The Na-flux method [1] is employed to grow large bulk GaN crystals for freestanding substrate. In the past, the polycrystal generation due to heterogeneous nucleation near gas-liquid interface was a crucial problem that inhibits a large crystal growth. This problem was solved by C addition to Na-Ga melts [2]; however, the fundamentals of the effect of C atoms and growth process under C-added condition are not understood. We previously reported that C and N atoms are strongly bonded in Ga-Na melts and it prevents Ga-N bond formation and GaN heterogeneous nucleation [3]. In this study, we simulated C-added Na-flux GaN growth on GaN(0001) surface using first-principles calculations and investigated the process of N incorporation into the crystal surface.

We used a first-principles molecular dynamics simulation program “STATE (Simulation Tool for Atom TEchnology)-Senri”. Figure 1 shows a simulation model of the C-added Na-flux growth, which was composed of 133 atoms. The bottom part was a GaN crystal. The GaN(000-1) surface was terminated by 3/4-charged H atoms. Na atoms were placed above the GaN(0001) surface as Na melt. We removed a N atom in the top layer of the GaN(0001) surface to open a N site. We initially put a CN cluster over the open N site at several heights. The N atom of the CN cluster was arranged on the side of the GaN crystal. The interatomic distance between the C and the N atoms was initially set to be 1.2 Å, which is stable distance in Na-Ga melts. We carried out structural optimization calculations for three CN cluster positions and compared total energy and C-N interatomic distance of them.

Figure 2 shows the atomic coordinates after the structural optimization. It seems that Figs. 2(a), 2(b) and 2(c) sequentially show the process of the N atom of the CN cluster will be incorporated in the GaN(0001) surface. The total energy and the C-N interatomic distance of them were listed in Table 1. These results show that the following two situations were energetically stable: (i) the CN cluster was on a Ga atom of the GaN(0001) surface (Fig. 2(a)) and (ii) the N atom of the CN cluster was at the N site in the GaN(0001) surface and the C atom moved away from the N atom (Fig. 2(c)). In addition, the total energy of the situation (ii) was smaller than that of the situation (i). Considering these results and our previous paper [3], we speculate the process of the C-added Na-flux GaN growth on GaN(0001) as follows: CN clusters generated in the melt are transported to the crystal surface, the CN clusters obtain sufficient energy to overcome the energy barrier corresponding to the result of Fig. 2(b), the N atoms of the CN clusters are incorporated in the crystal surface and on the other hand the C atoms depart from the crystal surface. The GaN growth will develop by repeating these processes.

Figure 1  Simulation model of C-added Na-flux GaN growth.

Figure 2  Atomic coordinates after structural optimization calculation. (a) The CN cluster was on a Ga atom. (b) The N atom of the CN cluster bonded to Ga atoms. (c) The N atom of the CN cluster was at the N site in the (0001) surface.

Table 1 Relative total energy and C-N interatomic distance for the carbon-added Na-flux GaN growth shown in Fig 2. The energy for Fig. 2(c) was set to be zero.

[1] H. Yamane, M. Shimada, S. J. Clarke and F. J. DiSalvo, Chem. Mater. 9 (1997) 413.

[2] M. Imade, Y. Hirabayasi, Y. Konishi, H. Ukegawa, N. Moyoshi, M. Yoshimura, T. Sasaki, Y. Kitaoka and Y. Mori, Appl. Phys. Express 3 (2010) 075501.

[3] T. Kawamura, H. Imabayashi, Y. Yamada, M. Maruyama, M. Imade, M. Yoshimura, Y. Mori and Y. Morikawa, Jpn. J. Appl. Phys. in press.

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