- Email: [email protected]
Modulation of the work function of fullerenes C60 and C70 by alkali-metal adsorption: A theoretical study
Physics Letters A 377 (2013) 2676–2680
Contents lists available at ScienceDirect
Physics Letters A www.elsevier.com/locate/pla
Modulation of the work function of fullerenes C60 and C70 by alkali-metal adsorption: A theoretical study Hong Liang a , Shunfu Xu a,b,∗ , Weihui Liu b , Yueqiang Sun a , Xiangfa Liu a , Xinqing Zheng a , Sen Li a , Qiang Zhang a , Ziliang Zhu a , Xiaochun Zhang a , Chengguo Dong a , Chun Li b , Guang Yuan b,c , Hitenori Mimura b a b c
Institute of Architecture and Engineering, Weifang University of Science and Technology, Weifang 262700, China Department of Physics, Institute of Information Science and Engineering, Ocean University of China, Qingdao 266100, China Research Institute of Electronics, University of Shizuoka, Hamamasu 432-8011, Japan
a r t i c l e
i n f o
Article history: Received 10 April 2013 Received in revised form 1 August 2013 Accepted 2 August 2013 Available online 8 August 2013 Communicated by R. Wu Keywords: Alkali metal Fullerene Adsorption position Vacancy defect First-principles calculation
a b s t r a c t The impact of alkali-metal (Li/Na/Cs) adsorption on work function of fullerenes C60 and C70 was investigated by first-principles calculations. After adsorption, the work functions of fullerenes C60 and C70 decrease distinctly and vary linearly with the electronegativity of the alkali metal elements, and the positions where the alkali atoms are adsorbed considerably influence the work functions. On the contrary, a vacancy defect elevates the work functions of the fullerenes C60 and C70 . The variation in the work functions rests with variation in Fermi level (which are attributed to charge transfer) and variation in vacuum levels (which are attributed to the induced dipole moments). Moreover, alkali-metal adsorption can also improve the electric conductivity of a fullerene mixture of C60 and C70 . © 2013 Elsevier B.V. All rights reserved.
1. Introduction C60 , a fascinating molecule formed as a truncated icosahedron with 20 hexagonal and 12 pentagonal faces, and 60 vertices, was discovered by Kroto et al. [1] in 1985. Since then, a new form of pure carbon, called fullerene [2], has received considerable attention as potential candidates for future nanoelectronics and has been extensively studied. C60 represents the most identifiable member of the first molecular carbon allotrope existing in universe long before it was discovered. Different kinds of the fullerenes, in the form of C60 , C70 , C76 , C82 and C84 molecules, were found in a family of minerals known as shungites [3]. Field emission characteristics and electronic structures of C60 molecules were investigated experimentally by Lin et al. [4]. The work function of C60 polycrystal films is about 4.69–4.72 eV, which is close to the work function of graphene [5]. Hebard et al. [6,7] found that C60 and C70 become conductive when doped with alkali metals, and potassium-doped C60 can act as a high-temperature superconductor at 18 K.
*
Corresponding author at: Institute of Architecture and Engineering, Weifang University of Science and Technology, Weifang 262700, China. Tel.: +86 0532 66781204. E-mail addresses: [email protected] (S. Xu), [email protected] (G. Yuan). 0375-9601/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.physleta.2013.08.007
The first-principles calculations indicated that the work functions of (5, 5)/(9, 0) single-walled carbon nanotube with a capped edge can be distinctly modulated by alkali-metal adsorption, and electronegativity of the alkali atom plays a dominant role in the work functions of adatom–fullerene systems [8–10]. However, issues regarding the field emission characteristics of fullerenes with alkali-metal adatoms remain. In this Letter, we report the results of work functions in the axial and radial directions of fullerenes (C60 and another fairly common fullerene: C70 ) with different alkalimetal adatoms (Li/Na/Cs) based on first principles calculations. The calculation results show that the electronegativity of the alkali metals is crucial in manipulating the work functions of fullerenes C60 and C70 . The effect of vacancy defect and adsorption position of different alkali metals on the field emission characteristics of fullerenes is also investigated. 2. Calculation details Fig. 1 shows theoretical models of the selected fullerenes C60 and C70 . A vacancy defect was made by removing a carbon atom from the tip (pentagon or hexagon) of the fullerenes C60 and C70 (which was labeled as T in Fig. 1(a)–(b)). An alkali-metal adatom (Li/Na/Cs) was initially located above the center of the pentagons or hexagons (which was labeled as P1 –P4 in Fig. 1(a) for the C60 and in Fig. 1(b) for the C70 ) for the perfect fullerenes (P-fullerene),
H. Liang et al. / Physics Letters A 377 (2013) 2676–2680
2677
Fig. 1. Side and top views of (a) perfect fullerene C60 and (b) perfect fullerene C70 marked with the adsorption position P1 –P5 and defect position T.
and nearby the vacancy defect for the defective fullerenes (Dfullerene). The axial and radial directions of the fullerenes and the X /Y / Z axis were defined in Fig. 1. Our calculations were performed within first-principles DFT (density functional theory) under GGA (generalized gradient approximation) of Perdew, Burke, and Ernzerhof (PBE) [11]. The energy cutoff in the plane-wave basis set is 30 Ry. Ultra-soft pseudopotentials (USPP) are used to describe the valence electrons interaction with the ion cores. The Brillouin zone was sampled using the Γ point approximation. The atomic positions were optimized until all components of all force was less than 1.0 × 10−4 a.u. The fullerenes C60 and C70 were constructed within the same tetragonal supercell with a vacuum width of 30 Å in the axial direction and 20 Å in the radial direction to avoid interactions between adjacent fullerenes. The adatom–graphene system lacks inversion symmetry and therefore has a net electric-dipole moment perpendicular to the surface. To remove spurious dipole interactions between periodic images along the Z direction, we applied corrections to the local electrostatic potential and the total energy (Dipole and potential correction (DPC) method by Neugebauer et al.) [12,13]. The work function W F was defined as the minimum energy which was necessary to extract an electron far from Fermi level into the vacuum level
WF = φ − E f where φ represents the vacuum level and E f represents the Fermi level. The vacuum level was determined by the electrostatic potential in the vacuum region, and was a sufficient distance from the fullerenes C60 and C70 in the Z / X direction that the value converged. All the calculations were performed using the PWscf code in the Quantum ESPRESSO suite [14,15]. 3. Results and discussions According to the present calculations, the work function of the P-fullerene C60 along the axial/radial direction ( Z -axis/ X -axis, Z -W F / X-W F ) is 5.02/5.02 eV, and the Z -W F / X-W F of P-fullerene C70 is 5.00/5.00 eV. In contrast, the work function of the Dfullerene C60 along the axial/radial direction ( Z -axis/ X -axis, Z -W F / X-W F ) is 5.12/5.11 eV, and the Z -W F / X-W F of D-fullerene C70 is
Fig. 2. (a) Axial work functions of P- and D-fullerenes with Li/Na/Cs on P1 vs. electronegativity. (b) Axial and radial work functions of the P-fullerene C60 with Li/Na/Cs on P2 –P4 vs. electronegativity.
5.26/5.25 eV. The difference is derived from the orientation of the alkali-metal adatoms and the distribution of the carbon atoms. As an example, the tip of the D-fullerene C60 is more sharp and the distance between the two adjacent carbon layers is less than that of the P-fullerene C60 , which builds up the capability of binding electrons for the D-fullerene C60 . Therefore, the work functions of the D-fullerenes are slightly higher than that of the P-fullerenes. After alkali-metal adsorption, the work functions of all the Pfullerenes and D-fullerenes along the Z -axis and the X -axis decrease significantly. The Z -W F / X-W F of the P- and D-fullerene C60 with alkali-metal adatoms are lower than that of the P- and Dfullerene C70 with the same adatoms. However, the Z -W F / X-W F of the D-fullerenes with alkali-metal adatoms are higher than that of the P-fullerenes with the same adatoms. The Z -W F and X-W F correspond with the work functions of fullerenes with alkali-metal adatoms on their surface and in their grooves, respectively. Fig. 2(a) summarizes the axial work functions of P- and Dfullerenes C60 and C70 with alkali-metal adatoms on P1 plotted against the electronegativity of the alkali metal elements. All the work functions of fullerenes increase linearly with the electronegativity of the alkali metal elements. Table 1 lists the slopes of these linear curves. The slopes are comparable with that of the Gordy– Thomas equation (W F = 2.3χ + 0.34) [16,17], which is a linear relationship between the work functions and electronegativity. The slopes of the X-W F are more consistent with the Gordy–Thomas
2678
H. Liang et al. / Physics Letters A 377 (2013) 2676–2680
Table 1 Slopes of the linear curves for P- and the D-fullerenes C60 and C70 with alkali-metal adatoms. Z -W F of P-fullerene C60 –P1
X-W F of P-fullerene C60 –P1
Z -W F of D-fullerene C60 –P1
X-W F of D-fullerene C60 –P1
Z -W F of P-fullerene C70 –P1
Z -W F of D-fullerene C70 –P1
3.50
2.53
3.42
2.71
3.75
2.92
Z -W F of P-fullerene C60 –P2
X-W F of P-fullerene C60 –P2
Z -W F of P-fullerene C60 –P3
X-W F of P-fullerene C60 –P3
Z -W F of P-fullerene C60 –P4
X-W F of P-fullerene C60 –P4
2.80
2.54
1.98
2.68
1.71
2.54
equation than that of the Z -W F . In Fig. 2(b), similarly, the axial and radial work functions of P-fullerene C60 with alkali-metal adatoms on different positions (P2 –P4 ) also exhibit a linear relationship with electronegativity of the alkali metal elements. The slopes of all these linear curves in Fig. 2 depend on the adsorption position and the vacancy defect. When the adsorption position shifts from P1 to P4 , the slopes of the axial work functions Z -W F of P-fullerene C60 decrease markedly. However, the slope of the radial work function X-W F changes little. Therefore, P-fullerene C60 has the lowest work functions with alkali-metal adatoms on P1 in the axial direction and on P3 in the radial direction. The linear curves in Fig. 2(a)–(b) can also predict the work functions of fullerenes with other alkali-metal adatoms such as K and Rb. Furthermore, other metal adatoms are presumed to have similar effects as alkali metals on decreasing or increasing the axial and radial work functions of C60 , C70 and other fullerenes (C76 , C82 and C84 , etc.). The linear relationships between the work functions of fullerenes and the electronegativity of the alkali-metal adatoms imply that the work functions of fullerenes C60 and C70 can be simply modulated by different alkali-metal adsorption. The work functions can be influenced by either an enhanced (reduced) surface dipole moments or a lowering (rising) of the intrinsic bulk Fermi levels [18]. Our calculations show that the changes of the work functions are mainly attribute to the shifts in the Fermi levels. For example, the shift of the Fermi levels after Li/Na/Cs adsorption on P1 is 0.94/1.10/1.45 eV for the P-fullerene C60 , while the corresponding variations in the Z -W F and X-W F are 1.07/1.27/1.74 eV and 0.91/1.06/1.39 eV, respectively. Fig. 3(a) plots the Fermi levels of P- and D-fullerene C60 with alkali-metal adatoms on P1 versus electronegativity. All the Fermi levels decrease linearly with electronegativity, indicating the changes in the Fermi levels are dominated by the electronegativity of alkalimetal adatoms. The Fermi levels of the fullerene C60 with alkali metals are slightly higher than that of the fullerene C70 with alkali metals. However, the Fermi levels of the D-fullerene C60 with alkali metals are slightly lower than that of the D-fullerene C70 with alkali metals. Fig. 3(a) also shows the dipole moments along the Z -axis of P-fullerene/D-fullerene C60 with alkali-metals on P1 plotted as a function of electronegativity of the alkali metal elements. All the dipole moments increase linearly with the electronegativity, suggesting that the changes in the dipole moments are dominated by the electronegativity of the alkali metal elements. Fig. 3(b) presents vacuum levels as functions of induced dipole moments along the Z -axis for P-fullerenes C60 with alkali-metal adatoms on different adsorption positions (P1 –P4 ). All vacuum levels increase linearly with the dipole moments, indicating that the changes in the vacuum levels in the axial direction is mainly due to the changes in the dipole moments along the Z -axis. After alkalimetal adsorption, the induced dipole moments decrease the vacuum levels, leading to a small decrease in the work functions. The relationship between these physical quantities of the P-fullerene C70 and D-fullerenes with alkali-metal adatoms is similar to that of the P-fullerene C60 with alkali-metal adatoms.
Fig. 3. (a) Fermi levels and dipole moments along the Z axis of P- and D-fullerene C60 with Li/Na/Cs on P1 vs. electronegativity. (b) Relation between the vacuum levels and dipole moments along the Z -axis of the P-fullerene C60 with Li/Na/Cs on P1 –P4 .
Because the electronegativity of the alkali metals is less than that of the carbon atoms (the electronegativity of C/Li/Na/Cs is 2.55/0.98/0.93/0.79 [16,17], respectively), the electrons of alkalimetal adatoms on the fullerenes are ionized due to the effect of the surface state [19], and the electrons are easily transferred from the alkali-metal adatoms to fullerenes. Fig. 4 shows the 2D/3D differential charge density distributions (DCDD) of the P-fullerene C60 and C70 with the lithium adatom on P1 . The differential charges accumulate between Li and the six nearest-neighbor C atoms on the tips, presenting the properties of π orbitals of the C atoms. Therefore, the Li adatom is predicted to donate the great mass of its outer valence-electrons to the neighboring π orbitals of
H. Liang et al. / Physics Letters A 377 (2013) 2676–2680
2679
Fig. 5. Density of states (DOS) of the P-fullerenes and D-fullerenes before and after Li adsorption. The Fermi levels are set to 0 eV.
Fig. 6. Projected density of states (PDOS) of the carbon atoms in the first layer of the P-fullerene C60 and the Li atom (on P1 ).
Fig. 4. 3D and 2D contours of differential charge density distributions (DCDD) of (a) Li–P-fullerene C60 and (b) Li–P-fullerene C70 . Black and red balls represent carbon atoms and Li atoms, respectively. Blue and yellow represent positive and negative charge distributions, respectively. DCDD is defined as C = C (fullerene + Li) − C (fullerene) − C (Li). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this Letter.)
the fullerenes. This causes elevation of the Fermi levels and a great atomic dipole moment (which decrease the vacuum levels), thereby a quick linear decrease of the work function. Compared with the P-fullerenes with the Li adatom, there is an asymmetric contour of the DCDD for the D-fullerenes with the Li adatom. The DCDD of the P-fullerenes and D-fullerenes with the Na/Cs adatom is similar to that of the P-fullerenes with the Li adatom. However, the Na/Cs adatom are more efficient in charge transfer and elevation of the Fermi levels due to their smaller electronegativity. Because the diameter of Li/Na/Cs atoms is comparable with that of the size of hexagon or pentagon rings of fullerenes, alkali metals can reduce the spatial extension of the p electrons into the vacuum by forming chemical bonds with fullerenes and assist fullerenes in keeping their electrons, resulting in repulsion among the energy states [20]. We take Li adsorption for example of alkali-metal adsorption. Fig. 5 shows the density of states (DOS) of the P-fullerenes C60 and C70 before and after Li adsorption. As shown in this figure, the P-fullerenes C60 and C70 present semiconducting properties. The DOS of the P-fullerenes C60 and C70 shifts towards the low-energy side after Li adsorption, leading
to more occupation of fullerene states. That is to say, the highest occupied molecular orbital (HOMO) shifts towards a higher energy. The Li adsorption enhances the DOS value at Fermi levels of the P-fullerenes, transforming the pristine semiconducting properties into metallic properties. It’s consistent with the abovementioned changes in the Fermi levels of the P-fullerenes C60 and C70 . The D-fullerenes show metallic properties and the DOS near the Fermi levels do not change significantly after Li adsorption. This phenomenon indicates that alkali-metal adsorption may resolve two questions: to decrease high work functions of fullerenes and improve electric conductivity of fullerene mixtures. The DOS of the P-fullerenes and D-fullerenes with the Na/Cs adatom is similar to that of the P-fullerenes and D-fullerenes with the Li adatom. The projected density of states (PDOS) can provide detailed information relevant to the electronic structure of the adsorption systems. Fig. 6 shows the PDOS of the Li atom (on P1 ) and carbon atoms in the first layer of the P-fullerene C60 . After adsorption, augmentation of the DOS value near the Fermi level is mainly derived from the 2p z and 2p x + 2p y orbitals of the carbon atoms and the 2p x + 2p y orbitals of the Li atom. This result indicates a charge transfer from the 2s orbital of the Li atom to the neighboring 2p x + 2p y orbitals of the Li atom and 2p z orbitals of the carbon atoms on the tip. After adsorption, the 2p x + 2p y states of the fullerene C60 are partly occupied and a broad resonance with 2p z state of carbon atoms exists near the Fermi level. This result implies that the Li–C60 interaction and the decrease in work function come mainly from hybridization of the three states. These phenomena are consistent with the charge redistribution in Fig. 4. The charge transfer from a higher energy level of the Li atom to a lower
2680
H. Liang et al. / Physics Letters A 377 (2013) 2676–2680
energy level of the P-fullerene increases the Fermi levels and decreases the vacuum levels, and then influences the work functions. Similar results of PDOS are found for Na/Cs-fullerene systems. 4. Summary The first-principles calculations show that the work functions of fullerenes C60 and C70 can be effectively modulated by alkali-metal adsorption and the electronegativity of the alkali atoms plays a dominant role in the work functions of the adatom–fullerene systems. After adsorption, the work functions of fullerenes C60 and C70 decrease distinctly, and the work functions of the D-fullerene are slightly higher than that of the P-fullerenes. The variations in the work functions are mainly attributed to changes in the Fermi levels. Furthermore, the adsorption positions considerably influence the work functions. In addition, the alkali-metal adsorption converts the semiconducting properties of P-fullerenes C60 and C70 into metallic properties. Acknowledgements We acknowledge the developers of XCrySDen [21,22] (a crystalline and molecular structure visualization program) and VESTA [23,24] (a three-dimensional visualization system for electronic and structural analysis). This work is supported by the fund from National Natural Science Foundation of China (Grants 41076057 and 60907007), a Project of Shandong Province Higher Educational Science and Technology Program (Grant No. J13LJ52) and Doctoral Science Foundation of Weifang University of Science and Technology (Grant No. W13K015).
References [1] H.W. Kroto, J.R. Heath, S.C. O’Brien, R.F. Curl, R.E. Smalley, Nature (London) 318 (1985) 162. [2] R.F. Curl, R.E. Smalley, Sci. Am. 264 (1991) 54. [3] P.R. Buseck, S.J. Tsipursky, R. Hettich, Science 257 (1992) 215. [4] M.E. Lin, R.P. Andres, R. Reifenberger, D.R. Huffmen, Phys. Rev. B 47 (1993) 7546. [5] M. Shiraishi, K. Shibata, R. Maruyama, M. Ata, Phys. Rev. B 68 (2003) 235414. [6] R.C. Haddon, A.F. Hebard, M.J. Rosseinsky, D.W. Murphy, S.J. Duclos, K.B. Lyons, B. Miller, J.M. Rosamilia, R.M. Fleming, A.R. Kortan, S.H. Glarum, A.V. Makhija, A.J. Muller, R.H. Eick, S.M. Zahurak, R. Tycko, G. Dabbagh, F.A. Thiel, Nature 350 (1991) 320. [7] A.F. Hebard, M.J. Rosseinsky, R.C. Haddon, D.W. Murphy, S.H. Glarum, T.T.M. Palstra, A.P. Ramirez, A.R. Kortan, Nature 350 (1991) 600. [8] S.F. Xu, G. Yuan, C. Li, W.H. Liu, H. Mimura, J. Phys. Chem. C 115 (2011) 8928. [9] S.F. Xu, G. Yuan, C. Li, Z.J. Jia, H. Mimura, Appl. Phys. Lett. 96 (2010) 233111. [10] S.F. Xu, G. Yuan, C. Li, H. Mimura, J. Vac. Sci. Technol. B 29 (2011) 04E101. [11] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. [12] C.Y.He.Z.Z. Yu, L.Z. Sun, J.X. Zhong, J. Comput. Theor. Nanosci. 9 (2012) 16. [13] J. Neugebauer, M. Scheffler, Phys. Rev. B 46 (1992) 16067. [14] http://www.quantum-espresso.org/. [15] P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G.L. Chiarotti, M. Cococcioni, I. Dabo, A.D. Corso, S. de Gironcoli, S. Fabris, G. Fratesi, R. Gebauer, U. Gerstmann, C. Gougoussis, A. Kokalj, M. Lazzeri, L. Martin-Samos, N. Marzari, F. Mauri, R. Mazzarello, S. Paolini, A. Pasquarello, L. Paulatto, C. Sbraccia, S. Scandolo, G. Sclauzero, A.P. Seitsonen, A. Smogunov, P. Umari, R.M. Wentzcovitch, J. Phys.: Condens. Matter 21 (2009) 395502. [16] S. Yamamoto, Appl. Surf. Sci. 251 (2005) 4. [17] W. Gordy, W.J.O. Thomas, J. Chem. Phys. 24 (1956) 439. [18] B. Shan, K. Cho, Phys. Rev. Lett. 94 (2005) 236602. [19] R.Q. Wu, K.L. Chen, D.S. Wang, N. Wang, Phys. Rev. B 38 (1988) 3180. [20] M. Khazaei, A.A. Farajian, H. Mizuseki, Y. Kawazoe, Comput. Mater. Sci. 36 (2006) 152. [21] http://www.xcrysden.org/. [22] A. Kokalj, Comput. Mater. Sci. 28 (2003) 155. [23] http://www.geocities.jp/kmo_mma/index-en.html. [24] K. Momma, F.J. Izumi, Appl. Crystallogr. 41 (2008) 653.
Contents lists available at ScienceDirect
Physics Letters A www.elsevier.com/locate/pla
Modulation of the work function of fullerenes C60 and C70 by alkali-metal adsorption: A theoretical study Hong Liang a , Shunfu Xu a,b,∗ , Weihui Liu b , Yueqiang Sun a , Xiangfa Liu a , Xinqing Zheng a , Sen Li a , Qiang Zhang a , Ziliang Zhu a , Xiaochun Zhang a , Chengguo Dong a , Chun Li b , Guang Yuan b,c , Hitenori Mimura b a b c
Institute of Architecture and Engineering, Weifang University of Science and Technology, Weifang 262700, China Department of Physics, Institute of Information Science and Engineering, Ocean University of China, Qingdao 266100, China Research Institute of Electronics, University of Shizuoka, Hamamasu 432-8011, Japan
a r t i c l e
i n f o
Article history: Received 10 April 2013 Received in revised form 1 August 2013 Accepted 2 August 2013 Available online 8 August 2013 Communicated by R. Wu Keywords: Alkali metal Fullerene Adsorption position Vacancy defect First-principles calculation
a b s t r a c t The impact of alkali-metal (Li/Na/Cs) adsorption on work function of fullerenes C60 and C70 was investigated by first-principles calculations. After adsorption, the work functions of fullerenes C60 and C70 decrease distinctly and vary linearly with the electronegativity of the alkali metal elements, and the positions where the alkali atoms are adsorbed considerably influence the work functions. On the contrary, a vacancy defect elevates the work functions of the fullerenes C60 and C70 . The variation in the work functions rests with variation in Fermi level (which are attributed to charge transfer) and variation in vacuum levels (which are attributed to the induced dipole moments). Moreover, alkali-metal adsorption can also improve the electric conductivity of a fullerene mixture of C60 and C70 . © 2013 Elsevier B.V. All rights reserved.
1. Introduction C60 , a fascinating molecule formed as a truncated icosahedron with 20 hexagonal and 12 pentagonal faces, and 60 vertices, was discovered by Kroto et al. [1] in 1985. Since then, a new form of pure carbon, called fullerene [2], has received considerable attention as potential candidates for future nanoelectronics and has been extensively studied. C60 represents the most identifiable member of the first molecular carbon allotrope existing in universe long before it was discovered. Different kinds of the fullerenes, in the form of C60 , C70 , C76 , C82 and C84 molecules, were found in a family of minerals known as shungites [3]. Field emission characteristics and electronic structures of C60 molecules were investigated experimentally by Lin et al. [4]. The work function of C60 polycrystal films is about 4.69–4.72 eV, which is close to the work function of graphene [5]. Hebard et al. [6,7] found that C60 and C70 become conductive when doped with alkali metals, and potassium-doped C60 can act as a high-temperature superconductor at 18 K.
*
Corresponding author at: Institute of Architecture and Engineering, Weifang University of Science and Technology, Weifang 262700, China. Tel.: +86 0532 66781204. E-mail addresses: [email protected] (S. Xu), [email protected] (G. Yuan). 0375-9601/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.physleta.2013.08.007
The first-principles calculations indicated that the work functions of (5, 5)/(9, 0) single-walled carbon nanotube with a capped edge can be distinctly modulated by alkali-metal adsorption, and electronegativity of the alkali atom plays a dominant role in the work functions of adatom–fullerene systems [8–10]. However, issues regarding the field emission characteristics of fullerenes with alkali-metal adatoms remain. In this Letter, we report the results of work functions in the axial and radial directions of fullerenes (C60 and another fairly common fullerene: C70 ) with different alkalimetal adatoms (Li/Na/Cs) based on first principles calculations. The calculation results show that the electronegativity of the alkali metals is crucial in manipulating the work functions of fullerenes C60 and C70 . The effect of vacancy defect and adsorption position of different alkali metals on the field emission characteristics of fullerenes is also investigated. 2. Calculation details Fig. 1 shows theoretical models of the selected fullerenes C60 and C70 . A vacancy defect was made by removing a carbon atom from the tip (pentagon or hexagon) of the fullerenes C60 and C70 (which was labeled as T in Fig. 1(a)–(b)). An alkali-metal adatom (Li/Na/Cs) was initially located above the center of the pentagons or hexagons (which was labeled as P1 –P4 in Fig. 1(a) for the C60 and in Fig. 1(b) for the C70 ) for the perfect fullerenes (P-fullerene),
H. Liang et al. / Physics Letters A 377 (2013) 2676–2680
2677
Fig. 1. Side and top views of (a) perfect fullerene C60 and (b) perfect fullerene C70 marked with the adsorption position P1 –P5 and defect position T.
and nearby the vacancy defect for the defective fullerenes (Dfullerene). The axial and radial directions of the fullerenes and the X /Y / Z axis were defined in Fig. 1. Our calculations were performed within first-principles DFT (density functional theory) under GGA (generalized gradient approximation) of Perdew, Burke, and Ernzerhof (PBE) [11]. The energy cutoff in the plane-wave basis set is 30 Ry. Ultra-soft pseudopotentials (USPP) are used to describe the valence electrons interaction with the ion cores. The Brillouin zone was sampled using the Γ point approximation. The atomic positions were optimized until all components of all force was less than 1.0 × 10−4 a.u. The fullerenes C60 and C70 were constructed within the same tetragonal supercell with a vacuum width of 30 Å in the axial direction and 20 Å in the radial direction to avoid interactions between adjacent fullerenes. The adatom–graphene system lacks inversion symmetry and therefore has a net electric-dipole moment perpendicular to the surface. To remove spurious dipole interactions between periodic images along the Z direction, we applied corrections to the local electrostatic potential and the total energy (Dipole and potential correction (DPC) method by Neugebauer et al.) [12,13]. The work function W F was defined as the minimum energy which was necessary to extract an electron far from Fermi level into the vacuum level
WF = φ − E f where φ represents the vacuum level and E f represents the Fermi level. The vacuum level was determined by the electrostatic potential in the vacuum region, and was a sufficient distance from the fullerenes C60 and C70 in the Z / X direction that the value converged. All the calculations were performed using the PWscf code in the Quantum ESPRESSO suite [14,15]. 3. Results and discussions According to the present calculations, the work function of the P-fullerene C60 along the axial/radial direction ( Z -axis/ X -axis, Z -W F / X-W F ) is 5.02/5.02 eV, and the Z -W F / X-W F of P-fullerene C70 is 5.00/5.00 eV. In contrast, the work function of the Dfullerene C60 along the axial/radial direction ( Z -axis/ X -axis, Z -W F / X-W F ) is 5.12/5.11 eV, and the Z -W F / X-W F of D-fullerene C70 is
Fig. 2. (a) Axial work functions of P- and D-fullerenes with Li/Na/Cs on P1 vs. electronegativity. (b) Axial and radial work functions of the P-fullerene C60 with Li/Na/Cs on P2 –P4 vs. electronegativity.
5.26/5.25 eV. The difference is derived from the orientation of the alkali-metal adatoms and the distribution of the carbon atoms. As an example, the tip of the D-fullerene C60 is more sharp and the distance between the two adjacent carbon layers is less than that of the P-fullerene C60 , which builds up the capability of binding electrons for the D-fullerene C60 . Therefore, the work functions of the D-fullerenes are slightly higher than that of the P-fullerenes. After alkali-metal adsorption, the work functions of all the Pfullerenes and D-fullerenes along the Z -axis and the X -axis decrease significantly. The Z -W F / X-W F of the P- and D-fullerene C60 with alkali-metal adatoms are lower than that of the P- and Dfullerene C70 with the same adatoms. However, the Z -W F / X-W F of the D-fullerenes with alkali-metal adatoms are higher than that of the P-fullerenes with the same adatoms. The Z -W F and X-W F correspond with the work functions of fullerenes with alkali-metal adatoms on their surface and in their grooves, respectively. Fig. 2(a) summarizes the axial work functions of P- and Dfullerenes C60 and C70 with alkali-metal adatoms on P1 plotted against the electronegativity of the alkali metal elements. All the work functions of fullerenes increase linearly with the electronegativity of the alkali metal elements. Table 1 lists the slopes of these linear curves. The slopes are comparable with that of the Gordy– Thomas equation (W F = 2.3χ + 0.34) [16,17], which is a linear relationship between the work functions and electronegativity. The slopes of the X-W F are more consistent with the Gordy–Thomas
2678
H. Liang et al. / Physics Letters A 377 (2013) 2676–2680
Table 1 Slopes of the linear curves for P- and the D-fullerenes C60 and C70 with alkali-metal adatoms. Z -W F of P-fullerene C60 –P1
X-W F of P-fullerene C60 –P1
Z -W F of D-fullerene C60 –P1
X-W F of D-fullerene C60 –P1
Z -W F of P-fullerene C70 –P1
Z -W F of D-fullerene C70 –P1
3.50
2.53
3.42
2.71
3.75
2.92
Z -W F of P-fullerene C60 –P2
X-W F of P-fullerene C60 –P2
Z -W F of P-fullerene C60 –P3
X-W F of P-fullerene C60 –P3
Z -W F of P-fullerene C60 –P4
X-W F of P-fullerene C60 –P4
2.80
2.54
1.98
2.68
1.71
2.54
equation than that of the Z -W F . In Fig. 2(b), similarly, the axial and radial work functions of P-fullerene C60 with alkali-metal adatoms on different positions (P2 –P4 ) also exhibit a linear relationship with electronegativity of the alkali metal elements. The slopes of all these linear curves in Fig. 2 depend on the adsorption position and the vacancy defect. When the adsorption position shifts from P1 to P4 , the slopes of the axial work functions Z -W F of P-fullerene C60 decrease markedly. However, the slope of the radial work function X-W F changes little. Therefore, P-fullerene C60 has the lowest work functions with alkali-metal adatoms on P1 in the axial direction and on P3 in the radial direction. The linear curves in Fig. 2(a)–(b) can also predict the work functions of fullerenes with other alkali-metal adatoms such as K and Rb. Furthermore, other metal adatoms are presumed to have similar effects as alkali metals on decreasing or increasing the axial and radial work functions of C60 , C70 and other fullerenes (C76 , C82 and C84 , etc.). The linear relationships between the work functions of fullerenes and the electronegativity of the alkali-metal adatoms imply that the work functions of fullerenes C60 and C70 can be simply modulated by different alkali-metal adsorption. The work functions can be influenced by either an enhanced (reduced) surface dipole moments or a lowering (rising) of the intrinsic bulk Fermi levels [18]. Our calculations show that the changes of the work functions are mainly attribute to the shifts in the Fermi levels. For example, the shift of the Fermi levels after Li/Na/Cs adsorption on P1 is 0.94/1.10/1.45 eV for the P-fullerene C60 , while the corresponding variations in the Z -W F and X-W F are 1.07/1.27/1.74 eV and 0.91/1.06/1.39 eV, respectively. Fig. 3(a) plots the Fermi levels of P- and D-fullerene C60 with alkali-metal adatoms on P1 versus electronegativity. All the Fermi levels decrease linearly with electronegativity, indicating the changes in the Fermi levels are dominated by the electronegativity of alkalimetal adatoms. The Fermi levels of the fullerene C60 with alkali metals are slightly higher than that of the fullerene C70 with alkali metals. However, the Fermi levels of the D-fullerene C60 with alkali metals are slightly lower than that of the D-fullerene C70 with alkali metals. Fig. 3(a) also shows the dipole moments along the Z -axis of P-fullerene/D-fullerene C60 with alkali-metals on P1 plotted as a function of electronegativity of the alkali metal elements. All the dipole moments increase linearly with the electronegativity, suggesting that the changes in the dipole moments are dominated by the electronegativity of the alkali metal elements. Fig. 3(b) presents vacuum levels as functions of induced dipole moments along the Z -axis for P-fullerenes C60 with alkali-metal adatoms on different adsorption positions (P1 –P4 ). All vacuum levels increase linearly with the dipole moments, indicating that the changes in the vacuum levels in the axial direction is mainly due to the changes in the dipole moments along the Z -axis. After alkalimetal adsorption, the induced dipole moments decrease the vacuum levels, leading to a small decrease in the work functions. The relationship between these physical quantities of the P-fullerene C70 and D-fullerenes with alkali-metal adatoms is similar to that of the P-fullerene C60 with alkali-metal adatoms.
Fig. 3. (a) Fermi levels and dipole moments along the Z axis of P- and D-fullerene C60 with Li/Na/Cs on P1 vs. electronegativity. (b) Relation between the vacuum levels and dipole moments along the Z -axis of the P-fullerene C60 with Li/Na/Cs on P1 –P4 .
Because the electronegativity of the alkali metals is less than that of the carbon atoms (the electronegativity of C/Li/Na/Cs is 2.55/0.98/0.93/0.79 [16,17], respectively), the electrons of alkalimetal adatoms on the fullerenes are ionized due to the effect of the surface state [19], and the electrons are easily transferred from the alkali-metal adatoms to fullerenes. Fig. 4 shows the 2D/3D differential charge density distributions (DCDD) of the P-fullerene C60 and C70 with the lithium adatom on P1 . The differential charges accumulate between Li and the six nearest-neighbor C atoms on the tips, presenting the properties of π orbitals of the C atoms. Therefore, the Li adatom is predicted to donate the great mass of its outer valence-electrons to the neighboring π orbitals of
H. Liang et al. / Physics Letters A 377 (2013) 2676–2680
2679
Fig. 5. Density of states (DOS) of the P-fullerenes and D-fullerenes before and after Li adsorption. The Fermi levels are set to 0 eV.
Fig. 6. Projected density of states (PDOS) of the carbon atoms in the first layer of the P-fullerene C60 and the Li atom (on P1 ).
Fig. 4. 3D and 2D contours of differential charge density distributions (DCDD) of (a) Li–P-fullerene C60 and (b) Li–P-fullerene C70 . Black and red balls represent carbon atoms and Li atoms, respectively. Blue and yellow represent positive and negative charge distributions, respectively. DCDD is defined as C = C (fullerene + Li) − C (fullerene) − C (Li). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this Letter.)
the fullerenes. This causes elevation of the Fermi levels and a great atomic dipole moment (which decrease the vacuum levels), thereby a quick linear decrease of the work function. Compared with the P-fullerenes with the Li adatom, there is an asymmetric contour of the DCDD for the D-fullerenes with the Li adatom. The DCDD of the P-fullerenes and D-fullerenes with the Na/Cs adatom is similar to that of the P-fullerenes with the Li adatom. However, the Na/Cs adatom are more efficient in charge transfer and elevation of the Fermi levels due to their smaller electronegativity. Because the diameter of Li/Na/Cs atoms is comparable with that of the size of hexagon or pentagon rings of fullerenes, alkali metals can reduce the spatial extension of the p electrons into the vacuum by forming chemical bonds with fullerenes and assist fullerenes in keeping their electrons, resulting in repulsion among the energy states [20]. We take Li adsorption for example of alkali-metal adsorption. Fig. 5 shows the density of states (DOS) of the P-fullerenes C60 and C70 before and after Li adsorption. As shown in this figure, the P-fullerenes C60 and C70 present semiconducting properties. The DOS of the P-fullerenes C60 and C70 shifts towards the low-energy side after Li adsorption, leading
to more occupation of fullerene states. That is to say, the highest occupied molecular orbital (HOMO) shifts towards a higher energy. The Li adsorption enhances the DOS value at Fermi levels of the P-fullerenes, transforming the pristine semiconducting properties into metallic properties. It’s consistent with the abovementioned changes in the Fermi levels of the P-fullerenes C60 and C70 . The D-fullerenes show metallic properties and the DOS near the Fermi levels do not change significantly after Li adsorption. This phenomenon indicates that alkali-metal adsorption may resolve two questions: to decrease high work functions of fullerenes and improve electric conductivity of fullerene mixtures. The DOS of the P-fullerenes and D-fullerenes with the Na/Cs adatom is similar to that of the P-fullerenes and D-fullerenes with the Li adatom. The projected density of states (PDOS) can provide detailed information relevant to the electronic structure of the adsorption systems. Fig. 6 shows the PDOS of the Li atom (on P1 ) and carbon atoms in the first layer of the P-fullerene C60 . After adsorption, augmentation of the DOS value near the Fermi level is mainly derived from the 2p z and 2p x + 2p y orbitals of the carbon atoms and the 2p x + 2p y orbitals of the Li atom. This result indicates a charge transfer from the 2s orbital of the Li atom to the neighboring 2p x + 2p y orbitals of the Li atom and 2p z orbitals of the carbon atoms on the tip. After adsorption, the 2p x + 2p y states of the fullerene C60 are partly occupied and a broad resonance with 2p z state of carbon atoms exists near the Fermi level. This result implies that the Li–C60 interaction and the decrease in work function come mainly from hybridization of the three states. These phenomena are consistent with the charge redistribution in Fig. 4. The charge transfer from a higher energy level of the Li atom to a lower
2680
H. Liang et al. / Physics Letters A 377 (2013) 2676–2680
energy level of the P-fullerene increases the Fermi levels and decreases the vacuum levels, and then influences the work functions. Similar results of PDOS are found for Na/Cs-fullerene systems. 4. Summary The first-principles calculations show that the work functions of fullerenes C60 and C70 can be effectively modulated by alkali-metal adsorption and the electronegativity of the alkali atoms plays a dominant role in the work functions of the adatom–fullerene systems. After adsorption, the work functions of fullerenes C60 and C70 decrease distinctly, and the work functions of the D-fullerene are slightly higher than that of the P-fullerenes. The variations in the work functions are mainly attributed to changes in the Fermi levels. Furthermore, the adsorption positions considerably influence the work functions. In addition, the alkali-metal adsorption converts the semiconducting properties of P-fullerenes C60 and C70 into metallic properties. Acknowledgements We acknowledge the developers of XCrySDen [21,22] (a crystalline and molecular structure visualization program) and VESTA [23,24] (a three-dimensional visualization system for electronic and structural analysis). This work is supported by the fund from National Natural Science Foundation of China (Grants 41076057 and 60907007), a Project of Shandong Province Higher Educational Science and Technology Program (Grant No. J13LJ52) and Doctoral Science Foundation of Weifang University of Science and Technology (Grant No. W13K015).
References [1] H.W. Kroto, J.R. Heath, S.C. O’Brien, R.F. Curl, R.E. Smalley, Nature (London) 318 (1985) 162. [2] R.F. Curl, R.E. Smalley, Sci. Am. 264 (1991) 54. [3] P.R. Buseck, S.J. Tsipursky, R. Hettich, Science 257 (1992) 215. [4] M.E. Lin, R.P. Andres, R. Reifenberger, D.R. Huffmen, Phys. Rev. B 47 (1993) 7546. [5] M. Shiraishi, K. Shibata, R. Maruyama, M. Ata, Phys. Rev. B 68 (2003) 235414. [6] R.C. Haddon, A.F. Hebard, M.J. Rosseinsky, D.W. Murphy, S.J. Duclos, K.B. Lyons, B. Miller, J.M. Rosamilia, R.M. Fleming, A.R. Kortan, S.H. Glarum, A.V. Makhija, A.J. Muller, R.H. Eick, S.M. Zahurak, R. Tycko, G. Dabbagh, F.A. Thiel, Nature 350 (1991) 320. [7] A.F. Hebard, M.J. Rosseinsky, R.C. Haddon, D.W. Murphy, S.H. Glarum, T.T.M. Palstra, A.P. Ramirez, A.R. Kortan, Nature 350 (1991) 600. [8] S.F. Xu, G. Yuan, C. Li, W.H. Liu, H. Mimura, J. Phys. Chem. C 115 (2011) 8928. [9] S.F. Xu, G. Yuan, C. Li, Z.J. Jia, H. Mimura, Appl. Phys. Lett. 96 (2010) 233111. [10] S.F. Xu, G. Yuan, C. Li, H. Mimura, J. Vac. Sci. Technol. B 29 (2011) 04E101. [11] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. [12] C.Y.He.Z.Z. Yu, L.Z. Sun, J.X. Zhong, J. Comput. Theor. Nanosci. 9 (2012) 16. [13] J. Neugebauer, M. Scheffler, Phys. Rev. B 46 (1992) 16067. [14] http://www.quantum-espresso.org/. [15] P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G.L. Chiarotti, M. Cococcioni, I. Dabo, A.D. Corso, S. de Gironcoli, S. Fabris, G. Fratesi, R. Gebauer, U. Gerstmann, C. Gougoussis, A. Kokalj, M. Lazzeri, L. Martin-Samos, N. Marzari, F. Mauri, R. Mazzarello, S. Paolini, A. Pasquarello, L. Paulatto, C. Sbraccia, S. Scandolo, G. Sclauzero, A.P. Seitsonen, A. Smogunov, P. Umari, R.M. Wentzcovitch, J. Phys.: Condens. Matter 21 (2009) 395502. [16] S. Yamamoto, Appl. Surf. Sci. 251 (2005) 4. [17] W. Gordy, W.J.O. Thomas, J. Chem. Phys. 24 (1956) 439. [18] B. Shan, K. Cho, Phys. Rev. Lett. 94 (2005) 236602. [19] R.Q. Wu, K.L. Chen, D.S. Wang, N. Wang, Phys. Rev. B 38 (1988) 3180. [20] M. Khazaei, A.A. Farajian, H. Mizuseki, Y. Kawazoe, Comput. Mater. Sci. 36 (2006) 152. [21] http://www.xcrysden.org/. [22] A. Kokalj, Comput. Mater. Sci. 28 (2003) 155. [23] http://www.geocities.jp/kmo_mma/index-en.html. [24] K. Momma, F.J. Izumi, Appl. Crystallogr. 41 (2008) 653.