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InN growth on BaTiO3 (111) substrates: A first-principles study
Journal of Crystal Growth 395 (2014) 98–103
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Journal of Crystal Growth journal homepage: www.elsevier.com/locate/jcrysgro
InN growth on BaTiO3 (111) substrates: A first-principles study Jianli Wang a,n, Gang Tang a, Long Pu a, X.S. Wu b a b
Department of Physics, China University of Mining and Technology, Xuzhou 221116, China Nanjing National Laboratory of Microstructures, Laboratory of Solid State Microstructures, College of Physics, Nanjing University, Nanjing 210093, China
art ic l e i nf o
a b s t r a c t
Article history: Received 11 January 2014 Received in revised form 5 March 2014 Accepted 14 March 2014 Communicated by M. Uwaha Available online 21 March 2014
The surface stability of the polar (111) BaTiO3 surfaces is systematically studied by first-principle calculations. Surface energy and atomic relaxation have been calculated for BaO3 and Ti polar terminations in perovskite BaTiO3 ceramics. The specific adsorption sites at the initial growth stage and the atomic structure of InN on the BaTiO3 (111) substrate have been systematically investigated. The In adsorption atoms are more favorable than the N atoms for the BaTiO3 (111) surface. The energetically favorable In/BaO3 interface is pointed out among the atomic arrangements of the InN/BaTiO3 (111) interfaces. Oxygen vacancies in the first layer of the BaO3-terminated BaTiO3 substrate induce the occupied defect states of In 5s5p character at the energetically favorable In/BaO3 interface. & 2014 Elsevier B.V. All rights reserved.
Keywords: A1. Adsorption A1. First-principles calculations B1. InN B1. BaTiO3
1. Introduction Indium nitride (InN) is a promising material for near-infrared optoelectronics, high-efficiency solar cells, and high-speed electronics owing to its considerably narrower direct band gap (0.7–0.8 eV) [1,2] and superior electron transport characteristics in nitride semiconductors [1,3]. As the growth of high-quality InN single crystals is difficult due to the low dissociation temperature and high equilibrium vapor pressure of nitrogen molecules, this material is usually observed by the hetero-epitaxial growth. Meanwhile, InN has been usually grown using highly reactive nitrogen sources such as NH3 or N2 plasma, which cause nitridation of the substrate surfaces just before the epitaxial growth. This limits the substrates for the epitaxial growth of InN to chemically stable materials such as Si [4], SiC [5] and Al2O3 [6]. The suitable substrate materials play an important role for the highquality epitaxial growth. Development of semiconductor growth techniques on perovskite oxides substrates allows us to fabricate integrated devices which combine the unique properties of superconductors with the conventional semiconductor optical and electronic devices. Barium titanate (BaTiO3, BTO) is not only one of the most important ferroelectric material utilized for ceramic capacitors, ferroelectric random access memory, and piezoelectric devices [7,8], but also an important dielectric material from a technological standpoint due to its extremely high electrical permittivity. The phase transition behavior of BTO under (111) epitaxial strain [9] and the phonon modes of three polytypes of BTO [10] were investigated using density-functional theory (DFT) calculations. Meanwhile, BTO (111) n
Corresponding author. E-mail address: [email protected] (J. Wang).
http://dx.doi.org/10.1016/j.jcrysgro.2014.03.018 0022-0248/& 2014 Elsevier B.V. All rights reserved.
surfaces were epitaxially grown on SrTiO3 (STO) (111) substrates with a LaNiO3 conductive layer as a template using pulsed laser deposition [11]. Epitaxial BTO/STO dielectric superlattices were prepared with molecular layer order accuracy by ArF pulsed laser deposition. The superlattice with (001) orientation seems to be promising for ferroelectric devices owing to its large remanent polarization, while (111) for high frequency applications if a dielectric behavior can be found for them to give low dielectric relaxation in the microwave range [12]. Growth of InN on BTO is attractive since the integration of group III nitrides with perovskite oxides may develop new types of devices with novel functionalities. Advances in integrated multifunctional electronic and optoelectronic devices are crucially dependent on the fundamental understanding of the physical properties of the semiconductor–ferroelectric heterointerfaces due to progressing miniaturization. The interface morphology and microstructure play an important role in affecting the physical properties of layer structure materials. Thus further studies of the interface microstructure are necessary in order to investigate the influence of the interfacial structure on electronic properties and possibly establish relationships between interface microstructure. Although InN/BTO heterojunction shows many promising properties, there are few reports [13–15] on the epitaxial growth of InN films on BTO substrates to date. Epitaxial wurtzite InN thin films have been grown by metal-organic chemical vapor deposition on (111) STO substrates [13]. The InN films on STO substrates exhibit a strong photoluminescence emission around 0.78 eV. Then the valence band offset (VBO) of wurtzite InN/STO heterojunction was directly measured by x-ray photoelectron spectroscopy [14]. The VBO is determined to be 1.26 70.23 eV and the conduction band offset (CBO) is deduced to be 1.30 70.23 eV,
J. Wang et al. / Journal of Crystal Growth 395 (2014) 98–103
indicating the heterojunction has a type-I band alignment. X-ray photoelectron spectroscopy was used to measure the VBO of the InN/BTO heterojunction [15]. A type-I band alignment with the VBO of 2.25 70.09 eV and CBO of 0.15 70.09 eV is obtained. It is difficult to distinguish the interfacial layer in the experiment. We are interested in more detailed information regarding the initiative InN growth on BTO substrates. Such first-principles calculations can form the foundation for realistic simulations of the actual growth process.
2. Methodology The present self-consistent total-energy pseudopotential calculations are performed using the Vienna ab initio simulation package (VASP) [16]. The projector-augmented wave [17] method of Blöchl is used for the treatment of the core electrons. The electron exchange and correlation are treated within the generalized gradient approximation (GGA) using the Perdew–Burke–Ernzerhof [18] functionals. The Ti 3s3p, Ba 5s and In 4d [19] electrons are treated as valence electrons. A plane-wave cutoff energy of 500 eV is used throughout for the plane-wave set. The forces on each ion are relaxed to less than 0.02 eV/Å. The Brillouin-zone integrations are performed using a Gaussian smearing [20] of sigma¼ 0.2 eV. This would accelerate the convergence. The optimized lattice constant of cubic BTO (aBTO) used for constructing surface configurations is 4.036 Å, which is very close to experimental value of 4.00 Å [21] as well as other theoretical results. [22,23]. The InN lattice constants of the optimized wurtzite structure (a¼3.6137 Å, c¼5.8582 Å) [24] within GGA are in agreement with the theoretical values (a¼ 3.5848 Å, c¼5.8002 Å) [25] and the experimental values (a¼3.535 Å, c¼5.699 Å) [26]. We choose BTO (111) as a substrate because the (11 1) plane of BTO shares the threefold rotational symmetry with the (0001) plane of hexagonal InN. Both BaO3-terminated and Ti-terminated surfaces are considered, because they may be realized experimentally [27]. The theoretical lattice mismatch for InN is estimated to be 9.66%, if we assume the inplane alignment of InN [10–10]JBTO [ 101]. The different thickness InN/BTO heterostructures were deposited by metalorganic chemical vapor deposition [15]. The lattice mismatch may cause interfacial
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defects and then influence the electronic properties [15] of the films; however, the effect of the interface defects is hardly revealed only through experiments because of problems with reproducibility. We study the effect of the defects around the interface. For the theoretical modeling, the BTO surface structure is geometrically optimized using a symmetric slab [28], which avoids any artificial dipole–dipole interaction between the periodic images in the z-direction [29]. BaO3-terminated and Titerminated surfaces of BTO (111) are modeled by the periodic slabs shown in Fig. 1(a). For the BaO3-terminated surface, the slab consists of 10 BaO3 layers and nine Ti layers. Similarly, the Ti-terminated slab contains 10 Ti layers and nine BaO3 layers. In both cases, the slabs are isolated by six lattice constants width of vacuum regions. The total energy changed by less than 0.01% when the vacuum region is enlarged to 10 lattice constants in thickness. The z-axis is taken as normal to the surface. The calculations are done with a (6 6 1) Monkhorst–Pack [30] mesh. Increasing the mesh to (10 10 1), the surface energy differs by less than 0.01%.
3. Results and discussion 3.1. Surface energy and atomic relaxation of BTO (111) surfaces When we cleave the BaTiO3 (111) crystal, we can obtain two identical BaO3- or Ti-terminated surfaces to simplify the calculations. The relevant surface energy [31]ES ðαÞ (α ¼BaO3 or Ti) is ES ðαÞ ¼
i 1h i 1 h unrel unrel Eslab ðBaO3 Þ þ Eunrel Erel slab ðTiÞ nE bulk þ slab ðαÞ E slab ðαÞ ; 4N 2N
rel where Eunrel slab ðαÞ and E slab ðαÞ are the total energy of the unrelaxed α-terminated slab and the relaxed α-terminated slab, respectively. Ebulk is the bulk energy per formula unit in the cubic structure, and ¼ and ½ mean that in total four or two surfaces are created upon the crystal cleavage. N represents the number of the surface unit cell and n is the total number of bulk formula units in the slab. In our calculations the two 19 alternating layer BaO3- and Titerminated slabs represent together 19 bulk unit cells. Surfaces with
Fig. 1. (a) Three dimensional views of the BaO3-terminated and the Ti-terminated BTO (111) surfaces; the top view of the two surface layers of the BaO3-terminated (b) and (c) the Ti-terminated BTO (111) surfaces and the possible adsorption sites are marked by black spheres. H3 is the hollow site, top is the site directly above the surface atoms (abbreviated as TBa, TO and TTi), and T4 is the site directly above the sublayer (second layer) atoms.
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J. Wang et al. / Journal of Crystal Growth 395 (2014) 98–103
both terminations arise simultaneously under cleavage of the crystal and the relevant cleavage energy is distributed equally between created surfaces. The calculated surface energy per unit cell for BaO3-terminated BTO (111) surface (4.98 eV) is larger than that of Ti-terminated BTO (1 1 1) surface (3.66 eV), which is similar to SrTiO3 (111) and CaTiO3 (111) surfaces [32]. According to the results of the calculations, all metal (oxygen) atoms relax outward (inward, i.e. towards the bulk) for BaO3terminated BaTiO3 (111) surface and relax inward (outward) for Ti-terminated BaTiO3 (111) surface. For BaO3-terminated BaTiO3 (111) surface the upper layer metal Ba atom relaxes outwards by 6.47% of bulk lattice constant aBTO, but the upper layer O atom relaxes very slightly inwards by 0.23% of aBTO. Outward relaxation of the second layer Ti atom is 5.66% of aBTO. The upper layer Ti atom for Ti-terminated BaTiO3 (111) surface strongly (by 7.03% of aBTO) relaxes inwards. The second layer Ba atom relaxes inwards rather weakly (by 0.09% of aBTO), while the second layer O atom relaxes outwards by 4.89% of aBTO.
3.2. InN initial adsorption on defect-free BTO (111) surfaces For the adsorption studies presented here, only those with high symmetry adsorption sites are examined (see Fig. 1(b) and (c)). The coverage is defined as the number of the adatoms divided by the number of surface atoms. The adsorption energy per adsorption atom is defined by the equation [28,33] Eads ¼ ðEtotal Eref nEX Þ=n, where Etotal and Eref are the total energies of the adsorbed model and the clean surface model, respectively, n and EX are respectively the number and the energy of the adsorption atom X. To understand the initial growth and adsorption behavior of InN on BTO substrate, we firstly focus on the structures of In or
N adsorbate on BTO (111) under the lower coverage. The adsorption energies as well as the relaxations for In or N adatom on the BaO3-terminated and the Ti-terminated BTO (111) surfaces are calculated for different adsorption sites, and the results are summarized in Table 1. For the BaO3-terminated BTO (111) surface, 1/4 monolayer (ML) In adsorption at the H3 arrangement is the most stable. In atom will shift from TO site to H3 site and the total energy and the calculated relaxed atomic positions are the same. The adsorption energies of 1 ML In adsorption atoms at the H3 sites are shown to be lowered by 0.46 or 0.37 eV/atom than the structures at the T4 or TTi sites for the Ti-terminated BTO (111) surface. Meanwhile, the H3 sites for the BaO3-terminated surface are more favorable for In adsorption than the H3 sites for the Ti-terminated surface. An In adatom will favor an oxidizing rather than a reducing chemical environment. The distances between In adatoms and the underlying nearest O or Ti atoms are found to be 2.30 Å and 3.64 Å for the BaO3-terminated and Ti-terminated surfaces, respectively. For a higher coverage, the adsorption energies of ¾ML In adsorption atoms that occupy the H3, T4 and TBa adsorption sites are lowered by 0.01 eV/atom than that at the TO sites for the BaO3-terminated BTO (111) surface, an even lower adsorption energy of In adsorption atoms is obtained from 1 to 3 ML for the Ti-terminated STO (111) surface. The distances between In adatoms and the substrate nearest Ba or oxygen atoms are found to be 2.40 Å, 3.08 Å and 3.71 Å for the ¾ML In adatoms at the H3, T4, and TBa sites of the BaO3-terminated surface respectively. As for N adsorption on the BTO (111) surface, it does not present stable structures for both surface terminations under the lower coverage (refer to Table 1). The lowest formation energy of N atoms is 5.50 eV/atom at the H3 site of BaO3-terminated BTO (111) surface. For higher coverage, all the surface structures induced by adsorption of nitrogen are unstable for both surface
Table 1 The adsorption energy per adsorption atom and the distance between the adsorption In or N atom and BTO (111) surface atoms. BaO3-terminated surface T4
H3
1/4 ML In N
TO
Ead (eV)
In(N)–O (Å)
Ead (eV)
In(N)–O (Å)
Ead (eV)
In(N)–O (Å)
Ead (eV)
In(N)–Ba (Å)
2.10 5.50
2.30 1.30
1.77 5.87
2.38 1.47
– 7.65
— 1.85
0.18 7.90
3.58 2.78
H3, T4, TBa
3/4 ML In N
TBa
TO, TO, TO
Ead (eV)
In(N)–O(Ba) (Å)
Ead (eV)
1.27 4.72
2.40, 3.08, 3.71 5.15, 1.47, 3.84
1.26 5.09
In(N)–O (Å)
2.27 1.35
Ti-terminated surface T4
H3
1 ML In N
TTi
Ead (eV)
In(N)–Ti (Å)
Ead (eV)
In(N)–Ti (Å)
Ead (eV)
In(N)–Ti (Å)
1.04 7.27
3.64 3.60
0.58 6.98
4.30 3.67
0.67 5.97
3.15 1.90
H3, T4, TTi
3 ML In N
Ead (eV)
In(N)–Ti (Å)
1.16 4.99
3.88, 4.49, 3.08 3.04, 2.24, 2.15
J. Wang et al. / Journal of Crystal Growth 395 (2014) 98–103
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Fig. 2. Schematic of the In/BTO (111) interfaces showing the composition of each layer. Sixteen pseudo-hydrogen atoms (shown in white) are found at the top of the cell. The same schematic describes the N/BTO (111) interfaces, but with the elemental identity of the In and N atoms switched. For the reduced In/BaO3 interface, the oxygen vacancies are simulated by removing the oxygen atom from the first layer of the BaO3-terminated BTO surface. (a) the first In/BaO3 model, (b) the second In/BaO3 model and (c) In/Ti
Fig. 3. Ball model of the four interface layers of the unrelaxed first (a) and the unrelaxed second (b) In/BaO3 interface. The second In/BaO3 model (b) can be obtained by a translation of 1/3 unit cell length along the BTO ½110 of the first In/BaO3 model (a).
Fig. 4. Ball model of the interface layer of the second unrelaxed (a) and (b) relaxed In/BaO3 interface.
terminations. Thus the In adsorption atoms are more favorable than the N atoms for the BTO (111) surface. Among the structures examined, the BaO3-terminated BTO (111) surface induced by adsorbing ¼ ML In at H3 sites shows the lowest energy and thus is favorable. We have made no effort to introduce the temperature and pressure dependence here, so the results must be used with caution when addressing questions of the relative stability of surfaces under specific external conditions, i.e., the growth temperature, atmospheric pressure, etc.
3.3. InN/BTO interfaces The understanding and control of the interfaces are critical for the integration and fabrication of reliable heterostructures. A fundamental issue is atomic reconstruction: how the surface lattice symmetry differs from the bulk? The geometry of the heterostructures is schematically shown in Fig. 2 for the interfaces in the present study. As the adsorption configure of ¾ML In adsorption atoms that occupy the H3, T4 and TBa adsorption sites
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is stable for the BaO3-terminated BaTiO3 (111) surface under a higher coverage, we thus design the atomic arrangements of the first In/BaO3 interface model (Fig. 2(a)). If the In surfaces are translated to 1/6 of the length of the (2 2) unit cell along the [101] of BaTiO3 (see Fig. 3), the lattice matchings are still present. So we build the atomic arrangements of the second In/BaO3 interface model (Fig. 2(b)). The InN/BTO (111) heterointerfaces are modeled by a slab thickness of 10 atomic layers (ALs) of BTO and 10 ALs of InN [34,35]. We use lattice constants, a ¼b¼ 11.42 Å (¼ 2√2 aBTO) and c ¼69.91 Å ( ¼10√3 aBTO) for the heterostructures with In/BaO3 or In/Ti interface, in which the atomic structure relaxation is also performed under a fixed c/a in both
Fig. 5. Ball model of the interface layer of the second unrelaxed In/BaO3 interface.
Table 2 The z-axis distance between the In atom and BTO (111) surface nearest to Ba atoms at the second relaxed In/BaO3 interface (Å).
dIn1–Ba1 dIn2–Ba2 dIn3–Ba3 dIn4–Ba4
Defect-free
VO1
VO1 þVO2
VO1 þVO2 þ VO3
VO1 þ VO2 þ VO3 þ VO4
2.489 2.489 2.489 2.489
2.251 2.491 2.473 2.479
2.236 2.236 2.460 2.460
2.178 2.178 2.150 2.450
2.122 2.122 2.122 2.122
heterostructures. In the present InN/BTO (111) calculations, we allow all atoms to relax along the z axis. For the In-terminated surface, the dangling bonds in the bottom N layer are saturated with pseudo-hydrogen with a fractional charge of 3/4 in order to prevent unphysical charge transfer between the top and bottom slab surfaces [34–37]. For the N-terminated surface, we saturate the dangling bonds in the bottom In layer with pseudo-hydrogen with a fractional charge of 5/4. Adsorption was allowed on only one side of the exposed surfaces, with the dipole moment corrected accordingly in the z direction. We also examined InN/ BTO (111) heterostructures with oxygen vacancies; since the oxygen vacancy is known to significantly influence the physical properties of BTO [38]. The In/BaO3 interfaces are more energetically favorable [34] among the atomic arrangements of the InN/BTO (111) interfaces, which is in good agreement with the stable structure of the In atoms on the BaO3-terminated surface. Meanwhile, the second In/BaO3 interface is more favorable than the first In/BaO3 interface, because oxygen migrates from its initial position at the BTO (111) surface (see Fig. 4) and causes the shorter In–O bonds. Our results may help explain the atomic arrangements between the InN and the BTO (111) surfaces in the experiments [15]. For the second relaxed defect-free In/BaO3 interface, the interplanar spacing normal to the surface (2.489 Å) is larger than 1.681 Å (3cInN/16 þ p ffiffiffi 3aBTO/12). Our calculations of the interlayer distances are based on the metal ion (In and Ba) displacements [39]. After oxygen vacancies are introduced in the first layer of the BaO3-terminated BTO substrate (see Fig. 5), there is larger relaxation in comparison to that for the second defect-free In/BaO3 interface. The z-axis distances of In atoms and the underlying nearest Ba atoms near oxygen vacancies in Table 2 are found to be 2.251 Å, 2.236 Å, 2.178 Å and 2.122 Å for the second relaxed In/BaO3 interface with one, two, three and four oxygen vacancies, respectively. The interplanar distances of the second reduced In/BaO3 interface decrease with increasing the number of oxygen vacancy in the structures examined.
Fig. 6. The DOS of the second In/BaO3 heterojunction with/without oxygen vacancies. The solid black, red, and green curves correspond to the s, p, and d states, respectively, in (c)–(o). The vertical dotted line gives the location of the Fermi level. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
J. Wang et al. / Journal of Crystal Growth 395 (2014) 98–103
3.4. The effect of oxygen vacancy To further investigate the stability of oxygen vacancy for the first layer of the BaO3-terminated BTO substrate in Fig. 5, we calculated the formation energy of oxygen vacancies for the second In/BaO3 heterostructures. The formation energy, Ω, of oxygen vacancy can be calculated from Ω ¼ Etot ðV NO Þ Eref þ N O μO =N O where Etot ðV NO Þ is the energy of the supercell with oxygen vacancy, Eref is the energy of the defect-free supercell, N O is the number of oxygen vacancies, and μO is the chemical potential of the oxygen reservoir [40]. The formation energies of one oxygen vacancy are shown to be lowered by 0.03, 0.08 and 0.12 eV than that of the two, three and four oxygen vacancies. We analyze the electronic properties of the second In/BaO3 interface with/without oxygen vacancies. Qualitative insights into the electronic properties can be obtained by contrasting closely related electronic structures. As the partial density of states (PDOS) provide a general identification of the nature of the orbital, the effects of the interface atoms on the electronic properties of the interface can be obtained by contrasting the PDOS. Fig. 6 (a) displays the total density of states (TDOS) for the second defect-free In/BaO3 heterojunction. The upper valence band ranges are mainly composed of In 5s5p, N 2p, Ti 3d and O 2p states. After oxygen vacancies are introduced at the second In/BaO3 interface, some new occupied states generate at the upper valence band in comparison with TDOS for the second defect-free In/BaO3 heterojunction (Fig. 6(b)), which might impact on the interfacial electrically conducting. Compared to the PDOS of the interface layer atoms, the new occupied states should mainly attribute to the In 5s5p contributions. The difference between the In atoms may be caused by the dangling bonds of the In atom near oxygen vacancy. 4. Summary In summary, the structural and electronic properties of InN on the BTO (111) substrate are studied using the DFT. The calculated surface energy per unit cell for BaO3-terminated BTO (111) surface is larger than that of Ti-terminated BTO (111) surface. The BaO3terminated BTO (111) covered by 1/4 monolayer In adsorption atoms at H3 sites shows the lowest energy under the lower coverage, which does not necessarily correspond to a real superstructure due to the computer limitation. For a higher coverage, In adsorption atoms prefer to occupy the TO sites of the BaO3terminated BTO (111) surface. The second In/BaO3 interface is the most energetically favorable among the atomic arrangements of the InN/BTO (111) interfaces. After oxygen vacancies are introduced in the second In/BaO3 interface, the occupied states generate at the upper valence band. Our model can also be applied to other III-nitride/Perovskite oxide interfaces. Acknowledgment This work has been supported by NSFC 11347016 and the Fundamental Research Funds for the Central Universities under
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Grant no. 2014QNA65. We are grateful to the High Performance Computing Center of China University of Mining and Technology for the award of CPU hours to accomplish this work.
Appendix A. Supplementary material Supplementary data associated with this article can be found in the online version at http://dx.doi.org/10.1016/j.jcrysgro.2014.03.018.
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Journal of Crystal Growth journal homepage: www.elsevier.com/locate/jcrysgro
InN growth on BaTiO3 (111) substrates: A first-principles study Jianli Wang a,n, Gang Tang a, Long Pu a, X.S. Wu b a b
Department of Physics, China University of Mining and Technology, Xuzhou 221116, China Nanjing National Laboratory of Microstructures, Laboratory of Solid State Microstructures, College of Physics, Nanjing University, Nanjing 210093, China
art ic l e i nf o
a b s t r a c t
Article history: Received 11 January 2014 Received in revised form 5 March 2014 Accepted 14 March 2014 Communicated by M. Uwaha Available online 21 March 2014
The surface stability of the polar (111) BaTiO3 surfaces is systematically studied by first-principle calculations. Surface energy and atomic relaxation have been calculated for BaO3 and Ti polar terminations in perovskite BaTiO3 ceramics. The specific adsorption sites at the initial growth stage and the atomic structure of InN on the BaTiO3 (111) substrate have been systematically investigated. The In adsorption atoms are more favorable than the N atoms for the BaTiO3 (111) surface. The energetically favorable In/BaO3 interface is pointed out among the atomic arrangements of the InN/BaTiO3 (111) interfaces. Oxygen vacancies in the first layer of the BaO3-terminated BaTiO3 substrate induce the occupied defect states of In 5s5p character at the energetically favorable In/BaO3 interface. & 2014 Elsevier B.V. All rights reserved.
Keywords: A1. Adsorption A1. First-principles calculations B1. InN B1. BaTiO3
1. Introduction Indium nitride (InN) is a promising material for near-infrared optoelectronics, high-efficiency solar cells, and high-speed electronics owing to its considerably narrower direct band gap (0.7–0.8 eV) [1,2] and superior electron transport characteristics in nitride semiconductors [1,3]. As the growth of high-quality InN single crystals is difficult due to the low dissociation temperature and high equilibrium vapor pressure of nitrogen molecules, this material is usually observed by the hetero-epitaxial growth. Meanwhile, InN has been usually grown using highly reactive nitrogen sources such as NH3 or N2 plasma, which cause nitridation of the substrate surfaces just before the epitaxial growth. This limits the substrates for the epitaxial growth of InN to chemically stable materials such as Si [4], SiC [5] and Al2O3 [6]. The suitable substrate materials play an important role for the highquality epitaxial growth. Development of semiconductor growth techniques on perovskite oxides substrates allows us to fabricate integrated devices which combine the unique properties of superconductors with the conventional semiconductor optical and electronic devices. Barium titanate (BaTiO3, BTO) is not only one of the most important ferroelectric material utilized for ceramic capacitors, ferroelectric random access memory, and piezoelectric devices [7,8], but also an important dielectric material from a technological standpoint due to its extremely high electrical permittivity. The phase transition behavior of BTO under (111) epitaxial strain [9] and the phonon modes of three polytypes of BTO [10] were investigated using density-functional theory (DFT) calculations. Meanwhile, BTO (111) n
Corresponding author. E-mail address: [email protected] (J. Wang).
http://dx.doi.org/10.1016/j.jcrysgro.2014.03.018 0022-0248/& 2014 Elsevier B.V. All rights reserved.
surfaces were epitaxially grown on SrTiO3 (STO) (111) substrates with a LaNiO3 conductive layer as a template using pulsed laser deposition [11]. Epitaxial BTO/STO dielectric superlattices were prepared with molecular layer order accuracy by ArF pulsed laser deposition. The superlattice with (001) orientation seems to be promising for ferroelectric devices owing to its large remanent polarization, while (111) for high frequency applications if a dielectric behavior can be found for them to give low dielectric relaxation in the microwave range [12]. Growth of InN on BTO is attractive since the integration of group III nitrides with perovskite oxides may develop new types of devices with novel functionalities. Advances in integrated multifunctional electronic and optoelectronic devices are crucially dependent on the fundamental understanding of the physical properties of the semiconductor–ferroelectric heterointerfaces due to progressing miniaturization. The interface morphology and microstructure play an important role in affecting the physical properties of layer structure materials. Thus further studies of the interface microstructure are necessary in order to investigate the influence of the interfacial structure on electronic properties and possibly establish relationships between interface microstructure. Although InN/BTO heterojunction shows many promising properties, there are few reports [13–15] on the epitaxial growth of InN films on BTO substrates to date. Epitaxial wurtzite InN thin films have been grown by metal-organic chemical vapor deposition on (111) STO substrates [13]. The InN films on STO substrates exhibit a strong photoluminescence emission around 0.78 eV. Then the valence band offset (VBO) of wurtzite InN/STO heterojunction was directly measured by x-ray photoelectron spectroscopy [14]. The VBO is determined to be 1.26 70.23 eV and the conduction band offset (CBO) is deduced to be 1.30 70.23 eV,
J. Wang et al. / Journal of Crystal Growth 395 (2014) 98–103
indicating the heterojunction has a type-I band alignment. X-ray photoelectron spectroscopy was used to measure the VBO of the InN/BTO heterojunction [15]. A type-I band alignment with the VBO of 2.25 70.09 eV and CBO of 0.15 70.09 eV is obtained. It is difficult to distinguish the interfacial layer in the experiment. We are interested in more detailed information regarding the initiative InN growth on BTO substrates. Such first-principles calculations can form the foundation for realistic simulations of the actual growth process.
2. Methodology The present self-consistent total-energy pseudopotential calculations are performed using the Vienna ab initio simulation package (VASP) [16]. The projector-augmented wave [17] method of Blöchl is used for the treatment of the core electrons. The electron exchange and correlation are treated within the generalized gradient approximation (GGA) using the Perdew–Burke–Ernzerhof [18] functionals. The Ti 3s3p, Ba 5s and In 4d [19] electrons are treated as valence electrons. A plane-wave cutoff energy of 500 eV is used throughout for the plane-wave set. The forces on each ion are relaxed to less than 0.02 eV/Å. The Brillouin-zone integrations are performed using a Gaussian smearing [20] of sigma¼ 0.2 eV. This would accelerate the convergence. The optimized lattice constant of cubic BTO (aBTO) used for constructing surface configurations is 4.036 Å, which is very close to experimental value of 4.00 Å [21] as well as other theoretical results. [22,23]. The InN lattice constants of the optimized wurtzite structure (a¼3.6137 Å, c¼5.8582 Å) [24] within GGA are in agreement with the theoretical values (a¼ 3.5848 Å, c¼5.8002 Å) [25] and the experimental values (a¼3.535 Å, c¼5.699 Å) [26]. We choose BTO (111) as a substrate because the (11 1) plane of BTO shares the threefold rotational symmetry with the (0001) plane of hexagonal InN. Both BaO3-terminated and Ti-terminated surfaces are considered, because they may be realized experimentally [27]. The theoretical lattice mismatch for InN is estimated to be 9.66%, if we assume the inplane alignment of InN [10–10]JBTO [ 101]. The different thickness InN/BTO heterostructures were deposited by metalorganic chemical vapor deposition [15]. The lattice mismatch may cause interfacial
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defects and then influence the electronic properties [15] of the films; however, the effect of the interface defects is hardly revealed only through experiments because of problems with reproducibility. We study the effect of the defects around the interface. For the theoretical modeling, the BTO surface structure is geometrically optimized using a symmetric slab [28], which avoids any artificial dipole–dipole interaction between the periodic images in the z-direction [29]. BaO3-terminated and Titerminated surfaces of BTO (111) are modeled by the periodic slabs shown in Fig. 1(a). For the BaO3-terminated surface, the slab consists of 10 BaO3 layers and nine Ti layers. Similarly, the Ti-terminated slab contains 10 Ti layers and nine BaO3 layers. In both cases, the slabs are isolated by six lattice constants width of vacuum regions. The total energy changed by less than 0.01% when the vacuum region is enlarged to 10 lattice constants in thickness. The z-axis is taken as normal to the surface. The calculations are done with a (6 6 1) Monkhorst–Pack [30] mesh. Increasing the mesh to (10 10 1), the surface energy differs by less than 0.01%.
3. Results and discussion 3.1. Surface energy and atomic relaxation of BTO (111) surfaces When we cleave the BaTiO3 (111) crystal, we can obtain two identical BaO3- or Ti-terminated surfaces to simplify the calculations. The relevant surface energy [31]ES ðαÞ (α ¼BaO3 or Ti) is ES ðαÞ ¼
i 1h i 1 h unrel unrel Eslab ðBaO3 Þ þ Eunrel Erel slab ðTiÞ nE bulk þ slab ðαÞ E slab ðαÞ ; 4N 2N
rel where Eunrel slab ðαÞ and E slab ðαÞ are the total energy of the unrelaxed α-terminated slab and the relaxed α-terminated slab, respectively. Ebulk is the bulk energy per formula unit in the cubic structure, and ¼ and ½ mean that in total four or two surfaces are created upon the crystal cleavage. N represents the number of the surface unit cell and n is the total number of bulk formula units in the slab. In our calculations the two 19 alternating layer BaO3- and Titerminated slabs represent together 19 bulk unit cells. Surfaces with
Fig. 1. (a) Three dimensional views of the BaO3-terminated and the Ti-terminated BTO (111) surfaces; the top view of the two surface layers of the BaO3-terminated (b) and (c) the Ti-terminated BTO (111) surfaces and the possible adsorption sites are marked by black spheres. H3 is the hollow site, top is the site directly above the surface atoms (abbreviated as TBa, TO and TTi), and T4 is the site directly above the sublayer (second layer) atoms.
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both terminations arise simultaneously under cleavage of the crystal and the relevant cleavage energy is distributed equally between created surfaces. The calculated surface energy per unit cell for BaO3-terminated BTO (111) surface (4.98 eV) is larger than that of Ti-terminated BTO (1 1 1) surface (3.66 eV), which is similar to SrTiO3 (111) and CaTiO3 (111) surfaces [32]. According to the results of the calculations, all metal (oxygen) atoms relax outward (inward, i.e. towards the bulk) for BaO3terminated BaTiO3 (111) surface and relax inward (outward) for Ti-terminated BaTiO3 (111) surface. For BaO3-terminated BaTiO3 (111) surface the upper layer metal Ba atom relaxes outwards by 6.47% of bulk lattice constant aBTO, but the upper layer O atom relaxes very slightly inwards by 0.23% of aBTO. Outward relaxation of the second layer Ti atom is 5.66% of aBTO. The upper layer Ti atom for Ti-terminated BaTiO3 (111) surface strongly (by 7.03% of aBTO) relaxes inwards. The second layer Ba atom relaxes inwards rather weakly (by 0.09% of aBTO), while the second layer O atom relaxes outwards by 4.89% of aBTO.
3.2. InN initial adsorption on defect-free BTO (111) surfaces For the adsorption studies presented here, only those with high symmetry adsorption sites are examined (see Fig. 1(b) and (c)). The coverage is defined as the number of the adatoms divided by the number of surface atoms. The adsorption energy per adsorption atom is defined by the equation [28,33] Eads ¼ ðEtotal Eref nEX Þ=n, where Etotal and Eref are the total energies of the adsorbed model and the clean surface model, respectively, n and EX are respectively the number and the energy of the adsorption atom X. To understand the initial growth and adsorption behavior of InN on BTO substrate, we firstly focus on the structures of In or
N adsorbate on BTO (111) under the lower coverage. The adsorption energies as well as the relaxations for In or N adatom on the BaO3-terminated and the Ti-terminated BTO (111) surfaces are calculated for different adsorption sites, and the results are summarized in Table 1. For the BaO3-terminated BTO (111) surface, 1/4 monolayer (ML) In adsorption at the H3 arrangement is the most stable. In atom will shift from TO site to H3 site and the total energy and the calculated relaxed atomic positions are the same. The adsorption energies of 1 ML In adsorption atoms at the H3 sites are shown to be lowered by 0.46 or 0.37 eV/atom than the structures at the T4 or TTi sites for the Ti-terminated BTO (111) surface. Meanwhile, the H3 sites for the BaO3-terminated surface are more favorable for In adsorption than the H3 sites for the Ti-terminated surface. An In adatom will favor an oxidizing rather than a reducing chemical environment. The distances between In adatoms and the underlying nearest O or Ti atoms are found to be 2.30 Å and 3.64 Å for the BaO3-terminated and Ti-terminated surfaces, respectively. For a higher coverage, the adsorption energies of ¾ML In adsorption atoms that occupy the H3, T4 and TBa adsorption sites are lowered by 0.01 eV/atom than that at the TO sites for the BaO3-terminated BTO (111) surface, an even lower adsorption energy of In adsorption atoms is obtained from 1 to 3 ML for the Ti-terminated STO (111) surface. The distances between In adatoms and the substrate nearest Ba or oxygen atoms are found to be 2.40 Å, 3.08 Å and 3.71 Å for the ¾ML In adatoms at the H3, T4, and TBa sites of the BaO3-terminated surface respectively. As for N adsorption on the BTO (111) surface, it does not present stable structures for both surface terminations under the lower coverage (refer to Table 1). The lowest formation energy of N atoms is 5.50 eV/atom at the H3 site of BaO3-terminated BTO (111) surface. For higher coverage, all the surface structures induced by adsorption of nitrogen are unstable for both surface
Table 1 The adsorption energy per adsorption atom and the distance between the adsorption In or N atom and BTO (111) surface atoms. BaO3-terminated surface T4
H3
1/4 ML In N
TO
Ead (eV)
In(N)–O (Å)
Ead (eV)
In(N)–O (Å)
Ead (eV)
In(N)–O (Å)
Ead (eV)
In(N)–Ba (Å)
2.10 5.50
2.30 1.30
1.77 5.87
2.38 1.47
– 7.65
— 1.85
0.18 7.90
3.58 2.78
H3, T4, TBa
3/4 ML In N
TBa
TO, TO, TO
Ead (eV)
In(N)–O(Ba) (Å)
Ead (eV)
1.27 4.72
2.40, 3.08, 3.71 5.15, 1.47, 3.84
1.26 5.09
In(N)–O (Å)
2.27 1.35
Ti-terminated surface T4
H3
1 ML In N
TTi
Ead (eV)
In(N)–Ti (Å)
Ead (eV)
In(N)–Ti (Å)
Ead (eV)
In(N)–Ti (Å)
1.04 7.27
3.64 3.60
0.58 6.98
4.30 3.67
0.67 5.97
3.15 1.90
H3, T4, TTi
3 ML In N
Ead (eV)
In(N)–Ti (Å)
1.16 4.99
3.88, 4.49, 3.08 3.04, 2.24, 2.15
J. Wang et al. / Journal of Crystal Growth 395 (2014) 98–103
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Fig. 2. Schematic of the In/BTO (111) interfaces showing the composition of each layer. Sixteen pseudo-hydrogen atoms (shown in white) are found at the top of the cell. The same schematic describes the N/BTO (111) interfaces, but with the elemental identity of the In and N atoms switched. For the reduced In/BaO3 interface, the oxygen vacancies are simulated by removing the oxygen atom from the first layer of the BaO3-terminated BTO surface. (a) the first In/BaO3 model, (b) the second In/BaO3 model and (c) In/Ti
Fig. 3. Ball model of the four interface layers of the unrelaxed first (a) and the unrelaxed second (b) In/BaO3 interface. The second In/BaO3 model (b) can be obtained by a translation of 1/3 unit cell length along the BTO ½110 of the first In/BaO3 model (a).
Fig. 4. Ball model of the interface layer of the second unrelaxed (a) and (b) relaxed In/BaO3 interface.
terminations. Thus the In adsorption atoms are more favorable than the N atoms for the BTO (111) surface. Among the structures examined, the BaO3-terminated BTO (111) surface induced by adsorbing ¼ ML In at H3 sites shows the lowest energy and thus is favorable. We have made no effort to introduce the temperature and pressure dependence here, so the results must be used with caution when addressing questions of the relative stability of surfaces under specific external conditions, i.e., the growth temperature, atmospheric pressure, etc.
3.3. InN/BTO interfaces The understanding and control of the interfaces are critical for the integration and fabrication of reliable heterostructures. A fundamental issue is atomic reconstruction: how the surface lattice symmetry differs from the bulk? The geometry of the heterostructures is schematically shown in Fig. 2 for the interfaces in the present study. As the adsorption configure of ¾ML In adsorption atoms that occupy the H3, T4 and TBa adsorption sites
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is stable for the BaO3-terminated BaTiO3 (111) surface under a higher coverage, we thus design the atomic arrangements of the first In/BaO3 interface model (Fig. 2(a)). If the In surfaces are translated to 1/6 of the length of the (2 2) unit cell along the [101] of BaTiO3 (see Fig. 3), the lattice matchings are still present. So we build the atomic arrangements of the second In/BaO3 interface model (Fig. 2(b)). The InN/BTO (111) heterointerfaces are modeled by a slab thickness of 10 atomic layers (ALs) of BTO and 10 ALs of InN [34,35]. We use lattice constants, a ¼b¼ 11.42 Å (¼ 2√2 aBTO) and c ¼69.91 Å ( ¼10√3 aBTO) for the heterostructures with In/BaO3 or In/Ti interface, in which the atomic structure relaxation is also performed under a fixed c/a in both
Fig. 5. Ball model of the interface layer of the second unrelaxed In/BaO3 interface.
Table 2 The z-axis distance between the In atom and BTO (111) surface nearest to Ba atoms at the second relaxed In/BaO3 interface (Å).
dIn1–Ba1 dIn2–Ba2 dIn3–Ba3 dIn4–Ba4
Defect-free
VO1
VO1 þVO2
VO1 þVO2 þ VO3
VO1 þ VO2 þ VO3 þ VO4
2.489 2.489 2.489 2.489
2.251 2.491 2.473 2.479
2.236 2.236 2.460 2.460
2.178 2.178 2.150 2.450
2.122 2.122 2.122 2.122
heterostructures. In the present InN/BTO (111) calculations, we allow all atoms to relax along the z axis. For the In-terminated surface, the dangling bonds in the bottom N layer are saturated with pseudo-hydrogen with a fractional charge of 3/4 in order to prevent unphysical charge transfer between the top and bottom slab surfaces [34–37]. For the N-terminated surface, we saturate the dangling bonds in the bottom In layer with pseudo-hydrogen with a fractional charge of 5/4. Adsorption was allowed on only one side of the exposed surfaces, with the dipole moment corrected accordingly in the z direction. We also examined InN/ BTO (111) heterostructures with oxygen vacancies; since the oxygen vacancy is known to significantly influence the physical properties of BTO [38]. The In/BaO3 interfaces are more energetically favorable [34] among the atomic arrangements of the InN/BTO (111) interfaces, which is in good agreement with the stable structure of the In atoms on the BaO3-terminated surface. Meanwhile, the second In/BaO3 interface is more favorable than the first In/BaO3 interface, because oxygen migrates from its initial position at the BTO (111) surface (see Fig. 4) and causes the shorter In–O bonds. Our results may help explain the atomic arrangements between the InN and the BTO (111) surfaces in the experiments [15]. For the second relaxed defect-free In/BaO3 interface, the interplanar spacing normal to the surface (2.489 Å) is larger than 1.681 Å (3cInN/16 þ p ffiffiffi 3aBTO/12). Our calculations of the interlayer distances are based on the metal ion (In and Ba) displacements [39]. After oxygen vacancies are introduced in the first layer of the BaO3-terminated BTO substrate (see Fig. 5), there is larger relaxation in comparison to that for the second defect-free In/BaO3 interface. The z-axis distances of In atoms and the underlying nearest Ba atoms near oxygen vacancies in Table 2 are found to be 2.251 Å, 2.236 Å, 2.178 Å and 2.122 Å for the second relaxed In/BaO3 interface with one, two, three and four oxygen vacancies, respectively. The interplanar distances of the second reduced In/BaO3 interface decrease with increasing the number of oxygen vacancy in the structures examined.
Fig. 6. The DOS of the second In/BaO3 heterojunction with/without oxygen vacancies. The solid black, red, and green curves correspond to the s, p, and d states, respectively, in (c)–(o). The vertical dotted line gives the location of the Fermi level. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
J. Wang et al. / Journal of Crystal Growth 395 (2014) 98–103
3.4. The effect of oxygen vacancy To further investigate the stability of oxygen vacancy for the first layer of the BaO3-terminated BTO substrate in Fig. 5, we calculated the formation energy of oxygen vacancies for the second In/BaO3 heterostructures. The formation energy, Ω, of oxygen vacancy can be calculated from Ω ¼ Etot ðV NO Þ Eref þ N O μO =N O where Etot ðV NO Þ is the energy of the supercell with oxygen vacancy, Eref is the energy of the defect-free supercell, N O is the number of oxygen vacancies, and μO is the chemical potential of the oxygen reservoir [40]. The formation energies of one oxygen vacancy are shown to be lowered by 0.03, 0.08 and 0.12 eV than that of the two, three and four oxygen vacancies. We analyze the electronic properties of the second In/BaO3 interface with/without oxygen vacancies. Qualitative insights into the electronic properties can be obtained by contrasting closely related electronic structures. As the partial density of states (PDOS) provide a general identification of the nature of the orbital, the effects of the interface atoms on the electronic properties of the interface can be obtained by contrasting the PDOS. Fig. 6 (a) displays the total density of states (TDOS) for the second defect-free In/BaO3 heterojunction. The upper valence band ranges are mainly composed of In 5s5p, N 2p, Ti 3d and O 2p states. After oxygen vacancies are introduced at the second In/BaO3 interface, some new occupied states generate at the upper valence band in comparison with TDOS for the second defect-free In/BaO3 heterojunction (Fig. 6(b)), which might impact on the interfacial electrically conducting. Compared to the PDOS of the interface layer atoms, the new occupied states should mainly attribute to the In 5s5p contributions. The difference between the In atoms may be caused by the dangling bonds of the In atom near oxygen vacancy. 4. Summary In summary, the structural and electronic properties of InN on the BTO (111) substrate are studied using the DFT. The calculated surface energy per unit cell for BaO3-terminated BTO (111) surface is larger than that of Ti-terminated BTO (111) surface. The BaO3terminated BTO (111) covered by 1/4 monolayer In adsorption atoms at H3 sites shows the lowest energy under the lower coverage, which does not necessarily correspond to a real superstructure due to the computer limitation. For a higher coverage, In adsorption atoms prefer to occupy the TO sites of the BaO3terminated BTO (111) surface. The second In/BaO3 interface is the most energetically favorable among the atomic arrangements of the InN/BTO (111) interfaces. After oxygen vacancies are introduced in the second In/BaO3 interface, the occupied states generate at the upper valence band. Our model can also be applied to other III-nitride/Perovskite oxide interfaces. Acknowledgment This work has been supported by NSFC 11347016 and the Fundamental Research Funds for the Central Universities under
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Grant no. 2014QNA65. We are grateful to the High Performance Computing Center of China University of Mining and Technology for the award of CPU hours to accomplish this work.
Appendix A. Supplementary material Supplementary data associated with this article can be found in the online version at http://dx.doi.org/10.1016/j.jcrysgro.2014.03.018.
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