Theoretical investigation on the structural properties of ZnO grown on sapphire

We have investigated the growth mechanisms of ZnO on the c-plane sapphire(0001) substrates by the firstprinciples calculation. The first-principles total energy calculations of a sapphire slab with an isolated zinc adatom and an isolated oxygen adatom explain the experimental results such that the in-plane alignment between the ZnO and the sapphire is [1010]ZnO//[1120] sapphire. Moreover, from the experimental and theoretical results of GaN/sapphire growth mechanisms, the change of the polarity is very important for the migration barrier energy. The relative total energies for the isolated zinc adatom on the sapphire(0001) surface is very small while that for the isolated oxygen adatom on the sapphire(0001) surface is very large. When analogizing these relative energies with the experimental and theoretical results of GaN/sapphire growth mechanisms, we expect that the polarity of grown ZnO film on the sapphire substrate is the O-polarity. And the polarity of the direct growth of ZnO on the sapphire (0001) substrate does not change from the O-polarity under any growth conditions without using the low-temperature amorphous ZnO buffer layer. [DOI: 10.1380/ejssnt.2006.544]


I. INTRODUCTION
In recent years, great progress in epitaxial growth techniques of ZnO has made it possible to fabricate blue light emitting diodes and laser diodes as GaN [1].ZnO gradually becomes a new focus in material research because it has a large direct band gap (energy gap = 3.3 eV, while energy gap = 3.4 eV for GaN) at room temperature, a high exciton binding energy (binding energy = 60 meV, while binding energy = 28 meV for GaN) and a direct transition character.Recently, it has been also recognized that the crystalline polarity of ZnO films has strong influence on the film characteristics as the group III-nitride films, such as the surface morphology and the electron mobility [2][3][4].The main reason for the difficulty of the crystal growth of ZnO is considered to be the lattice mismatch between the ZnO(0001) epitaxial layer and the substrate material such as the sapphire(0001).The sapphire (0001) is used as the substrate for the growth of ZnO, because the lattice mismatch is only about 18%.Moreover, it should be considered seriously that we have almost no knowledge about 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 * Corresponding author: fujiwara@kjaro.damp.tottori-u.ac.jp substrate crystal is sapphire (0001), but 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 so that the low-temperature buffer layer technique is necessary to obtain the ZnO crystal.
At present, rf -plasma-assisted molecular beam epitaxial (rf -MBE) is applied successfully to the crystal growth of ZnO film on sapphire (0001) substrate [5].The growth temperature of ZnO film on sapphire(0001) substrate is usually about 650 • C. It was shown that the in-plane alignment between ZnO and the sapphire were grown [1010]ZnO//[1120]sapphire by rf -MBE [5].And this inplane alignment between ZnO and the sapphire is also shown by electron cyclotron resonance-assisted molecular beam epitaxy [2] and the first-principles calculation [3].However, the adsorbed model of the first-principles calculation is the adsorption Zn-O molecule on the sapphire (0001) surface.The factors that determine the Zn or O adatoms are still unclear.The polarities of the ZnO crystals were grown by laser molecular beam epitaxy [4] and rf -MBE [5].However, the factors that determine the ZnO film polarity are still unclear.For further improvements in the crystalline quality and full control of the ZnO film polarity, it is very important to understand the mechanism of the early stage of the growths of ZnO on the sapphire substrates.
Therefore, in this paper, we investigate the dynamics of the isolated Zn adatom and the isolated O adatom on the c-plane sapphire(0001) surface using the firstprinciples calculation.The abrupt interface without the low-temperature amorphous buffer layers enables us to characterize the interfacial structure and the growth ISSN 1348-0391 c 2006 The Surface Science Society of Japan (http://www.sssj.org/ejssnt)mechanism of ZnO at the early stage.

II. COMPUTATIONAL METHOD
The first-principles calculations based on the density functional theory with the Troulier-Martin type GGA pseudopotentials [6,7] were performed to investigate the local interfacial structure.Similar calculations have been applied recently for epitaxial growth of GaN [8,9].We used the non-conserving pseudopotential [10,11] for Al, and the ultrasoft pseudopotential [12] for Zn, and O.The Zn-3d electrons were treated as part of the valence band.The wave functions were expanded within a plane-wave basis set with a cutoff energy of 30Ry and the primitive first Brillouin Zone was sampled with 4 k-points.We employed Al-terminated sapphire(0001) surface, unit cells containing six layers of sapphire, relax the top four layers in addition to the adatoms and (2 × 2) periodicity.

III. RESULTS AND DISCUSSION
We have calculated the total energy for the adsorption of the isolated Zn atom and the isolated O atom on the Alterminated sapphire (0001) surface, giving immediate insight into stable site and diffusivity.By fixing the adatom laterally at five adsorption sites with high symmetry; L1, L2, L3, H3 and T4 shown in Fig. 1, and allowing the adatom height to relax, we have calculated the total energy.The adsorption sites of L1, L2 and L3 are on-top site for Al atom of the first, second and third (topmost) layer from the underlying layer of Al-terminated sapphire(0001) surface.These points are expected to be cols or peaks in the potential energy surface.Table I lists the total energy values for the sapphire slab with the isolated Zn adatom or the isolated O adatom at each high-symmetry site.In this table, the total energy for the most stable sites for each atomic species is set to be zero.
As can be seen in this table, the most stable adsorption site for Zn atom is H3 site and for O atom is T4 site, respectively.However, Zn adatom has little difference of relative energy of each adsorption sites.T4 site of the most stable site for O adatom is on-top site for O atom of Al-terminated sapphire(0001) surface.The interaction of adatom and the Al-terminated sapphire(0001) surface is very important.The binding energy of Zn adatom on the Al-terminated sapphire(0001) surface is 0.14 eV.The binding energy of O adatom on the Al-terminated sapphire(0001) surface is 4.19 eV.Thus, the binding energy of Zn adatom on the Al-terminated sapphire(0001) surface is low, however, the binding energy of Zn adatom on the Al-terminated sapphire(0001) surface is high.Then by adsorption of the isolated oxygen on the Al-terminated sapphire(0001) surface, the surface structure is that the The interaction of adatom and the Al-terminated sapphire(0001) surface is very important.The binding energy of Zn adatom on the Al-terminated sapphire(0001) surface is 0.14 eV.The binding energy of O adatom on the Al-terminated sapphire(0001) surface is 4.19 eV.Thus, the binding energy of Zn adatom on the Al-terminated sapphire (0001) surface is much smaller than that of O adatom.
We investigate the in-plane alignment of [1010]ZnO//[1120]sapphire from the results of the first-principles total energy calculation for the sapphire slab with the isolated Zn adatom and the isolated O adatom on the surface.As we discussed in Ref. [13], if we assume that the crystal growth on the sapphire(0001) surface proceeds while keeping the first atom which sits on the most stable site, the oxygen atom at T4 leads to the observed in-plane alignment [1010]ZnO//[1120]sapphire as seen in Fig. 1.It can be considered that zinc is unrelated to the in-plane alignment because Zn adatom has little difference of relative energy of each adsorption sites on the Al-terminated sapphire (0001) surface.This calculated result is the same as the theoretical result [3], and explains the experimental result [2,5] quite well.
We investigate the polarity of ZnO crystal growth from the results of the first-principles total energy calculation for the sapphire slab with the isolated Zn adatom and the isolated O adatom at the sapphire(0001) surface.In recent experimental results [13], the polarity of grown GaN film on the sapphire substrate is Ga-polarity when buffering by Al-rich AlN layer before GaN growth, and N-polarity under other growth conditions.On the other hand, the calculation result [13] has shown the diffusivity of Al, Ga and N atom on the sapphire(0001) surface.The energy differences between the most stable site and the second stable site for Al, Ga and N are 0.74 eV, 0.22 eV and 1.4 eV, respectively.In the initial growth of the GaN film on the sapphire(0001) substrate, the change in atomic species of the first layer on the sapphire(0001) surface explains the experiment result of the change in the polarity quite well.The change in the polarity of GaN film on the sapphire(0001) substrate shows that it is important that the relative energy difference between the most stable site and the second stable site for the atomic species on the Al-terminated sapphire(0001) surface and the atomic specie of the first atomic layer on the Al-terminated sap-phire(0001) surface.We have considered that the adatom diffusion is due to the relative energy difference between the most stable site and the second stable site adsorbed on the Al-terminated sapphire(0001) surface.The polarity of grown ZnO film on the sapphire(0001) substrate is considered from these results.In Table I, the relative energy differences between the most stable site and the second stable site for Zn and O are 0.01 eV and 1.65 eV, respectively.Since the relative total energies for Zn adatom on the sapphire is similar to that for Ga adatom as we discussed above, we expect that the polarity of grown ZnO film on the sapphire(0001) surface is O-polarity under every growth conditions without using the low-temperature amorphous buffer layer.Moreover, this calculation result explains the experiment results [4,5] quite well.

IV. CONCLUSION
The first-principles calculations of the sapphire slab with an adatom explain the experimental results such as the in-plane alignment.It has been theoretically revealed that the in-plane alignment between the ZnO and sapphire is [1010]ZnO//[1120]sapphire. When analogizing these relative energies with the experimental and theoretical results of GaN/sapphire growth mechanisms, we expect that the polarity of grown ZnO film on the sapphire substrate is the O-polarity.And the polarity of the direct growth of ZnO on the sapphire(0001) substrate does not changes from the O-polarity under any growth conditions without using the low-temperature amorphous ZnO buffer layer.These results indicate that theoretical calculation can be a powerful tool to understand the growth mechanisms of the ZnO on an atomic scale.

FIG. 1 :
FIG. 1: Top and side views of the Al-terminated c-plane sapphire(0001) surface.The solid lines indicate the unit cell of the surface.The dashed circles labeled L1, L2, L3, H3, and T4 are the possible adsorption sites with high symmetry.The most stable adsorption site for Zn atom is H3 site and T4 site for O atom, respectively.However, Zn adatom has little difference of relative energy of each adsorption sites.

TABLE I :
Total energy values of the sapphire slab with a Zn or O adatom at various adsorption sites with high symmetry.The energy values for the most stable sites are set at zero.The unit of the energy is eV. of the nearest Al atom goes up about 0.48 Å and the position of the nearest O atom fall down about 0.08 Å.From the calculated result, it is shown that the oxygen adsorbed structure is not O-O contact but O-Al contact.