ARTICLE pubs.acs.org/JPCC
Transport Properties of a Squeezed Carbon Monatomic Ring: A Route to a Negative Differential Resistance Device Ming Qiu, Zhenhua Zhang,* Zhiqiang Fan, Xiaoqing Deng, and Jinbo Pan School of Physics and Electronic Science, Changsha University of Science and Technology, Changsha 410114, People’s Republic of China ABSTRACT: Based on a first-principles approach, the transport behaviors for undeformed and deformed carbon cumulene monatomic rings are investigated. The distinct negative differential resistance (NDR) behaviors can be observed in a certain range of deformations. The analysis on the microscopic nature reveals that the electronic transmission strength, position of molecular levels, and spatial distribution of molecular states can be altered by the applied bias and horizontal pressure, which are intrinsic origins of NDR behaviors. Our work suggests that a carbon atomic ring is a potential NDR device when deformations occur.
’ INTRODUCTION A lot of investigations have demonstrated that carbon-based nanomaterials, such as carbon nanowires, graphene, and carbon nanotubes, possess favorable electrical structures for developing future nanodevices. Recently, based on a first-principles method, Larade et al.1 investigated the transport characteristics of carbon atomic wires in contact with two Al electrodes and found that the shift of electron states induced by moleculeelectrode coupling is a key factor of negative differential resistance (NDR) behaviors. Yuzvinsky et al.2 reported that NDR behaviors appear for the carbon nanotube while its diameter shrank to a carbonchain-like structure. Khoo et al.3 found the NDR behaviors in both even and odd carbon monatomic wires sandwiched between two capped metallic carbon nanotube electrodes by applying a density functional theory (DFT). The calculated results showed that the states of carbon monatomic wires can be hybridized or tuned by the electron states of the cap. Fan et al.4 showed us that NDR behaviors can be changed with the deformation in a squashed C60 molecular device and suggested that the origin of the behaviors is the shift of a wide transmission valley between two first frontier orbitals at different bias voltages. Using a DFT plus nonequilibrium Green’s function (DFT/ NEGF) approach, the NDR behaviors were presented in carbon nanowires by García-Suarez et al.5 and Deng et al.6 when they were capped with endgroups or contacted directly to two asymmetric electrodes, respectively. The NDR also has been found in many physical systems with various mechanisms, such as the polaron model,7 bias induced phase transition,8 orbital symmetry mismatch,9 intermolecular interaction,10 weaker coupling between core molecule and electrodes,11 and so on. Pulling long linear carbon atomic wires from graphene or carbon nanotubes might be an important method for building carbon atomic nanostructures in the future.2,12,13 r 2011 American Chemical Society
’ MODEL AND METHOD Carbon atoms can not only form a monatomic chain, which has been studied widely as stated above, but also enable one to constitute a stable monocyclic ring.14 In this work, we investigate the NDR behaviors induced by geometric deformations for such a carbon ring. This process is to model the continuous deformations of a monatomic ring when it is squeezed by an STM tip. The devices we construct are shown in Figure 1. A two-probe system is composed of a cumulene monatomic ring with 12 carbon atoms and 2 flat Au (111) electrodes. We use two S as endgroups to connect the ring onto the top site of the electrodes symmetrically. The other models are structured by that the monatomic ring is squashed with electrodes along the X axis gradually when the distance between endgroups and electrodes is sustained ideally. The coefficient ε (ε = (y x)/y) is used to characterize the deformation degree of a ring, where x is the distance between two transversal carbon atoms and y is the maximal distance of two longitudinal carbon atoms perpendicular to x, as shown in Figure 1. We name the models as M1 (x = 5.06 Å, without deformation), M2 (x = 4.64 Å and ε = 0.17), M3 (x = 4.54 Å and ε = 0.20), M4 (x = 4.38 Å and ε = 0.25), M5 (x = 4.01 Å and ε = 0.33), and M6 (x = 3.41 Å and ε = 0.50). The bond length in model M1 is about 1.296 Å, which is close to the result of 1.28 Å.14 In the calculations, the system we study is divided into three areas: the left electrode, right electrode, and central scattering area. The two layer atoms on each electrode are included in the scattering area to screen the potential effect of the embedded molecule to the electrodes. We employ normconserving pseudopotentials15 to represent the atomic core and double ζþ double polarization basis sets to expand the valence Received: January 21, 2011 Revised: April 20, 2011 Published: May 25, 2011 11734
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Figure 1. Schematic of the device: (a) model M1, (b) model M2, (c) model M3, (d) model M4, (e) model M5, and (f) model M6. Figure 2. Calculated currents as a function of applied bias for our models.
states of electrons. The generalized gradient approximation (GGA) in Perdew, Burke, and Ernzerhof form16 is used for the exchange and correlation function. The details of such a theoretical method can be found in refs 17 and 18.
’ RESULTS AND DISCUSSION First, we compute self-consistently the currentvoltage (IV) characteristics of six models in a bias range from 0 to 2.4 V, as shown in Figure 2. From this figure, we can see that the obvious Ohmic behavior can be observed for model M1 (M2M4) below a bias of 1.9 V (1.4 V), and the current curves of models M5 and M6 also present at low bias. While ε e 0.33, the currents in M5 below 1.5 V and the currents in M2M4 below 1.7 V are bigger than that in M1; while ε comes to 0.50, currents become obviously weakened at high bias. It is interesting to see that the IV curves of models M2M4 are relatively similar. The currents decrease to about 4% from 1.4 to 1.9 V due to deformations, and remarkable NDR behaviors appear in such a bias region, corresponding to the peak-to-valley ratios n = 1.14, 1.15, and 1.20, respectively. For model M5, the NDR behavior occurs under a bias ranged from 1.4 to 1.8 V (n = 1.10). These indicate that NDR behaviors can be observed obviously in our systems if ε e 0.33 and suppressed largely if ε > 0.33. These indicate that NDR behaviors can be observed obviously in our systems if ε e 0.33 and suppressed largely if ε > 0.33. This may be because the sharp change in electronic structures is induced by the geometrical structure after ε > 0.33 and the sensitivity of the electronic structures to bias is very low, leading to the weakened transport nonlinearity; that is, the NDR behavior almost vanishes in M6 if ε > 0.33. To present an explanation for the results above, we calculate transmission spectra T (E) at the equilibrium state, which is the most intuitive representation of quantum transport behaviors, as shown in Figure 3. As can been seen, the main resonant levels are the LUMO (the lowest unoccupied molecular orbital), which is closer to the Fermi energy than other levels and has certain transmission coefficients from our calculations for models M1M5, except model M6, whose resonant level is the HOMO (the highest occupied molecular orbital), at lower bias. When deformations occur, the LUMO peak in model M1 shifts to higher energy with an enhanced transmission coefficient for models M2M5 and passes the Fermi level to lower energy to become the higher HOMO peak for model M6. These results can be rationalized by the M€ulliken population analysis, which shows that the core molecule is electron-accepting and electronic charges transferred from the electrodes are 0.0743 e, 0.1085 e, 0.1123 e,
Figure 3. Transmission spectra of six models at zero bias. The Fermi energy is set to zero.
0.1153 e, 0.1035 e, and 0.0580 e for models M1M6, respectively. For models M2M5, obviously, the core molecule obtains more charges than that in model M1, a rising of the electronelectron repulsion in the core molecule to move its level to higher energy,5 whereas for model M6, the case is just the opposite. On comparison with model M4, the core molecule of model M5 loses a little charge and the LUMO peak moves close to the Fermi energy. The fact that the LUMO passes the Fermi level to become the HOMO for model M6 can be clearly observed from Table 1, where the molecular state of level 31 (LUMO) in model M1 is very similar to level 30 (HOMO) in model M6. The above calculations predict that the electronic structure of the carbon cumulene monatomic ring can be tuned greatly by geometric deformations. To explain the distinct NDR behaviors fully, we plot the representative transmission spectra of models M2M4 in the bias range of [1.3, 2.1 V] and model M5 in the bias range of [1.3, 1.9 V] in steps of 0.2 V, as shown in Figure 4. The integration of the transmission coefficient in the bias window [Vb/2, Vb/2] is equal to the current,18 where Vb is the magnitude of the bias voltage. In Figure 3, the shapes of transmission spectra for four models are basically similar. An evident broader resonance occurs in models M2M4 as compared with model M5. It indicates that the deformations with ε e 0.25 can increase the electronic transmission and delocalization of molecular states obviously. However, as ε increases to 0.33, the big π orbital perpendicular to the plane of the ring14 is squeezed intensely and the transport performance has 11735
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Table 1. MPSH of Models M1M6 at a Certain Bias in Real Space
Figure 4. Transmission spectra of models M2M4 in the bias range of [1.3, 2.1 V] and model M5 in the bias range of [1.3, 1.9 V] in steps of 0.2 V.
’ CONCLUSION Based on a first-principles approach, the negative differential resistance (NDR) behaviors of a cumulenic monatomic ring are investigated. The results show that distinct NDR behaviors can be observed in a certain deformation range. The analysis of transmission spectra and the MPSH of molecular orbitals indicates that the electronic transmission strength and distributions of molecular states can be tuned by applied bias and geometric deformations induced by the horizontal pressure, which is the intrinsic origin of these NDR behaviors. Our work suggests that a carbon atomic ring is a potential NDR device when deformations occur. ’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected]. been weakened. The electronic transmission and current is smaller in model M5. With the bias increasing, the resonant peaks for models M2M5 shift to lower energies due to a decrease of the charge in core molecules by the bias and are suppressed in a certain bias region, leading thus to the exhibition of NDR behavior. Interestingly, the LUMO resonant peaks for models M2M4 move to even lower energies, passing the Fermi energy, to become the HOMO peaks at a bias of 1.9 V. In Table 1, the molecular projected self-consistent Hamiltonian (MPSH) of main contribution molecular states, referred to as levels 2932, within the bias window for models M2M5 in the real space are shown. They are important molecular orbitals for quantum transport,19 by which NDR behaviors can be explained intuitively. For models M2M4, the MPSH for levels 2932, is very similar, which indicates that it is not almost affected by deformations with 0.17 e ε e 0.25. The distribution of MPSH for level 32 from the whole core molecule (at 1.4 V) alters obviously into the left part (at 1.9 V), which presents the intrinsic origin of NDR behaviors. In model M5, the molecular state for level 31 changes from a delocalization on the whole core molecule (at 1.4 V) to a localization on its lower part (at 1.8 V), which results in a decreasing of resonant tunneling and the exhibition of NDR behavior.
’ ACKNOWLEDGMENT This work was supported by the National Natural Science Foundation of China (Grant Nos. 61071015 and 60771059), the Scientific Research Fund of Hunan Provincial Education Department (Grant Nos. 08A005 and 08C110). ’ REFERENCES (1) Larade, B.; Taylor, J.; Mehrez, H.; Guo, H. Phys. Rev. B 2001, 64, 075420. (2) Yuzvinsky, T. D.; Mickelson, W.; Aloni, S.; Begtrup, G. E.; Kis, A.; Zettl, A. Nano Lett. 2006, 6, 2718. (3) Khoo, K. H.; Neaton, J. B.; Son, Y. W.; Cohen, M. L.; Louie, S. G. Nano Lett. 2008, 8, 2900. (4) Fan, Z. Q.; Chen, K. Q.; Wan, Q.; Zou, B. S.; Duan, W. H.; Shuani, Z. Appl. Phys. Lett. 2008, 92, 263304. (5) García-Suarez, V. M.; Lambert, C. J. Nanotechnology 2008, 19, 455203. (6) Deng, X. Q.; Zhou, J. C.; Zhang, Z. H.; Zhang, H.; Qiu, M.; Tang, G. P. Appl. Phys. Lett. 2009, 95, 163109. (7) Galperin, M.; Ratner, M. A.; Nitzan, A. Nano Lett. 2005, 5, 125. 11736
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