Indian Journal of Pure & Applied Physics Vol. 54, July 2016, pp. 427-430
Ab initio calculation of electron transport in armchair graphane nano structure containing graphene quantum dot Naveen Kumar a*, Jyoti Dhar Sharmaa & P K Ahluwaliab a
b
Department of Physics, Shoolini University, Bajhol, Solan, 173 212, India Department of Physics, Himachal Pradesh University, Shimla, 171 005, India Received 29 October 2013; revised 27 January 2015; accepted 4 April 2015
First principle quantum transport calculations have been performed for armchair graphane nano structures containing graphene quantum dots (QD) of increasing sizes. Each QD has been formed by creating vacancies in the H lattice of graphane. TranSIESTA has been used for calculating transport properties with nonequilibrium Green's function approach within density functional theory. Transmission functions, electron density of states and current-voltage characteristics have been calculated using graphene electrodes. Band structure, electron density of states and zero bias conductance (transmission function) have been found to be in consonance with each other. The current in V-I characteristics shows non linear fluctuating pattern and tends to saturate as the voltage is increased. The value of current is graphene QD size dependent. The current lies in the range of nano ampere (for QD consisting of 16 contiguous vacancies) to femto ampere (for QD consisting of 6 contiguous vacancies). Keywords: Graphene, Graphane, Quantum dot, DFT, Electron transport, TranSIESTA
1 Introduction Graphene, being a single atomic layer of graphite, has attracted a great deal of interest since it was isolated in 20041-4. Due to unique transport characteristics graphene is a strong candidate for replacing silicon in future electronic devices5. A pristine graphene is a semimetal and a graphene sheet can be chemically converted into a graphane layer through reacting with hydrogen atoms6,7. Graphane is a wide band gap semiconductor and because of its structure and low dimensionality, it provides a fertile ground for fundamental science and technological applications4,8-12. The introduction of a cluster of vacancies in hydrogen sub lattice of graphane leads to formation of graphene quantum dot (QD). QD’s or artificial atoms are one of the most intensely studied systems4,13-17. QD's have enormous potentials for applications ranging from ballistic transport to novel lasers to quantum information processing. The study of electronic transport in nano structures is of current theoretical and experimental interests18-29. In the present study the changes in electronic transport in the presence of QD as vacancies have been explored in the hydrogen sub lattice of graphane. The nanostructures forming the scattering region —————— *Corresponding author (E-mail:
[email protected])
consist of 50C atoms in the form of 1×6×8 super cell and H atoms lie in chair conformation. QD, a cluster of vacancies in hydrogen sub lattice of graphane, has been modeled by pulling out hydrogen atoms from graphane. The size of the QD was varied from six contiguous vacancies to ten contiguous vacancies, fourteen contiguous vacancies and sixteen contiguous vacancies thus increasing the size of graphene quantum dot (Fig. 1). The nanostructures are named as GQDi, i=1, 2, 3 and 4, respectively. We have systematically explored graphane nano structures containing graphene QD of four sizes with 48C+42H (GQD1 containing six contiguous H vacancies in the form of one unsaturated C hexagon), 48C+38H (GQD2 containing ten contiguous H vacancies in the form of two contiguous unsaturated C hexagon), 48C+34H (GQD3 containing fourteen contiguous H vacancies in the form three contiguous unsaturated C hexagons) and 48C+32H (GQD4 containing sixteen contiguous H vacancies) with H-atoms in chair conformation. These nano structures form the scattering region connected to graphene electrodes on both sides (Fig. 1). 2 Simulation Details The calculations have been performed within the framework of density functional theory (DFT) as implemented in SIESTA code30,31. Very well tested,
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Fig. 1—Optimized graphane nano structure containing graphene quantum dot (GQD2) with graphene electrodes
norm conserving, relativistic Troullier Martin pseudopotentials have been used for both carbon and hydrogen. The exchange and correlation energies are treated within the generalized gradient approximation (GGA) according to the Perdew, Burke and Ernzerhof (PBE) parameterization. Throughout the geometry optimization, numerical atomic orbitals with single zeta polarization (SZP) basis set with confinement energy of 0.02 Ry were used. The Brillouin zone was sampled using Monkhorst-Pack scheme with a 1×11×40 mesh for the calculations and 250 Ry meshcutoff energy was used. An interaction between adjacent graphene layers was hindered by a spacing of 20 Å. The electronic transport properties were studied by the nonequilibrium Green’s function techniques, within the Keldysh formalism31, based on density functional theory (DFT) as implemented in the TranSIESTA module21,31 within the SIESTA code. The current through the contact region was calculated using Landauer-Buttiker formula18: (1) where G0 = 2(e2/h) is the unit of quantum conductance and T(E, Vb) is the transmission probability of electrons incident at an energy E through the device under the potential bias Vb. The electrochemical potential difference between the left and right electrodes is: (2) 3 Results and Discussion Figure 2 shows the band structure, electron density of states and zero bias conductance (transmission function) for pristine graphane and two graphane nano structures containing different sized graphene quantum dots (GQD2 and GQD4). As the size of quantum dot is increased, the number of peaks appearing around the Fermi energy increases. It is clear that the graphs of the band structure, electron
Fig. 2—Band structure (left), Electron Density of states (middle) and Zero Bias Conductance (right) of graphane and graphane containing graphene quantum dot, GQD2 & GQD4
Fig. 3—Transmission function for graphane and graphane nano structure containing different sized graphene quantum dot for 0.0 V, 0.5 V and 1.0 V
density of states and zero bias conductance are in consonance with each other. Figure 3 shows the transmission function for pristine graphane and four graphane nano structures containing different sized graphene quantum dot (GQDi i = 1, 2, 3 and 4 ) for 0.0 V, 0.5 V and 1.0 V. Energy has been rescaled so that Fermi energy lies at 0 eV. As the size of quantum dot increases the number of peaks appearing around the Fermi energy increase. It is clear that the graph of transmission function varies with applied voltage. Figure 4 shows the Voltage-Current (V-I) characteristics for pristine graphane and graphane nano structures containing different sized graphene quantum dot. The current has been plotted in log scale as the fluctuations are very large. It is observed that in
KUMAR et al.: ELECTRON TRANSPORT IN ARMCHAIR GRAPHANE NANO STRUCTURE
Fig. 4—Voltage-Current (V-I) characteristics for graphane and graphane containing graphene quantum dot, GQDi, i = 1, 2, 3 and 4 Table 1—Current in each nano structure at 0.5 V and 1.0 V Nano-structure C48H48 C48H42 C48H38 C48H34 C48H32
Current (A) 0.5 V 7.45098546E-14 1.42272340E-15 1.99472192E-14 1.00063870E-11 3.62475842E-10
1.0 V 3.18791346E-13 2.47497812E-14 3.45045535E-13 1.33213089E-10 4.25046169E-09
the V-I characteristics current shows non-linear fluctuating behaviour and tends to saturate with rise in voltage. The applied voltage is increased from 0.0 V to 1.0 V in the steps of 0.05 V. As the QD is introduced in the graphane nanostructure, the current is found to decrease, as compared to pristine graphane, in the case of GQD1 and GQD2 nano structures and lies in the range of 10-18 A to 10-15 A. In the case of GQD3 and GQD4 the current is more than that in the pristine graphane nanostructure and lies in the range of 10-12 A to 10-9 A. Table 1 shows current in each nano structure at 0.5 V and 1.0 V. As the QD is introduced in graphane the current first decreases and as the size of the QD increases, the current increases. The nanostructure C48H32 (GQD4) shows maximum rise in current as compared to pristine graphane. This type of behaviour is expected from higher sized QD with availability of more conduction electrons. 4 Conclusions An ab initio computational study of quantum electron transport has been undertaken for graphane nano structures containing graphene QD of different size. It has been observed that: (i) The graphs of the band structure, electron density of state and zero bias conductance for each nanostructure are in consonance with each other.
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(ii) As the QD is introduced in pristine graphane nano structure, peaks appear around the Fermi energy in the graphs of the electron density of state and transmission function and the number of peaks increase as the size of QD is increased. (iii) The graph of transmission function varies as the voltage is increased. (iv) Current in the V-I characteristics shows non-linear fluctuating behaviour and tends to saturate with rise in voltage. (v) As the QD is introduced in the graphane nanostructure, the current is found to decrease, as compare to pristine graphene, in the case of GQD1 and GQD2 nano structures and lies in the range of 10-18 A to 10-15 A. In the case of GQD3 and GQD4 the current is more than that in the pristine graphane nanostructure and lies in the range of 10-12 A to 10-9 A. Thus the current is QD size dependent. It is clear that the presence of QD significantly changes the electronic transport properties of graphane nanostructures, as compared to pristine graphane, increasing the possibility of vast applications in microelectronics devices. Acknowledgement Authors acknowledge SIESTA team for SIESTA code. References 1
Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y, Dubonos S V, Grigorieva I V & Firsov A A, Science, 306 (2004) 666. 2 Geim A K & Novoselov K S, Nature Mater, 6 (2007) 183. 3 Molitor F, Guttinger G, Stampfer C, Droscher S, Jacobsen A, Ihn T & Ensslin K, J Phys Condens Matter, 23 (2011) 243201. 4 Abergel D S L, Apalkov V, Berashevich J, Ziegler K & Tapash Chakraborty, Adv Phys, 59 (2010) 261. 5 Julia Berashevich & Tapash Chakraborty, Nanotechnology, 21 (2010) 355201. 6 Sofo J O, Chaudhari A S & Barber G D, Phys Rev B, 75 (2007) 153401. 7 Elias D C, Nair R R, Mohiuddin T M G, Morozov S V, Blake P, Halsall M P, Ferrari A C, Boukhvalov D W, Katsnelson M I, Geim A K & Novoselov K S, Science, 323 (2009) 610. 8 Boukhvalov D W, Katsnelson M I & Lichtenelson A I, Phys Rev B, 77 (2008) 035427. 9 Flores M Z S, Autreto P A S, Legoas S B & Galvao D S, Nanotechnology, 20 (2009) 465704. 10 Sharma Jyoti Dhar, Ahluwalia P K & Kumar Naveen, AIP Conf Proc, 1393 (2011) 321. 11 Kumar Naveen, Sharma Jyoti Dhar, Kumar Ashok & Ahluwalia P K, AIP Conf Proc,1512 (2013) 192. 12 Pumera Martin & Wong Colin Hong An, Chem Soc Rev, 42 (2013) 5987.
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13 Chakraborty T, Quantum Dots, A survey of the properties of artificial atoms,(Elsevier, Amsterdam, New York) 1999. 14 Silvestrov P G & Efetov K B, Phys Rev Lett, 98 (2007) 016802. 15 Singh Abhishek K, Penev Evgeni S & Yakobson Boris I, ACS Nanotecnology, 4 (2010) 3510. 16 Liu Fei, Jang Min-Ho, Dong Hyun Ha, Kim Je-Hyung, Cho Yong-Hoon & Seo Tae Seok, Adv Mater, 25 (2013) 3657. 17 Sharma Jyoti Dhar, Sharma Munish, Kumar Naveen & Ahluwalia P K, J Phys Conf Ser, 472 (2013) 012010. 18 Datta Supriya, Electronic Transport in Mesoscopic systems, Cambridge Studies in Semiconductor Physics and Microelectronic Engineering, vol 3, (Cambridge University Press), 1997. 19 Massimiliano di ventra, Electrical Transport in Nanoscale Systems, (Cambridge University Press), 2008. 20 Taylor Jeremy, Guo Hong & Wang Jian, Phys Rev B, 63 (2001) 121104. 21 Brandbyge Mads, Mozos Jose-Luis, Ordejon Pablo, Taylor Jeremy & Stokbro Kurt, Phys Rev B, 65 (2002) 165401. 22 Topsakal M, Bagci V M K & Ciraci S, Phys Rev B, 81 (2010) 205437.
23 Saloriutta Karri, Hancock Yvette, Karkkainen Asta, Karkkainen Leo, Puska Martti J & Jauho Antti-Pekka, Phys Rev B, 83 (2011) 205125. 24 Martins Steven E, Withers Freddie, Dubois Marc, Craciun Monica F & Russo Saverio, New J Phys, 15 (2013) 033024. 25 Kumar Naveen, Sharma Munish, Sharma Jyoti Dhar & Ahluwalia P K, AIP Conf Proc, 1536 (2013) 139. 26 Sharma Jyoti Dhar, Kumar Naveen, Sharma Munish & Ahluwalia P K, AMST-2012 Conf Proc, LAP LAMBERT Academic Publishing, Germany, pp 55-60. 27 Sun B Y & Wu M W, Phys Rev B, 88 (2013) 235422. 28 Valencia Daniel, Lu Jun-Qiang, Wu Jian, Lui Feng, Zhai Feng & Jiang Yong-Jin, arXiv:1308.1013v1 (2013). 29 Zhang Hang, Huand Jhao-Wun, Velasco Jr Jairo, Myhro Kevin, Matt Maldonado, Tran David Dung, Zhao Zeng, Wang Fenglin, Lee Yongjin, Liu Gang, Bao Wenzhong & Lau Chun Ning, arXiv:1308.1182v1 (2013). 30 Soler J M, Artacho E, Gale J D, Garclia A, Junquera J, Ordejon P & Portal D S, J Phys Condens Matter, 14 (2002) 2745. User's Guide, SIESTA 3.0-beta-15, www.icmab.es/siesta. 31 Keldysh L V, Zh Eksp Teor Fiz, 47 (1964) 1515 & Sov Phys JETP, 20 (1965) 1018.
