Elastic constants, composition, and piezolectric polarization in InxAl1−xN: Fromab initiocalculations to experimental implications for the applicability of Vegard's rule

Abstract

We present a theoretical analysis on the applicability of Vegard's linear rule in In x Al 1−x N alloys in relation to strain related elastic and piezoelectric properties. We derive the elastic stiffness constants and biaxial coefficients, as well as the respective deviations from linearity (Vegard's rule) by using ab initio calculations. The stress-strain relationships to extract composition from the lattice parameters are derived in different coordinate systems for In x Al 1−x N with an arbitrary surface orientation. The error made in the composition extracted from the lattice parameters if the deviations from linearity are not taken into account is discussed for different surface orientations, compositions and degrees of strain in the In x Al 1−x N films. The strain induced piezoelectric polarization is analyzed for In x Al 1−x N alloys grown pseudomorphically on GaN. The polarization values are compared with those obtained from our experimental data for the lattice parameters. We establish the importance of the deviation from linearity to correctly determine the piezoelectric polarization and also a smooth, not particular piezoelectric response at GaN lattice matched conditions.

Inapplicability of Martin transformation to elastic constants of zinc-blende and wurtzite group-III nitride alloys

“…A dotted line represents the result obtained for In x Al 1Àx N in Ref. 32, whereas a dashed line corresponds to the ideal value of the c/a ratio equal to ffiffi 8 3 q % 1:633. For binary nitrides, the largest deviation of the c/a ratio from the ideal value is obtained for AlN and the smallest for GaN.…”

Validity of Vegard’s rule for Al1−xInxN (0.08 < x < 0.28) thin films grown on GaN templates

“…In conclusion, uncertainties in the lattice parameters and stiffness constants of the binaries have an effect of the same order of magnitude as the modification to Vegard's rule described in equation (1). Note that the errors introduced by incorrect stiffness parameters or bowing can be much higher for the case of semipolar material than for the c-plane samples investigated here [47].…”

“…Composition and strain contributions must then be separated by relating the parallel, ε xx , and perpendicular, ε zz , components of the deformation with the elastic constants of the alloy [45]. This is done in terms of the distortion factor D [41]: [46,47].…”

Assessing structural, free-charge carrier, and phonon properties of mixed-phase epitaxial films: The case of InN

“…(25) can be neglected. We note that in group-III nitride films grown on off-axis oriented sapphire substrates the strain in the basal plane is anisotropic ( xx = yy ) and has more complex behavior (see [21,42] This would result in a blueshift of the E 1 (TO) phonon. However, our films are grown directly on sapphire and the normal strains may differ from the pseudomorphic growth situation.…”

“…Structural, phonon, dielectric and free-charge carrier parameters of ZB InN in comparison with previously published experimental results: TO phonon frequency ω TO,ZB , high-frequency dielectric function limit ε ∞,ZB , static dielectric constant ε 0,ZB , N and μ are the bulk free electron concentration and mobility, respectively, N s is the electron accumulation density at the surface, and a ZB is the lattice parameter. nitride films with an arbitrary surface orientations is given by [42] A z zz = A x xx + A y yy ,…”