Microsc. Microanal., page 1 of 7 doi:10.1017/S1431927614000737
© MICROSCOPY SOCIETY OF AMERICA 2014
The Near Edge Structure of Hexagonal Boron Nitride Nicholas L. McDougall,1,* Rebecca J. Nicholls,2 Jim G. Partridge,1 and Dougal G. McCulloch1 1 2
Department of Physics, School of Applied Sciences, RMIT University, GPO Box 2476 V, Melbourne, Victoria 3001, Australia Department of Materials, University of Oxford, Parks Rd, Oxford, Oxfordshire, OX1 3PH, UK
Abstract: Hexagonal boron nitride (hBN) is a promising material for a range of applications including deep-ultraviolet light emission. Despite extensive experimental studies, some fundamental aspects of hBN remain unknown, such as the type of stacking faults likely to be present and their influence on electronic properties. In this paper, different stacking configurations of hBN are investigated using CASTEP, a pseudopotential density functional theory code. AB-b stacking faults, in which B atoms are positioned directly on top of one another while N atoms are located above the center of BN hexagons, are shown to be likely in conventional AB stacked hBN. Bandstructure calculations predict a single direct bandgap structure that may be responsible for the discrepancies in bandgap type observed experimentally. Calculations of the near edge structure showed that different stackings of hBN are distinguishable using measurements of core-loss edges in X-ray absorption and electron energy loss spectroscopy. AB stacking was found to best reproduce features in the experimental B and N K-edges. The calculations also show that splitting of the 1s to π* peak in the B K-edge, recently observed experimentally, may be accounted for by the presence of AB-b stacking faults. Key words: hBN, stacking faults, first principles, CASTEP, NES, EELS, ELNES, XAS, XANES
I NTRODUCTION Boron nitride (BN) is a synthetic material that exhibits many interesting properties (Riedel, 1994; Mirkarimi et al., 1997). It is analogous to carbon in having both a cubic diamond-like phase (cBN) and a hexagonal graphite-like phase (hBN). cBN is second only to diamond in hardness, but unlike diamond does not readily oxidize or dissolve in ferrous materials at elevated temperature (Riedel, 1994). This makes cBN a desirable coating for cutting tools; improving lifetime and reducing wear. Similar in bonding and structure to graphite, hBN consists of hexagonal rings of B and N atoms bonded strongly in-plane and weakly between planes. The ease of sliding between the basal planes makes hBN a useful solid lubricant (Watanabe et al., 1991), which unlike graphite is electrically insulating. hBN is a wide bandgap semiconductor with high thermal and chemical stability making it a promising material for compact deep-ultraviolet light emitting devices with applications including water purification, sterilization, and communication (Watanabe et al., 2004, 2009; Nebel, 2009). Realization of hBN devices requires an in-depth knowledge of its structure and electronic properties. Despite extensive experimental studies of hBN (Solozhenko et al., 2001; Watanabe et al., 2006; Song et al., 2010; Majety et al., 2012), fundamental properties including the nature and magnitude of the bandgap are in dispute. Both direct and indirect bandgaps have been reported, with values ranging from 3.6 to 7.1 eV (Solozhenko et al., 2001; Watanabe et al., 2004). These inconsistencies are commonly attributed to defects within the hBN crystal, such as stacking faults (Watanabe et al., 2009). Several ab-initio Received November 28, 2013; accepted March 21, 2014 *Corresponding author. [email protected]
theoretical studies have investigated the energetics of different stacking configurations in hBN. These found that in addition to the conventional AB stacking (in which layers are arranged with alternating B and N atoms aligned in the < 0001 > direction), other low energy stacking arrangements are possible (Liu et al., 2003; Constantinescu et al., 2013). Calculations of the electronic structure have shown that different stacking configurations produce a range of different bandgap energies that can be both direct and indirect (Liu et al., 2003; Yin et al. 2011). Evidence for stacking configurations other than AB have also been found in high-resolution transmission electron microscopy (TEM) images of chemical vapor deposited or exfoliated hBN layers (Warner et al., 2010; Kim et al., 2013; Shmeliov et al., 2013). Electronic structure calculations are useful in interpreting experimental results from core-loss electron energy loss spectroscopy (EELS) (Egerton, 1996) and X-ray absorption spectroscopy (XAS) (Stöhr, 1992). These techniques are capable of probing the local bonding arrangements and have the potential to characterize the microstructure in hBN materials, including the types of defects present. Here, we investigate the energetics and electronic structure of different stacking configurations in hBN using the ab-initio code CASTEP (Clark et al., 2005). The near edge structure (NES), which is measured in core-loss features in EELS and XAS, has also been calculated to enable experimental identification of the different possible stacking configurations in hBN materials.
MATERIALS
AND
METHODS
Theoretical investigations of the structural and electronic properties of hBN were carried out using the pseudopotential density functional theory (DFT) code CASTEP (v6.1) within
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Figure 1. hBN crystal structures of five potential stacking configurations investigated in this study. These structures are separated into two groups differing by a 60° rotation; Group I on the top row and Group II on the bottom row. Note that in stacking AD, there are two different atomic environments for both B and N (inequivalent atoms), shown in the two different views AD1 and AD2.
the local density approximation exchange correlation functional. Calculations performed using the generalized gradient functional (GGA-PBE) produced similar results with little discernible differences. The analysis tool OptaDOS (Nicholls et al., 2012) was used to calculate the density of states (DOS) and NES, including instrumental- and lifetimebroadening effects not available within CASTEP. Five hBN stacking configurations (AB, AB-b, AB-n, AA, and AD) have been considered as shown in Figure 1. A four atom unitcell with lattice parameters a = 2.504 Å, and c = 6.661 Å (Solozhenko et al., 2001) was used in the bandstructure and single point energy minimization calculations, while the NES was calculated using a 128 atom 4 × 4 × 2 supercell. This supercell was found to be sufficiently large to minimize effects of core-hole – core-hole interactions. In all calculations, the electronic wavefunctions were expanded using plane waves with a 500 eV kinetic energy cut-off and on-the-fly generated pseudopotentials, enabling the inclusion of core holes (Gao et al., 2009). A 20 × 20 × 4 Monkhorst-Pack grid (Monkhorst & Pack, 1976) generated the k-points for the unit-cell calculations and a 5 × 5 × 2 Monkhorst-Pack grid was used to generate the k-points for the supercell calculations, corresponding to an equal maximum k-point spacing of 0.023 Å−1 in the a-direction and 0.038 Å−1 in the c-direction for each system. A Pulay density mixing scheme was used in the
self-consistent field calculations with a minimum total energy/ atom convergence tolerance of 5 × 10−7 eV. The NES calculations were performed with unexcited adsorbing atoms, and various core-hole treatments. The inclusion of core-holes was implemented by charge removal of a 1s electron from the target atom, while smearing a neutralizing charge over the system. A 0.1 eV Gaussian function was used for the fixed smearing scheme of the DOS and a 0.6 eV Lorentzian instrumental broadening with a 0.1 eV lifetime broadening was applied to each NES spectrum. Each of the five structures in Figure 1 can be transformed into one another by gliding one basal plane relative to the other and/or rotation about the c-axis. Based on the transformations required, these structures can be split into two groups (as shown in Table 1). Within either group, structures require a 1.446 Å translation of one basal plane relative to the other to be converted into another structure. While between groups, a 60° rotation is necessary. The relative stability and the likelihood of transitions between stackings was investigated using a series of single point energy minimization calculations in which neighboring basal planes were shifted relative to one another in steps of 0.1446 Å. There are two different atomic environments for both B and N in the AD stacking, known as inequivalent atoms. These are shown in Figure 1 using two different views, labeled AD1 and AD2. The NES of B and N in stacking AD was calculated from an average of the spectra from both inequivalent atoms. Experimental EELS and XAS were collected from hBN powder synthesized under high temperature and high pressure conditions (HT–HP) obtained from Goodfellows (Huntingdon, England) for comparison with the calculated NES. The EELS spectra were collected using a JEOL 2100 F TEM equipped with a Tridiem Gatan Imaging Filter. An accelerating voltage of 120 kV was used, resulting in an EELS energy resolution (measured by the FWHM of the zero loss peak) of 0.7 eV. The spectra were collected under magic angle conditions (Hebert et al., 2006) utilizing the experimental methods presented by Daniels et al. (2003) and it was found that the magic angle conditions were approximately four times the collection angle (Hebert et al. 2004). Magic angle conditions produce an isotropic average with no orientation dependence on the NES, aiding the comparison of NES spectra of anisotropic materials. XAS was performed on the soft X-ray beam line at the Australian Synchrotron at an energy resolution of better than 0.1 eV. A horizontally polarized X-ray beam was used and the spectra were collected with the specimen tilted at an angle of 45° to the beam. The intensity of the X-rays was maximized at each energy using an Elliptically Polarized Undulator (Danfysik). The spectra were collected using the Auger electron yield and an electron flood gun was employed to minimize sample charging.
RESULTS
AND
DISCUSSION
The energy/atom for each stacking configuration is shown in Table 1. Stackings AB and AD were found to have the lowest energy/atom while AA had the highest, in agreement with
Near Edge Structure of Hexagonal Boron Nitride Table 1.
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Structural Properties of the Five Crystal Structures of hBN Considered Here.
Group hBN Group I
hBN Group II
Structure AB AB-b AB-n AA AD
Space Group 194 (P63/mmc) 194 (P63/mmc) 194 (P63/mmc) 187 (P-6m2) 156 (P3m1)
Fraction Coordinates (unit-cell) B: B: B: B: B: B:
(23 ; 13 ; 34) (0; 0; 34) (13 ; 23 ; 34) (13 ; 23 ; 34) (0; 0; 14) (13 ; 23 ; 34)
N: N: N: N: N: N:
(13 ; 23 ; 34) (13 ; 23 ; 34) (0; 0; 34) (23 ; 13 ; 34) (0; 0; 34) (23 ; 13 ; 14)
Eg (eV)
Total Energy (eV/atom) − 180.588 − 180.587 − 180.574 − 180.571 − 180.588
4.07 3.61 3.15 3.04 4.22
Indirect Direct Indirect Indirect Indirect
Also shown are the total energy/atom and bandgaps of each structure calculated using CASTEP.
previous calculations (Liu et al., 2003; Constantinescu et al., 2013). Bandstructure calculations (not shown) were used to determine the nature and magnitude of the bandgap for each of the five structures (Table 1). Our results show that stacking AA has the lowest bandgap (3.04 eV), followed by stacking AB-n (3.15 eV). Stackings AB-b and AB have bandgaps 3.61 and 4.07 eV, respectively. Stacking AD is found to have the highest bandgap energy (4.22 eV). These bandgaps compare well with those predicted by previous DFT calculations (Liu et al., 2003; Yin et al., 2011). Our theoretical values are smaller than those observed experimentally, which range between 3.6 and 7.1 eV (Solozhenko et al., 2001; Watanabe et al., 2004). DFT calculations are known to underestimate the value of the bandgap (Liu et al., 2003), so these values are expected to be lower than those found experimentally. All stacking configurations have an indirect bandgap, with the exception of AB-b, which was found to have a direct bandgap, in agreement with previous DFT calculations (Liu et al., 2003; Yin et al., 2011). Since both direct and indirect bandgaps have been reported in the literature, this result indicates that AB-b stacking defects could be responsible for the direct bandgaps observed experimentally. To determine the relative stabilities of stacking configurations, basal plane energy minimization calculations were performed. Figure 2a shows the change in total energy/atom relative to the AB structure for transitions between stackings in Group I. The insets show the direction of slippage of adjacent basal planes along the < 21 10 > direction as the AB stacking transforms to AB-b, AB-n and back to AB. Given the hexagonal structures three-fold symmetry, the potential energy barrier for translation is also equivalent for either the < 1210 > or < 1 120 > direction of slippage. The AB stacking was found to have the lowest energy of those in Group I, with the highest energy structure AB-n consisting of layers in which N atoms are directly on top of one another while B atoms are located above the center of BN hexagons. The equivalent structure AB-b in which B atoms are directly on top of one another is only slightly higher in energy than AB suggesting that AB-b is a probable stacking fault in hBN. Figure 2b shows a similar transition for the Group II structures AA and AD. Note that the structures in Figure 2b are related to those in Figure 2a by a 60° rotation, as shown in inset Figure 2c for the transition between AB-b and AD1. The AA structure in which both B and N atoms are on top of one another has the highest
energy of any stacking considered. AD (see Fig. 1) has an energy/atom similar to that of AB suggesting that it is also likely to occur as a stacking fault in hBN. However, the need to rotate in order to transform between AB and AD indicates that it may be less likely to occur than AB-b. The relative energy differences between the different stacking configurations are consistent with those published previously (Liu et al., 2003; Constantinescu et al., 2013). Since several stackings have energies within 0.001 eV of each other and are therefore predicted to coexist in experimentally synthesized BN, it would be advantageous to be able to discern between the stackings using their NES. The B and N K-edges from the AB structure calculated using different core-hole treatments are shown with EELS and
Figure 2. Change in total energy/atom for transitions between stacking configurations (relative to the AB structure) for (a) Group I and (b) Group II structures. The insets show the atomic configurations as adjacent basal planes slid relative to one another, allowing conversion between structures within each group. The inset (c) shows how structures require a 60° rotation to transform between groups.
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Figure 3. The calculated B K-edge for the AB stacking configuration (a) without a core-hole, (b) with a partial core-hole (3/4 of a 1s electron) and (c) with a full core-hole, compared with EELS and XAS experimental spectra.
XAS experimental data in Figures 3 and 4, respectively. Some differences in the EELS and XAS spectra may be accounted for by the increased energy resolution of the XAS technique. In addition, these techniques sample from different depths, with XAS the more surface sensitive. Therefore, surface related defects and/or surface contaminants are likely to produce additional features in the XAS. Our EELS and XAS experimental data is consistent with that published previously (Arenal et al., 2007; Peter et al., 2009). The main features in Figures 3 and 4 have been labeled i–v. Peaks i and ii are associated mainly with 1s to π* and 1s to σ* transitions, respectively. Peak iii originates from antibonding interactions involving N-2s orbitals to B-2pxy orbitals. Peak iv originates from antibonding interactions involving N-2pxy orbitals to B-2pxy orbitals (Tanaka et al., 1999). Peak v has been assigned to a σ* resonance (Berns et al., 1997). For the B K-edge, the theoretical spectra were shifted so that the onset of the first 1s to σ* peak (labeled ii) was aligned with the experimental data. Each spectrum was also normalized to the intensity of peak iii. Three different core-hole treatments were considered: no core-hole (Fig. 3a); a partial core-hole (3/4 of a 1s electron) (Fig. 3b); and a full corehole (Fig. 3c). The calculated NES with no core-hole compares well with a previous DFT study on the AB stacking
Figure 4. The calculated N K-edge for the AB stacking configuration (a) without a core-hole, (b) with a partial core-hole (3/4 of a 1s electron) and (c) with a full core-hole, compared with EELS and XAS experimental spectra.
(Wang et al., 2009). Previous work on cBN found that partial core-holes were required to correctly reproduce experimental data (McCulloch et al., 2012). The calculation without a core-hole (Fig. 3a) showed the weakest agreement with the experimental data, while the full core-hole calculation (Fig. 3c) dramatically overestimated the intensities of peaks i and ii. All calculations produce incorrect positions of peak v. Overall, the partial core-hole calculation was found to best reproduce the experimental B K-edge, with the exception of peaks iii and iv, which are ~1 eV lower than in the experiment. The major discrepancy in the calculations compared to the XAS data is that the doublet at ii is not found. The physical origin of the doublet is unknown. However, recent work has shown that boron vacancies, not included in our calculations, can be readily found in hBN (Meyer et al., 2009) and these may give rise to the observed splitting. Figure 4 shows the calculated N K-edge for the AB stacking using the same core-hole treatments as used in the B K-edge, compared with EELS and XAS experimental data. The calculated spectra have been shifted and normalized to peak ii. The partial core-hole treatment (Fig. 4b) provides good agreement with most of the features seen experimentally. The full core-hole calculation (Fig. 4c) also predicts the spectrum shape seen experimentally; however the relative intensities of the peaks are not well reproduced.
Near Edge Structure of Hexagonal Boron Nitride
Figure 5. Calculated B K-edges from five potential stacking configurations of hBN compared with the experimental EELS spectrum.
The B and N K-edge spectra of the five stacking configurations investigated are compared in Figures 5 and 6, respectively. Given that the partial core-hole treatment provided the best agreement with both the experimental B and N K-edges, these treatments were used in the calculations of the other stacking configurations. In the case of the B K-edges (Fig. 5), AB, AB-b, and AD stackings provide good agreement with the experimental data. As discussed above, these three structures are also found to have the lowest energies. The most significant changes occurring as a function of stacking configuration are in the positions and intensities of peaks iii and v. In the case of the N K-edges (Fig. 6), peaks i, iii, and iv are most sensitive to changes in stacking. In particular, there are significant variations in the vicinity of the 1s to π* peak (i) as the bonding environment between layers changes. Stacking AB best reproduced the experimental features in the N K-edge, while the high energy structures AA and AB-n provided the worst agreement with experiment. The calculations in Figures 5 and 6 show that the different stacking configurations are distinguishable using EELS or XAS. Previous work has shown evidence for a splitting of the B K-edge 1s to π* peak in XAS (Li et al., 2012, 2013). The origin of this splitting is not well understood and has been attributed to either coupling of core excitons to lattice vibrations or to stacking faults (Li et al., 2012).
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Figure 6. Calculated N K-edges from five potential stacking configurations of hBN compared with the experimental EELS spectrum.
Figure 7 shows an enlargement of the 1s to π* peak of our XAS spectrum, which also shows evidence of splitting. To determine if stacking faults could account for this splitting, the calculated spectra of all stackings were examined in the vicinity of the 1s to π* peak. The three low energy structures (AB, AB-b, and AD) have been superimposed onto the XAS spectrum. Note that a reduced broadening of a 0.1 eV Lorentzian instrumental broadening with a 0.1 eV lifetime broadening was applied. Both the AB and AD 1s to π* peaks are located at similar energies and are aligned with the more intense region of the split peak. The position of the 1s to π* peak for the AB-b stacking was found to be located near the lower energy feature of the split peak. This result suggests that the origin of the split peak may well be due to the presence of stacking faults, in particular AB-b.
CONCLUSIONS The energetics and core-loss NES of five different stacking configurations in hBN have been studied. Energy minimization calculations indicate the AB and AD structures have the lowest energies, followed by AB-b. Since rotation is necessary to transform between AB and AD, stacking faults of the type AB-b are more likely in a conventional hBN structure with AB stacking. The magnitude of the bandgaps of all five stackings were calculated and found in the range
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the support of the Australian National Computational Infrastructure National Facility (NCI-NF). Finally, the authors gratefully acknowledge support provided by the Australian Research Council (ARC) and the Australian Academy of Sciences.
REFERENCES
Figure 7. XAS spectrum of the B K-edge in the vicinity of the 1s to π* peak showing that this peak is split. Superimposed are the calculated B K-edges from the AB, AB-b, and AD configurations.
of 3.0–4.2 eV. AB-b stacking was the only structure predicted to have a direct bandgap. This result indicates AB-b stacking defects may be responsible for the discrepancies in bandgap type observed experimentally. NES calculations reproduced the main features of the core-loss edges observed experimentally in EELS and XAS, provided core-holes were included. A comparison between the NES of the different stacking configurations revealed that the AB stacking best reproduced the B and N K-edges. These calculations also show that the recent experimentally observed splitting of the 1s to π* peak in the B K-edge may be accounted for by the presence of AB-b stacking faults. Finally, the results show that it is possible to distinguish between the different stacking configurations of hBN using the NES, opening up the possibility of characterizing stacking faults in hBN using EELS in high-resolution scanning transmission electron microscopes.
ACKNOWLEDGMENTS The authors gratefully acknowledge the facilities, and the scientific and technical assistance, of the Australian Microscopy & Microanalysis Research Facility at the RMIT Microscopy & Microanalysis Facility, at RMIT University. The authors also would like to gratefully acknowledge Dr. Desmond Lau for painstaking EELS acquisitions, the Australian Synchrotron and
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© MICROSCOPY SOCIETY OF AMERICA 2014
The Near Edge Structure of Hexagonal Boron Nitride Nicholas L. McDougall,1,* Rebecca J. Nicholls,2 Jim G. Partridge,1 and Dougal G. McCulloch1 1 2
Department of Physics, School of Applied Sciences, RMIT University, GPO Box 2476 V, Melbourne, Victoria 3001, Australia Department of Materials, University of Oxford, Parks Rd, Oxford, Oxfordshire, OX1 3PH, UK
Abstract: Hexagonal boron nitride (hBN) is a promising material for a range of applications including deep-ultraviolet light emission. Despite extensive experimental studies, some fundamental aspects of hBN remain unknown, such as the type of stacking faults likely to be present and their influence on electronic properties. In this paper, different stacking configurations of hBN are investigated using CASTEP, a pseudopotential density functional theory code. AB-b stacking faults, in which B atoms are positioned directly on top of one another while N atoms are located above the center of BN hexagons, are shown to be likely in conventional AB stacked hBN. Bandstructure calculations predict a single direct bandgap structure that may be responsible for the discrepancies in bandgap type observed experimentally. Calculations of the near edge structure showed that different stackings of hBN are distinguishable using measurements of core-loss edges in X-ray absorption and electron energy loss spectroscopy. AB stacking was found to best reproduce features in the experimental B and N K-edges. The calculations also show that splitting of the 1s to π* peak in the B K-edge, recently observed experimentally, may be accounted for by the presence of AB-b stacking faults. Key words: hBN, stacking faults, first principles, CASTEP, NES, EELS, ELNES, XAS, XANES
I NTRODUCTION Boron nitride (BN) is a synthetic material that exhibits many interesting properties (Riedel, 1994; Mirkarimi et al., 1997). It is analogous to carbon in having both a cubic diamond-like phase (cBN) and a hexagonal graphite-like phase (hBN). cBN is second only to diamond in hardness, but unlike diamond does not readily oxidize or dissolve in ferrous materials at elevated temperature (Riedel, 1994). This makes cBN a desirable coating for cutting tools; improving lifetime and reducing wear. Similar in bonding and structure to graphite, hBN consists of hexagonal rings of B and N atoms bonded strongly in-plane and weakly between planes. The ease of sliding between the basal planes makes hBN a useful solid lubricant (Watanabe et al., 1991), which unlike graphite is electrically insulating. hBN is a wide bandgap semiconductor with high thermal and chemical stability making it a promising material for compact deep-ultraviolet light emitting devices with applications including water purification, sterilization, and communication (Watanabe et al., 2004, 2009; Nebel, 2009). Realization of hBN devices requires an in-depth knowledge of its structure and electronic properties. Despite extensive experimental studies of hBN (Solozhenko et al., 2001; Watanabe et al., 2006; Song et al., 2010; Majety et al., 2012), fundamental properties including the nature and magnitude of the bandgap are in dispute. Both direct and indirect bandgaps have been reported, with values ranging from 3.6 to 7.1 eV (Solozhenko et al., 2001; Watanabe et al., 2004). These inconsistencies are commonly attributed to defects within the hBN crystal, such as stacking faults (Watanabe et al., 2009). Several ab-initio Received November 28, 2013; accepted March 21, 2014 *Corresponding author. [email protected]
theoretical studies have investigated the energetics of different stacking configurations in hBN. These found that in addition to the conventional AB stacking (in which layers are arranged with alternating B and N atoms aligned in the < 0001 > direction), other low energy stacking arrangements are possible (Liu et al., 2003; Constantinescu et al., 2013). Calculations of the electronic structure have shown that different stacking configurations produce a range of different bandgap energies that can be both direct and indirect (Liu et al., 2003; Yin et al. 2011). Evidence for stacking configurations other than AB have also been found in high-resolution transmission electron microscopy (TEM) images of chemical vapor deposited or exfoliated hBN layers (Warner et al., 2010; Kim et al., 2013; Shmeliov et al., 2013). Electronic structure calculations are useful in interpreting experimental results from core-loss electron energy loss spectroscopy (EELS) (Egerton, 1996) and X-ray absorption spectroscopy (XAS) (Stöhr, 1992). These techniques are capable of probing the local bonding arrangements and have the potential to characterize the microstructure in hBN materials, including the types of defects present. Here, we investigate the energetics and electronic structure of different stacking configurations in hBN using the ab-initio code CASTEP (Clark et al., 2005). The near edge structure (NES), which is measured in core-loss features in EELS and XAS, has also been calculated to enable experimental identification of the different possible stacking configurations in hBN materials.
MATERIALS
AND
METHODS
Theoretical investigations of the structural and electronic properties of hBN were carried out using the pseudopotential density functional theory (DFT) code CASTEP (v6.1) within
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Figure 1. hBN crystal structures of five potential stacking configurations investigated in this study. These structures are separated into two groups differing by a 60° rotation; Group I on the top row and Group II on the bottom row. Note that in stacking AD, there are two different atomic environments for both B and N (inequivalent atoms), shown in the two different views AD1 and AD2.
the local density approximation exchange correlation functional. Calculations performed using the generalized gradient functional (GGA-PBE) produced similar results with little discernible differences. The analysis tool OptaDOS (Nicholls et al., 2012) was used to calculate the density of states (DOS) and NES, including instrumental- and lifetimebroadening effects not available within CASTEP. Five hBN stacking configurations (AB, AB-b, AB-n, AA, and AD) have been considered as shown in Figure 1. A four atom unitcell with lattice parameters a = 2.504 Å, and c = 6.661 Å (Solozhenko et al., 2001) was used in the bandstructure and single point energy minimization calculations, while the NES was calculated using a 128 atom 4 × 4 × 2 supercell. This supercell was found to be sufficiently large to minimize effects of core-hole – core-hole interactions. In all calculations, the electronic wavefunctions were expanded using plane waves with a 500 eV kinetic energy cut-off and on-the-fly generated pseudopotentials, enabling the inclusion of core holes (Gao et al., 2009). A 20 × 20 × 4 Monkhorst-Pack grid (Monkhorst & Pack, 1976) generated the k-points for the unit-cell calculations and a 5 × 5 × 2 Monkhorst-Pack grid was used to generate the k-points for the supercell calculations, corresponding to an equal maximum k-point spacing of 0.023 Å−1 in the a-direction and 0.038 Å−1 in the c-direction for each system. A Pulay density mixing scheme was used in the
self-consistent field calculations with a minimum total energy/ atom convergence tolerance of 5 × 10−7 eV. The NES calculations were performed with unexcited adsorbing atoms, and various core-hole treatments. The inclusion of core-holes was implemented by charge removal of a 1s electron from the target atom, while smearing a neutralizing charge over the system. A 0.1 eV Gaussian function was used for the fixed smearing scheme of the DOS and a 0.6 eV Lorentzian instrumental broadening with a 0.1 eV lifetime broadening was applied to each NES spectrum. Each of the five structures in Figure 1 can be transformed into one another by gliding one basal plane relative to the other and/or rotation about the c-axis. Based on the transformations required, these structures can be split into two groups (as shown in Table 1). Within either group, structures require a 1.446 Å translation of one basal plane relative to the other to be converted into another structure. While between groups, a 60° rotation is necessary. The relative stability and the likelihood of transitions between stackings was investigated using a series of single point energy minimization calculations in which neighboring basal planes were shifted relative to one another in steps of 0.1446 Å. There are two different atomic environments for both B and N in the AD stacking, known as inequivalent atoms. These are shown in Figure 1 using two different views, labeled AD1 and AD2. The NES of B and N in stacking AD was calculated from an average of the spectra from both inequivalent atoms. Experimental EELS and XAS were collected from hBN powder synthesized under high temperature and high pressure conditions (HT–HP) obtained from Goodfellows (Huntingdon, England) for comparison with the calculated NES. The EELS spectra were collected using a JEOL 2100 F TEM equipped with a Tridiem Gatan Imaging Filter. An accelerating voltage of 120 kV was used, resulting in an EELS energy resolution (measured by the FWHM of the zero loss peak) of 0.7 eV. The spectra were collected under magic angle conditions (Hebert et al., 2006) utilizing the experimental methods presented by Daniels et al. (2003) and it was found that the magic angle conditions were approximately four times the collection angle (Hebert et al. 2004). Magic angle conditions produce an isotropic average with no orientation dependence on the NES, aiding the comparison of NES spectra of anisotropic materials. XAS was performed on the soft X-ray beam line at the Australian Synchrotron at an energy resolution of better than 0.1 eV. A horizontally polarized X-ray beam was used and the spectra were collected with the specimen tilted at an angle of 45° to the beam. The intensity of the X-rays was maximized at each energy using an Elliptically Polarized Undulator (Danfysik). The spectra were collected using the Auger electron yield and an electron flood gun was employed to minimize sample charging.
RESULTS
AND
DISCUSSION
The energy/atom for each stacking configuration is shown in Table 1. Stackings AB and AD were found to have the lowest energy/atom while AA had the highest, in agreement with
Near Edge Structure of Hexagonal Boron Nitride Table 1.
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Structural Properties of the Five Crystal Structures of hBN Considered Here.
Group hBN Group I
hBN Group II
Structure AB AB-b AB-n AA AD
Space Group 194 (P63/mmc) 194 (P63/mmc) 194 (P63/mmc) 187 (P-6m2) 156 (P3m1)
Fraction Coordinates (unit-cell) B: B: B: B: B: B:
(23 ; 13 ; 34) (0; 0; 34) (13 ; 23 ; 34) (13 ; 23 ; 34) (0; 0; 14) (13 ; 23 ; 34)
N: N: N: N: N: N:
(13 ; 23 ; 34) (13 ; 23 ; 34) (0; 0; 34) (23 ; 13 ; 34) (0; 0; 34) (23 ; 13 ; 14)
Eg (eV)
Total Energy (eV/atom) − 180.588 − 180.587 − 180.574 − 180.571 − 180.588
4.07 3.61 3.15 3.04 4.22
Indirect Direct Indirect Indirect Indirect
Also shown are the total energy/atom and bandgaps of each structure calculated using CASTEP.
previous calculations (Liu et al., 2003; Constantinescu et al., 2013). Bandstructure calculations (not shown) were used to determine the nature and magnitude of the bandgap for each of the five structures (Table 1). Our results show that stacking AA has the lowest bandgap (3.04 eV), followed by stacking AB-n (3.15 eV). Stackings AB-b and AB have bandgaps 3.61 and 4.07 eV, respectively. Stacking AD is found to have the highest bandgap energy (4.22 eV). These bandgaps compare well with those predicted by previous DFT calculations (Liu et al., 2003; Yin et al., 2011). Our theoretical values are smaller than those observed experimentally, which range between 3.6 and 7.1 eV (Solozhenko et al., 2001; Watanabe et al., 2004). DFT calculations are known to underestimate the value of the bandgap (Liu et al., 2003), so these values are expected to be lower than those found experimentally. All stacking configurations have an indirect bandgap, with the exception of AB-b, which was found to have a direct bandgap, in agreement with previous DFT calculations (Liu et al., 2003; Yin et al., 2011). Since both direct and indirect bandgaps have been reported in the literature, this result indicates that AB-b stacking defects could be responsible for the direct bandgaps observed experimentally. To determine the relative stabilities of stacking configurations, basal plane energy minimization calculations were performed. Figure 2a shows the change in total energy/atom relative to the AB structure for transitions between stackings in Group I. The insets show the direction of slippage of adjacent basal planes along the < 21 10 > direction as the AB stacking transforms to AB-b, AB-n and back to AB. Given the hexagonal structures three-fold symmetry, the potential energy barrier for translation is also equivalent for either the < 1210 > or < 1 120 > direction of slippage. The AB stacking was found to have the lowest energy of those in Group I, with the highest energy structure AB-n consisting of layers in which N atoms are directly on top of one another while B atoms are located above the center of BN hexagons. The equivalent structure AB-b in which B atoms are directly on top of one another is only slightly higher in energy than AB suggesting that AB-b is a probable stacking fault in hBN. Figure 2b shows a similar transition for the Group II structures AA and AD. Note that the structures in Figure 2b are related to those in Figure 2a by a 60° rotation, as shown in inset Figure 2c for the transition between AB-b and AD1. The AA structure in which both B and N atoms are on top of one another has the highest
energy of any stacking considered. AD (see Fig. 1) has an energy/atom similar to that of AB suggesting that it is also likely to occur as a stacking fault in hBN. However, the need to rotate in order to transform between AB and AD indicates that it may be less likely to occur than AB-b. The relative energy differences between the different stacking configurations are consistent with those published previously (Liu et al., 2003; Constantinescu et al., 2013). Since several stackings have energies within 0.001 eV of each other and are therefore predicted to coexist in experimentally synthesized BN, it would be advantageous to be able to discern between the stackings using their NES. The B and N K-edges from the AB structure calculated using different core-hole treatments are shown with EELS and
Figure 2. Change in total energy/atom for transitions between stacking configurations (relative to the AB structure) for (a) Group I and (b) Group II structures. The insets show the atomic configurations as adjacent basal planes slid relative to one another, allowing conversion between structures within each group. The inset (c) shows how structures require a 60° rotation to transform between groups.
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Figure 3. The calculated B K-edge for the AB stacking configuration (a) without a core-hole, (b) with a partial core-hole (3/4 of a 1s electron) and (c) with a full core-hole, compared with EELS and XAS experimental spectra.
XAS experimental data in Figures 3 and 4, respectively. Some differences in the EELS and XAS spectra may be accounted for by the increased energy resolution of the XAS technique. In addition, these techniques sample from different depths, with XAS the more surface sensitive. Therefore, surface related defects and/or surface contaminants are likely to produce additional features in the XAS. Our EELS and XAS experimental data is consistent with that published previously (Arenal et al., 2007; Peter et al., 2009). The main features in Figures 3 and 4 have been labeled i–v. Peaks i and ii are associated mainly with 1s to π* and 1s to σ* transitions, respectively. Peak iii originates from antibonding interactions involving N-2s orbitals to B-2pxy orbitals. Peak iv originates from antibonding interactions involving N-2pxy orbitals to B-2pxy orbitals (Tanaka et al., 1999). Peak v has been assigned to a σ* resonance (Berns et al., 1997). For the B K-edge, the theoretical spectra were shifted so that the onset of the first 1s to σ* peak (labeled ii) was aligned with the experimental data. Each spectrum was also normalized to the intensity of peak iii. Three different core-hole treatments were considered: no core-hole (Fig. 3a); a partial core-hole (3/4 of a 1s electron) (Fig. 3b); and a full corehole (Fig. 3c). The calculated NES with no core-hole compares well with a previous DFT study on the AB stacking
Figure 4. The calculated N K-edge for the AB stacking configuration (a) without a core-hole, (b) with a partial core-hole (3/4 of a 1s electron) and (c) with a full core-hole, compared with EELS and XAS experimental spectra.
(Wang et al., 2009). Previous work on cBN found that partial core-holes were required to correctly reproduce experimental data (McCulloch et al., 2012). The calculation without a core-hole (Fig. 3a) showed the weakest agreement with the experimental data, while the full core-hole calculation (Fig. 3c) dramatically overestimated the intensities of peaks i and ii. All calculations produce incorrect positions of peak v. Overall, the partial core-hole calculation was found to best reproduce the experimental B K-edge, with the exception of peaks iii and iv, which are ~1 eV lower than in the experiment. The major discrepancy in the calculations compared to the XAS data is that the doublet at ii is not found. The physical origin of the doublet is unknown. However, recent work has shown that boron vacancies, not included in our calculations, can be readily found in hBN (Meyer et al., 2009) and these may give rise to the observed splitting. Figure 4 shows the calculated N K-edge for the AB stacking using the same core-hole treatments as used in the B K-edge, compared with EELS and XAS experimental data. The calculated spectra have been shifted and normalized to peak ii. The partial core-hole treatment (Fig. 4b) provides good agreement with most of the features seen experimentally. The full core-hole calculation (Fig. 4c) also predicts the spectrum shape seen experimentally; however the relative intensities of the peaks are not well reproduced.
Near Edge Structure of Hexagonal Boron Nitride
Figure 5. Calculated B K-edges from five potential stacking configurations of hBN compared with the experimental EELS spectrum.
The B and N K-edge spectra of the five stacking configurations investigated are compared in Figures 5 and 6, respectively. Given that the partial core-hole treatment provided the best agreement with both the experimental B and N K-edges, these treatments were used in the calculations of the other stacking configurations. In the case of the B K-edges (Fig. 5), AB, AB-b, and AD stackings provide good agreement with the experimental data. As discussed above, these three structures are also found to have the lowest energies. The most significant changes occurring as a function of stacking configuration are in the positions and intensities of peaks iii and v. In the case of the N K-edges (Fig. 6), peaks i, iii, and iv are most sensitive to changes in stacking. In particular, there are significant variations in the vicinity of the 1s to π* peak (i) as the bonding environment between layers changes. Stacking AB best reproduced the experimental features in the N K-edge, while the high energy structures AA and AB-n provided the worst agreement with experiment. The calculations in Figures 5 and 6 show that the different stacking configurations are distinguishable using EELS or XAS. Previous work has shown evidence for a splitting of the B K-edge 1s to π* peak in XAS (Li et al., 2012, 2013). The origin of this splitting is not well understood and has been attributed to either coupling of core excitons to lattice vibrations or to stacking faults (Li et al., 2012).
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Figure 6. Calculated N K-edges from five potential stacking configurations of hBN compared with the experimental EELS spectrum.
Figure 7 shows an enlargement of the 1s to π* peak of our XAS spectrum, which also shows evidence of splitting. To determine if stacking faults could account for this splitting, the calculated spectra of all stackings were examined in the vicinity of the 1s to π* peak. The three low energy structures (AB, AB-b, and AD) have been superimposed onto the XAS spectrum. Note that a reduced broadening of a 0.1 eV Lorentzian instrumental broadening with a 0.1 eV lifetime broadening was applied. Both the AB and AD 1s to π* peaks are located at similar energies and are aligned with the more intense region of the split peak. The position of the 1s to π* peak for the AB-b stacking was found to be located near the lower energy feature of the split peak. This result suggests that the origin of the split peak may well be due to the presence of stacking faults, in particular AB-b.
CONCLUSIONS The energetics and core-loss NES of five different stacking configurations in hBN have been studied. Energy minimization calculations indicate the AB and AD structures have the lowest energies, followed by AB-b. Since rotation is necessary to transform between AB and AD, stacking faults of the type AB-b are more likely in a conventional hBN structure with AB stacking. The magnitude of the bandgaps of all five stackings were calculated and found in the range
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the support of the Australian National Computational Infrastructure National Facility (NCI-NF). Finally, the authors gratefully acknowledge support provided by the Australian Research Council (ARC) and the Australian Academy of Sciences.
REFERENCES
Figure 7. XAS spectrum of the B K-edge in the vicinity of the 1s to π* peak showing that this peak is split. Superimposed are the calculated B K-edges from the AB, AB-b, and AD configurations.
of 3.0–4.2 eV. AB-b stacking was the only structure predicted to have a direct bandgap. This result indicates AB-b stacking defects may be responsible for the discrepancies in bandgap type observed experimentally. NES calculations reproduced the main features of the core-loss edges observed experimentally in EELS and XAS, provided core-holes were included. A comparison between the NES of the different stacking configurations revealed that the AB stacking best reproduced the B and N K-edges. These calculations also show that the recent experimentally observed splitting of the 1s to π* peak in the B K-edge may be accounted for by the presence of AB-b stacking faults. Finally, the results show that it is possible to distinguish between the different stacking configurations of hBN using the NES, opening up the possibility of characterizing stacking faults in hBN using EELS in high-resolution scanning transmission electron microscopes.
ACKNOWLEDGMENTS The authors gratefully acknowledge the facilities, and the scientific and technical assistance, of the Australian Microscopy & Microanalysis Research Facility at the RMIT Microscopy & Microanalysis Facility, at RMIT University. The authors also would like to gratefully acknowledge Dr. Desmond Lau for painstaking EELS acquisitions, the Australian Synchrotron and
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