Negative differential resistance in the unsymmetrical C121-based molecular junction

Physics Letters A 375 (2011) 2639–2643

Contents lists available at ScienceDirect

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

Negative differential resistance in the unsymmetrical C121 -based molecular junction P. Zhao a,∗ , D.S. Liu b,c , Y. Zhang a , Y. Su a , S.J. Li a , G. Chen a a b c

School of Physics, University of Jinan, Jinan 250022, China School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Jinan 250100, China Department of Physics, Jining University, Qufu 273155, China

a r t i c l e

i n f o

Article history: Received 27 March 2011 Received in revised form 10 May 2011 Accepted 20 May 2011 Available online 26 May 2011 Communicated by R. Wu Keywords: Fullerene Non-equilibrium Green’s function Electronic transport Negative differential resistance

a b s t r a c t Using first-principles density functional theory and non-equilibrium Green’s function formalism for quantum transport calculation, we have investigated the electronic transport properties of the unsymmetrical C121 -based molecular junction. Our results show that the current–voltage curve displays a negative differential resistance phenomenon in a certain bias voltage range. The mechanism for the negative differential resistance phenomenon is suggested. The present findings could be helpful for the application of the C121 molecule in the field of single molecular devices or nanometer electronics. © 2011 Elsevier B.V. All rights reserved.

1. Introduction In recent years, progresses in microfabrications and self-assembly techniques have made it possible to develop electronic devices at single molecular level [1]. A number of novel and promising physical properties, including single-electron characteristics [2], negative differential resistance (NDR) [3], rectification [4], electrical switching [5], and so on, have been found in various kinds of single molecular junctions. The most prominent among these is NDR effect, which is a very useful property due to its utility in molecular electronic devices such as molecular switch, logic cell and memory. NDR behavior has been found in many systems, such as oligo(phenylene ethynylene) (OPE) molecular junction with nitro and amino groups on the central phenyl ring [3], benzene molecular junction with donor/acceptor substitutions [6, 7], porphyrin junction with side groups [8], anthracene junction [9, 10], ferrocenyl-pentanethiolate junction [11], N-terminated carbon nanotube junction [12], metallic and semiconducting clusters [13], etc. In spite of a number of theoretical and experimental studies about NDR in various kinds of molecular devices, the origin of the mechanism leading to NDR is still under intense debate [3,14–16]. The C121 is the first synthesized ball-and-chain fullerene dimer in which two C60 fullerenes are linked by a C atom [17–19]. Because of a bridge space being introduced into this kind of

*

Corresponding author. Tel.: +86 531 8276 5976. E-mail address: [email protected] (P. Zhao).

0375-9601/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.physleta.2011.05.044

molecule, C121 possesses a unique structure and novel properties which are expected to have potential applications in fields such as artificial photosynthesis, novel molecular electronic devices and supramolecular chemistry [19]. It is well known that the conductive properties are of crucial importance in any device application. In the present work, we have investigated the electronic transport properties of the C121 molecule by a theoretical simulation that combines both first-principles density functional theory (DFT) and non-equilibrium Green’s function (NEGF) method. Our results show that the transport under low bias is determined by the lowest unoccupied molecular orbitals (LUMOs) of two C60 moieties, and their relative shifts with applied bias can lead to a NDR phenomenon in a certain bias voltage range. To our knowledge, this is the first DFT + NEGF study of the electronic transport properties of C121 molecule. 2. Model and method Three possible structures for C121 can be built based on the structures of the individual C60 moieties. The pristine C60 contains two different C–C bonds: the one at the junction of two six-membered rings (labeled as a [6, 6] C–C bond) and the other one at the junction of a five- and a six-membered rings (labeled as a [5, 6] C–C bond in Fig. 1(a)). It had been shown that the predominant isomer has a spiro C atom bridge that connects to one of the C60 cages through an open [5, 6] ring junction and to the other through a closed [6, 6] ring junction [18]. This unsymmetrical isomer is more stable than either of the symmetrical isomers, with

2640

P. Zhao et al. / Physics Letters A 375 (2011) 2639–2643

Fig. 1. (a) The two distinct C–C bonds in C60 are marked by the thick sticks with ‘[5, 6]’ and ‘[6, 6]’, respectively. (b) Optimized geometry of the C121 -based junction. The region in the box indicates the electrode, and the one between two boxes is the central scattering region. The gray, yellow spheres represent C and Au atoms, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this Letter.)

the bridging C atom attached to both C60 cages through closed [6, 6] ring junctions or attached to each cage through open [5, 6] ring junctions. Geometries of all isomers are optimized using the Vienna Ab-inito Simulation Package (VASP) package [20], and then the lowest-energy configuration, i.e., the unsymmetrical C121 , is used for the transport calculations. The electronic transport properties of C121 molecule are calculated with the Atomistix Toolkit (ATK2008.10) package [21,22], which is based on the combination of DFT with NEGF technique. As shown in Fig. 1(b), our calculations use such one two-probe system which has been well documented [23,24]. In practical theoretical simulations, such a two-probe system is divided into three regions: a left electrode, a central scattering region, and a right electrode. The semi-infinite electrodes are calculated separately to obtain the bulk self-energy. The scattering region includes the C121 molecule and a portion of the semi-infinite electrodes to screen the perturbation effect from the central region. In our system, two Au(100) leads with finite cross sections are modeled as the semiinfinite left and right electrodes. Each atomic layer in the leads contains 5 or 4 Au atoms. The distance between the left and right electrodes, d = 22.63 Å, is determined by a serial of optimization calculations with different fixed electrode–electrode distances using the VASP package. Then the atomic structure of the junction, including the molecular structure and the first two layers of the lead surface, are fully optimized by the ATK package by minimizing the atomic forces on the atoms to be smaller than 0.05 eV/Å. After optimization, the distance between the last plane of atoms in the left electrode and the leftmost C atom in the left C60 is found to be d1 = 2.99 Å, and the distance between the right electrode and the rightmost C atom in the right C60 is d2 = 2.95 Å. In our calculations, the exchange-correlation potential is described by the Perdew–Burke–Ernzerhof version of the generalized gradient approximation (GGA.PBE) [25]. Valence electrons are expanded in a single zeta plus polarization basis set (SZP) for Au atoms and a double zeta plus polarization basis set (DZP) for C atoms. Core electrons are modeled with the Troullier–Martins nonlocal pseudo-potential [26]. The electrode calculations are performed under periodical boundary conditions, and the Brillouin zone has been sampled with 1 × 1 × 100 points within the Monkhorst–Pack k-point sampling scheme. A mesh cutoff energy of 110 Ry and an energy shift of 0.01 Ry are selected to achieve a balance between the calculation efficiency and the accuracy. In addition, to avoid the interaction between the molecule and its periodic images, a

Fig. 2. The calculated I –V curves of the C121 -based junction. The inset shows the differential conductance against bias voltage (dI /dV –V ) curve.

large supercell dimension (20 Å) in the plane perpendicular to the transport direction is used. In NEGF theory, the transmission function T ( E , V ) of the system is a sum of transmission probabilities of all channels available at energy E under external bias voltage V [27]





T ( E , V ) = Tr Γ L ( V )G R ( E , V )Γ R ( V )G A ( E , V ) ,

(1)

where G R , A is the retarded and advanced Green’s function, coupling function Γ L , R are the imaginary parts of the left and right self-energies, respectively. Then, the current (I )–voltage (V ) characteristics are obtained from the Landauer–Bütiker formalism [27]

I (V ) =

2e h







f ( E − μ L ) − f ( E − μ R ) T ( E , V ) dE ,

(2)

where h is the Planck’s constant, e the electron charge, f the Fermi function, μ L , R the electrochemical potential of the left and right electrodes, and the difference in the electrochemical potentials is given by eV with the applied bias voltage V , i.e., μ L / R ( V ) = E F ± eV /2, E F the Fermi level of the system which is set to be zero in our calculations. 3. Results and discussion In Fig. 2, we describe the self-consistently calculated I –V characteristic curve of the C121 -based molecular junction at a bias up to ±1.4 V, which is reasonable in practical experimental measurements. As we expect, it is clear from Fig. 2 that the I –V curve presents unsymmetrical characteristic in the gross due to the unsymmetrical structure of C121 molecule under investigation. Meantime, we can see that the I –V curve reveals highly nonlinear feature. The current can be neglected until 0.2 (−0.3) V. Beyond 0.2 (−0.3) V, there is a rapid increase in current following the increase of bias voltage. As the bias voltage goes higher than 0.5 (−0.6) V, the current decreases abruptly. This decrease in current due to an increase in voltage is manifestation for the NDR feature of C121 , which are supported by the variations of differential conductance (dI /dV ) against bias voltage V , as shown in the inset of Fig. 2. To be specific, we can see clearly that the differential conductance is negative in the bias ranges of [0.5 V, 0.8 V] and [−0.6 V, −1.4 V]. We can evaluate the NDR phenomenon according to the magnitude of the peak-to-valley ratio (PVR) of current.

P. Zhao et al. / Physics Letters A 375 (2011) 2639–2643

2641

Fig. 3. The bias dependence of the transmission spectra under biases (a) 0, 0.5, 0.8 V and (b) 0, −0.6, −1.4 V, respectively. The energy origin is set to be the Fermi level E F . The region between the two vertical blue lines indicates the bias window. For clarity, the scale of vertical axis of the transmission spectra decreases with the increase in bias voltage. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this Letter.)

Fig. 4. The contour plots of the real space effective potential of the C121 -based junction at 0.5 and 0.8 V. Blue (red) represents low (high) effective potential. It shows the effective potential averaged along the plane perpendicular to the transport (i.e., the x– y plane), as function of the transport direction (z). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this Letter.)

For our system, the PVR is about 16 when the positive bias is applied. This value is bigger than many reported values [28,29], and is closed to the maximum value obtained by Lee et al. [30]. In order to understand the observed NDR behavior, we calculate the transmission spectrum of the C121 -based molecular junction for bias voltage 0, 0.5, 0.8 and −0.6, −1.4 V, respectively, as shown in Fig. 3. From Eq. (2), we know that only electrons with energies within the energy region, [μ L ( V ), μ R ( V )], contribute to the total current integral, which is called the bias window or integral window. Consider the fact that the E F is set to be zero, the region of the bias window is actually [− V /2, V /2]. Thus, the current is determined by T ( E , V ) in the bias window and is further only determined by the integral area in the bias window. For the zero-bias transmission spectrum, the magnitude of the transmission around the E F is 10−5 , that is, close to zero. However, there is a strong and

Fig. 5. The spatial distribution of the HOMO and LUMO of the C121 .

broad transmission peak in the range of 0.25 to 0.5 eV just above the E F (coming from the resonant tunneling between the LUMOs of two C60 moieties which can be seen later). It is clear that the I –V characteristic curve is determined by this transmission peak under low bias voltage. With the increase of positive (negative) bias voltage, this LUMOs-derived transmission peak is split in two parts (P1 and P2, as seen in Fig. 3). P1 shifts toward lower energies and moves into the bias window, resulting in an initial increase in current. P2 shifts toward higher energies and has no contribution to the current integral. However, the external bias voltage also simultaneously reduces the peak height significantly, decreasing the weight of the transmission spectrum in the bias window. The overall reduction in peak height outweighs increase from additional peak moving into the expanding bias window, leading to a net drop in current and the onset of NDR near 0.5 (−0.6) V. In order to understand the origin of those transmission peaks and the reason of their shifts with bias voltage, first of all, we calculate the real space effective potential, as shown in Fig. 4. It shows how the applied bias is distributed across the junction, i.e., where the voltage drops, where the resistance is [31]. The volt-

2642

P. Zhao et al. / Physics Letters A 375 (2011) 2639–2643

Fig. 6. The PDOS of the left (black line) and right (red line) C60 moieties under biases (a) 0, 0.5, 0.8 V and (b) 0, −0.6, −1.4 V, respectively. The energy origin is set to be the Fermi level E F . The arrow indicates the shift directions of PDOS with the increase in bias voltage. The characters L and R represent the left and right C60 , respectively. For clarity, the scale of vertical axis of the PDOS decreases with the increase in bias voltage. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this Letter.)

age drop over the molecular junction is obtained by calculating effective potential with zero bias (V 0 ) and the applied finite bias (V 1 = 0.5, 0.8 V) across the electrodes, which is defined as

U eff ( V ) = U eff ( V 1 ) − U eff ( V 0 ).

(3)

From the change in the potential, it can be seen that there is almost no voltage blockage across the left and right C60 moieties, and the voltage mainly drops around the bridge space. This indicates that the resistance of C121 mainly takes place in the bridge space. This is also supported by the spatial distribution of the highest occupied molecular orbital (HOMO) and LUMO of the C121 , as shown in Fig. 5. From Fig. 5, we can see that the HOMO and LUMO of C121 is mainly localized on the left and right C60 moieties, respectively. As a result, the bridge C atom plays the role of a barrier, and then electrons can only transported by resonant tunneling between two C60 moieties under low bias [29,32]. Next, we project the density of states (PDOS) onto the left (black line) and right (red line) C60 moieties at various bias voltage, respectively, as shown in Fig. 6. It is well known that the PDOS represents the discrete energy levels of the isolated molecule including the effects of energy shift and line broadening due to the molecule–electrode coupling. There is good correspondence between the peaks in the transmission spectrum and those in the PDOS. It can be seen clearly that, in the zero-bias case, PDOS peaks in the range of 0.25 to 0.5 eV just above the E F are mediated by the LUMOs while the peaks around −1.25 eV below the E F arises from the HOMOs of the left and right C60 moieties, respectively. It is obvious that these two sets of PDOS peaks (black and red lines) are not degenerate in energy due to asymmetry of the C121 molecule. However, there is the big overlap between them which leads to the strong peaks in the zero-bias transmission spectrum. With the increase of positive (negative) bias voltage, PDOS peaks coming from the left C60 shift toward lower (higher) energies while those from the right C60 shift toward higher (lower) energies. We can see more clearly form the diagram of the shifts of the energy levels of two C60 moieties with positive and negative biases, as shown in Fig. 7. When a positive (negative) bias is applied, the energy levels of the left C60 are shift down (up), while those of the right C60 are sifted up (down), which leads to the gap between them become bigger and bigger. As a result, the overlap between these two sets of PDOS peaks becomes smaller and smaller following the increase of bias voltage, which leads to the

Fig. 7. The diagram of the shifts of the energy levels of two C60 moieties under 0.5, 0, −0.6 V. The arrow indicates the shift directions of the energy levels with the increase in bias voltage. The horizontal dashed line indicates the Fermi level E F . The characters L and R represent the left and right C60 , respectively.

reduction in transmission peak height and the NDR behavior. Since the NDR is caused by relative shifts of the LUMO levels localized on two C60 moieties, it is possible to tune the position and magnitude of the NDR by applying a gate voltage, which can change the positions of the LUMO levels of two C60 s. 4. Summary In summary, we have investigated the electronic transport properties of the C121 -based molecular junction by applying NEGF formalism combined with the first-principles DFT. Our results show that the transport under low bias is determined by the LUMOs of two C60 moieties, and their relative shifts with applied bias can lead to an obvious NDR phenomenon in a certain bias voltage range. The present findings could be helpful for the application

P. Zhao et al. / Physics Letters A 375 (2011) 2639–2643

of the C121 molecule in the field of single molecular devices or nanometer electronics. Acknowledgements This work was jointly supported by the National Natural Science Foundation of China (Grant No. 11074146), the Natural Science Foundation of Shandong Province, China (Grant No. ZR2009AL004) and the Doctoral Foundation of University of Jinan, China (Grant No. XBS1004). References [1] R.P. Andres, T. Bein, M. Dorogi, S. Feng, J.I. Henderson, C.P. Kubiak, W. Mahoney, R.G. Osifchin, R. Reifenberger, Science 272 (1996) 1323. [2] T.R. Kelly, H.D. Silva, R.A. Silva, Nature (London) 401 (1999) 150. [3] J. Chen, M.A. Reed, A.M. Rawlett, J.M. Tour, Science 286 (1999) 1550. [4] M.K. Ng, D.C. Lee, L.P. Yu, J. Am. Chem. Soc. 124 (2002) 11862. [5] D.I. Gittins, D. Bethell, D.J. Schiffrin, R.J. Nichols, Nature (London) 408 (2000) 67. [6] M. Di Ventra, S.G. Kim, S.T. Pantelides, N.D. Lang, Phys. Rev. Lett. 86 (2001) 288. [7] Y. Luo, Y. Fu, J. Chem. Phys. 117 (2002) 10283. [8] M.Q. Long, K.Q. Chen, L.L. Wang, W. Qing, B.S. Zou, Z. Shuai, Appl. Phys. Lett. 92 (2008) 243303. [9] P. Zhao, C.F. Fang, C.J. Xia, Y.M. Wang, D.S. Liu, S.J. Xie, Appl. Phys. Lett. 93 (2008) 013113.

[10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32]

2643

Y. Xu, G. Zhang, B.W. Li, J. Phys. Chem. B 112 (2008) 16891. S.C. Wang, W.C. Lu, Q.Z. Zhao, J. Bernholc, Phys. Rev. B 74 (2006) 195430. P. Zhao, P.J. Wang, Z. Zhang, D.S. Liu, Phys. Lett. A 374 (2010) 1167. J.M. Seminario, R.A. Araujo, L.M. Yan, J. Phys. Chem. B 108 (2004) 6915. J.M. Seminario, A.G. Zacarias, J.M. Tour, J. Am. Chem. Soc. 122 (2000) 3015. J. Cornil, Y. Karzazi, J.L. Bredas, J. Am. Chem. Soc. 124 (2002) 3516. J. Taylor, M. Brandbyge, K. Stokbro, Phys. Rev. B 68 (2003) 121101(R). Y.L. Zhao, Z.L. Chen, H. Yuan, X.F. Gao, L. Qu, Z.F. Chai, G.M. Xing, S. Yoshimoto, E. Tsutsumi, K. Itaya, J. Am. Chem. Soc. 126 (2004) 11134. M. Fujitsuka, O. Ito, N. Dragoe, S. Ito, H. Shimotani, H. Takagi, K. Kitazawa, J. Phys. Chem. B 106 (2002) 8562. J.L. Segura, N. Martin, Chem. Soc. Rev. 29 (2000) 13. G. Kresse, J. Furthmuller, Phys. Rev. B 54 (1996) 11169. J. Taylor, H. Guo, J. Wang, Phys. Rev. B 63 (2001) 245407. M. Brandbyge, J.L. Mozos, P. Ordejon, J. Taylor, K. Stokbro, Phys. Rev. B 65 (2002) 165401. X.Q. Shi, Z.X. Dai, X.H. Zheng, Z. Zeng, J. Phys. Chem. B 110 (2006) 16902. Z.Q. Fan, K.Q. Chen, Q. Wan, B.S. Zou, W.H. Duan, Z. Shuai, Appl. Phys. Lett. 92 (2008) 263304. J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. N. Troullier, J. Martins, Phys. Rev. B 43 (1991) 1993. S. Datta, Electronic Transport in Mesoscopic Systems, Cambridge University Press, New York, 1995. R. Pati, M. McClain, A. Bandyopadhyay, Phys. Rev. Lett. 100 (2008) 246801. C.G. Zeng, H.Q. Wang, B. Wang, J.L. Yang, J.G. Hou, Appl. Phys. Lett. 77 (2000) 3595. S.U. Lee, R.V. Belosludov, H. Mizuseki, Y. Kawazoe, Small 5 (2009) 1769. J. Taylor, M. Brandbyge, K. Stokbro, Phys. Rev. Lett. 89 (2002) 138301. X.H. Zheng, W.C. Lu, T.A. Abtew, V. Meunier, J. Bernholc, ACS Nano 12 (2010) 7205.