Mechanical Properties in Dilute Nitrides

An ab initio approach
The equilibrium configuration achieved for a nitrogen pair interstitial.
The equilibrium configuration achieved for a nitrogen pair interstitial.

Besides the large reduction of the energy gap, experimental and theoretical N alloying of GaAs also produces a decrease of the lattice and elastic constants, and an increase of the conduction band effective mass. This work focus on the mechanical properties, specifically on the lattice and elastic constants as functions of the nitrogen concentration [1]. We study the range of validity of the Vegard's law for the lattice constants, as well as the bowing coefficients for the elastic constants. In particular, we show a strong deviation from the Vegard's law for the lattice constants in crystals whose As atoms have been replaced by a N-N, or an N-As molecules (Interstitial Substitution, IS), and we supply a set of ab initio bowing coefficients for the C11 and C12 elastic constants, whose ratios were previoulsy taken from other materials (GaInSb and SiGeC) to analyse experiments on GaAsN [R. S. Goldman, 2].

Interstitial substitutions in GaAsN alloys: atomic structures
Two configurations have been numerically studied with ABINIT. The first (second) deals with an N2 (NAs) IS in a pure GaAs crystal. The figure shows the equilibrium configuration achieved for a N2 IS.

Lattice and elastic constants for normal and interstitial substitutions in GaAsN alloys

The figure exhibits the elastic constant as functions of the nitrogen concentration for normal substitution (NS) and interstitial substitution (IS) crystals. Both NS and IS exhibit a bowing as functions of the nitrogen concentration. The values of the bowing ratio (whose values may be used in experiments on C11 and C12 as functions of x [R. S. Goldman, 2] b11/b12 are equal to 2.03, 1.85 and 1.47 at x=0.25, x=0.5 and x=0.75 for the NS, and equal to 3.2 (NAs) and 2.46 (NN) at x=0.25 and x=0.5 for the IS respectively.

Random distribution of nitrogen - VFF approach
The Valence Force Field (VFF) method has been used to study the influence of a randomly distributed N concentration on the lattice and elastic constants, as functions of the nitrogen concentration x. The following figure shows no deviation between the VFF lattice constants computed in ordered 8-atom supercells (diamond symbols) and disordered 216-atom supercells ('+' symbols). Same conclusion has been obtained for the elastic constants [1].

References
[1] G. Stenuit and S. Fahy, Calculated Mechanical Properties of GaNxAs1-x, submitted to PRB
[2] M. Reason, X. Weng, W. Ye, D. Dettling, S. Hanson, G. Obeidi and R. S. Goldman, J. Appl. Phys. 97 (2005) 103523.

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