Functionalization of monolayer MoS2 by substitutional ... - CiteSeerX

Physics Letters A 377 (2013) 1362–1367

Contents lists available at SciVerse ScienceDirect

Physics Letters A www.elsevier.com/locate/pla

Functionalization of monolayer MoS2 by substitutional doping: A first-principles study Qu Yue a , Shengli Chang a , Shiqiao Qin a , Jingbo Li b,∗ a b

College of Science, National University of Defense Technology, Changsha 410073, China State Key Laboratory for Superlattice and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083, China

a r t i c l e

i n f o

Article history: Received 7 November 2012 Received in revised form 12 March 2013 Accepted 27 March 2013 Available online 29 March 2013 Communicated by R. Wu Keywords: Substitutional doping Magnetic moment Half-metal First-principles calculations

a b s t r a c t Electron-beam mediated substitutional doping of monolayer MoS2 was recently demonstrated, opening a new way to modify its properties. Using first-principles calculations, the structural, electronic and magnetic properties of monolayer MoS2 doped with nonmetal and transition-metal atoms are investigated. All dopants are strongly bound to the structures, inducing interesting magnetic behaviors. While all H, B, N and F-doped monolayers have magnetic moment of 1.0 μB , V, Cr, Mn, Fe and Codoped ones attain 1.0, 4.0, 3.0, 3.0 and 1.0 μB , respectively. Additionally, MoS2 undergoes transition from semiconductor to half-metal in the presence of H, B or Cr doping. © 2013 Elsevier B.V. All rights reserved.

1. Introduction Two-dimensional nanomaterials such as graphene, transitionmetal dichalcogenide and boron nitride have been widely studied due to their remarkable physical properties and promising application in next-generation nanoelectronic devices [1–4]. In this context, monolayer MoS2 (1H-MoS2 ), one kind of transition-metal dichalcogenides, is of particular interest [5–18]. Recently, twodimensional 1H-MoS2 sheets have been successfully synthesized through different methods [19–21], and related nanotransistors working at room temperature have also been fabricated [22–24]. Motivated by the advances in experimental research, theoretical studies have been performed to explore the functionalization of 1H-MoS2 by decorating the pristine surface with adatoms or molecules [25–30]. For example, He et al. [25] investigated the adsorption of nonmetal (NM) atoms on pristine 1H-MoS2 and found that H, B, C, N and F atoms can induce local magnetic moments, whereas Ataca et al. [27] studied the implementation of local magnetism through the absorbtion of transition-metal (TM) atoms. Compared to the magnetism based on d or f orbitals of TM atoms, magnetism based on sp orbitals of NM atoms yields stronger longrange exchange-coupling interactions [25]. Additionally, the diffusion barrier of adatom on MoS2 sheet is found to be relatively small [26], thus we can expect that substitutionally doped 1HMoS2 could be fabricated by depositing impurity atoms on areas where vacancy defects have been previously produced in the sheet.

*

Corresponding author. E-mail address: [email protected] (J. Li).

0375-9601/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.physleta.2013.03.034

Very recently, Komsa et al. [31] observed the vacancy formation in 1H-MoS2 under exposure to 80 keV electron-beam irradiation inside a high-resolution transmission electron microscope (HRTEM) and then the filling of vacancies with substitutional impurity atoms, validating the above expectation. Furthermore, it provides a new opportunity to modify the properties of MoS2 sheet via the electron-beam mediated substitutional doping approach. Note that this doping scheme has been widely used to functionalize carbon tube, graphene, boron nitride and related structures [32–37]. Nevertheless, to our best knowledge, little is known about the influences of vacancy and substitutional impurity atoms on the electronic and magnetic properties of 1H-MoS2 until now. In order to fully understand and control the properties of impurity atom substituted MoS2 sheets, a systematic theoretical study is needed before considering them for applications. In this work, by means of the first-principles calculations, we investigate the effects of nonmetal and transition-metal atom substitutions on the electronic and magnetic properties of MoS2 sheets. It is found that the band gaps and magnetic moments can be modulated depending on different substitutional atoms, which strongly bind to the sheets. More interestingly, H, B and Cr-doped sheets become halfmetals with one spin channel being semiconducting and the other metallic. 2. Method First-principles spin-polarized calculations are performed on the basis of density-functional theory (DFT) using projectoraugmented wave (PAW) potentials [38]. The exchange-correlation

Q. Yue et al. / Physics Letters A 377 (2013) 1362–1367

interactions are treated by the generalized gradient approximation (GGA) with Perdew–Burke–Ernzerhof (PBE) functional [39]. The plane-wave cutoff energy is 400 eV. Monkhorst–Pack (MP) meshes [40] of 5 × 5 × 1 and 21 × 21 × 1 are employed for geometry optimization and calculation of density of states, respectively. The pristine MoS2 monolayer is modeled by a 4 × 4 supercell with 2

lateral size of 12.64 × 12.64 Å , which contains 32 S and 16 Mo atoms. The distance between adjacent monolayers is larger than 12 Å and hence the interaction between them can be eliminated. All the structures are fully relaxed by using the conjugate gradient method until the maximum Hellmann–Feynman forces acting on each atom is less than 0.02 eV/Å. Bader analysis [41] is used to calculate charge transformation. As our tests show that, whether including or excluding spin-orbit coupling does not affect the main results in the present work, the effect of spin-orbit coupling thus can be neglected. Numerical calculation is implemented by the Vienna ab initio simulation package (VASP) [42,43]. 3. Results and discussions We follow the two-step process to dope 1H-MoS2 , including vacancy creation and then incorporation of dopant into the vacancy site, as suggested by the electron-beam mediated substitutional doping scheme. We first turn to single S vacancy (VS ) in MoS2 sheet [Fig. 1(a)], which is energetically easier to be produced than Mo vacancy (VMo ) under electron-beam irradiation [31]. It is well known that 1H-MoS2 consists of a monatomic Mo-layer between

Fig. 1. Atomic structures of 1H-MoS2 with (a) VS defect and (b) substitutional dopant in VS . Dashed atom and bonds are vacant site. Side views of 1H-MoS2 with (c) NM atom and (d) TM atom substitutions in VS . The blue, yellow and red balls represent the Mo, S and dopant, respectively. h denotes the height between dopant and Mo-layer. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this Letter.)

1363

two monatomic S-layers like a sandwich structure. Mo and S atoms alternatively occupy corners of a hexagon. Herein, VS is obtained by removing one S atom from the 4 × 4 supercell of 1H-MoS2 . Vacancy formation energy (E f ) is defined as E f = E vac − ( E sheet − E i ), where E vac and E sheet are the total energies of 1H-MoS2 with and without VS , and E i is the energy of isolated S atom. For VS in 1H-MoS2 , structure relaxation shows that the neighboring Mo and S atoms have slightly displacements with respect to the vacancy site, which is different from the visibly reconstructed single vacancy in graphene sheet [44]. The calculated formation energy is 5.72 eV, in good agreement with the reported value of 5.89 ev [27]. Positive E f value indicates that the formation of VS is an endothermic process. As pristine 1H-MoS2 is nonmagnetic and direct semiconductor with gap of 1.9 eV [5], the structure with VS remains spin-unpolarized and thus this defect does not cause any magnetic moments. Nevertheless, VS gives rise to defect states in the band gap and modulates both the gap size and other electronic properties of host 1H-MoS2 . Based on the Bader analysis, charge transfer between Mo and S atoms is also examined. While the depletion of electrons on Mo atom is 1.05e in pristine 1HMoS2 , a comparable depletion of 0.92e occurs on the nearest Mo atom around VS in defective structure. Because insignificant variation of charge transfer is observed in the presence of vacancy, consequently no magnetism is induced. Now we study the electronic and magnetic properties of MoS2 sheet with substitutional defect representing single dopant embedded in the VS , as shown in Fig. 1(b). Varieties of NM atoms (H, B, C, N, O, F) and TM atoms (V, Cr, Mn, Fe, Co, Ni) are considered for a comprehensive comparison. Still, the calculations are carried out in the 4 × 4 supercell, with the impurity concentration corresponding to Θ = 1/48. The distance between two substitutional atoms is larger than 12 Å, and hence the interaction between them can be ignored. The binding energy (E b ) is calculated from the formula E b = E vac+subs − ( E vac + E subs ), where E vac+subs and E vac are total energies of defective 1H-MoS2 with and without substitutional dopant, and E subs is the energy of isolated dopant. Fig. 1(c) gives the typical atomic configuration of NM atom embedded in VS in MoS2 sheet. The height of each NM atom relative to middle Mo-layer, binding energy, total magnetic moment and excess charge on NM atom are presented in Fig. 2(a). As the distance between upper S-layer and middle Mo-layer is 1.57 Å, NM atom displaces downwards from the upper S-layer after relaxation. The binding energies show that all the foreign atoms can favorably be bound to vacancy site. Among these impurities, H has the weakest binding energy of −2.41 eV, whereas O has the strongest binding energy of −7.21 eV. Besides, it is found that the binding

Fig. 2. (a) Height of dopant from Mo-layer, h, binding energy, E b , total magnetic moment, μtotal and excess charge on dopant, ρ of 1H-MoS2 with NM atom substitution in VS . (b) The same caption as (a) but for the case of TM atom substitution. The NM (TM) atom concentration corresponds to Θ = 1/48.

1364


Table 1 Calculated values for 1H-MoS2 with substitutional dopant in VS at uniform concentration of Θ = 1/48. Height between dopant and Mo-layer (h, in Å), binding energy (E b , in eV), magnetic moments of the whole supercell (μtotal , in μB ) and dopant (μ, in μB ), excess charge on dopant(ρ , in e), energy difference between magnetic and nonmagnetic states ( E, in eV). Species

H

B

C

N

O

F

V

Cr

Mn

Fe

Co

Ni

h Eb

0.91 −2.41 1.00 0.00 0.333 −0.064

0.89 −4.96 1.00 0.05 0.230 −0.008

0.84 −6.75 ... ... 0.728 ...

0.96 −5.87 1.00 0.22 0.701 −0.062

1.06 −7.21 ... ... 0.903 ...

1.34 −4.19 1.00 0.07 0.675 −0.049

1.71 −3.91 1.00 1.26 −0.818 −0.171

1.98 −2.60 4.00 3.90 −0.677 −1.254

1.80 −3.35 3.00 3.60 −0.580 −2.128

1.73 −3.77 3.00 2.93 −0.395 −0.941

1.65 −3.80 1.00 1.28 −0.153 −0.158

1.66 −4.23

μtotal μ ρ E

... ... −0.046 ...

Fig. 3. Spin density isosurfaces of substituted 1H-MoS2 at Θ = 1/48. The dashed line denotes the 4 × 4 supercell used in the calculations, green and gray distributions 3

correspond to positive and negative values, respectively. The isosurface value is 0.001 e /Å . (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this Letter.)

energies obtained here are higher than those of adatoms on pristine MoS2 sheets [25], which implies that the NM-substituted structures are more stable than the latter and should be more favored for specific applications. The excess charge on the NM atom (ρ ) is obtained by subtracting the valence charge of the atom from the calculated charge on the atom. Positive ρ value indicates extra electrons transferred from sheet structure onto the substitutional atom. However, due to their weaker electronegativity, H and B atoms gain smaller excess electrons compared to other atoms from C to F. All relevant data is also listed in Table 1. In order to determine the ground state of NM-substituted 1HMoS2 , we calculate the energy difference between spin-polarized and spin-unpolarized states ( E). It is found that H, B, N and Fsubstituted structures have magnetic ground state while C-, and Osubstituted ones are spin-unpolarized. All the magnetic moments are 1.0 μB per supercell in the cases of H, B, N, F substitutions, which is similar to H, B, N and F-absorbed pristine structures. Nonetheless, the contributions of H, B, N, and F to total magnetic moments are unequal, namely, 0.4%, 4.8%, 22.4%, and 6.5%, respectively. The spin-resolved densities in Figs. 3(a)–3(d) show that the spin polarizations are mainly localized on dopants and neighboring atoms for H, and B substitutions, while rather larger spatial extensions of spin density are found for N, and F substitutions. Then, the effect of NM atom doping on the electronic properties of MoS2 sheet is understood by examining the corresponding total density of states (TDOS) and partial density of states (PDOS), as presented in Fig. 4. It is shown that impurity states appear in the band gaps of all doped structures except the O doping case, and the impurity states induced by H, C, and N dopants belong to deep-level ones in the gaps. Clearly these impurity states are mainly attributed to the hybridization between 2p states of NM atom and 4d states of nearest Mo atoms, with small contribution from the 3p states

of nearest S atoms. Because of larger extensions of spin density in N- and F-substituted structures, there also exist extra contributions from the 4d states of third-nearest Mo atoms in the two cases. Since the band gap of pristine sheet is evidently tuned after doping, the optical and transport properties would be significantly affected either. Then, similar calculations are performed for 1H-MoS2 with TM atom substitution in VS . Different from the case of NM atom doping, the TM atom moves upwards from the upper Slayer, as its typical configuration shown in Fig. 1(d). The binding energies of TM-substituted 1H-MoS2 [Fig. 2(b)] range from −2.6 to −4.23 eV, implying more stable configurations relative to TM-absorbed pristine ones. For instance, when E b are calculated to be −2.6, −3.35, −3.77, and −4.23 eV for sheets with Cr, Mn, Fe and Ni in VS , E b are −1.08, −1.37, −2.42, and −3.65 eV for pristine sheets with corresponding adatoms [27], respectively. Negative value of ρ indicates depletion of electrons on TM atom, contrary to the case of NM atom. Noting that the charge transfer from TM atom to the sheet decreases from V to Ni. The TM-substituted 1H-MoS2 are magnetic for elements from V to Co, and the total magnetic moments are 1.0, 4.0, 3.0, 3.0, and 1.0 μB per supercell, respectively [Fig. 2(b)]. The magnetic behaviors are interesting, by incorporating different TM dopants into VS , the magnetic moments of MoS2 structures can be modulated. Figs. 3(e)–3(i) show that the polarizations are mostly localized on V, Cr, Mn, Fe and Co atoms and the spatial extensions of spin density are small compared to those in N and F-substituted sheets. Nevertheless, for V, Cr and Mn, there still exists weak polarizations on the second-nearest Mo atoms, and the directions of polarization on nearest and second-nearest Mo atoms are antiparallel. Based on the TDOS and PDOS in Fig. 5, it is found that the impurity


1365

Fig. 4. The TDOS and PDOS of H, B, C, N, O and F-substituted 1H-MoS2 at Θ = 1/48. The plane of (a) is the TDOS, and (b)–(d) are the p states of NM atom (s and p states for H), d states of nearest Mo atom, and p states of nearest S atom around VS in the upper S-layer, respectively. Fermi level is denoted by the vertical dashed line.

states in the gaps primarily origin from both the 4d orbitals of TM atoms and nearest Mo atoms, indicating strong interactions between them. More interestingly, it can be seen that H, B and Cr-substituted MoS2 sheets behave as half-metals which can be utilized as spin filters. Their band structures are shown in Fig. 6. For H substitution, the sheet is metallic for up-spin channel and semiconductor with direct band gap of 1.20 eV at K for downspin channel. In contrast, B and Cr-substituted sheets behave as direct semiconductors for up-spin channel and metals for downspin channel, the corresponding band gaps are 1.61 eV at K and 1.15 eV at Γ , respectively. Furthermore, the magnetic coupling of H, B and Cr-substituted MoS2 monolayer are examined by adopting the 8 × 8 supercell containing 4 substitutes (namely, doubling the previous structures both in the x and y directions) and setting the initial magnetic moments to be ferromagnetic (FM) and antiferromagnetic (AFM) separately. FM couplings are then found for all the three systems at a distance of 12.64 Å, the corresponding total energy differences between FM and AFM couplings (E FM − E AFM ) are −15.9, −9.6 and −1.0 meV for H, B and Cr-substituted MoS2 monolayer, respectively. In contrast, AFM coupling are observed at the distance of 12.64 Å for H and F-absorbed MoS2 monolayer, where E FM − E AFM are equal to 6.3 and 3.8 meV, respectively [25]. Additionally, MoS2 with TM atom in Mo vacancy is also studied for comparison. The formation energy of VMo is 13.61 eV, indicating a more higher electron beam required to obtain this vacancy defect than VS . Although VMo fails to cause magnetism in the sheet, the situation becomes different when embedding TM atom into VMo , namely, V, Mn, Fe, Co and Ni atoms induce magnetic moments of 1.0, 1.0, 2.0, 3.0 and 4.0 μB , as listed in Table 2.

Table 2 Calculated values for properties of TM atom embedded in VMo , corresponding to the impurity concentration of Θ = 1/48. Binding energy (E b , in eV), magnetic moments of the whole supercell (μtotal , in μB ) and TM atom (μ, in μB ), excess charge on the TM atom (ρ , in e), energy difference between magnetic and nonmagnetic states ( E, in eV). Species

V

Eb

−12.23 1.00 0.30 −1.197 −0.013

μtotal μ ρ E

Cr

−10.54 ... ... −0.983 ...

Mn

Fe

Co

Ni

−9.22 1.00 0.92 −0.803 −0.128

−9.37 2.00 1.17 −0.678 −0.161

−8.47 3.00 0.92 −0.570 −0.180

−7.06 4.00 1.23 −0.569 −0.390

Meanwhile, because of the high formation energy of VMo , the substitutional TM atom is energetically favored at Mo vacancy site with E b ranging from −7.06 to −12.23 eV. Overall, these findings reveal a new route to fabricate spintronic devices based on MoS2 sheet. 4. Summary In summary, on the basis of the first-principles calculations, we study the magnetic and electronic properties of MoS2 sheets with substitutional NM (H, B, C, O, N and F) and TM (V, Cr, Mn, Fe, Co and Ni) atoms in VS defects. Calculated binding energies show that all the substitutional atoms are strongly bound to VS defects, resulting in different magnetic behaviors. While all the H, B, N and F-substituted MoS2 sheets attain total magnetic moment of 1.0 μB , V, Cr, Mn, Fe and Co dopants give rise to total magnetic moments

1366


Fig. 5. The TDOS and PDOS of V, Cr, Mn, Fe, Co and Ni-substituted 1H-MoS2 at Θ = 1/48. The plane of (a) is the TDOS, and (b)–(d) are the d states of TM atom, d states of nearest Mo atom, and p states of nearest S atom, respectively. Fermi level is denoted by the vertical dashed line.

electronic properties of 1H-MoS2 , which may be used for developing MoS2 based nanodevices for spintronics and other potential applications. Acknowledgements J.L. gratefully acknowledges financial support from the National Science Fund for Distinguished Young Scholar (Grant No. 60925016). This work is supported by the National Natural Science Foundation of China (NSFC) (Grant No. 11104347 and No. 11104349) and Advanced Research Foundation of National University of Defense Technology (Grant No. JC-02-19). References

Fig. 6. Band structures of H, B and Cr-substituted MoS2 . Red (blue) color corresponds to up-spin (down-spin) channel. Fermi level is set at 0. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this Letter.)

of 1.0, 4.0, 3.0, 3.0 and 1.0 μB in the sheets, respectively. Furthermore, as the band gaps are simultaneity tuned due to presence of the dopants, novel half-metallic behaviors can be achieved in the H, B and Cr-substituted sheets. Our results show that substitutional doping is an effective way to modulate the magnetic and

[1] K.S. Novoselov, D. Jiang, F. Schedin, T.J. Booth, V.V. Khotkevich, S.V. Morozov, A.K. Geim, Proc. Natl. Acad. Sci. USA 102 (2005) 10451. [2] A.K. Geim, K.S. Novoselov, Nature Mater. 6 (2007) 183. [3] A.H. Castro Neto, F. Guinea, N.M.R. Peres, K.S. Novoselov, A.K. Geim, Rev. Mod. Phys. 81 (2009) 109. [4] C.H. Jin, F. Lin, K. Suenaga, S. Iijima, Phys. Rev. Lett. 102 (2009) 195505. [5] K.F. Mak, C. Lee, J. Hone, J. Shan, T.F. Heinz, Phys. Rev. Lett. 105 (2010) 136805. [6] A. Splendiani, L. Sun, Y. Zhang, T. Li, J. Kim, C.-Y. Chim, G. Galli, F. Wang, Nano Lett. 10 (2010) 1271. [7] K.F. Mak, K. He, J. Shan, T.F. Heinz, Nature Nanotechnol. 7 (2012) 494. [8] S. Lebègue, O. Eriksson, Phys. Rev. B 79 (2009) 115409. [9] C. Ataca, M. Topsakal, E. Aktürk, S. Ciraci, J. Phys. Chem. C 115 (2011) 16354. [10] A. Kuc, N. Zibouche, T. Heine, Phys. Rev. B 83 (2011) 24513. [11] A. Molina-Sánchez, L. Wirtz, Phys. Rev. B 84 (2011) 155413. [12] P. Johari, V.B. Shenoy, ACS Nano 6 (2012) 5449. [13] Y. Ding, Y. Wang, J. Ni, L. Shi, S. Shi, W. Tang, Physica B 406 (2011) 2254.


[14] T. Cheiwchanchamnangij, W.R.L. Lambrecht, Phys. Rev. B 85 (2012) 205302. [15] Q. Yue, J. Kang, Z. Shao, X. Zhang, S. Chang, G. Wang, S. Qin, J. Li, Phys. Lett. A 376 (2012) 1166. [16] Z.Y. Zhu, Y.C. Cheng, U. Schwingenschlögl, Phys. Rev. B 84 (2011) 153402. [17] W.S. Yun, S.W. Han, S.C. Hong, I.G. Kim, J.D. Lee, Phys. Rev. B 85 (2012) 033305. [18] E.S. Kadantsev, P. Hawrylak, Solid State Commun. 152 (2012) 909. [19] J.N. Coleman, M. Lotya, A. O’Neil, S.D. Bergin, P.J. King, U. Khan, K. Young, A. Gaucher, S. De, R.J. Smith, et al., Science 331 (2011) 568. [20] Z. Zeng, Z. Yin, X. Huang, H. Li, Q. He, G. Lu, F. Boey, H. Zhang, Angew. Chem. Int. Ed. 50 (2011) 1. [21] A. Castellanos-Gomez, M. Barkelid, A.M. Goossens, V.E. Calado, H.S.J. van der Zant, G.A. Steele, Nano Lett. 12 (2012) 3187. [22] B. Radisavljevic, A. Radenovic, J. Brivio, V. Giacometti, A. Kis, Nature Nanotechnol. 6 (2011) 147. [23] B. Radisavljevic, M.B. Whitwick, A. Kis, ACS Nano 5 (2011) 9934. [24] Z. Yin, H. Li, H. Li, L. Jiang, Y. Shi, Y. Sun, G. Lu, Q. Zhang, X. Chen, H. Zhang, ACS Nano 6 (2012) 74. [25] J. He, K. Wu, R. Sa, Q. Li, Y. Wei, Appl. Phys. Lett. 96 (2010) 082504. [26] Y. Li, D. Wu, Z. Zhou, C.R. Cabrera, Z. Chen, J. Phys. Chem. Lett. 3 (2012) 2221. [27] C. Ataca, S. Ciraci, J. Phys. Chem. C 115 (2011) 13303. [28] D.C. Sorescu, D.S. Sholl, A.V. Cugini, J. Phys. Chem. B 107 (2003) 1988.

1367

[29] D.C. Sorescu, D.S. Sholl, A.V. Cugini, J. Phys. Chem. B 108 (2004) 239. [30] P.G. Moses, J.J. Mortensen, B.I. Lundqvist, J.K. Nørskov, J. Chem. Phys. 130 (2009) 104709. [31] H.-P. Komsa, J. Kotakoski, S. Kurasch, O. Lehtinen, U. Kaiser, A.V. Krasheninnikov, Phys. Rev. Lett. 109 (2012) 035503. [32] A.V. Krasheninnikov, P.O. Lehtinen, A.S. Foster, P. Pyykkö, R.M. Nieminen, Phys. Rev. Lett. 102 (2009) 126807. [33] X. Wei, M.-S. Wang, Y. Bando, D. Golberg, ACS Nano 5 (2011) 2916. [34] J.A. Rodríguez-Manzo, O. Cretu, F. Banhart, ACS Nano 4 (2010) 3422. [35] Y.G. Zhou, P. Yang, Z.G. Wang, X.T. Zu, H.Y. Xiao, X. Sun, M.A. Khaleel, F. Gao, Phys. Chem. Chem. Phys. 13 (2011) 7378. [36] H. Sahin, ¸ R.T. Senger, S. Ciraci, J. Appl. Phys. 108 (2010) 074301. [37] C. Ataca, E. Aktürk, H. Sahin, ¸ S. Ciraci, J. Appl. Phys. 109 (2011) 013704. [38] P.E. Blochl, Phys. Rev. B 50 (1994) 17953. [39] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. [40] H.J. Monkhorst, J.D. Pack, Phys. Rev. B 13 (1976) 5188. [41] G. Henkelman, A. Arnaldsson, H. Jonsson, Comput. Mater. Sci. 36 (2006) 354. [42] G. Kresse, J. Hafner, Phys. Rev. B 47 (1993) 558. [43] G. Kresse, J. Furthmuller, Phys. Rev. B 54 (1996) 11169. [44] P.O. Lehtinen, A.S. Foster, Y. Ma, A.V. Krasheninnikov, R.M. Nieminen, Phys. Rev. Lett. 93 (2004) 187202.