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Density functional calculations of the binding energies and adatom diffusion on

strained AlN (0001) and GaN (0001) surfaces

Article  in  Materials Research Society symposia proceedings. Materials Research Society · January 2007

DOI: 10.1557/PROC-1040-Q06-02

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Density functional calculations of the binding energies and adatom diffusion on strained AlN (0001) and GaN (0001) surfaces

Vibhu Jindal, James Grandusky, Neeraj Tripathi, Mihir Tungare, and Fatemeh Shahedipour-Sandvik College of Nanoscale Science and Engineering, University at Albany, 255 Fuller Road, Albany, NY, 12203

ABSTRACT

Density functional calculations were carried out to study the binding energies and diffusion barriers of various adatoms on AlN and GaN (0001) surfaces. The binding energies and potential energy surfaces were investigated for Al, Ga, and N adatoms on both Al (Ga) terminated and N terminated (0001) surfaces of AlN (GaN). Calculations were performed to investigate the diffusion paths and obtain diffusion energy barriers of these adatoms. It was found that the N adatom on N terminated AlN and GaN surfaces faces a high diffusion barrier due to strong N-N bond. The Al and Ga adatom on Al (Ga) terminated AlN (GaN) surfaces showed lower diffusion barriers due to the weak metallic bonds. However, the diffusion barrier for an Al adatom was always larger than that of a Ga adatom on any surface. To investigate the effect of strain on diffusion barriers the surfaces were subjected to a hydrostatic compressive and tensile strain in the range of 0 to 5%. The diffusion energy barrier for N adatom on N terminated AlN and GaN surfaces decreased when the strain state was changed from tensile to compressive. In contrast, Al and Ga adatoms show continuous increase in diffusion barriers from tensile to compressively strained Al (Ga) terminated AlN (GaN) surfaces. INTRODUCTION

III-Nitride based devices have become very important in the past decade for

applications in optoelectronic and electronic devices [1]. Although, there has been great progress on epitaxial growth of high quality AlInGaN device structures, deeper fundamental understanding of the growth mechanisms for homoepitaxy and heteroepitaxy of such layers is required [2-3]. Considerable theoretical efforts have been made in order to gain insight on physical processes such as adsorption, desorption, and diffusion of various adatoms on clean and adsorbate-covered GaN surfaces [4-6]. However, the influence of strain on such physical processes in III-Nitride systems is not very well known. The effect of strain on surface diffusion properties is not only of general scientific interest but also of technological importance. Strain plays an important role in any lattice mismatched heteroepitaxial growth system [7-8]. Phenomena occurring due to strain such as formation of quantum dots and nanostructures (transition of growth mode from 2D to 3D), coarsening of 2D island arrays, alloy fluctuation and phase ordering, emphasize the role of strain in a heteroepitaxial system [9-13]. Understanding of the effect of strain is also essential in homoepitaxy as the substrates often contain large impurity concentrations and residual strain [14]. This has driven the focus towards the development of a fundamental understanding of the effect of strain on kinetic processes such as binding energies and diffusion of adatoms on III-nitride surfaces. This work is

Mater. Res. Soc. Symp. Proc. Vol. 1040 © 2008 Materials Research Society 1040-Q06-02

targeted at understanding the effect of strain on diffusion of adatoms such as Al, Ga, and N on Al (Ga) and N terminated AlN (GaN) (0001) surfaces.

COMPUTATIONAL METHOD

Self-consistent first principle density functional theory (DFT) calculations were performed using the density functional formalism and the local density approximation (LDA). Ceperley-Alder [15] function was used for the exchange-correlation potential as parameterized by Troullier and Martins [16] to generate norm-conserving pseudopotentials in the Kleinman-Bylander form [17]. All calculations were performed using the SIESTA (Spanish Initiative for Electronic Simulations with Thousands of Atoms) code [18]. The pseudopotentials are generated with the 3s2 3p1 and 2s2 2p2 electronic configurations for Al and N respectively. The Ga 3d electrons were included in the valence and cut off radii of 2.0, 2.0, 2.2, and 2.2 were used for the s, p, d, and f orbitals. Well-converged results were obtained for lattice constants and bulk moduli of the AlN (GaN) with the mesh-cutoff energy of 400 (100) Ry and k-grid-cutoff of 7 (7) Å respectively. For bulk calculations a k-grid sampling of 9×9×6 was generated using the Monkhorst-Pack [19] scheme, while for supercell calculations only the gamma point was used. Atom positions were allowed to relax until atomic forces were less than 0.002 eV/Å. From these calculations, lattice constants of a=3.100 Å, c=4.973 Å (a=3.181 Å, c=5.176 Å) were obtained which are in agreement with experimental values [20-21] of a=3.11 Å, c=4.98 Å (a=3.189 Å, c=5.178 Å) for AlN (GaN) respectively. Surface calculations were performed on a 2×2×2 supercell with a 20 Bohr vacuum region above the surface. This cell was found to be sufficient for isolating the surface and for obtaining surface energies that were converged within ~20 meV. RESULTS AND DISCUSSIONS

The aim of this work is to study the adatom binding energies and diffusion barriers on the strained AlN and GaN (0001) surfaces. This was done by calculating the potential energy surfaces for adatoms by letting them relax in c-direction on Al (Ga) and N terminated (0001) AlN (GaN) surfaces. The minimum energy positions for these adatoms on the surfaces were identified upon relaxation. This allowed determination of the diffusion pathways and the diffusion barriers for adatoms. Hopping type of diffusion mechanism was considered for all the calculations presented in this paper. Later, we investigated the strain dependencies of diffusion in order to study the hetero- and homoepitaxy on strained surfaces.

It is a common practice to label the relevant energy sites in potential energy surface plots while addressing the adatom diffusion process. Fig. 1(a) and 1(b) show the N terminated and Al (Ga) terminated III-Nitride (0001) surfaces. There are two sites of primary interest, fcc and hcp, labeled as H1, H2 and F in Fig. 1. The H1 and H2 are hcp sites where H1 is denoting the hcp site on top of surface atoms while H2 denotes the hcp site on top of atoms which are below the surface atoms. Fig. 2 shows potential energy surface (PES) mapping for Al diffusion on unstrained N terminated AlN (0001) surface along with the atomic positions in the cell.

Fig 1: Ball and stick diagram for (a) N terminated and (b) Al (Ga) terminated (0001) AlN (GaN) surface showing hcp (H1 and H2) and fcc (F) sites

The minimum energy positions identified are fcc (F) and hcp (H2) positions for Al adatom on unstrained N terminated AlN (0001) surfaces. The fcc (F) and hcp (H2) positions were found to have similar energy values (within the accuracy of calculations), showing that both positions are equally likely to possess minimum energy configuration. The H1 hcp positions were, however, of high energy indicating that the adatom will not bond at these positions in equilibrium. Al adatom at the hcp position above another subsurface atom (H2), or the fcc position above no subsurface atoms (F) minimizes the energy by sharing the electrons with three surface N atoms. The most preferable pathway of diffusion in this structure would likely take place from the hcp to fcc energy minima or vice versa. The diffusion barrier for such type of diffusion pathway was calculated to be 2.28 eV. This value is comparable to the bond energy of ~2.9 eV between Al and N in AlN. The minimum energy positions and diffusion pathways for Al and Ga adatoms on N terminated unstrained AlN and GaN surfaces were found to be at similar fcc and hcp positions as above. However, the PES of N adatom on N terminated surface (Fig. 3) shows only one minimum energy position.

Fig 2: (a) PES for Al adatom on N terminated (0001) AlN surface (b) PES for

Al (Ga)

N H2

H1

H1 H2

H2 H1

F

H1

H2

H2 H1

H1 H2

F

Al adatom overlaid with ball and stick model for N terminated (0001) AlN surface.

Fig 3: (a) PES for N adatom on N terminated (0001) AlN surface, and (b) PES for

The lowest energy site for the N adatom on N terminated surface is the hcp position (H1) which is directly above the N atom on the surface. The strong binding of the N adatom to the N atom on the surface leads to very high diffusion barriers (2.59 eV on AlN and 3.12 eV on GaN) and limits the diffusion of the N adatom on N-terminated III-Nitride surfaces. Al adatom on unstrained Al terminated AlN (0001) surface (Fig. 4) again shows two local minimum energy positions (fcc (F) and hcp (H2) positions surrounded by three Al atoms on surface). The fcc energy position (F) corresponds to a local minima while the hcp position resembles a global minima with significant energy difference between the two energy positions. There was no direct diffusion pathway available for the Al adatom to diffuse from one hcp global minimum energy position to another. The Al adatom would have to first diffuse to the saddle fcc position (F) from the global minimum energy hcp position (H2) and then to the adjacent hcp-like spot. The resultant PES for N adatom on the Al terminated surface is shown in Fig. 5. It was found that the N adatom prefers to bind to three Al atoms and sit in the fcc (F) location with another low energy hcp location (H2) between the three Al atoms.

Fig 4: (a) PES for Al adatom on Al terminated (0001) AlN surface, and (b) PES for Al adatom overlaid with ball and stick model for Al terminated (0001) AlN surface.

N adatom overlaid with ball and stick model for N terminated (0001) AlN surface.

Fig 5: (a) PES for N adatom on Al terminated (0001) AlN surface (b) PES for

The ideal hcp location (H2), a single bond directly above the Al atom, is much higher in energy in comparison to the fcc position (F). So far these calculations provide one with insight into the evaluation of the binding energies, diffusion pathways, and diffusion barriers for different adatom-surface combinations for unstrained AlN and GaN. It has been well established that the strain resulting from heteroepitaxy due to lattice mismatch would have a strong impact on the surface morphology for thermodynamic reasons. To investigate and correlate the effect of strain on surface diffusion, GaN and AlN lattices were subjected to a hydrostatic compressive and tensile strain in the range of 0 to 5%. Figure 6(a) shows the effect of strain on adatom diffusion on a strained N terminated (0001) surface for AlN and GaN. The diffusion barrier of N adatom on N terminated surfaces was pretty high on both AlN and GaN (0001) surfaces. This can limit the diffusion of N adatom on these surfaces. However, the diffusion barrier for N adatom reduced when the strain was changed from tensile to compressive. In contrast, the Al and Ga adatoms show maximum diffusion barrier at a compressive strain between 1 to 2% for these strained surfaces.

Fig 6: Effect of strain on diffusion barriers for adatoms on (a) N terminated

N adatom overlaid with ball and stick model for Al terminated (0001) AlN surface.

AlN and GaN (0001) surface (b) Al (Ga) terminated AlN (GaN) (0001) surface.

The diffusion barriers decreased from the peak value when the strain changed to higher compressive strain or tensile strain. The diffusion barriers for Al adatoms were always larger than Ga adatoms on the same surface. The diffusion barriers for Al and Ga adatoms on the Al (Ga) terminated surface were relatively very small due to the weak metallic bonds. Hence, the diffusion of Al or Ga adatoms will be much faster on Al (Ga) terminated surfaces due to low diffusion barriers as compared to N terminated AlN (GaN) surfaces. The diffusion barrier decreased when the surfaces were subjected to strain from highly compressive to tensile.

CONCLUSION

DFT calculations were carried out to generate potential energy surfaces for Al (Ga) and N adatoms on Al (Ga) and N terminated (0001) AlN (GaN) surfaces. The binding energies, diffusion paths, and diffusion barriers were calculated for various adatom-surface combinations. It was found that the N adatom on N terminated AlN and GaN surfaces yielded high diffusion barriers due to strong N-N bond whereas the Al and Ga adatoms on Al (Ga) terminated AlN (GaN) showed low diffusion barriers due to the weak metallic bonds. However, diffusion barriers for Al adatoms were always larger than Ga adatom on any surface. Further calculations were carried out on strained surfaces in order to obtain a better understanding of the effects of strain on diffusion barriers of adatoms on AlN and GaN surfaces. The diffusion barriers constantly decreased for N adatom on N terminated AlN and GaN surfaces from highly tensile strained to compressively strained surfaces. Similar results for Al and Ga adatoms on N terminated AlN and GaN surfaces show a maximum in diffusion barrier for surfaces strained compressively between 1 to 2%. The Al and Ga adatoms show a linear decrease in diffusion barrier as the Al (Ga) terminated surfaces were subjected to strain from compressive to tensile for AlN (GaN).

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