give the band structure of infinite slab of bulk wurtzite structure with the same planar $\left(11\overline{2}\right)$ surfaces as $zb1$ nanowires does. Zero of energy is set at the Fermi level $E_F$. The widening of the band gap upon the termination of dangling bonds by hydrogen is shown by (green) dark-shaded regions for $N=31$, 73, and surface.

Figure 9

(Color online) Same as in Fig. 8 but for $zb2$ structure. The shaded region in the band structure of $zb2–37$ corresponds to the band gap opened after the passivation of dangling bonds with hydrogen. $zb2–19$ and $zb2–61$ nanowires are not passivated with hydrogen