Ordered structures in III-Nitride ternary alloys
Graphical abstract
Introduction
Nitride alloys have been recognized as materials of significant importance for optoelectronic devices [1]. Although various studies on wurtzite nitride alloys have been reported [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], the effect of the metallic mixing (ordered-disordered structures) on the electronic and optical characteristics is still under investigation. There have been many theoretical studies for the bandgap dependence on the alloy concentrations [12], [13], [14], [15], [16], but the results are based on a large set of different structural configurations, disordered and ordered. The disordered structures can be described as randomly distributed metallic atoms in a supercell, while on the ordered structures the atoms occupy specific crystallographically defined sites in the lattice. In the experimentally observed cases disordered as well as ordered structural configurations may coexist in these alloys. However, in all the cases the arrangement of the metallic atoms in the structures is driven by the several growth parameters. In order to investigate the distribution of the metallic atoms in both the disordered and ordered structures, various computational approaches have been implemented [17], [18], [19], [20] taking into account the required formation energy. Initially Northrup et al. [21], proposed a model in order to explain simple 1 × 1 ordering with alternating Ga and Al/In rich layers. Recently Xu et al. [5], concluded by the use of first principles calculations in seven low-energy order structural configurations for 2 × 2 × 1 16-atom GaxAl1−xN supercells. The concept of Special Quasirandom Structures (SQS) has also been employed [17]. The method generates structures by occupying all possible lattice sites in a given supercell and successfully provides optimal disordered states within the frame of a periodic supercell approximation. The exhaustive algorithms scale poorly with the number of atoms, limiting the method to small supercells. Gan et al. [15] used this method to calculate the thermodynamic properties of wurtzite and zinc-blende InxGa1−xN alloys producing optimal, but still disordered, 32-atom structures for x = 1/4, 1/2 and 3/4. An alternative approach by de Carvalho et al. [16] uses the cluster expansion method [18], [19], in which InxGa1−xN and InxAl1−xN alloy structures are divided into a number of clusters, which are grouped into classes according to lattice symmetry. The authors used 16-atom 2 × 2 × 1 supercells and found more or less ordering along the main crystallographic directions. Atomic ordering has been identified also experimentally in GaxAl1−xN and InxGa1−xN alloys [6], [7], [8], [9], [10], [11], [22], [23], [24], [25]. Ordering in GaxAl1−xN films grown by plasma assisted molecular beam epitaxy has been investigated by Moustakas et al. [9], [10], [11]. The researchers have found that GaxAl1−xN exhibits a 1 × 1 monolayer cation ordering along the [0 0 0 1] direction. They have identified three types of spontaneously formed superlattice structures with periodicities of 2, 7, and 12 monolayers.
In an effort to clarify the issues of alloy ordering, we combine powerful evolutionary algorithms, density functional theory (DFT) calculations and molecular dynamics (MD) simulations with interatomic potentials (IP) in the investigation of the three III-Nitride ternary alloys. DFT models consisting of 32 atoms and MD models consisting of 104 atoms are used. The symmetry of the 2 × 2 × 2 supercell model used in the present study concluded on specific ordered structures exhibiting local formation energy minima by both IP and DFT based calculations at x = 0.25, 0.50 and 0.75 of the metallic atoms for the GaxAl1−xN, InxGa1−xN and InxAl1−xN ternary alloys.
Section snippets
Computational methods
The USPEX structure prediction code [20] in combination with the VASP ab initio simulation package [26] is implemented in order to reveal energetically favorable structures of the GaxAl1−xN, InxGa1−xN and InxAl1−xN alloys for the full range of compositions. USPEX employs a powerful evolutionary algorithm to predict the stable structures of a given composition of atoms. In this case bulk crystal enthalpy optimizations with fixed compositions are performed for the ternary alloys. In order to
Results
In Table 1, the lattice constants and bandgap values for AlN, GaN and InN calculated under LDA, GGA and HSE approaches are presented. In agreement with the literature [40] the obtained values show that LDA underestimates and GGA overestimates the equilibrium lattice parameters, while the parameters obtained from HSE are in good agreement with the experimental values. As shown in Table 1, the bandgaps are underestimated in LDA and GGA, i.e. InN has a negative bandgap in both methods. Again, the
Conclusions
In this work we investigate primarily the preferable structures of the nitride ternary alloys and secondly their energetics and structural and electronic properties. A 2 × 2 × 2 32-atom supercell is used and the energetically preferable structures are determined using the USPEX code in conjunction with the VASP package. The obtained structures are isomorphic for the three alloys and are described in detail. The formation energies of the structures show local minima when plotted against the cation
Acknowledgements
The authors are grateful to Prof. Th. Kehagias and Prof. G.P. Dimitrakopulos for valuable discussions. This research was co-financed by the European Union (European Social Fund – ESF) and Greek national funds through the Operational Program “Education and Lifelong Learning” of the National Strategic Reference Framework (NSRF) – Research Funding Program: THALES, Project: NITPHOTO. Computations were supported by the LinkSCEEM-2 project, funded by the European Commission under the 7th Framework
References (54)
- et al.
Comput. Mater. Sci.
(2014) - et al.
Comput. Mater. Sci.
(2015) - et al.
J. Cryst. Growth
(2002) - et al.
Mater. Sci. Eng., B
(2001) - et al.
J. Phys. Chem. Solids
(2003) J. Comput. Phys.
(1995)- et al.
Comput. Mater. Sci.
(2003) - Class for Physics of the Royal Swedish Academy of Sciences, Scientific background on the Nobel prize in Physics 2014,...
- et al.
Comput. Mater. Sci.
(2015) - et al.
J. Phys. Chem. C
(2012)
Appl. Phys. Lett.
J. Appl. Phys.
Appl. Phys. Lett.
J. Appl. Phys.
Appl. Phys. Lett.
Phys. Rev. B
Phys. Rev. B
Phys. Rev. B
Phys. Rev. Lett.
Phys. Rev. B
J. Chem. Phys.
Appl. Phys. Lett.
Appl. Phys. Lett.
J. Appl. Phys.
Appl. Phys. Lett.
Appl. Phys. Lett.
Cited by (13)
Modeling the structural characterization of nanostructures
2020, Frontiers of NanoscienceCitation Excerpt :The active regions of device structures consist of strained nanostructures due to lattice mismatch; moreover, a vast variety of defects are also identified. The strain induced in such systems, owing to mismatch or to extensive defects, modifies their electronic, electrical, and thermal characteristics [11,12] and alters their optoelectronic properties [13,14]. Consequently, the importance of investigating the strain characteristics of these materials is obvious, especially considering the variety of heterostructured cases that appear in the nanostructures of real devices, in addition to the strain induced by the presence of multiple dislocations [15,16].
Physical, photochemical, and extended piezoelectric studies of orthorhombic ZnSnN <inf>2</inf> nanocolumn arrays
2019, Applied Surface ScienceCitation Excerpt :Traditional III-nitrides include GaN, InN, and AlN [7]. Their wide applications to optoelectronics [8], including blue light-emitting diodes [9], generators [10], and sensors [11], can be achieved by using energy band gap (Eg) modification. However, Ga and In are limited resources on earth, and In is also environmentally unfriendly.
Ab initio investigation of the AlN:Er system
2017, Computational Materials ScienceCitation Excerpt :The results include the previously mentioned 4 × 4 × 4 256-atom supercell with an Er concentration of approximately 0.78% (1/128). All possible configurations are checked for a 2 × 2 × 2 32-atom supercell with the two Er atoms in a detailed examination that leads to the energetically preferable configuration, which is found to be an ordered structure in accordance with the results concerning ternary nitride compounds presented in Ref. [5]. The calculations also bring to light the change of nature of the bandgap of the ternary compound, which is direct only at 0.78% and switches to indirect for larger concentrations.
Strain and elastic constants of GaN and InN
2017, Computational Condensed MatterCitation Excerpt :The active regions of device structures consist of strained heterostructured nanostructures due to lattice mismatch. The strain induced in such systems modifies their electronic band structure and alters their optoelectronic properties [4,5]. Thus, it is important to investigate the elastic properties of these materials under different strain states that appear in the nanostructures of the real devices, i.e. short period superlattices, QWs and quantum dots.
Bandgap engineering of indium gallium nitride layers grown by plasma-enhanced chemical vapor deposition
2022, Journal of Vacuum Science and Technology A: Vacuum, Surfaces and Films