SCIENCE CHINA Physics, Mechanics & Astronomy • Research Paper •
August 2011 Vol.54 No.8: 1438–1442 doi: 10.1007/s11433-011-4408-8
Electronic structure and optical property of boron doped semiconducting graphene nanoribbons CHEN AQing1, SHAO QingYi2*, WANG Li1 & DENG Feng1 2
1 School of New Energy Engineering, Leshan Vocational & Technical College, Leshan 614000, China; Laboratory of Quantum Information Technology, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China
Received December 22, 2010; accepted April 1, 2011; published online June 30, 2011
We present a system study on the electronic structure and optical property of boron doped semiconducting graphene nanoribbons using the density functional theory. Energy band structure, density of states, deformation density, Mulliken popular and optical spectra are considered to show the special electronic structure of boron doped semiconducting graphene nanoribbons. The C—B bond form is discussed in detail. From our analysis it is concluded that the Fermi energy of boron doped semiconducting graphene nanoribbons gets lower than that of intrinsic semiconducting graphene nanoribbons. Our results also show that the boron doped semiconducting graphene nanoribbons behave as p-type semiconducting and that the absorption coefficient of boron doped armchair graphene nanoribbons is generally enhanced between 2.0 eV and 3.3 eV. Therefore, our results have a great significance in developing nano-material for fabricating the nano-photovoltaic devices. B-doped graphene nanoribbons, electronic structure, optical property, density functional theory PACS: 73.22.-f, 78.30.Na, 78.67.-n
1 Introduction The photovoltaic effect involves the generation of electrons and holes in a semiconductor device under illumination and the subsequent charge collection at opposite electrodes. The graphene applied in the solar cell was mainly used as windows of electrodes in solid-state solar cells [1] and as a competitor for indium thin oxide (ITO) resulting from its chemically stable, robust, flexible and room-temperature ballistic transport [2]. But graphene films exhibit the resistivity of several hundred ohms. Graphene has become the focus of nano-science among nano-electronics, nano-sensors, photonic and nano-mechanical devices because of the remarkable physical and chemical properties [2,3]. The studies of graphene application focus on gas detection [4] and solar cells [5]. Recently, graphene nanoribbons (GNRs),
synthesized experimentally with room-temperature mobilities of about 10000 cm2/(V∙s) [6], have been studied in rapidly growing fields [7–10]. Being similar to single-walled carbon nanotubes (SWNTs), the one-dimensional atomic structure of GNRs is a single layered graphene with a finite width. So, they were expected to present electronic properties similar to those of SWNTs. It is predicted that the nanoribbons with zigzag edges have metallic characteristics [9] and those with armchair edges were viewed as semiconductors whose band gap is a function of their width [10]. It was reported that the photovoltaic device fabricated by carbon nanotubes owned high conversion efficiency, indicating the future ultra-efficient photovoltaic devices [11]. The GNRs whose geometric structure is similar to carbon nanotubes also have the potential in the application of ultra-efficient nano-photovoltaic devices. It is well known that chemical doping can produce p-type or n-type transistors, which are crucial for building logic functions or photovol-
*Corresponding author (email:
[email protected]) © Science China Press and Springer-Verlag Berlin Heidelberg 2011
phys.scichina.com
www.springerlink.com
Chen A Q, et al.
Sci China Phys Mech Astron
taic devices. In carbon-based materials, p-type (n-type) doping can be achieved by boron (nitrogen) atom substitution within the carbon matrix [12]. The development of nano-photovoltaic devices is the trend of the study on solar cells in the future, especially on solar cells with graphene and carbon nanotube hybrid systems. With the aim to design solar cells based on the graphene and carbon nanotube hybrid systems, it is important to study the electronic and optical properties of the B-doped GNRs. Our results suggest that the B-doped GNRs perform p-type semiconductor and the absorption coefficient of GNRs is enhanced in the range of light wavelength after B atoms are present. Therefore, our study on the electronic structure and optical properties of boron doped semiconducting GNRs has a great significance in the development of nano-photovoltaic devices. Theoretical studies, based mainly on tight-binding approximations, have been employed in properties of various graphene including doped graphene sheet [13,14], doping effects on charge transport in GNRs [15] and optical properties of GNRs [16]. So in this paper, the first principle based on density function theory is employed to calculate all the relevant properties.
2 Geometric structure and electronic structure To study the electronic structure of GNRs applied to nano-photovoltaic device, the armchair graphene nanoribbons (AGNRs) with the width of 5 atoms have been chosen. The AGNRs terminated by hydrogen were periodic cells with 42 atoms. We performed unpolarized energy band calculations based on the density functional theory [17] within the generalized gradient approximation [18]. We also used norm conserving pseudo potentials [19,20], as implemented in the SIESTA code [21,22]. We employed a double zeta basis function with polarization orbitals [23], a confining energy shift of 0.05 eV, and a mesh cutoff energy of 200 Ry for the grid integration. The Brillouin zone was sampled by using a Monkhorst-Pack [24] scheme with a (1×1×20) k-point sampling. Periodic boundary conditions were used in the simulations. A vacuum region of 10 Å was used in order to separate the layer and its images in the direction perpendicular to the plane. Figure 1 shows the optimized geometry structure of B-doped AGNRs. One C atom located on a corner of hexagon is substituted by one B atom forming C—B bond. The length of C—B bond indicated by alphabet A and B is 1.4994 Å and 1.3944 Å, respectively, while the length of C—C bond in intrinsic GNRs is 1.42 Å. It is apparent that the angle of C—B—C bond is the same as that of C—C—C bond. The difference between the radius of C atom and B atom is assumed as the reason for the change of bond length. Another important reason we consider is the form of C—B bond. In order to discuss the form of C—B bond deeply, the
August (2011) Vol. 54 No. 8
1439
deformation charge density and Mulliken population are calculated. We defined deformation charge density as the difference ∆ρ(r) = ρ(r)−ρatm(r), where ρ(r) is electron density distribution and ρatm(r) is the sum of density of the free atoms of the structure, in other word, the valence density minus the sum of atomic valence densities. So the deformation charge density shows the electron redistribution owing to substitution doping of boron directly. Figures 2(a) and (b) show the deformation charge density of intrinsic and B-doped AGNRs, respectively. ∆ρ(r) is positive in the black areas and negative in the gray areas. Comparing Figure 2(a) with (b), it is obvious that the distribution of electrons is non-uniform when B atom replaces C atom. These C—B bonds (indicated by black circle in Figure 2(b)) have more electrons than C—C bond. Therefore, we assume that electrons transfer from C atoms to B atom. The Mulliken population analysis below accounts for our assumption. Table 1 lists the charge population of B atom and three C atoms surrounding B atom. The total charge of B atom is 3.952 which is larger than that of C atom in B-doped AGNRs. Comparing the charge of C atom in intrinsic AGNRs with that in B-doped AGNRs, it is not difficult to conclude that B atom captures electrons from the nearest C atom when the B—C bond formed, which is responsible for the p-type performance of B-doped AGNRs. With respect to the electrons which transfer to B atom, we can also conclude that they are from the p orbital of C atoms by Mulliken population analysis from Table 1. The C18, C20 and C22 are indexed as Figure 1. The band structure of the B-doped AGNRs is different from intrinsic AGNRs, just as Figure 3 shows. Figures 3(a) and (b) are the band structure of intrinsic and B-doped AGNRs, respectively. Figure 3(c) shows the PDOS of B-doped AGNRs. The energy gap which has great impact on the properties of device fabricated by semiconductors, especially on photovoltaic devices, scales inversely with the ribbon width [25,26]. The energy gap of intrinsic AGNRs
Figure 1
The optimized geometry structure of B-doped AGNRs.
1440
Figure 2 Table 1
C18 C20 C22 B
Chen A Q, et al.
Sci China Phys Mech Astron
August (2011) Vol. 54 No. 8
Deformation charge density of intrinsic and B-doped AGNRs. The black and gray areas represent the positive and negative ∆ρ(r), respectively. Mulliken population of C18, C20, C22 and B atoms Intrinsic AGNRs s orbital p orbital Total charges charges charge 0.934 3.021 3.955 0.946 3.047 3.993 0.934 3.021 3.955 − − −
B-doped AGNRs s orbital p orbital Total charges charges charge 0.923 2.842 3.765 0.925 2.873 3.798 0.923 2.842 3.765 1.2 2.752 3.952
Because the B impurity can capture electrons from the highest occupied band, holes are produced. The impurity level below the Fermi level is derived mainly from the fact that the occupied electronic states are concentrated around the B substitutional site. By above analysis it is obtained that B dopants act as hole donor and the B-doped AGNRs have p-type semiconducting behaviour.
3 Optical properties
Figure 3 (a) and (b) are the energy band structure of intrinsic and B-doped AGNRs, respectively. (c) shows the PDOS of B-doped AGNRs.
is about 0.338 eV which agrees with the value of hydrogen terminated AGNRs [26], which illustrates that our calculation is reliable. It is novel to note that the gap gets wider with the value of about 0.5 eV and the Fermi energy level shift from −4.37 eV to −5.07 eV after B atom is injected into the AGNRs replacing C atoms. The reasons for the wider gap are similar to our previous study on doped carbon nanotubes [27]. When B atom is injected into the C sheet, the symmetry of AGNRs is broken and π and π* bands become asymmetric, which leads to the widening of the energy gap. Wider energy gap is usually beneficial to the application of semiconducting GNRs. In order to investigate the energy band of B-doped AGNRs, further PDOS is calculated as shown in Figure 3(c). The B impurity level not only locates below the Fermi energy level but also below the valence band, which agrees with Panchakarla’s results [28]. The acceptor level and the impurity level are indexed by the dot line and dash line, respectively. The acceptor level arises from the highest occupied level of the intrinsic 5AGNRs.
The optical response of B-doped AGNRs was obtained by using first-order time-dependent pertubation theory [29]. The dipolar transition matrix elements between occupied and unoccupied single electron eigenstates are calculated. And the calculation was carried out in the momentum space formulation, as implemented in SIESTA. The AGNRs with the width of 5 (5AGNRs), 6 (6AGNRs), 7 (7AGNRs) and 8 (8AGNRs) carbon atoms were considered to study the relationship between the width and the optical absorption. It is to note that band gap oscillations behave with the widths, which agree with the Verónica Barone’s results [26]. We show here only the optical absorption for the case with the light polarization vector along the vertical direction of the ribbon length. Absorption coefficients of 5AGNRs, 6AGNRs, 7AGNRs, and 8AGNRs are shown in Figures 4(a)–(d). It is worthy of noting that there is an absorption peak at the energy which is a little higher than the energy gap for intrinsic AGNRs. So, it is deduced that the optical absorption for intrinsic AGNRs mainly arises from the inter-band transitions between the last valence and the first conduction bands, localized in k space near the Γ point. In the gray area of Figure 4, the doped AGNRs have a higher absorption coefficient than that of the intrinsic AGNRs. The reason for the enhanced absorption coefficient of B-doped AGNRs is mainly derived from the fact that the presence of B impurity enhances the electron-hole interaction and the impurity state thus provides a competing path for optical excitations so that the B-doped AGNRs becomes favorable to create electron-hole pairs that then form bound excitons (excitonic transition) enhancing the photo-absorption. As a result, the absorption intensity of B-doped AGNRs between 2.0 eV
Chen A Q, et al.
Sci China Phys Mech Astron
August (2011) Vol. 54 No. 8
1441
Figure 4 The absorption coefficients of intrinsic AGNRs and B-doped AGNRs for 5AGNRs, 6AGNRs, 7AGNRs and 8AGNRs are shown in (a)–(d), respectively. In the grey area, the B-doped AGNRs have a greater absorption coefficient than the intrinsic AGNRs for 5AGNRs, 7AGNRs and 8AGNRs.
and 3.3 eV is generally larger than that of the intrinsic AGNRs. In addition, it is well known that the energy of sunlight which the earth receives mainly varies from 1.38 eV to 3.26 eV. Therefore, the B-doped AGNRs are prospective nano-materials in the application to photovoltaic devices.
Key Research Project in Science and Technology of Leshan (Grant No. 2011GZD050). 1 2 3
4 Conclusion In this paper, we have studied the geometry structure, electronic structure and optical response of B-doped AGNRs with the first principle based on density functional theory. Our results show that the B atom captures electrons from the nearest C atom when the B—C bond formed, which results in AGNRs perform p-type semiconductor. What is more, generally, the absorption intensity of B-doped AGNRs between 2.0 eV and 3.3 eV is larger than that of the intrinsic AGNRs, which indicates the great potential application in photovoltaic device for GNRs. Therefore, our studies have great significance in exploring the nano-photovoltaic devices, especially in designing solar cells with graphene and carbon nanotube hybrid systems.
4 5 6 7 8 9
10 11
12 13
This work was supported by the Natural Science Foundation of Fujian Province of China (Grant No. A0220001), Science Research Project of Leshan Vocational & Technical College (Grant No. KY2011001) and the
14
Wang X, Zhi L J, Müllen K. Transparent, conductive graphene electrodes for dye-sensitized solar cells. Nano Lett, 2008, 8: 323–327 Geim K. Graphene: Status and prospects. Science, 2009, 324: 1530–1534 Novoselov K S, Geim A K, Morozov S V, et al. Two-dimensional gas of massless Dirac fermions in graphene. Nature, 2005, 438: 197–200 Lu G H, Ocola L E, Chen J H. Gas detection using low-temperature reduced graphene oxide sheets. Appl Phys Lett, 2009, 94: 083111 Li X M, Zhu H W, Wang K L, et al. Graphene-on-silicon Schottky junction solar cells. Adv Mater, 2010, 22: 2743–2748. Novoselov K S, Geim A K, Morozov S V, et al. Electric field effect in atomically thin carbon films. Science, 2004, 306: 666–669. Peres N M R, Castro Neto A H, Guinea F. Conductance quantization in mesoscopic graphene. Phys Rev B, 2006, 73: 195411 Gunlycke D, Lawler H M, White C T. Room-temperature ballistic transport in narrow graphene strips. Phys Rev B, 2007, 75: 085418 Nakada K, Fujita M. Edge state in graphene ribbons: Nanometer size effect and edge shape dependence. Phys Rev B, 1996, 54: 17954– 17961 Motohiko E. Peculiar width dependence of the electronic properties of carbon nanoribbons. Phys Rev B, 2006, 73: 045432 Gabor N M, Zhong Z H, Bosnick K, et al. Extremely efficient multiple electron-hole pair generation in carbon nanotube photodiodes. Science, 2009, 325: 1367–1371 Way B M, Dahn J R. Preparation and characterization of BxC1−x thin films with the graphite structure. Phys Rev B, 1992, 46: 1697– 1702 Garcia1 L E, Baltazar S E, Romero1 A H, et al. Influence of S and P doping in a graphene sheet. J Comput Theor Nanosci, 2008, 5: 1–9 Pontes R B, Fazzio A, Dalpian G M. Barrier-free substitutional doping of graphene sheets with boron atoms: Ab initio calculations. Phys
1442
15
16 17 18 19 20 21
22
Chen A Q, et al.
Sci China Phys Mech Astron
Rev B, 2009, 79: 033412 Biel B, Blase X, Triozon F, et al. Anomalous doping effects on charge transport in graphene nanoribbons. Phys Rev B, 2009, 102: 096803 Hsu H, Reichl L E. Selection rule for the optical absorption of graphene nanoribbons. Phys Rev B, 2007, 76: 045418 Capelle K. A bird’s-eye view of density-functional theory. J Phys, 2006, 36: 1318–1343 Perdew J P, Burke K, Ernzerhof M. Generalized gradient approximation made simple. Phys Rev Lett, 1996, 77: 3865–3868 Troullier N, Martins J L. Efficient pseudopotentials for plane-wave calculations. Phys Rev B, 1991, 43: 1993–2006 Kleinman L, Bylander D M. Efficacious form for model pseudopotentials. Phys Rev Lett, 1982, 48: 1425–1428 Ordejón P, Artacho E, Soler J M. Self-consistent order-N density-functional calculations for very large systems. Phys Rev B, 1996, 53: R10441–10443 Soler J M, Artacho E, Gale J D, et al. The SIESTA method for ab initio order-N materials simulation. J Phys- Condes Matter, 2002, 14:
23
24 25 26
27
28
29
August (2011) Vol. 54 No. 8
2745–2779 Artacho E, Sánchez-Portal D, Ordejón P, et al. Linear-scaling ab-initio calculations for large and complex systems. Phys Status Solidi B-Basic Solid State Phys, 1999, 215: 809–817 Monkhorst H J, Pack J D. Special points for Brillouin-zone integrations. Phys Rev B, 1976, 13: 5188–5192 Han M Y, Özyilmaz B, Zhang Y, et al. Energy band-gap engineering of graphene nanoribbons. Phys Rev Lett, 2007, 98: 206805 Barone V, Hod O, Scuseria G E. Electronic structure and stability of semiconducting graphene nanoribbons. Nano Lett, 2006, 6: 2748– 2754 Chen A Q, Shao Q Y, Li Z. Special electronic structures and quantum conduction of B/P co-doping carbon nanotubes under electric field using the first principle. J Nanopart Res, 2011, 13: 2275– 2283 Panchakarla L S, Subrahmanyam K S, Saha S K, et al. Synthesis, structure, and properties of boron- and nitrogen-doped graphene. Adv Mater, 2009, 21: 4726–4730 Economou E N. Green’s Functions in Quantum Physics. Berlin: Springer, 1983
