Conference-ISSS-7-Systematic Theoretical Investigations on Surface Reconstruction and Adatom Kinetics on AlN Semipolar Surfaces

The surface reconstructions and adatom kinetics on AlN(11̄02) and AlN(11̄01) surfaces in the presence of H2 molecules are investigated on the basis of density-functional theory calculations. Our surface phase diagram calculations demonstrate that the H-incorporated surfaces are invariably stable over the wide range of H2 pressure. We find that under the growth condition the adsorption energy of Al adatom on AlN(11̄02) surface is much larger than that on AlN(11̄01) surface. Furthermore, we find that the diffusion behavior of Al adatom on AlN(11̄01) surface is significantly influenced by the presence of hydrogen. These results suggest that impact of hydrogen ambient during the metal-organic vapor-phase epitaxy growth on AlN(11̄02) surface is quite different from that on AlN(11̄01) surface. [DOI: 10.1380/ejssnt.2015.239]


INTRODUCTION
AlN and related alloy semiconductors are promising materials for optoelectronic devices at deep ultra violet spectral regions [1].To fabricate these devices, the growth of high quality AlN layers has been actively studied by using epitaxial growth, such as metal-organic vapor-phase epitaxy (MOVPE) [2].The epitaxial growth of AlN has been conventionally grown along polar [0001] direction.However, this results in polarization electric fields that reduce the radiative efficiency.In order to reduce the effect of polarization fields, the epitaxial growth along nonpolar and semipolar orientations has been intensively carried out [3,4].The optimization of epitaxial growth condition on these surface orientations is thus one of important issues to improve crystalline quality.This can be achieved through the understanding surface reconstructions and elemental growth processes [5].
It has been recently reported that the epitaxial growth of AlN strongly depends on hydrogen ambient in the MOVPE [6,7].More importantly, the growth of AlN on semipolar (1 102) orientations is sensitive to H 2 pressure: high-density pits consisting of AlN(1 101) surface are formed under relatively low H 2 pressure conditions while smooth AlN(1 102) surface is obtained under high H 2 pressure conditions at initial growth processes.Furthermore, high-density pits perfectly disappear if high H 2 pressure is changed to low H 2 pressure after the growth of AlN(1 102) epilayer whose thickness is ∼ 100 nm [7].These experimental results inspire us to carry out theoretical investigations on the growth processes of AlN on semipolar orientations in the presence of H 2 molecules.In our previous studies, surface reconstructions and growth kinetics on polar and nonpolar AlN surfaces have been theoretically investigated on the basis of density-functional calculations [8,9].In this study, we extend our approach for the surface reconstructions and adatom kinetics on semipolar AlN(1 102) and AlN(1 101) surfaces.In particular, effects of hydrogen atoms on the structural stability and adatom kinetics on these semipolar surfaces under growth conditions are clarified by using surface phase diagrams, which take account of the growth conditions such as temperature and pressure.

II. COMPUTATIONAL PROCEDURE
Our DFT calculations are performed within the planewave pseudopotential approach using the generalized gradient approximation [10].We use norm-conserving pseudopotentials for Al and H atoms and ultrasoft pseudopotential for N atom [11,12].The conjugate gradient technique is utilized both for electronic structure calculations and for geometry optimization [13,14].The valence wave functions are expanded by the plane-wave basis set with a cutoff energy of 28 Ry.The surfaces on AlN(1 102) and AlN(1 101) are simulated using (1 × 2) and (2 × 2) slab models, respectively, which consist of eight atomic layers and an approximately 9 Å vacuum region.The bottom surface of slab is passivated with artificial hydrogen atoms [15] and lower four layers are fixed at ideal positions.The computations have been performed using Tokyo Ab initio Program Package (TAPP) [16].
The reconstructions on AlN(1 102) and AlN(1 101) surfaces depending on temperature and pressure are determined by comparing the chemical potential in gas phase (µ gas ) with adsorption energy (E ad ) [17].The chemical potentials of ideal gas such as Al atom and H 2 molecule (µ Al and µ H , respectively) are given by the following equations: Here, k B is the Boltzmann's constant, T is the gas temperature, g is the degree of degeneracy of electron energy level, and p Al (p H2 ) is pressure of Al atom (H 2 molecule).ζ trans , ζ rot , and ζ vib are the partition functions for translational, rotational, and vibrational motions, respectively.The adsorption energy E ad is obtained by ISSN 1348-0391 c ⃝ 2015 The Surface Science Society of Japan (http://www.sssj.org/ejssnt) Volume 13 (2015) Takemoto, et al.
where E total is total energy of surface with adatoms, E surface is the total energy of surface without adatoms, and E atom is total energy of isolated atom.Using the chemical potentials and adsorption energy, the adsorption and desorption behaviors on the surfaces under growth condition are obtained as functions of temperature and pressure.The structure corresponding to adsorbed surface is favorable when E ad is less than µ gas , whereas desorbed surface is stabilized when µ gas is less than E ad .
In order to investigate the adsorption and kinetics of Al adatom on the surface, the potential-energy surfaces (PES) are calculated by the adsorption energy of Al atom at various positions.We use 36 inequivalent lateral positions to sample the AlN(1 102)-(1 × 2) and AlN(1 101)-(2 × 2) unit cells.Based on the results of PES, diffusion length and surface lifetime of Al adatom on the surface are estimated using the Monte Carlo (MC) random-walk simulations [18].In the MC simulation procedure, the adsorption probability P ad (x) for Al adatom impinging on the specific lattice site x is given by assuming the localthermal equilibrium approximation written as where ∆µ(x) is the difference of Al chemical potential between site x and gas phase.The diffusion probability P diff (x → x ′ ) from the site x to x ′ is assumed in the Arrhenius form where diffusion pre-factor ν is 2k B T /h [19] and ∆E(x → x ′ ) is the local activation energy involving the adatom hopping from the site x to x ′ obtained by ab initio calculations.Two-dimensional periodic boundary conditions are imposed in the PES.The desorption probability P de (x) is written by Using these equations, we investigate the elemental growth process of Al adatom on AlN(1 102) and AlN(1 101) surfaces from adsorption to desorption via diffusion across the surface.

III. RESULTS AND DISCUSSION
We first clarify the surface reconstructions under the MOVPE growth conditions.Figure 1 shows surface phase diagrams on AlN(1 102) and AlN(1 101) surfaces as functions of temperatures and H 2 pressures at Al pressure of 1 × 10 −3 Torr.We have examined more than thirty and fifty candidates of surface structures on AlN(1 102) and AlN(1 101) surfaces, respectively.These surface phase diagrams demonstrate that there are several reconstructions depending on temperature and H 2 pressure.The surface phase diagram on AlN(1 102) surface shown in Fig. 1(a) reveals that the H-incorporated surfaces such as 2N de +Al-H and N de +N-H+Al-H appear under high H 2 pressure condition [20].The H atom on 2N de +Al-H tend to easily desorb from surface under low H 2 pressure condition and the surface without H atom (Al dim +2N de ) is stabilized.The metallic surface (bilayer) is stable over the wide range of H 2 pressures below ∼ 1200 K [21].Although two species of surface structures are stabilized, stable region of N de +N-H+Al-H is too small relative to that of 2N de +Al-H.Therefore, 2N de +Al-H mainly emerges under high H 2 pressure condition at typical growth temperatures (red line in Fig. 1).The stability of 2N de +Al-H can be interpreted by Al-H bond energy (−1.48 eV) and the electron counting rule [22].The energy of Al-H bond on AlN(1 102) surface is slightly smaller than that on AlN(0001) orientations (∼ −1.2 eV/atom) [8], so that stable region of 2N de +Al-H is larger than the H-incorporated surface on AlN(0001) surface.
In surface shown in Fig. 1(b) demonstrates that the Hincorporated surface (4N de +3Al-H) is considerably stable over the wide range of temperatures and H 2 pressures [20].This suggests that the reconstructions on AlN(1 101) surface are also insensitive to hydrogen ambient at typical growth temperatures ranging from 1300 to 1800 K.The stabilization of 4N de +3Al-H originates from the formation of stable Al-H bonds, whose energy (−1.54 eV/atom) is slightly smaller than that on AlN(1 102) surface.Although these surface orientations have N-polar, the ideal surfaces have two-coordinated N atoms.These two-coordinated N atoms on the ideal surfaces tend to desorb from surface, resulting in the formation of Al-H bonds.It should be noted that the surface reconstructions on semipolar AlN(1 101) surface are quite different from those on GaN(1 101) surface [23].
In order to analyze the growth processes on semipolar orientations, we clarify the adsorption behavior of Al adatom on AlN On the basis of the calculated PES, we furthermore per-form numerical analysis of adatom kinetics on the surface using the MC simulations.Figure 4

IV. CONCLUSIONS
We have systematically investigated surface reconstructions and adatom behaviors on AlN(1 102) and AlN(1 101) surfaces in the presence of H 2 molecules on the basis of DFT calculations.We have revealed that the Hincorporated surfaces emerge under growth conditions.This is because Al-H bonds are stable and H-incorporated surfaces on AlN(1 102) and AlN(1 101) satisfy the electron counting rule [22].We have also suggested that the adsorption behavior and kinetics of Al adatom, that are crucial for epitaxial growth, strongly depend on surface orientation: The growth on AlN(1 101) surface is much faster than that on AlN(1 102) surface under the MOVPE growth condition.

FIG. 1 .
FIG. 1. Calculated surface phase diagrams on (a) AlN(1 102) and (b) AlN(1 101) surfaces as functions of temperature and H2 pressure at Al pressure of 1.32×10 −6 atm (1×10 −3 Torr).The hydrogen incorporated surfaces are stabilized in the regions emphasized by shaded areas.Top views of surface structures are also shown.Large and small circles represent Al and N atoms, respectively.Crosses denote H atoms attaching on the surface.Typical growth temperature range for AlN growth is shown by red lines.

FIG. 2 .FIG. 3 .
FIG. 2. Contour plots of the PES for an Al adatom for (a) 2N de +Al-H on AlN(1 102) surface, and (b) 4N de +3Al-H on AlN(1 101) surfaces.Top views of the surface unit cell with Al adatom located at the most stable site are also shown by dashed rectangles.Large yellow, purple, and small circles represent Al adatom, Al, and N atoms, respectively.Crosses denote H atoms attaching on the surface.Arrows denote the saddle points of PES.
FIG. 4. (a) Diffusion length L diff and (b) lifetime τ of Al adatom on the surface as a function of reciprocal temperature for 2N de +Al-H (purple) on AlN(1 102) surface and 4N de +3Al-H (yellow) on AlN(1 101) surface.
[7]ws the calculated diffusion length L diff and surface lifetime τ of Al adatom on AlN(1 102) and AlN(1 101) surfaces in typical growth temperature range.The calculated diffusion length for 2N de +Al-H on AlN(1 102) surface is an order of magnitude larger than that for 4N de +3Al-H on AlN(1 101) surface.This is because the energy barrier for diffusion in 2N de +Al-H is lower than that in 4N de +3Al-H.It is suggested that Al adatoms easily migrate on AlN(1 102) surface compared with that on AlN(1 101) surface.On the other hand, due to the adsorption energy difference between 2N de +Al-H and 4N de +3Al-H, the calculated surface lifetime for 2N de +Al-H on AlN(1 102) surface is two orders of magnitude smaller than that for 4N de +3Al-H on AlN(1 101) surface.This implies that AlN(1 101) surface grows more rapidly than AlN(1 102) surface because of the higher sticking probability for Al adsorption on the AlN(1 101) surface.Furthermore, the longer Al diffusion length on AlN(1 102) surface than that on AlN(1 101) surface indicates that AlN(1 102) surface is more smooth than AlN(1 101) surface.These insights derived from present calculations are qualitatively consistent with experimental observations[7].