Advances in Condensed Matter Physics

Volume 2016 (2016), Article ID 9435387, 7 pages

http://dx.doi.org/10.1155/2016/9435387

## Theoretical Investigation on Structural and Electronic Properties of InN Growth on Ce-Stabilized Zirconia (111) Substrates

^{1}Department of Chemistry and Environment Engineering, Anyang Institute of Technology, Anyang 455000, China^{2}Department of Mathematics and Physics, Anyang Institute of Technology, Anyang 455000, China

Received 21 November 2015; Accepted 23 February 2016

Academic Editor: Da-Ren Hang

Copyright © 2016 Yao Guo et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The structural and electronic properties of InN on Ce-stabilized zirconia (CeSZ) (111) substrates are investigated using first-principles calculations based on density functional theory with GGA + method. Surface energy calculations indicate that the structure of Ce-segregated surface is more energetically stable than that of Ce-segregation-free surface. Adsorption energies of indium and nitrogen atoms on both Ce-segregated and Ce-segregation-free CeSZ (111) surfaces at the initial growth stage have been studied. The results suggest that the first layer of InN films consists of a nitrogen layer, which leads to epitaxial relationships between InN (0001) // CeSZ (111) and InN // CeSZ . In addition, density of states (DOS) analysis revealed that the hybridization effect plays a crucial role in determining the interface structure for the growth of InN on CeSZ (111) surfaces. Furthermore, adsorption energies of indium atoms on the nitrogen layer have also been evaluated in order to investigate the lattice polarity determination for InN films. It was found that an indium atom preferentially adsorbs at the center of three nitrogen atoms stacked on the CeSZ substrate, which results in the formation of In-polarity InN.

#### 1. Introduction

Indium nitride (InN) is a promising material for high-speed electronic devices owing to its highest electron mobility [1–3] and saturation drift velocity [4] among the group III nitride. Growth of high-quality ultrathin InN films is necessary for the fabrication of InN-based devices since the device performance is often restricted by the threading dislocations and stacking faults at the interface [5]. Foreign substrates such as sapphire or GaN [6, 7] are usually employed for epitaxial growth of InN because of the lack of bulk InN crystals. However, the large lattice mismatches between InN and these substrates cause the formation of a high density of threading dislocations. In order to solve the problem above, development of lattice-matched substrates for InN is required. Among the various substrates, cubic phase zirconia substrates serve as a promising candidate for InN growth because they share a threefold rotational symmetry with the InN (0001) surface and have small lattice mismatch [8]. For example, the use of yttria-stabilized zirconia (YSZ) substrates provides reduced defect density and abrupt InN/YSZ interfaces [9]. In fact, the fluorite-type zirconia could be stabilized by the addition of different dopants. The stabilized cubic zirconia has its own characteristic structures which are dopant-independent [10]. The introduction of new dopants into zirconia that replaces yttrium is a straightforward strategy because the interaction between the dopant and the InN film is quite different.

Ceria-stabilized zirconia (CeSZ) is known as heterogeneous catalysis in the area of automotive pollution control [11]. On the other side, CeSZ is an ideal substrate owing to the small lattice mismatch between the InN film and the substrate. In fact, it has been experimentally determined that Ce atoms stabilize the cubic structure of zirconia and the Ce dopant segregation on the CeSZ (111) surface could be obtained due to the cation redistribution at high temperatures [12]. However, the feasibility of epitaxial growth of InN films on CeSZ (111) has not yet been investigated to date. Hence, a clear understanding of the InN/CeSZ interface microstructure is especially meaningful. To investigate the influence of the interfacial structure on electronic properties and the possible epitaxial relationships in the interface, the mechanism of growth of InN layers on CeSZ (111) substrates is discussed on the basis of first-principles calculations.

#### 2. Computational Method

The theoretical calculations have been carried out in the framework of the ab initio density functional theory using the software MedeA VASP package [13]. The electron exchange and correlation were treated within the generalized gradient approximation (GGA-PBE) [14]. The wavefunctions were expanded in a plane-wave basis set with a cutoff energy of 800 eV. The electron-ion interactions were described by the full-potential PAW method [15]. The electron configurations of the pseudopotentials for In, N, Zr, Ce, and O are , , , , and , respectively. All calculations involving Ce were performed at the GGA + level with a Hubbard parameter eV for the Ce orbitals [16]. The oxygen-terminated surface was employed because it was more stable than the Zr terminated or O-O terminated [17]. The slab contained twelve atomic layers (four O-Zr-O trilayers) separated from each other by a vacuum layer of 15 Å in the perpendicular direction to eliminate any interactions between the adjacent slabs. In the optimization process, the layers in the bottom O-Zr-O trilayer were fixed at the bulk positions, while the top layers were fully relaxed with convergence criteria of 0.05 eV/Å. The supercell consisted of a 2 × 2 array of CeSZ (111) surface unit cells. The Brillouin-zone integration was calculated with a 2 × 2 × 1 k-point grid, which was generated using the Monkhorst-Pack method [18]. We also performed the test with a denser 4 × 4 × 1 k-point grid and found that the difference in total energy is less than 1 × 10^{−4} eV/atom. Therefore, the 2 × 2 × 1 k-point grid is sufficient for the calculation. Similar computational details are described elsewhere [19].

#### 3. Results and Discussion

For necessity of later calculations, the equilibrium lattice of CeSZ was investigated in total energy versus lattice parameter. A stoichiometric CeZrO_{4} cubic structure in the 1 × 1 × 1 unit cell is employed for the calculation. Figure 1 shows that the total energy of CeSZ bulk was calculated using GGA + and GGA and plotted as a function of the lattice constant. The effective Hubbard parameter of 3 eV and 5 eV was used in the calculation as the GGA + approach. The eV calculation corresponds to unmodified GGA. It allows a direct comparison of the two methods. Introducing into the GGA methods results in an increase of lattice constant so that eventually GGA + may predict the experimental lattice constant Å [20]. Therefore, the value of eV as suggested by Nolan et al. [16] was employed for the later calculations.