Comparison between experimental and theoretical determination of the local structure of the $\mathrm{Ga}{\mathrm{As}}_{1-y}{\mathrm{N}}_y$ dilute nitride alloy

We present a combined experimental and theoretical study of the local structure of the $\mathrm{Ga}{\mathrm{As}}_{1-y}{\mathrm{N}}_y$ dilute nitride alloy. Experimental results obtained by x-ray absorption spectroscopy have been compared with first-principles density-functional supercell calculations and with the predictions of three different valence force field models. Both experiments and calculations find that inclusion of N induces static disorder in the $\mathrm{Ga}\text{−}\mathrm{As}$ bond length distribution. An increase of the $\mathrm{Ga}\text{−}\mathrm{As}$ bond length upon N incorporation in gallium arsenide has been observed; this is due to the competing effects of the decrease of the free lattice parameter and the tensile strain due to pseudomorphic growth. The different theoretical calculations reproduce more or less accurately this bond length expansion; we discuss the performance of the different valence force field models in predicting the measured bond lengths.

Figure 1

Background-subtracted Ga $K$-edge XAFS spectra; V106, $y=0.0084$; V112, $y=0.0142$; V118: $y=0.0268$.

Figure 2

Magnitude of the Fourier transforms of the Ga $K$-edge XAFS: experimental data (continuous line) and fits (dots).

Figure 3

Calculated $\mathrm{Ga}\text{−}\mathrm{As}$ bond length distributions at various N concentrations. The different symbols represent different values of $y$: from top to bottom $y=0.03,0.06,0.09$.

Figure 4

(a) Experimental composition dependence of the $\mathrm{Ga}\text{−}\mathrm{As}$ bond length compared to the predictions of first-principles DFT calculations and three different VFF models for strained alloys; bold continuous line, least-squares fit; dotted lines, $1\sigma$ error; dashed lines, $2\sigma$ error. (b) DFT and VFF predictions for unstrained alloys.

Figure 5

Simulated $\mathrm{Ga}\text{−}\mathrm{As}$ distance in epi-strained $\mathrm{Ga}{\mathrm{As}}_{1-y}{\mathrm{N}}_y$ vs N concentration. Solid line, linear fit; dashed lines connect data points and are a guide to the eye.

Figure 6

Comparison between predicted and measured variance trends as a function of N concentration $y$; symbols, experimental data; full line, prediction by $\mathrm{B}+\text{strain}$ model; dotted line, prediction by DFT calculations.