Analysis of Unstable Two-Phase Region in Wurtzite Group III Nitride Ternary Alloy Using Modified Valence Force Field Model

Abstract

The Group III-nitride ternary system is studied with respect to an unstable two-phase region in the phase field. The unstable two-phase region is analyzed using a strictly regular solution model. The interaction parameter used in the analysis is obtained from a strain energy calculation using the valence force field model, modified for both wurtzite and zinc-blende structures to avoid overestimation of the strain energy. The structural deviation from an ideal wurtzite structure in InN, GaN, and AlN is also taken into account in our model. According to the calculated results of the interaction parameters, the critical temperature for wurtzite InGaN, InAlN, and GaAlN are found to be 1967 K, 3399 K, and 181 K, respectively. This suggests that, at a typical growth temperature of 800–1000°C a wide unstable two-phase region exists in both InGaN and InAlN. In order to show the validity of our calculation results, we compare the calculated results and the experimental results using the calculation of the interaction parameter for the InGaAs system. The calculated results agree well with the experimental results.

First principles phase diagram calculations for the wurtzite-structure systems AlN–GaN, GaN–InN, and AlN–InN

“…Surprisingly, the GaN-InN and AlN-InN FPPD phase diagrams are predicted to be approximately symmetric; this is in contrast to the VFF calculations of Takayama et al 22,23 in which symmetric phase diagrams are assumed at the outset. …”

“…The FPPD results for CE Hamiltonians that exclude F vib , Table II Table III, where they are compared to the VFF results of Takayama et al 22,23 To facilitate calculation of phase diagrams ͑CALPHAD͒-type 31 modeling, Redlich-Kister polynomial representations of the Gibbs energy were fitted to the FPPD phase boundaries ͑Figs. 3͒, and the resulting coefficients are listed in Table IV.…”

“…Therefore, the absence of odd-order terms is aprediction, not a choice, or an implicit assumption, whereas it is a choice in the VFF plus strictly regular solution model approach. 22,23 Cluster expansions of molar volumes as functions of bulk composition are plotted in Fig. 4; where 1 mole equals a mole of exchangeable cations.…”

“…Empirical valence force field ͑VFF͒ calculations for wurtzite-structure solid solutions 22,23 predict miscibility gaps with consolute temperatures T C of 171 K for AlN-GaN, 1668 K for GaN-InN, and 3399 K for AlN-InN. Takayama et al 22,23 also report T C = 1676 K and T C = 1678 K for GaNInN in the ideal wurtzite and zinc blende structures, respectively, and Adhikari and Kofke 24 reports T C = 1678 K, for zinc blende structure GaN-InN.…”

“…Takayama et al 22,23 also report T C = 1676 K and T C = 1678 K for GaNInN in the ideal wurtzite and zinc blende structures, respectively, and Adhikari and Kofke 24 reports T C = 1678 K, for zinc blende structure GaN-InN. These calculations combine VFF formulations of the excess enthalpy with strictly regular solution models, a methodology that has two serious limitations: ͑1͒ it necessarily yields symmetric miscibility gaps with X C = 0.5, and ͑2͒ ignores clustering ͑short-range order͒ and therefore a potentially significant contribution to the configurational entropy.…”