Epitaxial growth of ZnO crystal on the Si-terminated 6H-SiC(0001) surface using the first-principles calculation∗

The dynamics of the zinc and the oxygen adatom supplied as atomic zinc and atomic oxygen on the 6H-SiC(0001) surface is investigated using the first-principles calculation. The result reveals that the on top site is unstable for the zinc and the oxygen on the 6H-SiC(0001) surface. However, the oxygen is stable at the on top site near a Zn adatom. Our calculation shows that the optimized growth condition for the growth of ZnO on 6H-SiC(0001) is Zn-polarity ZnO crystal grown under the stoichiometric growth condition. [DOI: 10.1380/ejssnt.2006.254]


I. INTRODUCTION
Zinc oxide (ZnO) is very important for their application in blue-emitting diodes and laser diodes [1] as well as GaN [2]. At present, metal organic chemical vapor deposition (MOCVD) is applied successfully to the crystal growth of ZnO, but the growth temperature is usually around 500 • C [3][4][5][6]. The molecular beam epitaxial (MBE) growth technique is possible, but the growth speed is very slow and it is known that the growth of ZnO single crystal is very difficult.
The main reason for the difficulty of the crystal growth of ZnO(0001) is considered to be the lattice mismatch (∼ 18%) of ZnO(0001) epitaxial layers with the substrate material such as sapphire(0001). Hence, SiC(0001) is used as the substrate for the growth of ZnO, because the lattice mismatch is only about 5%. However, it should be considered seriously that we have almost no knowledge of the mechanism of growth of ZnO(0001).
In order to obtain the ZnO crystal using the epitaxial growth, we should prepare the substrate crystal different from ZnO, because the bulk ZnO single crystal is still very difficult to obtain. Thus, the heteroepitaxial growth is necessary for the growth of ZnO. The most popular substrate crystal is sapphire(0001). However, it is very difficult to cleave a grown ZnO crystal from the sapphire substrate. Moreover, the lattice mismatch is very large between ZnO and sapphire (∼ 18%) so that the lowtemperature buffer layer technique is necessary to obtain the ZnO crystal.
In order to avoid the lattice mismatch problem, we should determine a crystal having hexagonal symmetry with a very close lattice constant compared with ZnO crystal. One of the well-known candidates for the substrate of the epitaxial growth of ZnO is SiC. The lattice mismatch is about 5%. Since it is possible to obtain the SiC crystal with a diameter of more than 4-inch, SiC can be considered to be the most suitable substrate for ZnO.
Because of the very small lattice mismatch, the direct epitaxial growth of ZnO(0001) seems to be possible on SiC(0001). For the direct growth of ZnO(0001) on the SiC substrate, the optimization of the growth condition is required. However, to optimize the growth condition, determining the dynamics of the zinc adatom and the oxygen adatom on SiC(0001) surface is necessary. If we consider the growth of Zn-polarity ZnO(0001), the oxygen adatom should be placed at the top of the Si atom of the topmost Si-terminated SiC(0001) surface. And if we consider the growth of O-polarity ZnO(0001), the zinc adatom should be placed at the top of the Si atom of the topmost Si-terminated SiC(0001) surface.
Therefore, in this study, we investigate the dynamics of the zinc adatom and the oxygen adatom on the Si-terminated SiC(0001) surface using the first-principles calculation. We use 6H-SiC(0001) surface as the typical substrate. The energy difference between the H3, T4 and the site corresponding to the wurtzite lattice structure is not affected significantly by the difference of the polytype of SiC because of the equivalence of the topmost two layers among them. Thus, other polytype of SiC substrate are covered by this study.

II. CONPUTATIONAL METHOD
The present calculations are based on the density functional theory (DFT) within LDA [7] and GGA [8,9]. We use the norm-conserving pseudopotential for Si, and ultrasoft pseudopotential for C, Zn and O. The wave functions are expanded in a plane-wave basis set with a cutoff energy of 30Ry and the primitive first Brillouin zone is sampled with 4k-points. We employ unit cells containing twelve layers of SiC, relax the top six atomic layers in addition to the adatom and (2 × 2) periodicity. The bottom C dangling bonds are saturated by hydrogen atoms in order to maintain a bulk-like configuration. The vacuum region is 10Å.

III. RESULTS AND DISCUSSION
First, we calculate the total energy for the adsorption of the zinc and the oxygen adatom on the Si-terminated 6H-SiC(0001) surface, giving immediate insight into stable sites, migration paths and migration barrier energies. Fixing the adatom laterally at the sites L, H3, T4, A, B and C for Fig.1 and allowing the adatom height to relax calculate the total energy. L denotes the site for the original wurtzite lattice structure. The energies calculated by LDA are shown in Fig. 2, where we show the relative total energy for the six adsorption sites from the most stable site energy. Especially, L, B, H3 and T4 are important, because adsorption to L site binds to one danglingbond, adsorbed to B site binds to two dangling-bonds and adsorbed to H3 and T4 sites bind to three danglingbonds. Thus, the results of the energies calculated by LDA method and GGA method with other same computational condition are shown in Table I where we show the relative total energy for the four adsorption sites from the most stable site energy. For the Zn adatom the most stable adsorption site on the Si-terminated 6H-SiC(0001) surface is the T4 site in Fig. 2, solid line. Fig. 2, solid line also reveals that the energetically lowest transition path is the B site and the H3 site. The B site is significantly higher in energy of 0.41 eV by LDA method and 0.40 eV by GGA method. Therefore, to hop from one T4 site to the next, the Zn adatom diffuses along the B site over the H3 site which is the transition site leading to barrier  Fig. 2, dashed line. Fig. 2, dashed line also reveals that the energetically lowest transition local path is the H3 site. The energetically lowest transition path beyond the hexagon is the C site. The C site is significantly higher in energy of 1.24 eV by LDA method and 1.27 eV by GGA method. Therefore, to hop from one B site to the next, the O adatom diffuses along the C site which is the transition site leading to a barrier energy of 1.2 eV. The L site is unstable for adsorption of the O adatom: the relative energy is 1.14 eV by LDA method and 1.12 eV by GGA method. The origin of the relative energy comes from the fact that an isolated oxygen atom has two bonds. At the B site, the oxygen adatom uses all two bonds with three Si atoms of the topmost layer. However, at the L site, the zinc adatom uses only one bond for adsorption and the remaining one bond are dangling bonds. Thus, the crystal growth will be very difficult after constructing such a structure.
At the L site, each of an isolated atomic species is unstable at the L site. However, the Zn-O interaction doesnft consider. In the actual situation of the epitaxial growth, the ZnO reconstructed structure surface on the Si-terminated 6H-SiC(0001) substrates when the Zn adatom bind to the O adatom. Therefore, we investigate the dynamics of the O adatom on the Si-terminated 6H-SiC (0001) with the local adsorbed Zn surface and the dynamics of the Zn adatom on the Si-terminated 6H-SiC (0001) with the local additional O adatom surface using the first-principles calculation.
Second, we perform the total energy calculation for the dynamics of the oxygen adatom on the additional zinc adatom on the Si-terminated 6H-SiC (0001) surface. Figure 3 shows the initial surface structure that is one T4 site adsorbed Zn atom on the Si-terminated 6H-SiC (0001) (2 × 2) surface. Fixing the adatom laterally at the sites L, H3, T4, L-Zn, H3-Zn and T4-Zn and allowing the adatom height to relax calculate the total energy. '-Zn' of L-Zn, H3-Zn and T4-Zn means that the oxygen adsorption site is nearer to the Zn adatom on the Si-terminated 6H-SiC (0001) surface structure. T4-Zn site means that the oxygen adsorption site is located on the T4 site near the Zn adatom. T4 site means that the oxygen adsorption site is located on the tetrahedral of three topmost Si atoms and one C atom in the Si-terminated 6H-SiC (0001) surface. The results of the energies calculated by LDA method and GGA method with other same computational condition are shown in Table II, we show the total energy values of the six adsorption sites relative to the site with the most stable energy. The most stable site for the oxygen adatom is the L site. When the oxygen adatom is at the L site, the zinc adatom shifts from the T4 site of initial setting to the H3 site nearer to oxygen adatom and up to the topmost atomic layer. This structure is the most stable structure of the six adsorbed structure. And the ZnO/6H-SiC(0001) interface structure at this time is the zinc blend structure. The higher possibility of the initial optimized growth condition for the heteroepitaxy growth of ZnO on the Si-terminated 6H-SiC(0001) surface is the Zn-polarity ZnO crystal grown under the stoichiometric growth condition. The polarity of the ZnO crystalline on the Si-terminated 6H-SiC(0001) slab is Zn polarity using MOCVD by A. B. M. Almamun Ashrafi, et al. [5]. The theoretical energy calculations of the Si-terminated 6H-SiC(0001) slab with an adatom explain the experimental results for the polarity quite well. However, when the ZnO   crystal grown under the stoichiometric growth condition, there is also possibility of the O-polarity of ZnO crystal on the Si-terminated 6H-SiC(0001) surface. Third, we perform the total energy calculation for the dynamics of the zinc adatom on the additional oxygen adatom on the Si-terminated 6H-SiC (0001) surface. For O adatom the most stable adsorption site on the Siterminated 6H-SiC(0001) surface is the B site. However, we consider that the zinc adatom at the B site prevent the oxygen adatom at the L site and the zinc adatom at the H3 site for the second stable site is possible to the oxygen adatom at the L site. Figure 4 shows the initial surface structure that is one H3 site adsorbed Zn adatom on the Si-terminated 6H-SiC(0001) (2 × 2) surface.  Table II, we show the total energy values of the six adsorption sites relative to the site with the most stable energy. The most stable site for the zinc adatom of the six adsorption sites is the L site. However, the reconstructed structure of one O adatom at the L sites on one Zn adatom at the T4 sites on Si-terminated 6H-SiC(0001) (2 × 2) surface is more energetically unstable than that of one O adatom at the L sites and the zinc adatom shifts from the T4 site of initial setting to the H3 site nearer to oxygen adatom and up to the topmost atomic layer. This reason is the state of two dangling-bonds of oxygen atom that bind with other two dangling-bonds is stable. Because one in two danglingbond of oxygen adatom doesn't bind, one O adatom on one Zn adatom on Si-terminated 6H-SiC(0001) (2 × 2) surface is more energetically unstable. From these results, one O adatom at the L sites and one Zn adatom at the T4 sites are unstable on the Si-terminated 6H-SiC(0001) (2 × 2) surface structure under the stoichiometric growth condition. Thus, when the ZnO crystal grown under the stoichiometric growth condition, there is not possibility of the O-polarity of ZnO crystal on the Si-terminated 6H-SiC(0001) surface.

IV. CONCLUSIONS
In conclusion, the results of the energies calculated by LDA method and GGA method are similar to the relative energy values. We found that the most stable adsorption site for the zinc adatom on the Si-terminated 6H-SiC(0001) surface is the T4 site and for the oxygen adatom on the Si-terminated 6H-SiC(0001) surface is the B site. They are unstable for L adatom site on the Si-terminated 6H-SiC(0001) surface. The ZnO crystal growth mechanism is unclear from the dynamics of the isolated atomic species on the Si-terminated 6H-SiC(0001) surface. However, the Zn-O interaction on the Si-terminated 6H-SiC(0001) surface is very important. The stable site of the oxygen adatom is L site when the surface structure is the Si-terminated 6H-SiC(0001) (2×2) surface with one additional the zinc adatom at T4 site. When the oxygen adatom is at the L site, the zinc adatom shifts from the T4 site of initial setting to the H3 site nearer to oxygen adatom and up to the topmost atomic layer. Since one Zn adatom at the T4 sites and one O adatom at the L sites are stable on Si-terminated 6H-SiC(0001) (2 × 2) surface, the initial optimized growth condition for the heteroepitaxy growth of ZnO on 6H-SiC(0001) is Zn-polarity ZnO crystal grown under the stoichiometric growth condition.