Abstract
1. Introduction
Graphene, a single layer of sp2- bonded carbon atoms having a 2D honeycomb lattice, is the primary element for all other graphitic forms like fullerenes and carbon nanotubes (CNTs) etc.[
The application of external perpendicular electric field is the most efficacious method to open and tune bandgap because it tears inversion symmetry without carrier mobility being affected notably in bi-layer graphene (BLG)[
Graphitic carbon nitride (g-C3N4), appraised to be the most stable allotropes of C3N4 under ambient conditions, has enticed substantial considerations because of its propitious application in electronic devices[
Figure 1.(Color online) Proposed heterostructures (a) G/g-C3N4/h-BN in ABA stack and (b) g-C3N4/G/h-BN in AAA stack.
2. Methodology
All the calculations have been performed on Quantumwise Atomistix Toolkit (ATK) simulation package[
The electron difference density, a comparison between the electron density of a many-body system to the superposition of individual atom-based electron density is given by:
Band structure and bandgap calculation of optimized structures have been done using ATK-SE (semi-empirical) Extended Huckel method[
To calculate the distance between two graphene layers, van der Waals interactions are included. The long-range van der Waals interaction is included through the semi-empirical Grimme correction (DFT-D2) by adding a term to the DFT total energy and given by:
where the value of
The density mesh cutoff of 75 Hartree and tolerance of 10−5 Hartree has been used with the Pulay mixer algorithm[
3. Results and discussions
The hexagonal boron nitride h-BN, sometimes referred to as ‘white graphene’, has lattice structure similar to grapheme. The lattice mismatch is about of 1.5% only[
There is no bandgap in the BLG in Bernal (AB) stack at 0 V/nm as shown by Fig. 2(a). It can be seen from the figure that there are two almost parallel conduction bands beyond the two almost parallel valence bands near the Fermi level of the Bernal stacked BLG without any gating i.e. absence of an external electric field. The conduction band minimum (CBM) and the valence band maximum (VBM) touch each other around the K-point, if no electric field is applied, resulting in zero bandgap. An external perpendicular electric field is applied by means of two metallic plates (one at the top Et and one at the bottom Eb to induce the bandgap in BLG. As the field is applied, two effects are produced: (i)
Figure 2.(Color online) Band structure of BLG in Bernal (AB) stack at (a) 0 and (b) 4 V/nm.
The interlayer distance of various optimized graphene structures are shown in Tables 1 and 2. The vectors d1 and d2 represent distance between neighboring in-plane carbon atoms. The ‘–’ in tables represent not-applicable cases. It has been found that interlayer distance of various graphene structures decrease with increasing electric field in comparison to zero electric field. It implies that due to the application of an electric field, the structures get slightly distorted. Bandgap comparison for structures in Bernal stack and hexagonal stack are shown in Figs. 3 and 4.
Figure 3.(Color online) Bandgap in Bernal stack w.r.t. (a) Electric field (E) keeping interlayer distance
Figure 4.(Color online) Bandgap in hexagonal stack w.r.t. (a) Electric field (
It is observed from these figures that bandgap is dependent on interlayer spacing as well as stacking pattern. It can be seen from Figs. 3(b) and 4(b) that as the interlayer spacing approaches 4.0 Å, the bandgap also approaches zero for all the structures. This is because of such large interlayer spacing’s; there is hardly any interaction between the layers. As smaller interlayer spacing is approached (towards 2 Å), the bandgap is found to increase with decrease in interlayer spacing.
The layers having these charges interact with each other and build a field themselves, depending on the interlayer spacing. The π-orbitals overlap of neighboring layers increases with high charge density. This overlap is greater in hexagonal stack structures because of its geometry and less in Bernal stack structures. Hence the bandgap is greater in hexagonal stack structures as shown in Figs. 3(b) and 4(b).
The structural stability of the heterostructures, is assessed by the binding energy (Eb). Binding energies for different structures have been calculated using formulae given in Table 3. ‘n’ is the number of C atoms in the graphene, EC is the total energy of carbon atoms. Eheterostructure is the energy of the heterostructure, EG is the energy of graphene, EBN is the energy of hexagonal boron nitride and EC3N4 is the energy of graphitic Carbon Nitride with lattice parameter being same. The negative values of binding energy indicate the stable heterostructures. The heterostructures are more favorable if the binding energy is more negative i.e. higher |Eb| value. The C3N4/G/C3N4-AAA has the highest stability among the various structures studied as represented by Fig. 5. g-C3N4/G/h-BN-AAA is the best choice, since the effective mass is lowest of all the structures (Table 4) implying that it exhibits high carrier mobility, while the band gap is significantly opened. The results of the present work indicate that the properties of graphene heterostructures are affected by stacking pattern and the applied electric fields.
Figure 5.(Color online) Binding energies for (1) GBL -AB stack, (2) GBL-AA, (3) G/BN-AB, (4) G/BN-AA, (5) G/C3N4-AB, (6) G/C3N4-AA, (7) BN/G/BN-AB, (8) BN/G/BN-AA, (9) C3N4/G/C3N4-ABA, (10) C3N4/G/C3N4-AAA, (11) G/C3N4/BN- ABA, and (12) C3N4/G/BN-AAA.
Table Infomation Is Not EnableTable Infomation Is Not EnableThe effective mass is closely related to the carrier mobility. The effective mass (of electrons and holes) is calculated as
4. Conclusion
Sandwich heterostructures C3N4/G/BN-AAA and G/C3N4/BN-ABA have been proposed and investigated and their properties have been compared using DFT with other reported structures. C3N4/G/BN-AAA turns out to be the best choice among all the structures studied because it offers lowest effective mass i.e. higher carrier mobility with significant bandgap opening. The results suggest that effectively controlling the stacking patterns and applying a perpendicular electric field significantly affect the properties of the heterostructures and open up exciting opportunities for the development of electronic and optoelectronic devices.
References
[1] A K Geim, K S Novoselov. The rise of graphene. Nat Mater, 6, 183(2007).
[2] M Gupta, N Gaur, P Kumar et al. Tailoring the electronic properties of a Z-shaped graphene field effect transistor via B/N doping. Phys Lett A, 379, 710(2015).
[3] K S Novoselov, A K Geim, S Morozov. Electric field effect in atomically thin carbon films. Science, 306, 666(2004).
[4] X R Wang, Y J Ouyang, X L Li et al. Room-temperature all semiconducting sub-10-nm Graphene nanoribbon field-effect transistors. Phys Rev Lett, 100, 206803(2008).
[5] G Giovannetti, P A Khomyakov, G Brocks et al. Substrate induced band gap in graphene on hexagonal boron nitride: Ab initio density functional calculations. Phys Rev B, 76, 073103(2007).
[6] Z M Ao, F M Peeters. electric field activated hydrogen dissociative adsorption to nitrogen-doped graphene. J Phys Chem C, 114, 14503(2010).
[7] J Zhou, M M Wu, X Zhou et al. Tuning electronic and magnetic properties of Graphene by surface modification. Appl Phys Lett, 95, 103108(2009).
[8] S M Choi, S H Jhi, Y W Son. Effects of strain on electronic properties of graphene. Phys Rev B, 81, 081407(2010).
[9] Y Zhang, T T Tang, C Girit et al. Direct observation of a widely tunable bandgap in bilayer graphene. Nature, 459, 820(2009).
[10] W Tao, G Qing, L Yan et al. A comparative investigation of an AB- and AA-stacked bilayer graphene sheet under an applied electric field: A density functional theory study. Chin Phys B, 21, 067301(2012).
[11] A A Avetisyan, B Partoens, F M Peeters. Stacking order dependent electric field tuning of the band gap in graphene multilayers. Phys Rev B, 81, 115432(2010).
[12] J Zhu, P Xiao, H Li et al. Graphitic carbon nitride: synthesis, properties, and applications in catalysis. ACS Appl Mater Interf, 6, 16449(2014).
[13] X R Li, Y Dai, Y D Ma et al. Graphene/g-C3N4 bilayer: considerable band gap opening and effective band structure engineering. Phys Chem Chem Phys, 16, 4230(2014).
[14] M M Dong, C He, W X Zhang et al. Tunable and sizable bandgap of g-C3N4/Graphene/g-C3N4 sandwich heterostructure: a Van Der Waals density functional study. J Mater Chem C, 5, 3830(2017).
[15] W Hu, Z Y Li, J L Yang. Structural, electronic, and optical properties of hybrid silicene and graphene nanocomposite. J Chem Phys, 139, 154704(2013).
[16]
[17] S Smidstrup, D Stradi, J Wellendorff et al. First-principles Green's-function method for surface calculations: A pseudopotential localized basis set approach. Phys Rev B, 96, 195309(2017).
[18] M Schlipf, F Gygi. Optimization algorithm for the generation of ONCV pseudopotentials. Comp Phys Commun, 196, 36(2015).
[19] M J Van Setten, M Giantomassi, E Bousquet et al. The PseudoDojo: Training and grading a 85 element optimized norm-conserving pseudopotential table. Comp Phys Comm, 226, 39(2018).
[20] K Stokbro, D E Petersen, S Smidstrup et al. Semiempirical model for nanoscale device simulations. Phys Rev B, 82, 075420(2010).
[21] P Pulay. Convergence acceleration of iterative sequences, The case of SCF iteration. Chem Phys Lett, 73, 393(1980).
[22] J Wang, F Ma, M Sun. Graphene, hexagonal boron nitride, and their heterostructures: properties and applications. RSC Adv, 7, 16801(2017).
[23] R K Ghosh, S Mahapatra. Proposal for graphene-boron nitride heterobilayer based tunnel FET. IEEE Trans Nanotechnol, 12, 665(2013).
[24] A Ramasubramaniam, D Naveh, E Towe. Tunable band gaps in bilayer graphene/h-BN heterostructures. Nano Lett, 11, 1070(2011).
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