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And Fluorographene-Based Quantum Dots Mozhgan N Article pubs.acs.org/JPCC Graphane- and Fluorographene-Based Quantum Dots Mozhgan N. Amini, Ortwin Leenaerts, Bart Partoens,* and Dirk Lamoen* CMT-Group and EMAT, Department of Physics, University of Antwerp, Groenenborgerlaan 171, B-2020 Antwerp, Belgium ABSTRACT: With the help of first-principles calculations, we investigate graphane/ fluorographene heterostructures with special attention for graphane and fluorographene- based quantum dots. Graphane and fluorographene have large electronic band gaps, and we show that their band structures exhibit a strong type-II alignment. In this way, it is possible to obtain confined electron states in fluorographene nanostructures by embedding them in a graphane crystal. Bound hole states can be created in graphane domains embedded in a fluorographene environment. For circular graphane/ fluorographene quantum dots, localized states can be observed in the band gap if the size of the radii is larger than approximately 4 to 5 Å. raphene and its chemical derivatives, graphane and fluorine atoms with hydrogen atoms. Similarly, one can also G fluorographene, are the subject of numerous investiga- make fluorine-based QDs in a graphane crystal by substituting tions at the moment. The interesting physical phenomena that some hydrogen atoms with fluorine atoms. We show that are related to 2D electron gases as found in, for example, graphane dots contain localized hole states while fluorogra- heterostructures, are readily obtainable in these naturally 2D phene dots have bound electron states. crystals. Some advantages of graphane and fluorographene QDs over Graphene is in its pristine form a zero-gap semiconductor, graphene dots can be expected. First, there is a smaller lattice but it is possible to create a substantial electronic band gap by mismatch between graphane and fluorographene in comparison confinement or chemical functionalization. The gaps that can with graphene and graphane or graphene and fluorographene. be obtained by cutting graphene into nanoribbons range in Second, one can also expect these functionalized dots to be theory from 0 to ∼2.5 eV,1 while experimental gaps are found more stable because all of the carbon atoms are saturated. This up to 0.5 eV.2 Chemical functionalization leads to band gaps should be contrasted with graphene dots embedded in HG or − larger than 3 eV.3 8 This has motivated some research on FG, where the boundary between both materials will become graphene nanostructures (e.g., nanoribbons and quantum dots more chemically reactive and is often magnetic.15 (QDs)) embedded in functionalized graphene materials such as This paper is organized as follows: We first give the − graphane9 11 (HG) and fluorographene12 (FG). Partial computational details of our simulations, followed by a detailed functionalization creates graphene islands or nanoroads of comparison of the properties of graphane and fluorographene. which the boundaries are formed by the semiconducting Because the band alignment is the most important factor functionalized graphene.12,13 In practice, such structures are determining the properties of the graphane/fluorographene supposed to be formed by partial dehydrogenation (defluori- heterostructures, we examine this property in the next section. nation) of graphane (fluorographene) by exposure to, for This band alignment is used to construct graphane/ example, a laser beam,14 or by selective functionalization of the fluorographene QDs, which are subsequently investigated. graphene layer. By changing the size and the shape of these Finally, we give a summary of our work in the last section. nanostructures their electronic and magnetic properties can be 9,10,12,15 controlled. The realizability of such structures has been ■ COMPUTATIONAL DETAILS experimentally demonstrated by the creation of multiquantum fi dots in graphane.11 We perform rst-principles density functional theory (DFT) In this work, we examine the possibility of graphane-based calculations within the local density approximation (LDA), the and fluorographene-based nanostructures, especially QDs. generalized gradient approximation (GGA) of Perdew, Burke, fl and Ernzerhof,16 and the screened hybrid functional of Heyd, Graphane and uorographene have similar band gaps but 17 very different ionization potentials.4 This can be expected to Scuseria, and Ernzerhof (HSE06), as implemented in the 18 − cause a type-II alignment of their band structures, which can be Vienna ab initio simulation package. Electron ion inter- exploited in graphene-based heterostructures. Instead of actions are treated using projector-augmented wave poten- creating graphene domains inside graphane or fluorographene, we consider domains of one functionalized material inside the Received: May 23, 2013 other. We demonstrate that it is possible to build a graphane- Revised: July 15, 2013 based QD into a fluorographene crystal by substituting some Published: July 15, 2013 © 2013 American Chemical Society 16242 dx.doi.org/10.1021/jp405079r | J. Phys. Chem. C 2013, 117, 16242−16247 The Journal of Physical Chemistry C Article Figure 1. Electronic band structure of HG (a) and FG (b) calculated with the HSE06 xc-functional. The energy corresponding to the valence band maximum is put to zero. a Table 1. Structural and Electronic Properties of HG and FG for Different xc-Functionals graphane fluorographene LDA GGA HSE06 LDA GGA HSE06 a 2.508 2.541 2.522 2.557 2.609 2.582 d CX 1.117 1.110 1.104 1.365 1.382 1.364 d CC 1.516 1.537 1.526 1.555 1.583 1.568 θ CCX 107.3 107.4 107.4 108.3 107.9 108.1 θ CCC 111.6 111.5 111.5 110.7 111.0 110.8 E gap 3.385 3.477 4.383 2.963 3.103 4.933 m e 0.761 0.768 0.750 0.363 0.366 0.352 m lh 0.202 0.195 0.182 0.312 0.305 0.264 m hh 0.463 0.473 0.438 0.863 0.893 0.731 IE 4.962 4.740 5.383 8.066 7.911 8.952 a a d d θ θ Lattice constant, , and the bond lengths, CX and CC (with X = H or F), are given in angstroms. The bond angles, CCX and CCC, are given in ° E ff m degrees ( ) and the band gap, gap, and ionization energy, IE, are give in electronvolts. The e ective masses of electrons, e, and light and heavy m m holes, lh and hh, are given in units of the free electron mass. − tials.19 21 The C (2s22p2), H (1s1), and F (2s22p5) electrons with a valence band (VB) that is degenerate at the Γ point and are treated as valence electrons. For unit cell calculations of a nondegenerate conduction band (CB). This gives rise to pure HG and FG, the electron wave functions are described three types of quasiparticles in the system, namely, electrons using a plane-wave basis set with a cutoff energy of 600 eV, and and heavy and light holes. a24× 24 × 1 k-point grid is used to sample the Brillouin zone. A summary of the calculated structural (lattice parameters, Calculations for QD systems are performed with a lower energy bond lengths, and angles) and electronic (band gap, effective cutoff of 400 eV. Relaxations are done with a single k-point, masses, and ionization energy) properties of graphane and while finer 4 × 4 × 1 k-point grids are used to calculate the fluorographene is given in Table 1. (projected) density of states (P)DOS. A vacuum space of 15 Å Let us first compare the results of the various functionals. is used to reduce the interaction between periodic images of the Those obtained with the hybrid functional (HSE06) are pure FG and HG system and a vacuum space of 10 Å for the believed to be the most accurate,22 especially for electronic QD structures. Convergence with respect to self-consistent properties such as the band gap and the ionization potential.23 iterations was assumed when the total energy difference − The structural parameters roughly vary with 1%, and the between different cycles was less than 10 4 eV and the HSE06 functional gives values between those of LDA and geometry relaxation tolerance was better than 0.01 eV/Å. GGA. Furthermore, the difference between graphane and fluorographene is consistent for all functionals. Therefore, we ■ RESULTS can assume that, for our purpose, the structure is well- Before discussing the formation of QDs in graphane/ described, independent of the specific functional. The fluorographene heterostructures, we investigate the character- electronic properties show some substantial variation, although istics of these two materials separately. The properties that the results from LDA and GGA are very similar. It can be seen concern us here are both structural and electronic, and we make from Table 1 that the electronic band gap and the ionization use of different exchange-correlation (xc) functionals (LDA, energy, defined as the difference between the valence band PBE-GGA, and HSE06) to examine these. The latter is maximum (VBM) and the vacuum level, are significantly larger importanttounderstandtheinfluence of the level of for the hybrid functional. computation on the obtained results. The electronic band If we compare graphane to fluorographene, some important structures of graphane and fluorographene are shown in Figure differences can be observed. The lattice parameter of graphane 1. It is seen that both materials are large-gap semiconductors is ∼2% smaller than that of fluorographene. This is small 16243 dx.doi.org/10.1021/jp405079r | J. Phys. Chem. C 2013, 117, 16242−16247 The Journal of Physical Chemistry C Article enough to match the two materials without introducing too much strain. However, this strain can change the size of the band gap and the effective masses of graphane and fluorographene in a heterostructure. Therefore, we performed some test calculations on strained HG and FG. These calculations show that the changes of the electronic properties are on the same order as the strain (∼2%) and can therefore be neglected.
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