An empirical potential approach to structural stability of GaNxAs1−x
Introduction
GaN-based III–V alloys are important for optical device applications, which are of considerable practical concern. In particular, GaNxAs1−x have been paid much attention in recent years because of their potential application to long-wave length laser diodes with high temperature stability [1]. In order to fabricate GaNxAs1−x, there have been some fundamental studies from both theoretical and experimental viewpoints. Neugebauer and Van de Walle performed ab initio calculations and suggested that GaNxAs1−x have strong miscibility gap because of the lattice mismatch between GaN and GaAs [2]. Foxon et al. found that GaNxAs1−x films grown by MBE is phase separated at x∼0.2 [3]. Furthermore, the promising range of x as no phase separation is confirmed to be x<0.15 [4] and x>0.98 [5]. However, very few studies are currently available in the literature on the miscibility over the entire concentration range in GaNxAs1−x. This is because of the complexity of the structural stability between wurtzite (W) and zinc blende (ZB) structures.
W and ZB structures are generally found in a number of semiconductors including GaAs (ZB) and GaN (W). Depending on the details of growth parameters, a number of compound semiconductors in the bulk form and thin films can be prepared in either form. Despite the importance of the W–ZB structural stability, there have been very few systematic studies even in the bulk form [6], [7]. In our previous studies, a simple systematization of structural trends in the bulk form has been accomplished by simple description of energy difference ΔEW–ZB between W and ZB [8], [9]. This description developed a new empirical potential applicable to the structural stability between W and ZB [10]. In this paper, we perform theoretical analyses of system energy for hypothetical W- and ZB-GaNxAs1−x to determine the concentration of the phase transition in W–ZB polytypism, using our new empirical potentials. The calculated results are discussed in terms of electrostatic energy and strain energy contributions, where bond length difference in W- and ZB-GaNxAs1−x is closely related to the phase transition concentration. Based on the stable structures for GaNxAs1−x, the excess energies are calculated to investigate the miscibility of GaNxAs1−x.
Section snippets
Computational methods
To investigate the system energy for ZB- and W-GaNxAs1−x, we employ our simple energy formula [10]. This is given byHere, E0 is the cohesive energy estimated by conventional empirical interatomic potential Vij for i−j atom pairs [11], [12]. The rij is the distance between the atoms, Zi the effective coordination number of atom i, Ri the minimum distance
Results And discussion
Fig. 2 shows the calculated cohesive energy of ZB-GaNxAs1−x with their error bars within 20 (meV/atom). This confirms that averaging the energies of 100 samples is enough for estimating the final cohesive energies. Fig. 3 shows the calculated cohesive energy difference ΔE between ZB- and W-GaNxAs1−x. The calculated results show that ZB-GaAs is more stable than W-GaAs by 10.1 (meV/atom) at x=0, whereas ZB-GaN is less stable than W-GaN by 4.5 (meV/atom) at x=1.0. This is consistent with
Conclusion
In this paper, structural stability of GaNxAs1−x including ZB–W structures and miscibility is systematically investigated based on a newly developed empirical potential, which incorporates electrostatic energies due to bond charges and ionic charges. Using the empirical potential, the system energies were successfully calculated for bulk GaNxAs1−x over the entire concentration range. The calculated results predict that ZB structured GaNxAs1−x is stable in the range of x<0.4, whereas W form
Acknowledgements
This work was partly supported by JSPS Research for the Future Program in the Area of Atomic Scale Surface and Interface Dynamics.
References (14)
- et al.
J. Crystal Growth
(1995) - et al.
J. Crystal Growth
(2001) - et al.
J. Crystal Growth
(2002) J. Crystal Growth
(1974)- et al.
J. Crystal Growth
(2000) - et al.
Jpn. J. Appl. Phys.
(1996) - et al.
Phys. Rev. B
(1995)