Strain relaxation and band-gap tunability in ternary ${\text{In}}_x{\text{Ga}}_{1-x}\text{N}$ nanowires

The alloy formation enthalpy and band structure of InGaN nanowires were studied by a combined approach of the valence-force field model, Monte Carlo simulation, and density-functional theory (DFT). For both random and ground-state structures of the coherent InGaN alloy, the nanowire configuration was found to be more favorable for the strain relaxation than the bulk alloy. We proposed an analytical formula for computing the band gap of any InGaN nanowires based on the results from the screened exchange hybrid DFT calculations, which in turn reveals a better band-gap tunability in ternary InGaN nanowires than the bulk alloy.

Figure 1

(Color online) Lowest energy structures for (a) bulk ${\text{In}}_{0.5}{\text{Ga}}_{0.5}\text{N}$ alloy and (b) ${\text{In}}_{0.5}{\text{Ga}}_{0.5}\text{N}$ NW. Here red/gray or white arrows in (b) indicate two N atoms bonded with $3\text{In}+1\text{Ga}$ or $3\text{Ga}+1\text{In}$.

Figure 2

(Color online) (a) Illustration for the core-shell model. (b) Strain energy dependence of ${\text{In}}_{0.5}{\text{Ga}}_{0.5}\text{N}$ NWs upon the radius of the NWs. The solid line is the fitted result according to the core-shell model [Eq. (2)]. The strain energies of the core part $\left(E_c\right)$ and shell part $\left(E_s\right)$ are indicated by horizontal lines.

Figure 3

(Color online) Estimated HSE06 band gaps (in eV) for ${\text{In}}_x{\text{Ga}}_{1-x}\text{N}$ NWs with the diameters $D$ using Eq. (6). The solid line is the contour line with $E_g=2.3\text{eV}$.