Intrinsic Metallic and Semiconducting Cubic Boron Nitride Nanofilms

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Intrinsic Metallic and Semiconducting Cubic Boron Nitride Nanofilms Zhuhua Zhang*,†,‡ and Wanlin Guo*,† †

State Key Laboratory of Mechanics and Control of Mechanical Structures, Key Laboratory for Intelligent Nano Materials and Devices of Ministry of Education and Institute of Nano Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China ‡ Department of Mechanical Engineering and Materials Science, Rice University, Houston, Texas 77005, United States S Supporting Information *

ABSTRACT: We show by density functional theory calculations with both hybrid and semilocal functionals that cubic boron nitride (111) nanofilms are intrinsically metallic and even turn into semiconductors once the thickness is less than 0.69 nm, which is in sharp contrast to the known insulating nature of boron nitride materials. The exceptional metallic or semiconducting band gap is due to a combined effect of thicknessdependent inbuilt electric polarization and labile near-gap states unique in the polar nanofilms. The band gap and dipole moment of the nanofilms can be further significantly tuned by applying an in-plane strain. These distinguished features of the boron nitride nanofilms are robust to surface passivation and can be enhanced by hybridizing with diamond films, thereby opening an exciting prospect of using the versatile cubic nanofilms in future electronic and piezoelectric devices. KEYWORDS: Boron nitride, metal, semiconductor, nanofilm, strain, density functional theory calculations

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different from those of diamond nanofilms. Still, no study on the electronic structures of BNNFs can be found. Here, we reveal by first-principles calculations with both hybrid and local functionals that the BNNFs are widely metallic and can even turn into semiconducting when the thickness is less than 0.69 nm, which is contrary to intrinsic electrical insulation in known BN materials. Interestingly, applying epitaxial strain can further significantly tune the electronic properties and the dipole moment of the BNNFs. It is practically important that these properties in the BNNFs are robust against variation in the surface chemical termination and can be enhanced when welded on a diamond film, thereby offering a wealth of opportunities for using the BNNFs in versatile electronic and piezoelectric devices, especially for allBN devices with atomically perfect semiconductor−metal interface to serve in extreme environments. The calculations are performed using projector-augmented wave potentials21−23 with a plane-wave basis within the generalized gradient approximation (GGA).24 Kinetic energy cutoff of 500 eV is chosen in the plane-wave expansion. Considering that the BNNFs are electrically polarized, the vacuum region along the normal of the nanofilm is carefully checked by increasing it to 200 Å to examine spurious dipole interactions between the neighboring BNNFs in repeated supercells. We find that a vacuum region of 16 Å is enough to achieve convergence in electronic properties of the BNNFs and

oron nitride (BN) is isomorphic to carbon in many lattice configurations and has attracted wide research attention due to both fundamental reason and its immense potential for applications.1−3 In particular, as an isoelectronic isomorph of diamond, cubic BN (c-BN) has received special interests since it not only offers a number of extreme properties comparable to diamond but also is superior to diamond in higher chemical and thermal stabilities.4 It has been shown that c-BN can be robust to high-temperature wetting of most molten metals and hence suitable for fabricating nanoscale devices operating in harsh environments. However, the realization of c-BN-based electronic devices is still a challenging task due largely to electrically insulating nature of c-BN with a band gap around 6.4 eV.5,6 Although extensive research efforts have been devoted to modifying the electronic properties c-BN structures,7−9 few of them can fit practical applications. In contrast, intrinsic metallic and semiconducting forms of c-BN are more appealing but have never been reported. Recent experimental10−15 and theoretical16−18 studies have demonstrated that few-layer graphene can be transformed into multilayer graphane by chemical functionalizations with structure identical to few-layer (111) oriented diamond nanofilms. In contrast to graphene that has zero gap,19 the diamond nanofilm becomes insulating independent of its thickness.18,20 Using similar experimental strategy, one should be able to transform few-layer hexagonal BN (h-BN) sheet into hydrogenated sp3-bonded BN film whose structure will be equivalent to that of c-BN(111) nanofilms (BNNFs). Unlike the diamond films, the BNNFs have spontaneous electric polarization due to ionic character of B−N bonds. Therefore, the intrinsic properties of BNNFs would be dramatically © XXXX American Chemical Society

Received: April 14, 2012 Revised: June 4, 2012

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thus adopted in the calculations. Dipole correction25 to total energy is considered owing to the intrinsic polarization of the BNNFs. The 2D Brillouin zone integration is sampled by 60 special k-points and all the atoms are allowed to relax until the force on each atom is less than 0.01 eV/Å. External electric field is simulated by planar dipole layer method.26 In addition, the hybrid density functional theory calculations are performed by using functional developed by Heyd, Scuseria, and Ernzerhof (HSE06), which combines the GGA and Hartree−Fock contributions to describe the short-range part of the exchange functional while uses only GGA to describe the long-range part and the correlation functional.27 For comparison, we also performed the electronic structure calculations using the Becke and Lee−Yang−Parr (B3LYP) functional28,29 as put into practice with the CASTEP code. The BNNF has a thickness characterized by the number of B−N double layers across the films. Here, we use the notation n-BNNF to describe a BNNF having n B−N double layers. The 1-BNNF is just the hydrogenated single-layer h-BN sheet.30 Figure 1 illustrates the atomic structures of the 2- and 3-

Figure 2. Thickness-dependent band gap in n-BNNFs calculated using different functionals. The gap of bulk c-BN calculated by HSE06 functional is also provided.

developed HSE06 functional, which gives more reliable energy gap with respect to experiments. For example, the band gap of c-BN calculated by HSE06 functional is 6.0 eV, close to experimental value of 6.4 eV.5,6 It is gratifying that the band gap calculated with the HSE06 functional in the 4-BNNF and thicker ones remain closed, further verifying their metallicity, whereas the band gap of semiconducting BNNFs are remarkably widened. Especially, the band gaps of 2- and 3BNNFs are increased to 1.85 and 0.24 eV, respectively, which are being dreamed in the zero-gap graphene and insulating hBN sheet. To be more convinced, we further carry out calculations using the hybrid B3LYP functional and find essentially the same thickness-dependent band gap as that from the HSE06 (Figure 2). So it is valid that the BNNFs are natural 2D metal or semiconductor of long pursuit in BN electronics, without aid of any dopants,32−34 dangling bond states,35−38 external electric fields39,40 or mechanical strain41−43 as previously exploited for sp2-bonded h-BN nanotubes and nanoribbons. The flexibility in realizing metallic and semiconducting BNNFs by varying thickness is a great advantage for constructing device architectures based on BNNFs. For example, we can conceive a metal−semiconductor junction by partially thinning a metallic BNNF through industrial lithographic process, so that the metal-semiconductor interface formed by thin and thick BNNFs can be atomically smooth with optimal contact resistance. We then explore the electronic properties of the BNNFs by examining their band structures. Since the band features are similar in different BNNFs, we choose the 3-BNNF as a model system. Figure 3a presents the GGA band structure of the 3BNNF, which has a direct band gap of 0.1 eV at the Γ point. The band gap is widened to 0.24 eV in the HSE06 band structure shown in Figure 3b, largely contributed by a rigid upshift of the conduction bands. The valence band maximum (VBM) is contributed by mixed 2px and 2py orbitals of subsurface N atoms near the B-end surface, while the conduction band minimum (CBM) is from the 2pz states of N atoms at the N-end surface, as illustrated in Figure 3c and Supporting Information Figure S3. Therefore, the electron and hole carriers will be spatially separated in the BNNF, which is highly desired for photovoltaic applications.44 However, the charge density of CBM is found several times sparser than the VBM. Especially, most of the CBM state was peaked at 2.2 Å from the N-end surface outside the nanofilm and adopts dispersion like nearly free electron (NFE) states along the film. Moreover, the three higher conduction band states also have the NFE-like character and show increased amount of peaks from 2 for the CBM+1 state to 4 for the CBM+3 state (Figure

Figure 1. Atomic configurations of BNNFs. Prospective views of the atomic structures of the (a) 2- and (b) 3-BNNFs. The numbers mark the B−N double layers.

BNNFs. The BNNF has one of its surfaces composed by B atoms and the other by N atoms, named as B-end and N-end surfaces, respectively. In the 3-BNNF, the length of the B−N bond within the B−N double layer is around 1.6 Å, longer than 1.56 Å in bulk c-BN, while that between two neighboring double layers is shortened to 1.5 Å. So the B−N double layers in BNNFs are bound together more tightly than in bulk c-BN. Such alternation in the B−N bond length across the nanofilm becomes more pronounced in a thinner BNNF, somewhat akin to the Jahn−Teller distortion in finite molecular systems.31 Since the BNNFs are naturally occurring phases, they all are confirmed to be highly stable through the ab initio molecular dynamic simulations and phonon spectra calculations (see Supporting Information Figure S1). Figure 2 shows the calculated band gap by different functionals as a function of thickness of the BNNF. The most surprising result is that all the n-BNNFs become metallic when n ≥ 4 with a critical thickness of 0.69 nm, which is in sharp contrast to known insulating nature in c- and h-BN structures. Only when n is less than 4, the n-BNNF becomes semiconducting but the band gap is dramatically reduced with increasing film thickness from 2.9 eV in the 1-BNNF to only 0.1 eV in the 3-BNNF. The above results reappear in the calculations with local density approximation (LDA). As both the GGA and LDA underestimate the band gap of most semiconductors, we perform calculations with the newly B

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silicon. These elegant electronic properties of the BNNFs are robust against the variation in surface terminations, such as in F- and OH-terminated BNNFs. To further elucidate the origin of the metallic and semiconducting BNNFs, we plot plane-averaged electrostatic potential along the normal of the film in Figure 4a. An averaged potential difference of 7.3 eV is found between the B-end and N-end surfaces due to the lower electronegativity of B atom than the N atom. Therefore, the BNNF is embedded with a vertical electric polarization pointing from the B-end surface to the N-end surface, which causes charges accumulation at the Nend surface and depletion from the B-end surface, as shown in Figure 4b. This intersurface charge transfer pushes up the levels of the states around the B-end surface and lowers those around the N-end surface, thereby reducing the band gap of the nanofilm. The energy gap of the BNNF is entirely determined by such inbuilt potential difference and not by the quantum confinement. The inbuilt potential difference is higher in a thicker nanofilm (Figure 4c) and therefore hastens a more pronounced intersurface charge transfer, as supported by comparing the total charge distribution (Supporting Information Figure S4). The enhanced charge transfer with increasing film thickness not only sharply reduces the band gap but also metallizes the BNNF when the transferred charge becomes sufficient for band occupation. Indeed, the conduction and valence bands of the 4-BNNFs overlap around the Γ point to become partially occupied (see Supporting Information Figure S5). This metallicity can persist in thicker BNNFs, as has been testified in the 48-BNNF with a thickness of 10 nm. Nevertheless, the decrease in the effective potential gradient (Figure 4c) across the nanofilms ensures that the metallicity will saturate for BNNFs thick enough, like the case in zigzag hBN nanoribbons whose band gap decreases with increasing ribbon width and converges to a value notably smaller than that of the 2D h-BN sheet.39,40

Figure 3. Electronic structures of the BNNFs. (a,b) Band structures of the 3-BNNF calculated by the (a) GGA with PBE and (b) HSE06 functional. (c) Plane-averaged charge density (solid lines) along the direction normal to the nanofilm for electronic states of the VBM, CBM, CBM+1, CBM+2, and CBM+3, respectively. The insets illustrate isosurface plots of the corresponding partial charge densities to these states.

3c). These states can be categorized into a series of Rydberglike image potential states,45 similar to those revealed in graphene and h-BN structures.46,47 As will be shown, the peculiar NFE-like conduction band states are crucial to yielding the metallic and semiconducting BNNFs. As a result of the NFE-like band dispersions, the electron and hole effective masses of the BNNF are calculated to be 1.0 m0 and 1.2 m0 (m0 is the mass of free electron), respectively, close to those in

Figure 4. Mechanism for metallic and semiconducting properties in BNNFs. (a) Plane-averaged electrostatic potential along the normal of the nanofilm. (b) Plane-integrated charge transfer upon formation of the 3-BNNF from isolated atoms. The insets show the position of the nanofilm in the same scale with the z-coordinate. (c) Plane-averaged potential difference between the two planes formed by the surface B and N atoms as well as the potential gradient across the film thickness as a function of n. (d) Band gap change in the 1- and 2-BNNFs as well as in h-BN nanoribbons as functions of wEext, where Eext is the strength of the external electric field and w is the nanofilm thickness or ribbon width. Diamonds filled with different colors represent the cases for nanoribbons with different widths. C

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To this end, it remains unclear why the inbuilt electric field becomes so powerful in reducing and even closing the gap in the BNNFs, especially considering that the band gap of zigzag h-BN nanoribbons is reduced rather limited by the inbuilt polarization.39,40 This can be readily understood when one recollects the distribution of the peculiar conduction band states in the 3-BNNF, most of which are dispersed as NFE states outside of the nanofilm. As such, these states are weakly bound to the nanofilm and their redistribution against variation in the inbuilt polarization will be unusually labile. An attractive image potential created by the polarization will drive these NFE-like states converging onto the vacuum level, following a swift drop in energy toward the Fermi level. The energy levels of these NFE-like states are specified by the screening properties along the normal of the nanofilms, which only depend on the film thickness. In stark contrast, the near-gap states in the h-BN ribbons mainly refer to the π and π* electronic states that are locked on the nanoribbons and therefore behave more inert to their inbuilt polarization. This difference is further analyzed on the Stark effect by applying an external electric field Eext, which changes the band gaps by introducing an additional potential difference wEext (w is the BNNF thickness or ribbon width) to the inbuilt potential difference. Figure 4d shows that the change in the band gap of BNNFs with wEext is much more pronounced than that in the BN nanoribbons. Especially, the slope of gap change in the 1BNNF with respect to wEext is nearly five times higher than that in nanoribbons, while that in the 2-BNNF is three times higher because of the enhanced screening effect due to its smaller band gap than the 1-BNNF. This distinction in Stark effect between the sp2 and sp3 nanostructures has not been reported ever before. Our above results have robustly proved that the BNNFs are metallic or semiconducting depending on their thickness. For practical applications, it is desirable to realize tunable band gap in the BNNFs so as to afford greater flexibility in design of nanodevices. One efficient route toward tuning the band gap is the strain engineering, which have been well developed for advanced silicon technology. Here, the strain is applied along the two basic vectors, a and b, of the BNNF, as shown in the inset of Figure 5b. Since the HSE06 calculations are quite expensive while the GGA correctly tracks the trends of thickness-dependent band gap in the BNNFs, we focus on the GGA results in the following. Figure 5a shows that the band gap of the BNNFs monotonically increases with increasing

strain from compressive to tensile. For example, the band gap of the 1-BNNF can be reduced from 3.24 to 2.57 eV by 4.6% compressive strain. In particular, the tensile strain can open a gap in the originally metallic 4-BNNF, which can reach 0.09 eV at 4.8% strain (see inset in Figure 5a). Such strain-induced metal−insulator transition can find practical applications in nanodevices, such as for an electric switch controlled by elastic strain. Note that the strain can be realized by placing the BNNFs on a flexible substrate, akin to the strategy for stretching graphene.48 The origin of strain-dependent band gap in the BNNFs can be understood by examining the band structures. The strain-induced change in band gap is mainly contributed by the shift of the VBM and less by the CBM (Supporting Information Figure S6). This is because the VBM of the BNNFs is an antibonding state with a nodal plane parallel to the normal of the nanofilm. As a result, an in-plane compressive strain will enhance the repulsion in the charge density and hence raises its energy level to reduce the band gap. In contrast, the nodal plane of the CBM state is normal to the nanofilm so the effect of strain on its level is marginal. With this physical mechanism, the strain-tunable band gap remains feasible for uniaxial strains arbitrarily applied along the nanofilm plane. Besides the energy gap, the strain applied to BNNF also modifies its spontaneous electric polarization and in turn modulates the dipole moment along the normal of the nanofilm. The total dipole moment per supercell of the BNNF can be defined as P=

∫supercell zρ(r)d r

where ρ(r) is the total charge density of the nanofilm including the core charge. Figure 5b shows that the dipole moment is monotonically reduced by compressive strain but increased by tensile strain. The strain-induced modulation in dipole moment becomes more significant in a thicker BNNF. Detailed charge analyses show that the change in dipole moment results from the strain-mediated charge redistribution between the B-end and N-end surfaces. This character akin to piezoelectricity is a remarkable merit for the BNNFs to find applications in nanoelectromechanical devices. Although the freestanding BNNFs possess versatile properties, it is still necessary to explore how the properties will be changed when welded on substrates. As diamond has been widely used as substrates for epitaxially growing c-BN nanofilm49−51 due to a good lattice match between them, we focus on the hybrid BN/diamond films. Here, three kinds of hybrid BN/diamond nanofilms are considered: (i) only the Bend surface is terminated by the diamond film consisting of m carbon layers, denoted as Cm(BN)n; (ii) only the N-end surface is terminated by the diamond film, denoted as (BN)nCm; (iii) both the surfaces are terminated with diamond films, denoted as Cm(BN)nCm. Figure 6a−c presents the GGA band structures of the (BN)3 C 3 , C 3(BN) 3 and C 3 (BN) 3 C 3 nanofilms, respectively. We find that the three hybrid nanofilms remain narrow-gap semiconductors, unlike the insulating diamond and c-BN. Moreover, the CBM (electron) and VBM (hole) states are still longitudinally separated in these hybrid nanofilms (Figure 6d−f). Especially, the distribution of electron carriers in the C3(BN)3 and C3(BN)3C3 films moves to the outer surface of the diamond segment connecting with the B-end surface of the BNNFs.

Figure 5. Strain-engineering of the (a) GGA band gap and (b) total dipole moment along the normal of the BNNFs. Inset in (a) is a magnified view of the band gap in the 4-BNNF as a function of strain. The strain is applied along both a and b vectors as illustrated in the inset in (b). D

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Figure 7. Thickness dependence of GGA band gap in hybrid BN/ diamond nanofilms. (a) Band gaps of the hybrid C3(BN)nC3, (BN)nC3, and C3(BN)n nanofilms as functions of n. (b) Band gaps of the hybrid Cm(BN)3Cm, (BN)3Cm, and Cm(BN)3 nanofilms as functions of m.

In conclusion, we have shown by intensive first-principles calculations with different levels of functionals that the c-BN (111) nanofilms can be intrinsically metallic and can even turn into semiconducting when the thickness is less than 0.69 nm. The exceptional electronic properties in the BNNFs are due to a combined effect of the labile near-gap electronic states and strong inbuilt electric polarization. Moreover, the coupling of applied in-plane strain to this inbuilt polarization can further effectively modulate the band gap and dipole moment of the BNNFs, even causing metal−insulator transition in the metallic nanofilms. It is important that these versatile properties in the BNNFs are robust to the surface chemical passivation and can be enhanced when the nanofilms are welded on diamond films. (We note that ZnO, considered earlier without passivation,52 can be studied in a similar way.) The novel intrinsic properties rank the c-BN nanofilm as an attractive functional material with great potential for electronics, piezoelectrics, and photovoltaics applications in harsh environments.

Figure 6. Electronic properties of hybrid BN/diamond nanofilms. (a) Band structures for the (BN)3C3 nanofilm together with the isosurface plots (6 × 10−4 e/Å3) of the partial charge densities corresponding to the CBM and VBM. Corresponding results for the C3(BN)3 and the C3(BN)3C3 nanofilms are present in (b) and (c), respectively.

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However, several distinct features appear upon the termination of diamond film. First, the flat band at 0.8 eV below the Fermi level now disappears in the C3(BN)3C3 and the C3(BN)3 films but is retained in the (BN)3C3 nanofilm. This localized H-derived band is due to the weak B−H bonds and drops far away from the Fermi level when the B−H bonds are replaced with stronger B−C bonds. Second, both the C3(BN)3C3 and the C3(BN)3 nanofilms have smaller band gaps than that of the 3-BNNF, while the (BN)3C3 film has a larger one. So selective surface termination for the BNNFs can enhance the metallicity or gap reduction, especially for the semiconducting 1- and 2-BNNFs. In order to attain a smaller gap in BNNFs, it is desirable to terminate the B-end and N-end surfaces with groups of high and low electron-negativities, respectively. Finally, we note that the lowest band at the M point (Figure 6a) in the Cm(BN)3Cm nanofilm drops quickly toward the Fermi level with increasing m. This state is from the carbon 2px and 2py states near the interface C−N bonds and its drop in energy is due to the weakened quantum confinement effect upon increasing thickness. The downshift of this band will result in an indirect energy gap in the Cm(BN)3Cm nanofilm once m > 4. An indirect band gap can also arise in the (BN)3Cm and Cm(BN)3 nanofilms at larger m. Nevertheless, as shown in Figure 7, the band gap of all the hybrid nanofilms decreases with increasing thickness of the BN segment but increases with increasing diamond thickness because the diamond segment gradually dominates the electronic properties of the whole nanofilms. These results point to an interesting band engineering for the hybrid nanofilms.

ASSOCIATED CONTENT

S Supporting Information *

Calculated phonon spectra of the BNNFs, band structures by B3LYP functional, charge transfer analysis, HSE06 band structures of the 4- and 6-BNNFs, and low-energy band structure of the 3-BNNF under different strains are collected. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: (Z.Z.) [email protected], [email protected]; (W.G.) [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is supported by the 973 Program (2012CB933403), National NSF (11172124, 91023026), Jiangsu Province NSF (BK2011722), MOE doctoral discipline Foundation (20113218120033), China and Jiangsu Province Postdoctoral Science Foundation (20110490132, 1002015B), and the Fundamental Research Funds for the Central Universities (NS2012067). Work at Rice Uiversity (Z.Z.) was supported by the U.S. Army Research Office MURI grant (W911NF-11-10362).

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