Optical advantages of graphene on the boron nitride in visible and SW-NIR regions

Abstract

We theoretically study the optical advantages of graphene on boron nitride for advanced materials. Firstly, the optical absorption properties of graphene and the boron nitride are investigated theoretically, respectively. It is found that there is a strong optical absorption in the visible and SW-NIR regions for graphene; while the optical absorption of boron nitride is in the deep-ultraviolet region. For the two layer complex of graphene on the boron nitride, theoretical calculations further reveal that the optical property of graphene in the visual region is almost not influenced by boron nitride. The three dimensional charge difference densities reveal the optical properties of electron–hole distribution on the optical excitation for the single layer graphene. The ground state interaction between the graphene and the boron nitride is mainly the van der Waals interactions via edge atoms between two layers. Furthermore, charge difference density reveals that there is no charge transfer between graphene and boron nitride in the visual region on electronic transitions. So, the optical properties of graphene are not influenced by boron nitride in the visible region, which reveals that the boron nitride is one of the best substrates for graphene-based nano-photonic devices.

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1 Introduction

Recently, graphene has attracted much attention in the fields of condensed matter physics and materials, because of its unique linear energy dispersion,¹ high mobility,^2,3 high thermal conductivity,⁴ excellent mechanical properties,^5,6 the optical properties of graphene quantum dots (GQDs)⁷ and so on.^8–11 Based on such characteristics, graphene has been widely investigated, both experimentally and theoretically,^1,12–14 and has been widely applied in many fields, such as fuel cells,¹⁵ quantum information processing,¹⁶ photovoltaic materials,¹⁷ controlling reactions,⁹ water purification,¹⁸ and optical modulation.¹⁹ On the other hand, the above mentioned properties of graphene are greatly influenced by the substrate.²⁰ There are additional carrier scattering and electron–phonon interactions from the commonly used SiO₂ substrate,²¹ which declined the quality of graphene. Recently, coupled plasmon–phonon polaritons in two dimensional (2D) van der Waals heterostructures of graphene/SiO₂ have been studied using near-field optical imaging and far-field spectroscopy.²²

It is reported that the single-domain graphene has been successfully epitaxial grown on hexagonal boron nitide (h-BN) substrate by the plasma-assisted deposition method.²³ The h-BN can maintain intrinsic physical properties of the graphene, because of its advantages, such as its atomically flat surface, no danging bonds and weak doping effects. Graphene have the advantages of large-area (except the limit by the size of the substrate), single-domain, high quality (the highest carrier mobility was 20 000 cm² V⁻¹ s⁻¹) and controllable layers (from 1 to 3 layers). More importantly, graphene on h-BN can from 2D superlattice structure with about 15 nm period,²⁴ due to the lattice mismatch, namely, moiré pattern. The energy band of graphene can be modified by the superlattice structure, extra new sets of Dirac points are produced at point M of superlattice's Brillouin zone.²⁵ Theoretical calculations showed that the 2D superlattice can regulate band structure of graphene,^26–28 and from additional Dirac point, which provides an effective mean to explore a series of new physical phenomena such as Hofstadter Butterfly spectroscopy.^28–30

In this paper, we theoretically study the electronic structures and optical properties of single layer graphene/h-BN at ground and excited states, using density functional theory (DFT), and time-dependent DFT (TD-DFT). The electronic structure study reveals the interaction between graphene and h-BN in detail. The charge different density (CDD) method demonstrates the photoinduced charge transfer in the visible and SW-NIR regions. Our results promote deeper understanding on the optical properties of graphene based 2D van der Waals heterostructures.

2 Theoretical methods

The models used in the calculations are shown in Fig. 1(a)–(d): graphene, h-BN, graphene/h-BN with top and side views, respectively. In model (a) and (b), there are six zigzag edges, and the H atoms are added to the edge atoms. All the calculations were performed with Gaussian 09 software.³¹ The ground-state geometries of graphene, h-BN and graphene/h-BN were optimized with density functional theory (DFT)³² using the B3LYP functional³³ and 6-31g(d) basis set. Their optical absorption spectra in the visible and SW-NIR regions were calculated with time-dependent DFT (TD-DFT)³⁴ using the B3LYP functional³⁵ and 6-31g(d) basis set. The charge transfer in the electronic transition was visualized using CDDs.³⁶

Fig. 1 The models used in the calculations are shown in (a)–(d): graphene, h-BN, graphene/h-BN with top and side views, respectively.

3 Results and discussion

Optical properties of single-layer graphene

The calculated optical absorption spectrum of single layer graphene can be seen from Fig. 2, which demonstrates that there are four absorption peaks in the visible and SW-NIR regions. The electron–hole distributions after optical excitation for six strong electronic transitions can be revealed by three dimensional CDD, see Fig. 3. For the electronic transition at 833 nm, it is found that the electrons can be transferred and assembled as four “electron” lines, which can promote electrons transfer by the external electric field. For the electronic transition at 616 nm, electron–holes are distributed in the internal and external rings of graphene, respectively. For the electronic transition at 557 nm, CDD reflects that the electrons can be transferred and assembled as four “hole” lines, which can promote holes transfer by external electric field. For the absorption peaks around 440–430 nm, there are three strong electronic transitions, and the charge distribution is complex. It is interesting for the electronic transitions at 434 and 428 nm in this strong absorption peak. Electrons transfer to the center from the edge for the electronic transitions at 434 nm, and holes distribute at the edge. While electrons and holes have a opposite distribution for the electronic transitions at 428 nm. So, there are three kinds of charge transfers for the absorption peak around 445–425 nm. It seems that there are two kinds of simultaneous collective electron oscillations (CEO) between the center and the edge of single layer graphene, but the orientation of CEO is opposite. These two kinds of CEOs can be considered as two opposite plasmonic modes. It is well known that the graphene plasmon is in the region of IR. But our theoretical studies reveal two kinds of CEOs between the center and edge of graphene, which is the evidence of graphene plasmon in the visual spectral region. But it is hard to observe the graphene plasmon in the visible and SW-NIR regions. This is because that there are two opposite orientations of CEOs, and energies of these two graphene plasmonic modes are almost superposed. If these two superposed graphene plasmonic modes can be well separated by doping or other methods, the graphene plasmonic modes in the visible and SW-NIR regions region can be applied in the fields of sensing, for example, graphene plasmon-enhanced Raman scattering (G-PERS) on the substrate of single layer.

Fig. 2 The calculated absorption spectra of the single-layer graphene, f stands for oscillator strength.

Fig. 3 Charge-transfer densities for the strong electronic transitions in the graphene, where the holes and electrons are represented in green and red, respectively.

Optical properties of single-layer h-BN substrate

The calculated optical absorption spectrum of h-BN in Fig. 4 demonstrates that there are three strong peaks and a shoulder around 210 nm in the deep ultraviolet region. The electron–hole distribution of optical excitation for six strong electronic transitions can be revealed by CDD in Fig. 5. For the electronic transitions at 210.52 nm and 208.63 nm, it is found that the electrons can be transferred and assembled at the edge of h-BN, there have no electrons in the middle of the model. For the electronic transition at 204.29 nm, 203.36 nm, 202.64 nm, 197.51 nm, electron–holes distribute in the internal and external rings of h-BN, respectively. And the electrons transfer and assemble not obviously compared with the above, but some electrons still transfer and assemble to the edge. So the calculations reveal that the absorption occurs in the deep ultraviolet region, and there is no absorption in the visual region. From this result, we can know that h-BN is a optical material in the visible region.

Fig. 4 The calculated absorption spectra of the single-layer h-BN, f stand for oscillator strength, f stands for oscillator strength.

Fig. 5 Charge-transfer densities for the strong electronic transitions in the h-BN, where the holes and electrons are represented in green and red, respectively.

The electronic structure and interaction of graphene/h-BN at ground state

The detailed interactions of graphene/h-BN by the van der Waals force at ground state can be revealed via the charge distribution of graphene/h-BN in Fig. 6(a). For graphene layer, there are electrons transferred and assembled between adjacent C atoms at the zigzag edge, so the adjacent atoms of graphene at zigzag edge are of positive and negative charges, respectively. The internal C atoms of the single layer are almost neutral, neither electrons transfer nor electrons assemble exist there. On the other hand, electrons and holes alternately transfer from the B atoms to the N atoms of the single h-BN layer, in which all the nitrogen atoms demonstrate electronegative, while all boron atoms show electropositive. Each electron of boron atoms can be transferred to the adjacent nitrogen atoms.

Fig. 6 Charge distribution of the graphene/h-BN heterostructure at ground state, where the holes and electrons are represented in green and red, respectively. The neutral atoms are represented in black.

For the heterostructure of graphene/h-BN, there are interact between the graphene layer and the h-BN layer by the van der Waals force at the edges. For the zigzag edge A in Fig. 6(b), they are mainly attractive force, since the correspond atoms between graphene and h-BN are of opposite charges. But for the adjacent zigzag edges, they are mainly the repulsive force, since the correspond atoms between graphene and h-BN are of same charges. So, the figure Fig. 6(a) and (b) reveal the interaction between the graphene/h-BN and the distribution of the electrons and holes at ground state, especially at the zigzag edges.

Optical properties of single layer graphene/h-BN substrate

The calculated optical absorption spectrum of single layer graphene on h-BN (graphene/h-BN) can be seen from Fig. 7, the absorption of graphene/h-BN is almost identical to the absorption spectrum of the monolayer graphene in the visible and SW-NIR regions, in which there are four optical peaks. CDDs reveal that there is no charge transfer between graphene and h-BN substrate in the visible region, and all charge transfers are within the graphene layer (see Fig. 8). Furthermore, the optical properties of charge transfer within graphene is almost the same as those in single layer graphene itself in Fig. 3.

Fig. 7 The calculated absorption spectra of the single-layer graphene on the single-layer h-BN substrate, f stand for oscillator strength, f stands for oscillator strength.

Fig. 8 Charge-transfer densities for the strong electronic transitions in single-layer on single-layer h-BN substrate with top and side views, where the green and the red stand for the hole and electrons, respectively.

To reveal the fine difference between absorption spectrum of graphene and that of graphene on h-BN substrate, we compare them in Fig. 9. It is found that the blue shift is quite small due to interlayer interaction via van der Waals force.

Fig. 9 The calculated absorption spectra of single-layer graphene and graphene/h-BN.

4 Conclusions

The optical advantages of graphene on boron nitride for advanced materials have been studied. The strong optical absorption spectra for graphene in the visible and SW-NIR regions and h-BN in the deep-ultraviolet region have been observed, respectively. For graphene/h-BN, it is further indicated that the optical property of graphene in the visible and SW-NIR regions is almost not influenced by boron nitride. The optical properties of electron–hole distribution of the optical excitation for the single layer graphene have been revealed by CDDs. It is found that the ground state interaction between the graphene and the boron nitride is mainly the van der Waals interaction via edge atoms between two layers. Furthermore, by optical excitation, CDD reveals that there is no charge transfer between graphene and boron nitride in the visual spectral region. Our theoretical studies reveal that the boron nitride is one of best substrates for graphene-based nano-photonic devices. Our results may provide deep understanding for applications of graphene/h-BN device on the optical and electric field.^37–40

Acknowledgements

This work was supported by the National Science Foundation of China (Grant No. 91436102, 11374353, 11544015 and 61307016) and the Program of Liaoning Key Laboratory of Semiconductor Light Emitting and Photocatalytic Materials.

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Footnote

† Contributed equally.

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