Computational Materials Science

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1 Computational Materials Science 65 (2012) Contents lists available at SciVerse ScienceDirect Computational Materials Science journal homepage: Tunable band gap in half-fluorinated bilayer graphene under biaxial strains C.H. Hu a, Y. Zhang a, H.Y. Liu b, S.Q. Wu a,, Y. Yang c, Z.Z. Zhu a,d, a Department of Physics and Institute of Theoretical Physics and Astrophysics, Xiamen University, Xiamen , China b School of Science, Jimei University, Xiamen , China c State Key Lab for Physical Chemistry of Solid Surfaces, Xiamen University, Xiamen , China d Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, Xiamen , China article info abstract Article history: Received 23 March 2012 Received in revised form 26 June 2012 Accepted 27 June 2012 Available online 14 August 2012 Keywords: Bilayer graphene Biaxial strain Tunable band gap Direct-to-indirect gap transition Opening and tuning of the band gap of bilayer graphene (BLG) is of particular importance for its utilization in nanoelectronics. We presented here the electronic structures of two types of stoichiometrically half-fluorinated BLGs (i.e. C 2 Fs) as well as those under biaxial compressive and tensile strains. Our results reveal that both C 2 Fs are semiconductor with large direct band gaps in their unstrained configurations. Under biaxial compressive strains, the band gaps of both C 2 Fs can be reduced. However, by applying biaxial tensile strains, both C 2 Fs undergo a direct-to-indirect band gap transition. Electronic nature of the strain-tuned band gaps has been discussed. Ó 2012 Elsevier B.V. All rights reserved. Graphene s unique band structure has led to a host of fascinating phenomena, exemplified by massless Dirac fermion physics [1 3] and anomalous quantum Hall effect [4 7]. Available studies suggest that the valence and conduction bands of graphene exhibit a linear dispersion degenerate near the so-called Dirac point, resulting in the effectively massless Dirac fermion character of the carriers [8]. With one more graphene layer added, BLG has an entirely different (and equally interesting) band structure [9] but still possesses a zero band gap that in some way limits its utilization in modern device physics and nanotechnology. To date, surface passivation such as hydrogenation [10 14] and fluorination [15 18] has attracted much interest due to its ability to create finite band gaps for single layer graphene (SLG) and BLG, enabling their potential applications in nanoelectronics and nanophotonics. In the case of SLG, it has been reported that the fully fluorinated and hydrogenated SLG could exhibit semiconducting behavior with large direct band gaps of about 3.0 [15 17,19,20] and 3.5 ev [11 13], respectively. Bringing the fluorinated SLG up to the level of technological application, the fluorinated SLG has been proved to be a good counterpart of Teflon [20], a possible channel material in transistor [21] and a wide band gap semiconductor with ultraviolet luminescence [22]. On the other hand, in the case of BLG, the great current interest in it is mainly based on the Corresponding authors. Address: Department of Physics and Institute of Theoretical Physics and Astrophysics, Xiamen University, Xiamen , China. Tel.: ; fax: addresses: wsq@xmu.edu.cn (S.Q. Wu), zzhu@xmu.edu.cn (Z.Z. Zhu). premise that its band gap can be tuned by external factors such as chemical doping [23,24], applied electric field [7,8,10,25 29] and mechanical strains lately [30]. In addition, the band gap of the pristine BLG is also proved to be mechanically tunable if strains are applied to the two layers [30]. The aforementioned studies and possible important applications of BLGs have motivated our studies on the electronic properties of BLGs subjected to both fluorination and mechanical strain. In this letter, we show that the band gap of BLG can be opened through half-fluorination and then be tuned in both magnitude and type by applying biaxial strains. Practically, a tunable band gap would be highly desirable because it would allow great flexibility in design and optimization of the graphene-based devices [9]. Such wide strain-tunable band gaps of the C 2 Fs, if realized, will promise their highly flexible application in these areas and especially the ultraviolet photodetectors [31]. Additionally, the direct-to-indirect band gap transition in the C 2 Fs is also expected to provide some guidance in their optoelectronic applications. The present calculations have been performed by using the Vienna ab initio simulation package (VASP) [32,33], which is based on the density functional theory, the plane-wave basis and the projector augmented wave (PAW) representation. The exchange correlation functional is treated within the local density approximation (LDA) [34,35]. The wave functions are expanded by plane waves with a kinetic energy cutoff of 450 ev. The Brillouin zone integrations are approximated by using a special k-point sampling of the Monkhorst Pack scheme [36] with a C-centered grid. All the calculations are modeled by a (1 1) unit cell (consisting of four C and two F atoms, half-fluorinated) with a vacuum /$ - see front matter Ó 2012 Elsevier B.V. All rights reserved.

2 166 C.H. Hu et al. / Computational Materials Science 65 (2012) Fig. 1. Side and top views of (a) AB-C 2 F and (b) AA-C 2 F, with unit cells shown by blue rhombuses. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) space of 20 Å in Z-direction to avoid the interactions between adjacent BLGs (see also Fig. 1). All the atomic configurations are fully relaxed until the Hellmann Feynman forces on all the atoms are smaller than 0.01 ev/å. Our spin-polarized calculations show that C 2 F is rather insensitive to the spin-polarized effect, therefore, all of the following calculations are based on the non-spin-polarization scheme. Despite the electronic energy gap is of great importance for BLG to be exploited in nanoelectronics and nanophotonics, switching off the conductivity to a desirable level remains challenging in epitaxial graphene [37]. In this regard, it is of particular interest to investigate the C 2 Fs which are semiconducting in their unstrained configurations. Similar to the C 2 H, the half-fluorination considered here is the highest fluorine concentration on BLG, because a higher F concentration may lead to a separation of the two graphene layers. In this work, two models of the C 2 Fs (as presented in Fig. 1a and b) are considered, respectively, based on the Bernaland Hexagonal-stacking BLG [23]. The non-fluorinated and fluorinated C atoms are denoted as C A and C B, respectively. Hereafter, the half-fluorinated Bernal and Hexagonal BLG are denoted as AB-C 2 F and AA-C 2 F, respectively. The calculated lattice constants, the intralayer C C bond lengths, the interlayer C C bond lengths, the C F bond lengths, the buckling heights, the band gaps and the binding energies of both C 2 Fs considered are listed in Table 1, where the buckling height (D z ) is the difference between the maximum and minimum Z-coordinates of the C atoms in the graphene layer (see Fig. 1). The binding energy is defined as E b ¼ 1 n ðe tot P E atom Þ; where n is the number of F atoms in each unit cell, and the E tot and E atom are the total energies of the system and atomic energy of each atom, respectively. Based on our DFT calculations (Table 1), the AB-C 2 F is shown to be a bit more stable than the AA-C 2 F by about 40 mev/c 2 F in their unstrained configurations, while both C 2 Fs are semiconducting with large direct band gaps of about 4.04 and 3.94 ev, respectively. Considering that the band gap values are based on the LDA calculations, the real band gaps of Table 1 The calculated lattice constants a (Å), intralayer C C bond lengths d C C (Å), interlayer C C bond lengths I C C (Å), C F bond lengths d C F (Å), buckling heights D z (Å), band gaps (ev) and binding energies E b (ev/c 2 F) of the AB-C 2 F and AA-C 2 F. C 2 F a d C C I C C d C F D z E g E b AB-C 2 F AA-C 2 F both C 2 Fs should be significantly larger. From Table 1, it can also be seen that the intralayer C C bond lengths, the C F bond lengths and the buckling heights of AB-C 2 F are almost the same as those of AA-C 2 F. However, the interlayer C C bond length in the AA- C 2 F (1.55 Å) is distinctly larger than that in the AB-C 2 F (1.54 Å). Since the opening and tuning of the band gap of BLG hold great significance for its extensive applications, the electronic properties of AB-C 2 F and AA-C 2 F modulated by applying biaxial strains are investigated. The calculated band structures of the two unstrained C 2 Fs, and those modulated by applying biaxial strains are summarized in Fig. 2a and b, where the valence band maximums (VBMs) of both unstrained C 2 Fs are chosen as the reference energies (i.e., 0 ev), respectively. In Fig. 2, the D- and E-points are just the energy levels of the lowest conduction bands of AB-C 2 FatC and M points, respectively. It is shown from Fig. 2 that both unstrained AB-C 2 F and AA-C 2 F are analogous in their band structures and exhibit direct band gaps. What is more, their band structures are still analogous to each other when they are loaded with biaxial strains, either compressive or tensile. By applying biaxial compressive strains, the band gaps of AB-C 2 F and AA-C 2 F are found to be gradually diminished and transformed from semiconductor to metal at the compressive strain around 17% (see left two panels of Fig. 2a and b, respectively). However, by applying biaxial tensile strain, the band gaps of both C 2 Fs are found to be scarcely changed in magnitude but undergo the direct-to-indirect transition (see right two panels of Fig. 2a and b, respectively). In order to have a microscopic understanding of the changes of the band gaps under biaxial strains, the partial densities of states (PDOS) of AB-C 2 F under 10%, 0% and 10% biaxial strains are given in Fig. 3a c, respectively. Moreover, the evaluated band and k-point partial decomposed charge densities at the specified points (e.g., D, VBM, E points in Fig. 2) of the unstrained AB-C 2 F are presented in Fig. 3d f, respectively. For the unstrained AB-C 2 F, as can be seen from Fig. 3b and d, the conduction band minimum (CBM, i.e., the D-point) is dominated by the p z p z antibonding states of C B F atoms and interlayer C A C A atoms. However, VBM is mainly contributed by the p x p y bonding states of C C atoms in each graphene layer and by those of F F atoms in each Fluorine layer, with no s- or p z -states involved (see Fig. 3b and e). Therefore, the VBM of AB-C 2 F is mainly sensitive to interactions between the x-y planar electronic orbitals while the CBM is only sensitive to the interactions between the electronic orbitals in the Z-direction. Indeed, from Fig. 3a c, it is revealed that the energy of D-point is almost indifferent to the biaxial compressive strain, which is attributed to the flexibility of the C B F and interlayer C A C A bonds along the Z

3 C.H. Hu et al. / Computational Materials Science 65 (2012) Fig. 2. Band structures of (a) AB-C 2 F and (b) AA-C 2 F in the unstrained configurations (0%) and those loaded with the biaxial compressive ( 17% and 10%) and tensile strains (5% and 10%). The zero energies in (a) and (b) are set to the VBMs of the unstrained AB-C 2 F and AA-C 2 F, respectively. Fig. 3. PDOS of the AB-C 2 F under biaxial strains of (a) 10%, (b) 0%, and (c) 10%, respectively, and the evaluated band and k-point decomposed charge densities for the unstrained AB-C 2 F at (d) D-point, (e) VBM and (f) E-point (see Fig. 2). The zero energy is set to the VBM of unstrained AB-C 2 F. direction, since the bonds of C B F and C A C A can adjust themselves easily along with the biaxial compressive strains. On the other hand, VBM is greatly influenced by the biaxial compressive strain, as seen from Fig. 3e, bonding between the p x p y orbitals of C C atoms in each graphene layer and of F F atoms in each fluorine layer will be strengthened by the compressive strains. This directly leads to the increase of the band-width of energy band around the VBM and consequently an upward shift of VBM in Fig. 2. Accordingly, the band gap of AB-C 2 F is gradually reduced along with the increasing compressive strain and transforms from semiconducting to metallic when the compressive strain is large enough (about 17%). However, because of the strong interatomic bonding in the graphene layers, the 17% compressive strain maybe too much than normal and might be unable to be realized in experiment at the moment, therefore, the value of strain 17% presented here is just a theoretical prediction. Under the biaxial tensile strain, it is suggested that the AB-C 2 F changes from a direct-gap to an indirect-gap semiconductor, as shown in the right two panels of Fig. 2a. The calculated CBM is located at C-point for the unstrained AB-C 2 F, however, it is transferred to the M-point when the loaded biaxial tensile strain is larger than about 5%. To explain such a phenomenon, the understanding of electronic states at E-point, as highlighted by red 1 solid circles in Fig. 2a, is of great importance. Based on our calculations on the site projected wave function character for each band, the 1 For interpretation of color in Figs. 2 and 4, the reader is referred to the web version of this article.

4 168 C.H. Hu et al. / Computational Materials Science 65 (2012) explain why the band gap of AB-C 2 F is larger than that of AA-C 2 F. From Fig. 4, by comparing the density of contour lines between the bonded atoms, it suggests that the intralayer sp 3 C C covalent bonds in both C 2 Fs are strengthened by the biaxial compressive strains but weakened by the biaxial tensile strains, while the C F bonds are found to be almost indifferent to the biaxial strains. In summary, first-principles DFT calculations have been performed to study the electronic properties of two C 2 Fs under different biaxial strains. Results show that both AB-C 2 F and AA-C 2 Fin their unstrained configurations are semiconducting with large direct band gaps of about 4.04 and 3.94 ev, respectively. Nonetheless, their band gaps are shown to be modulated by applying biaxial strains. That is, the biaxial compressive strains are shown to reduce their band gaps and could transform them from semiconductor to metals. However, under biaxial tensile strains, both C 2 Fs are found to be able to undergo direct-to-indirect band gap transition. Therefore, it is suggested that the electronic band gap of BLG can be opened through fluorination and tuned simply by applying biaxial strains, which might be of special importance for the utilization of BLG in nanoelectronics and nanophotonics. Acknowledgments Fig. 4. Deformation charge densities of the ð1 210Þ planes of (a)-(c) AB-C 2 F and (d)- (e) AA-C 2 F, with biaxial strains of 10%, 0% and 10%, respectively. eigen function at E-point is mainly contributed by the s and (p x, p y, p z ) orbitals of all C atoms, but with no character from F atoms, as presented in Fig. 3c and f. The character of electronic states at E- point suggests that the energy of E-point is sensitive to the intralayer sp 3 C C bonding. When AB-C 2 F is loaded with biaxial tensile strains, the intralayer sp 3 C C bonding tends to be weakened, leading to the lowered antibonding energy of E-point, as vividly shown in Fig. 2. On the other hand, the eigen function at D-point is mainly contributed by the p z p z anti-bonding states of C B F and C A C A atoms, as mentioned above. Therefore, the energy of D-point is quite insensitive to the biaxial tensile strain, giving rise to its little energy decrease under the tensile strains in Fig. 2. Different energy decreases of the points E and D in the band structure lead to the direct-to-indirect band gap transition in AB-C 2 F under the biaxial tensile strains. For the AA-C 2 F, the tunable magnitude and directto-indirect transition of band gap can also be explained in the same way when it is loaded with biaxial compressive and tensile strains, because its band structures are all very similar to those of AB-C 2 F, by comparison of Fig. 2a and b. To see the bonding characters in both C 2 Fs and those loaded with biaxial strains, the corresponding deformation charge densities of the ð1 210Þ plane are shown in Fig. 4, where the range and interval of the charge density contours are all the same in the six panels. The deformation charge density is defined as Dqð~rÞ ¼ qð~rþ P lq atom ð~r ~ R l Þ, where qð~rþ represents the total charge density of C 2 F and P lq atom ð~r ~ R l Þ the superposition of atomic charge densities. Charge accumulation is depicted by orange solid lines, and charge depletion is shown by blue dashed lines. From Fig. 4, it can be seen that the C C bonds are covalent and the C F bonds are mainly ionic mixed with covalent for both the unstrained C 2 Fs and those loaded with biaxial strains. In their unstrained configurations (Fig. 4b and e), the intralayer C C covalent bonds of AB-C 2 F and AA-C 2 F are almost in the same strength, as well as the case of C F bonds. But the interlayer C C covalent bonds of the AB-C 2 F are a bit stronger than those of the AA-C 2 F, attributed to the shorter interlayer C C bond lengths in the AB-C 2 F than those in the AA-C 2 F (see Table 1). Such bonding characters can also This work is supported by the National 973 Program of China (Grant Nos. 2007CB209702, 2011CB935903), the National Natural Science Foundation of China under Grant No References [1] A.K. Geim, K.S. Novoselov, Nat. Mater. 6 (2007) 183. [2] M.I. Katsnelson, K.S. Novoselov, A.K. Geim, Nat. Phys. 2 (2006) 620. [3] B. Huard, J.A. Sulpizio, N. Stander, K. Todd, B. Yang, D. Goldhaber-Gordon, Phys. Rev. Lett. 98 (2007) [4] K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, M.I. Katsnelson, I.V. Grigorieva, S.V. Dubonos, A.A. Firsov, Nature 438 (2005) 197. [5] Y.B. Zhang, Y.W. Tan, H.L. Stormer, P. Kim, Nature 438 (2005) 201. [6] K.S. Novoselov, E. McCann, S.V. Morozov, V.I. Fal ko, M.I. Katsnelson, U. Zeitler, D. Jiang, F. Schedin, A.K. Geim, Nat. 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