Effects of Electrodes and Nitrogen-Atom Locations on Electron

Article pubs.acs.org/JPCC

Effects of Electrodes and Nitrogen-Atom Locations on Electron Transport in C59N Molecular Junctions: A First-Principles Study Shundong Yuan,†,‡ Shiyan Wang,‡ Qunbo Mei,† Qidan Ling,*,†,§ Lianhui Wang,†,∥ and Wei Huang† †

Jiangsu Key Laboratory of Organic Electronics & Information Displays and Institute of Advanced Materials, Nanjing University of Posts and Telecommunications, Nanjing 210046, People’s Republic of China ‡ College of Science, China University of Petroleum, Qingdao 266580, People’s Republic of China § Fujian Key Laboratory of Polymer Materials and College of Chemistry and Materials Science, Fujian Normal University, Fuzhou 350108, People’s Republic of China ∥ Laboratory of Advanced Materials, Fudan University, 2205 Songhu Road, Shanghai 200438, People’s Republic of China ABSTRACT: The electron-transport properties of C59N molecular junctions with different electrodes (Au, Al, and CNT) are investigated by density functional theory (DFT) combined with the first-principle nonequilibrium Green’s function (NEGF). The current−voltage characteristics of all the models are calculated. The results show both electrode species and nitrogen-atom location may affect the transport properties of the C59N molecular junction. When the nitrogen atom of the C59N molecule is located close to one side of the junction, the rectifying behavior can be found in CNTelectrode models, while there is no observable rectification in metal-electrode models. The negative differential resistance may be observed in the C59N molecular junction using CNT electrodes when the nitrogen atom is at a certain location. The results are discussed through examining the transmission spectra, the molecular projected selfconsistent Hamiltonian states, and the projection of the density of states.

■

molecule, the originally delocalized π electrons in pure C60 become more localized around the substituted atoms.28 Therefore, the C59N molecule has intrinsic asymmetry in its molecular and electronic structures. The electron-transport properties of the C59N molecular junction have been investigated by several groups. Zhang et al.25 and Zhong et al.,26 respectively, investigated theoretically the electronic transport of a single C59N molecule sandwiched between two Au electrodes. Their results showed that the electron-transport properties of the single C59N molecule are significantly different from those of the C60 molecule. Zhao et al.29 reported a molecular rectifier based on a single C59N molecule in a double-barrier tunnel junction (DBTJ) via the single electron tunneling effect. In their experiment, a monolayer of the C59N molecule was deposited on the alkanethiol self-assembled monolayer (SAM) surfaces. Based on this experiment, Fang et al.30 investigated the electron-transport properties of a C59N molecule absorbed on the self-assembled alkanethiol monolayer through theoretical simulation. Their computational results reproduced the main rectifying features of the experimental observations. In this work, we perform a first-principles theoretical investigation on the electron-transport properties of several C59N molecular junctions. The calculation method is based on

INTRODUCTION The field of molecular electronics has attracted more and more attention among researchers all over the world in the past decades,1−6 since Aviram and Ratner first proposed the assumption of the molecular rectifier through a donor-σbridge-acceptor (DσA) molecule in 1974.7 Some attractive characteristics, such as molecular rectification, negative differential resistance, and molecular switching, have been found in the specific molecular devices through many experimental investigations. Significant advances have also been made in the field of theoretical studies for the molecular device.8−19 Fullerene C60 molecule is one of the most promising candidates for practical application in molecular devices and has been extensively studied as a core component of molecular devices,20−27 because of its unique physical and chemical properties. The electronic transport properties of single C60 molecule could be tuned by different methods. One of the effective methods is electron or hole doping, such as introducing N or B atom. Doping of C60 can be generally expected to change its electric conductivity due to modification in the density of states near the Fermi surface. A single C60 molecule is a semiconductor. C59N is an n-type doped fullerene, and thus is an n-type semiconductor. It is known that the molecular and electronic structures of pristine C60 are symmetric. All the C atoms in C60 are equivalent with sp2 hybridization and the π electrons in hexagonal rings are delocalized. However, the electrons in the hexagonal rings on C60 do not delocalize over the whole molecule.26 In the C59N © 2013 American Chemical Society

Received: July 25, 2013 Revised: December 16, 2013 Published: December 19, 2013 617

dx.doi.org/10.1021/jp407395d | J. Phys. Chem. C 2014, 118, 617−626

The Journal of Physical Chemistry C

Article

density functional theory (DFT) combined with the firstprinciples nonequilibrium Green’s function (NEGF), which is employed extensively in the theoretical studies of the electrontransport properties in molecular junctions.12,31−33 The effect of electrodes on the molecular device has been investigated by many groups.9,33−39 Their results demonstrated that the different electrodes can influence the transport properties of molecular device significantly. In these investigations, the work by Deng et al.36 suggested that the rectification characteristics of a molecular device are related to electrode materials (Au, Al, or Li) for discrimination of the coupling degree between the electrode and the molecule. In addition, the geometric orientation of the fullerene molecule between two electrodes may be different, and it will result in the different electrontransport properties, just as discussed in some work.21,40−42 For the C59N molecule, it means that the relative position of the nitrogen atom between two electrodes may vary with the different molecular orientations. However, the effects of different electrodes and nitrogen-atom locations on the transport properties of C59N molecular junctions have yet to be investigated. Therefore, the present work focuses on the two aspects, especially the former. The transport properties of the different molecular junctions in which the C59N molecule is sandwiched between the different electrodes (Au, Al, and carbon nanotube (CNT)) were investigated systemically. The current−voltage (I−V) characteristics of these molecular junctions were computed and compared. The calculated results show that both electrode material and nitrogen-atom location can affect the transport properties of the C59N molecular junction. For the C60 molecule, introduction of an N atom may result in magnetism. Accordingly, spin polarization may be an alternative consideration in the transport calculation. Zheng et al.27 investigated the spin polarization of a (C60)2 molecular junction with N doping. Their results suggested that spin polarization in the transmission of the molecular junction is negligible. The work by Zhang et al.25 did not consider the spin polarization at all. In the present work, the spin polarized transport calculation was also not performed.

program43 at the hybrid DFT/B3LYP44,45 level of theory with the 6-31G(d,p) basis set. The models and transport properties of the molecular junctions based on C59N molecule are obtained by using VNL/ ATK 2008.10 package,46 in which the theoretical framework is a combination of DFT and NEGF. The models of the C59N molecular junctions can be obtained following the next procedures. First, the optimized C59N molecule is translated into the central region between two electrodes. In Figure 1, the molecular junction is divided into three parts: left electrode, right electrode, and central scattering region. For the case of metal (M) electrodes, models A and B, the semi-infinite left and right electrodes are modeled by two M(111)−(4 × 4) surfaces (i.e., each layer consisting of sixteen metal atoms) with periodic boundary conditions, as employed in the previous work.30 There are three layers in each of the electrode unit cell and two layers in each side of the scattering region. Two armchair single-walled (2,2) CNTs and (5,5) CNTs are employed for the CNT-electrode models C and D, respectively. The open end of each nanotube has unsaturated dangling bonds, as the treatment in some previous investigations.21,41 There are four layers of carbon atoms (two unit cells) in each of the electrode unit cell and two layers of carbon atoms (one unit cell) in each side of the scattering region. In models A and B, the hexagon containing nitrogen atom (C5N) and the opposite C6 hexagon are parallel to the (111) surfaces of the metal electrodes (Au and Al). For models C and D, the C5N and C6 hexagons are parallel to the cross sections of the CNTs, and the CNT cylinder axis is aligned to the diameter of C59N sphere across the centers of the two hexagons. So, the same nitrogen-atom locations are introduced into models A, B, C, and D, and they show a certain degree of asymmetry on the model structure due to the nitrogen atom. In models A1 and C1, the nitrogen atom is located close to the middle of the scattering region and two opposite C6 hexagons are parallel to the electrode surfaces. In other words, models A1 and A (or C1 and C) differ only in the relative position of the nitrogen atom. Second, the plane−plane distance between the electrode and the C59N molecule is determined by examining the total energy of molecular junction as a function of the distance. The optimal distance corresponds to the lowest total energy. According to our calculation, the optimal plane−plane distance in the Au-electrode system is 2.10 Å, which is in agreement with the result in the previous study,25 and the distance in the Al-electrode system is 2.07 Å. Because of the little difference, the plane−plane distances in models A(A1) and B are set to be 2.10 Å uniformly so that their transport properties can be compared under the same condition. The plane−plane distance is 2.04 Å in the CNTelectrode systems. Third, the geometric configurations of all these models are optimized in ATK by using Quasi Newton algorithm within a force convergence criterion of 0.05 eV/Å. In the metal-electrode models, the C59N molecule is relaxed completely and all the electrode atoms are fixed as the recommendation from VNL/ATK 2008.10 package.46 In the CNT-electrode models, however, all the atoms included in the scattering region are relaxed, just as the treatment in the previous works.21,41 The transport properties of these molecular junctions are calculated after the above geometric optimizations. To achieve a balance between the calculation efficiency and accuracy, a single-ζ with polarization (SZP) basis set is chosen for all atoms and a mesh cutoff of 150 Ry is adopted. The exchange− correlation potential is described by the Perdew−Zunger local

■

COMPUTATIONAL MODELS AND METHODS The models of the C59N molecular junctions, which are treated as two-probe systems, are schematically illustrated in Figure 1. The models A(A1), B, C(C1), and D correspond to the molecular junctions using Au, Al, (2,2) CNT, and (5,5) CNT electrodes, respectively. The geometric structure of the single C59N molecule is optimized in advance through the Gaussian03

Figure 1. Models of the molecular junctions: single C59N molecule sandwiched between two X (X = Au, Al, (2,2) CNT, or (5,5) CNT) electrodes. Gray and blue balls in the central region represent C and N atoms, respectively. The dashed-line frame part is defined as the scattering region. 618



Article

density approximation (LDA.PZ).47,48 The convergence criterion of 1 × 10−5 is set for the grid integration to get accurate results. A k-point sampling of 2 × 2 × 200 for the metal-electrode models is used in the Brillouin zone of the entire molecular junction, while 1 × 1 × 100 sampling for the CNT-electrode models is used. The integral mixing parameter is set to 0.01. The calculation with higher parameters was also tested and the corresponding results have no obvious change. The current−voltage (I−V) characteristic of molecular junction can be obtained by the Landauer−Büttiker formula49−51 I(Vb) =

2e 2 h

∫μ

μR

model A matches closely that of model B, and the former is slightly larger than the latter. However, the curve of model A deviates gradually from the curve of model B when |V| is above 1.0 V, and the largest difference between their current magnitudes is 60 μA at −2.0 V. The result shows that the Al electrode may be more favorable for the electronic transport of C59N-based molecular junction than the Au electrode at the higher bias voltages. In general, the C59N molecule exhibits near ohmic behavior when it is sandwiched between two Au (or Al) electrodes, and both gold and aluminum are excellent electrode materials for the electric conduction of C59N molecule. As for models C and D, their I−V curves are nonlinear. Comparing with models A and B, the curves of models C and D are somewhat irregular for their evolution tendency. In model C, when the positive bias voltage is applied, the current increases slowly with the rising bias voltage up to 1.0 V where the current begins to increase rapidly. In the case of the negative bias voltage, the current increases rapidly in the bias regions of [−1.2, 0.0] V, and it is different from the case of the positive bias voltage. It is worth noting that the current decreases with an increase of the bias voltage at [1.6, 1.8] V or [−1.4, −1.2] V. The feature is the so-called negative differential resistance (NDR). The evolution of I−V curve in model D shows a similar feature and NDR phenomenon also occurs. In the molecular electronic device, NDR is also one of the most intriguing properties for its potential application on circuit. The substituted C60 molecules in the work by Yaghobi et al.52 also display NDR behavior. In the work25,26 mentioned above, the I−V characteristics of Au−C59N−Au molecular junction were also calculated, and their models are very similar to the model A in this work. However, each result is different from the others, including the magnitude of current and the evolution tendency of the I−V curve. It is supposed that the difference originates mainly from the different configurations of the molecular junctions, such as the separation distance between the C59N molecule and the electrode, the molecular spatial orientation. In Figure 2, it is obvious that the I−V curves of these models are asymmetric more or less at about zero bias, especially for models C and D. To characterize the asymmetric characteristics, the molecular rectifications are investigated. The rectification ratio is defined as

[f (E − μL ) − f (E − μR )]T (E , Vb) dE

L

(1)

where h is the Planck constant, e is the elementary charge, and 2e2/h = G0 is the conductance quantum. f is the Fermi function. μL and μR are the electrochemical potentials of the left and right electrodes: μL(Vb) = EF − eVb/2 and μR(Vb) = EF + eVb/2. EF is the Fermi energy of the electrode. [μL(Vb), μR(Vb)] denotes the energy region that contributes to the current integral and is defined as the bias window. T(E, Vb) is the total transmission probability for an incident electron at energy E under a bias voltage Vb.

■

RESULTS AND DISCUSSION Effects of Different Electrodes on the Transport Properties. The current−voltage (I−V) curves of models A, B, C, and D are presented in Figure 2. The currents in models

R (V ) = Figure 2. I−V curves of models A, B, C, and D in the bias range from −2.0 to +2.0 V. The positive current flows from the left electrode to the right electrode, and vice versa.

I(+V ) I(−V )

(2)

R(V) = 1, that is, the current at the positive bias is equal to that at the negative bias, meaning that there is no rectification, and the value of R(V) deviates more from 1, meaning the rectification effect is more obvious. The calculated R values in our models are all less than 1. As the reciprocal of the rectification ratio, that is, |I(−V)/I(+V)|, can also describe the rectifying effect, in order to facilitate discussion, the values of |I(−V)/I(+V)| are calculated. According to our calculation, the rectifying effect in model A approaches that in model B, and the rectifying effect in model C approaches that in model D. For simplicity and clarity, Figure 3 shows the dependence of |I(−V)/I(+V)| on the bias voltages only for models A and C. The rectification values of model A approximate the unit 1 in the applied bias range. The results suggest that the C59N molecule sandwiched between two Au (or Al) electrodes cannot show the noticeable rectification. It reflects that the asymmetry of the C59N molecule is negligible

A and B are 1 order of magnitude larger than those in model C and almost 2 orders of magnitude larger than those in model D. It is supposed that the difference is mainly due to the different C59N−electrode couplings. We will discuss it briefly through the projected density of states in the following text. As for the difference between models C and D, the actual atom−atom separations between the C59N molecule and (5,5) CNT are longer than those between the C59N molecule and (2,2) CNT, though the plane−plane distance between the C59N molecule and electrode in model C is the same as that in model D. It should be noted that the I−V curve of model B shows an approximate linear evolution tendency, while the I−V curve of model A shows a gentle change with a nonlinear tendency. In the bias range of −1.0 to +1.0 V, the current magnitude of 619



Article

Figure 4. Transmission spectra of models A and C at 0 V. The Fermi level is set to zero.

Figure 3. Rectification ratio |I(−V)/I(+V)| of models A and C at the different bias voltages.

in the metal-electrode environment. In comparison with model A, the rectifying effect in model C is obvious. The rectification values of model C are over 2.0 in a wide bias range of [0.4, 1.0] V, and the maximum is 2.7 at 0.4 V. In addition, all the values of |I(−V)/I(+V)| for model D in the bias range from 0.6 to 1.4 V are also larger than 2.0. So, our results show the electrode dependence of rectification in C59N molecular junction. It is supposed that the C59N molecule with a specific spatial orientation will likely show observable rectifying behavior under the condition of CNT electrodes. The rectification characteristics in the CNT−C59N−CNT molecular junctions may be considered in the practical applications in molecular electronics. Considering the rectification characteristics in model C, it seems that the current occurs in the direction from the non-Natom side to the N-atom side rather than in the contrary direction. In other words, in our models, the preferential transfer direction for the electron is from the N-atom side to the non-N-atom side. The preferential direction may originate from the unequal electrode-molecule couplings, just as the suggestion by us53 and Zhao et al.54 According to the Landauer−Büttiker formula, the transmission spectra within the bias window [μL(Vb), μR(Vb)] determine the current. The bias window is confined by the region [−Vb/2, +Vb/2] when the Fermi level is set to zero. To understand the electronic transport properties in our models, the transmission spectra in the energy range from −1.5 to +1.5 eV at the different bias voltages are calculated. The difference of the I−V characteristics for the four models mentioned above can be further understood by analyzing their transmission spectra. Figure 4 shows the transmission coefficient of models A and C as a function of energy at 0 V bias. The transmission coefficients of model A are larger prominently than those of model C. It results in the difference in their current values. The feature also indicates that the electron transmission in model A is easy, while the transmission in model C is somewhat difficult relatively. Since many transmission coefficients in model A are larger than 1, there should be several transmission channels near a specific energy. The rectifying behavior of model C can be analyzed qualitatively by its transmission spectra. Figure 5 plots the transmission spectra of model C as a function of energy at the different biases. Obviously, the peaks in the transmission spectra show a regular spatial distribution, especially for those below the Fermi level. In addition, the transmission peaks shift toward the lower energy region with the rising bias voltage. In

Figure 5. Transmission spectra of model C as a function of energy at the different biases. The Fermi level is set to zero. The region confined by the blue dashed lines and energy axis is the bias window.

Figure 5, the asymmetric feature for the transmission spectra at the positive and negative biases can be observed. In the bias window, the peaks which are around the Fermi level at 0 V bias are always prominent when the negative bias is applied. However, some of the peaks disappear at the positive biases. Therefore, the current values at the positive and negative biases are unequal and it results in the rectifying behavior in model C. In order to further analyze the rectifying behavior in models C and D, we also consider their electron transmission eigenstates in the specific molecular energy levels which are modified by the electrodes. Each eigenstate corresponds to a possible transmission tunneling channel. To obtain these transmission eigenstates, a method which was proven to be effective by the previous theoretical studies15,32,55 was employed. In this method, the self-consistent Hamiltonian of the molecular junction is projected onto the molecule, and then the molecular projected self-consistent Hamiltonian (MPSH) matrix is diagonalized. The MPSH state is the eigenstate of the molecule in the two-probe environment, and the self-energies of two electrodes are not included. The MPSH states delocalized on the whole scattering region will contribute to the transmission spectra, while the MPSH states localized on 620



Article

any one of the electrodes will not make any contribution to the transmission spectra.15,32,55 Therefore, the rectifying behavior can be analyzed by intuitively comparing the respective MPSH states at the corresponding positive and negative biases. In the present work, the MPSH states at +1.0 and −1.0 V of model D are chosen as the compared paradigms. The selfconsistent Hamiltonian of the molecular junction is projected onto all atoms in the scattering region so that the molecule− electrode coupling can be shown. Figure 6 illustrates the spatial distribution of the MPSH states 209 to 219 which their corresponding energy levels locate in the energy region confined by the bias window. At the bias of −1.0 V, MPSH states 210, 215, 216, and 218 are well delocalized. In addition, states 211, 213, 214, 217, and 219 are also delocalized. They all contribute to the transmission. At the bias of +1.0 V, MPSH states 209, 210, 211, 213, 214, 215, 216, and 218 contribute to the transmission. On the whole, the MPSH states at −1.0 V are more delocalized than those at +1.0 V. Therefore, the contribution to the transmission from the MPSH states at −1.0 V is greater than that at +1.0 V. It results in the rectification effect at 1.0 V in model D. For the difference of the rectification between the metalelectrode model and CNT-electrode model in this work, we can analyze its origin qualitatively. The rectifying behavior corresponds to the preferential electron transfer direction, which originates from the unequal electrode−molecule couplings. So, it is supposed that the asymmetric electrode− molecule couplings should be the most crucial factor for the rectifying behavior in the C59N molecular junctions. In the case of metal electrodes (for example, Au electrode), the asymmetry of the electronic structure of the C59N molecule is almost eliminated for the almost equivalent Au−N and Au−C couplings. In other words, the asymmetry of the C59N molecule is too weak in the metal-electrode environment to bring prominent unequal electron-transport performance in the opposite directions. In the case of CNT electrodes, however, the asymmetry of the electronic structure of the C59N molecule is relatively prominent because of the unequal C−C and C−N couplings. Therefore, there is an obvious difference for the electronic transport in the opposite directions in the CNTelectrode environment. In order to confirm the above supposition, the projected density of states (PDOS) in models A and C is studied, respectively. It is known that the PDOS can give us information on how much the molecular orbitals contribute to the eigenstate of the whole open system and how strongly the molecule couples with the electrodes at a certain energy.56,57 In this work, the density of states is projected onto the left electrode atoms in the scattering region (L), the C5N hexagon close to left electrode, the C6 hexagon close to right electrode, and the right electrode atoms in the scattering region (R), respectively, so that the degree of the molecule−electrode coupling can be examined. Figure 7 shows the dependence of PDOS on the electron energy at zero bias for models A and C, respectively. In Figure 7(a1)-(a2), the PDOS spectra of the left Au electrode and right Au electrode are very similar; however, there is a difference between the PDOS spectra of the C5N and C6 hexagons. It shows that N doping may increase the density of states around the doping site. It should be noted that the PDOS magnitude of the two hexagons is far less than that of the electrode. As a result, in Figure 7(a3), the PDOS spectrum of the left electrode with the C5N hexagon is also very close to that of the right electrode with the C6 hexagon, just as the

Figure 6. Spatial distribution of MPSH states 209 to 219 at +1.0 and −1.0 V in model D. The isovalue is 0.03. The states which make no contribution to the transmission are not shown.

spectra in Figure 7(a1). The feature shows that the electrode− molecule couplings on both sides of model A are almost equivalent. Therefore, in the metal-electrode model, there is no noticeable difference for the electron transport in the positive and negative directions. In Figure 7(b1), the PDOS spectra of the left CNT electrode and the right CNT electrode also show a good similarity, especially for the locations of peaks. In Figure 7(b2), the PDOS 621



Article

also be analyzed briefly through the PDOS. According to the comparison between Figure 7(a3) and (b3), the PDOS values of the electrode surface with the C5N (or C6) hexagon in model A are larger than those in model C. Therefore, the C59N− electrode coupling in model A is stronger than that in model C. The stronger coupling is related to the larger electronic transport probability from the electrode to the C59N molecule. Accordingly, the current value in model A is larger than that in model C. Effects of Nitrogen-Atom Locations on the Transport Properties. The electron-transport properties of models A1 and C1 are studied and compared with models A and C, respectively, so that we can clarify the effects of different nitrogen-atom locations while keeping the position of the fullerene molecule fixed. Figure 8a shows the I−V curves of

Figure 7. Dependence of PDOS on the electron energy at zero bias: (a1)−(a3) correspond to model A; (b1)−(b3) correspond to model C. L and R represent the left and right electrode atoms in the scattering region, respectively. The Fermi level is set to be the origin of energy and denoted by the blue dashed line.

values around the Fermi level of the C5N hexagon are larger than those of the C6 hexagon obviously. According to the comparison between Figure 7(b1) and (b2), it can be seen that there is little difference in the magnitude of the PDOS values around the Fermi level of the hexagons and the electrodes. Consequently, as shown in Figure 7(b3), the PDOS values around the Fermi level of the left electrode with C5N hexagon are larger than those of the right electrode with C6 hexagon. The PDOS around the Fermi level plays a crucial role in the transmission of the incident electron. Therefore, it shows a certain difference for the electron-transport performance in the positive and negative directions in the circumstance of CNT electrodes. Our results also show that even a single doping atom in C60 molecule may bring about some noticeable changes in the electron-transport properties, just as suggested by Zhong et al.26 The above-mentioned difference of the currents between the metal-electrode models and the CNT-electrode models can

Figure 8. Comparison of I−V curves: (a) models A and A1; (b) models C and C1.

models A1 and A in the bias range of [0, 2.0] V. It can be seen that the two curves nearly coincide with each other. This feature suggests that the different nitrogen-atom locations do not bring observable change to the electron-transport characteristics in the metal-electrode circumstance. The I−V curves of models C1 and C in the bias range of [−2.0, 2.0] V are shown in Figure 8b, and the difference between them can be found. The currents in model C1 are less than those in model C over most of the bias range except the positive 0.2 to 1.0 V. In model C1, the current values at the positive and negative biases do not show significant difference, and it is unlike the case in model C. That is, there is no apparent rectifying behavior in model C1. However, model C1 shows an obvious NDR behavior for a certain range at the higher positive biases. As mentioned above, 622



Article

Figure 9. Transmission spectra (black solid curve) and PDOS spectra (red dashed curve) of model C1 in the energy range from −2.0 to +2.0 eV at the different positive bias voltages: (a) 0.8 V, (b) 1.2 V, (c) 1.4 V, and (d) 1.6 V, respectively. The region between the blue dashed vertical lines is the bias window.

NDR phenomena also appear in model C, but it is trivial and the corresponding bias range is limited. In model C1, NDR behavior appears in the bias range of [0.8, 1.4] V. In order to evaluate the NDR feature in model C1, the corresponding peakto-valley ratio (PVR) of the current is calculated, and the result is 1.388. Fan et al.24 investigated the transport properties of several C60 molecular devices in which the C60 molecule is squashed and coupled to two Al electrodes. NDR is also found in their models. Our results suggest that the C59N molecule can exhibit NDR features more or less under the condition of CNT electrodes, and NDR may be enhanced when the location of the nitrogen atom changes. To explain the origin of NDR feature in model C1, the transmission spectra and the corresponding PDOS in the energy range from −2.0 to +2.0 eV at the positive bias voltages of 0.8 V, 1.2 V, 1.4 V, and 1.6 V are calculated and presented in Figure 9. A strong coupling makes electrons at a certain energy easily transmit across the molecule, and it may bring a large transmission coefficient at this energy. In Figure 9, it can be seen that there is a good correlation between the transmission

spectra and the PDOS spectra, especially for the position of their peaks. Now we can discuss the NDR feature in model C1 through the transmission spectra. It is clearly observed in Figure 9 that the peaks around the Fermi level shift toward the lower energy region with the rising positive bias. At the bias of 0.8 V, the peak at 0.2 eV is high and broad; in addition, a part of another similar peak at about 0.5 eV enters the bias window. It gives rise to a large current at 0.8 V. For the case of 1.2 and 1.4 V, however, the transmission peaks at 0.2 and 0.5 eV become lower, though the two peaks are located completely in the bias window. As for the peaks below the Fermi level in the bias window, there is no obvious change with the varying bias voltage. Consequently, the currents decrease when the bias voltage is increased from 0.8 to 1.4 V. Therefore, the NDR phenomenon appears in the bias range of [0.8, 1.4] V. The peak at about 0.75 eV at 1.4 V bias is located out of the bias window, and it enters the bias window at 1.6 V. It is the main origin for the current at 1.6 V increasing again. In model C1, the NDR phenomenon does not appear in the negative bias region except for a tiny NDR in the bias range of 623



Article

[−0.8, −0.6] V, and it is different from the case of the positive bias. Figure 10(a) plots the transmission spectra of model C1 as

2.0] eV are large and there are no gaps in the transmission spectra. That is to say, there are enough states in the Au electrodes with which to couple the molecular orbitals. This is the reason that NDR phenomenon does not appear in the metal-electrode models.

■

CONCLUSIONS In conclusion, we have investigated the electron-transport properties of the different molecular junctions, in which a single C59N molecule is sandwiched between the different electrodes (Au, Al, and CNT), using density functional theory (DFT) combined with nonequilibrium Green’s function (NEGF). Their current−voltage characteristics were calculated. The results show that both electrode material and nitrogen-atom location may affect the transport properties of the C59N molecular junctions. For the case of metal electrodes, both gold and aluminum are excellent electrode materials for the electric conduction of the C59N molecule. The C59N molecular junctions using CNT electrodes exhibit some interesting transport characteristics, although the conductivities using CNT electrodes are less than those using metal electrodes. When the nitrogen atom of the C59N molecule is located close to one of the electrodes, the rectifying behavior was found in the CNT-electrode models, while there was no observable rectification in the metal-electrode models. The negative differential resistance may be observed in the C59N molecular junction using CNT electrodes when the nitrogen atom is at a certain location. The results were discussed through examination of the transmission spectra, the molecular projected selfconsistent Hamiltonian states, and the projection of the density of states.

■

AUTHOR INFORMATION

Corresponding Author

*Tel: +86-25-8586 6333. Fax: +86-25-8586 6396. E-mail address: [email protected].

Figure 10. Transmission spectra as a function of energy: (a) model C1 at the different negative biases; (b) model A1 at the different positive biases. The region confined by the blue dashed lines and energy axis is the bias window.

Notes

The authors declare no competing financial interest.

■

a function of energy at the different negative biases. It can be seen that the transmission spectrum located in the bias window increases with the rising bias all along. As a result, the current values at the negative biases show the same increase trend. So, there is no apparent NDR phenomenon in the negative bias region. It is suggested that the difference of the I−V characteristics between the positive and negative biases should originate mainly from the different densities of states which are modified by the electrodes at the corresponding positive and negative biases. It is worth noting that the NDR phenomenon occurs more or less in the CNT-electrode models (C, D, and C1) but not in the metal-electrode models (A, B, and A1). Smeu et al.58 investigated the electron-transport properties of disubstituted benzene dithiol molecules bridging two metallic leads. In their results, NDR occurs in the 3 × 3 Au-electrode system, and it is attributed to the use of electrodes having band gaps in their PDOS/band structure. According to their explanation, no NDR would occur if there are no gaps in the transmission spectra over the energy range considered. Figure 10b shows the transmission spectra of model A1 at the different positive biases. It can be seen that these spectra vary little with the rising bias. All the transmission coefficients in the energy range of [−2.0,

ACKNOWLEDGMENTS This work was supported by the National Basic Research Program of China (973 Program, 2009CB930601), National Natural Science Foundation of China (NSFC 60976019, 90813010), Program for New Century Excellent Talents in University (NCET-07-0446), Specialized Research Fund for the Doctoral Program of Higher Education (SRFDP20093223110002), Scientific and Technological Innovation Teams of Colleges and Universities in Jiangsu Province (TJ207035, TJ208027).

■

REFERENCES

(1) Chen, J.; Reed, M. A.; Rawlett, A. M.; Tour, J. M. Large On-Off Ratios and Negative Differential Resistance in a Molecular Electronic Device. Science 1999, 286, 1550−1552. (2) Tour, J. M. Molecular Electronics. Synthesis and Testing of Components. Acc. Chem. Res. 2000, 33, 791−804. (3) Park, J.; Pasupathy, A. N.; Goldsmith, J. I.; Chang, C.; Yaish, Y.; Petta, J. R.; Rinkoski, M.; Sethna, J. P.; Abruna, H. D.; McEuen, P. L.; et al. Coulomb Blockade and the Kondo Effect in Single-Atom Transistors. Nature 2002, 417, 722−725. (4) Nitzan, A.; Ratner, M. A. Electron Transport in Molecular Wire Junctions. Science 2003, 300, 1384−1389.

624



Article

(28) Dong, J.; Jiang, J.; Yu, J.; Wang, Z. D.; Xing, D. Y. Nonlinear Optical Properties of the Substituted Fullerenes C59X (X=B,N). Phys. Rev. B 1995, 52, 9066−9070. (29) Zhao, J.; Zeng, C.; Cheng, X.; Wang, K.; Wang, G.; Yang, J.; Hou, J. G.; Zhu, Q. Single C59N Molecule as a Molecular Rectifier. Phys. Rev. Lett. 2005, 95, 045502. (30) Fang, C.; Zhao, P.; Cui, B.; Wang, L.; Liu, D.; Xie, S. Current Rectification in Single Molecule C59N: Effect of Molecular Polarity Induced Dipole Moment. Phys. Lett. A 2010, 374, 4465−4470. (31) Ke, S.; Baranger, H. U.; Yang, W. Electron Transport through Molecules: Self-Consistent and Non-Self-Consistent Approaches. Phys. Rev. B 2004, 70, 085410. (32) Staykov, A.; Nozaki, D.; Yoshizawa, K. Theoretical Study of Donor−π-Bridge−Acceptor Unimolecular Electric Rectifier. J. Phys. Chem. C 2007, 111, 11699−11705. (33) Cho, Y.; Kim, W. Y.; Kim, K. S. Effect of Electrodes on Electronic Transport of Molecular Electronic Devices. J. Phys. Chem. A 2009, 113, 4100−4104. (34) Seminario, J. M.; De La Cruz, C. E.; Derosa, P. A. A Theoretical Analysis of Metal-Molecule Contacts. J. Am. Chem. Soc. 2001, 123, 5616−5617. (35) Geng, W. T.; Nara, J.; Ohno, T. Adsorption of Benzene Thiolate on the (111) Surface of M(M=Pt, Ag, Cu) and the Conductance of M/Benzene Dithiolate/M Molecular Junctions: A First-Principles Study. Thin Solid Films 2004, 464−465, 379−383. (36) Deng, X. Q.; Zhou, J. C.; Zhang, Z. H.; Tang, G. P.; Qiu, M. Electrode Metal Dependence of the Rectifying Performance for Molecular Devices: A Density Functional Study. Appl. Phys. Lett. 2009, 95, 103113. (37) Kondo, H.; Nara, J.; Kino, H.; Ohno, T. Transport Properties of a Biphenyl-Based Molecular Junction Systemthe Electrode Metal Dependence. J. Phys.: Condens. Matter 2009, 21, 064220. (38) Ko, C.; Huang, M.; Fu, M.; Chen, C. Superior Contact for Single-Molecule Conductance: Electronic Coupling of Thiolate and Isothiocyanate on Pt, Pd, and Au. J. Am. Chem. Soc. 2010, 132, 756− 764. (39) Pan, J. B.; Zhang, Z. H.; Ding, K. H.; Deng, X. Q.; Guo, C. Current Rectification Induced by Asymmetrical Electrode Materials in a Molecular Device. Appl. Phys. Lett. 2011, 98, 092102. (40) Kaun, C.; Jorn, R.; Seideman, T. Spontaneous Oscillation of Current in Fullerene Molecular Junctions. Phys. Rev. B 2006, 74, 045415. (41) OuYang, F.; Xu, H.; Fan, T. All Carbon Nanoswitch Based on C70 Molecule: A First Principles Study. J. Appl. Phys. 2007, 102, 064501. (42) Saffarzadeh, A. Electronic Transport through a C60 Molecular Bridge: The Role of Single and Multiple Contacts. J. Appl. Phys. 2008, 103, 083705. (43) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A.; Vreven, T.; Kudin, K. N.; Burant, J. C.; et al. Gaussian 03, revision C.01; Gaussian, Inc., Wallingford CT, 2004. (44) Becke, A. D. A New Mixing of Hartree-Fock and Local DensityFunctional Theories. J. Chem. Phys. 1993, 98, 1372−1377. (45) Lee, C.; Yang, W.; Parr, R. G. Development of the Colle-Salvetti Correlation-Energy Formula into a Functional of the Electron Density. Phys. Rev. B 1988, 37, 785−789. (46) Atomistix ToolKit, v 2008.10; QuantumWise A/S (www. quantumwise.com). (47) Ceperley, D. M.; Alder, B. J. Ground State of the Electron Gas by a Stochastic Method. Phys. Rev. Lett. 1980, 45, 566−569. (48) Perdew, J.; Zunger, A. Self-Interaction Correction to DensityFunctional Approximations for Many-Electron Systems. Phys. Rev. B 1981, 23, 5048−5079. (49) Büttiker, M.; Imry, Y.; Landauer, R.; Pinhas, S. Generalized Many-Channel Conductance Formula with Application to Small Rings. Phys. Rev. B 1985, 31, 6207−6215. (50) Büttiker, M. Four-Terminal Phase-Coherent Conductance. Phys. Rev. Lett. 1986, 57, 1761−1764.

(5) Salomon, A.; Cahen, D.; Lindsay, S.; Tomfohr, J.; Engelkes, V. B.; Frisbie, C. D. Comparison of Electronic Transport Measurements on Organic Molecules. Adv. Mater. 2003, 15, 1881−1890. (6) Wassel, R. A.; Gorman, C. B. Establishing the Molecular Basis for Molecular Electronics. Angew. Chem., Int. Ed. 2004, 43, 5120−5123. (7) Aviram, A.; Ratner, M. A. Molecular Rectifiers. Chem. Phys. Lett. 1974, 29, 277−283. (8) Emberly, E. G.; Kirczenow, G. Theoretical Study of Electrical Conduction through a Molecule Connected to Metallic Nanocontacts. Phys. Rev. B 1998, 58, 10911−10920. (9) Yaliraki, S. N.; Kemp, M.; Ratner, M. A. Conductance of Molecular Wires: Influence of Molecule-Electrode Binding. J. Am. Chem. Soc. 1999, 121, 3428−3434. (10) Di Ventra, M.; Pantelides, S. T.; Lang, N. D. First-Principles Calculation of Transport Properties of a Molecular Device. Phys. Rev. Lett. 2000, 84, 979−982. (11) Seminario, J. M.; Zacarias, A. G.; Tour, J. M. Theoretical Study of a Molecular Resonant Tunneling Diode. J. Am. Chem. Soc. 2000, 122, 3015−3020. (12) Brandbyge, M.; Mozos, J.; Ordejón, P.; Taylor, J.; Stokbro, K. Density-Functional Method for Nonequilibrium Electron Transport. Phys. Rev. B 2002, 65, 165401. (13) Xue, Y.; Datta, S.; Ratner, M. A. First-Principles Based Matrix Green’s Function Approach to Molecular Electronic Devices: General Formalism. Chem. Phys. 2002, 281, 151−170. (14) Taylor, J.; Brandbyge, M.; Stokbro, K. Theory of Rectification in Tour Wires: The Role of Electrode Coupling. Phys. Rev. Lett. 2002, 89, 138301. (15) Stokbro, K.; Taylor, J.; Brandbyge, M.; Mozos, J. -L.; Ordejón, P. Theoretical Study of the Nonlinear Conductance of Di-thiol Benzene Coupled to Au(1 1 1) Surfaces via Thiol and Thiolate Bonds. Comput. Mater. Sci. 2003, 27, 151−160. (16) Ke, S.; Baranger, H. U.; Yang, W. Molecular Conductance: Chemical Trends of Anchoring Groups. J. Am. Chem. Soc. 2004, 126, 15897−15904. (17) Galperin, M.; Ratner, M. A.; Nitzan, A. Hysteresis, Switching, and Negative Differential Resistance in Molecular Junctions: A Polaron Model. Nano Lett 2005, 5, 125−130. (18) Yeganeh, S.; Galperin, M.; Ratner, M. A. Switching in Molecular Transport Junctions: Polarization Response. J. Am. Chem. Soc. 2007, 129, 13313−13320. (19) Smeu, M.; Wolkow, R. A.; Guo, H. Conduction Pathway of πStacked Ethylbenzene Molecular Wires on Si(100). J. Am. Chem. Soc. 2009, 131, 11019−11026. (20) Taylor, J.; Guo, H.; Wang, J. Ab Initio Modeling of Open Systems: Charge Transfer, Electron Conduction, and Molecular Switching of a C60 Device. Phys. Rev. B 2001, 63, 121104. (21) Gutierrez, R.; Fagas, G.; Cuniberti, G.; Grossmann, F.; Schmidt, R.; Richter, K. Theory of an All-Carbon Molecular Switch. Phys. Rev. B 2002, 65, 113410. (22) Sergueev, N.; Demkov, A. A.; Guo, H. Inelastic Resonant Tunneling in C60 Molecular Junctions. Phys. Rev. B 2007, 75, 233418. (23) Ono, T.; Hirose, K. First-Principles Study of ElectronConduction Properties of C60 Bridges. Phys. Rev. Lett. 2007, 98, 026804. (24) Fan, Z.; Chen, K.; Wan, Q.; Zou, B. S.; Duan, W.; Shuai, Z. Theoretical Investigation of the Negative Differential Resistance in Squashed C60 Molecular Device. Appl. Phys. Lett. 2008, 92, 263304. (25) Zhang, X.; Long, M.; Chen, K.; Shuai, Z.; Wan, Q.; Zou, B. S.; Zhang, Y. Electronic Transport Properties in Doped C60 Molecular Devices. Appl. Phys. Lett. 2009, 94, 073503. (26) Zhong, X.; Pandey, R.; Rocha, A. R.; Karna, S. P. Can SingleAtom Change Affect Electron Transport Properties of Molecular Nanostructures such as C60 Fullerene? J. Phys. Chem. Lett. 2010, 1, 1584−1589. (27) Zheng, X. H.; Wang, X. L.; Dai, Z. X.; Zeng, Z. Tuning the Transport Properties of a (C60)2 Bridge with Electron and Hole Dopings. J. Chem. Phys. 2011, 134, 044708. 625



Article

(51) Büttiker, M. Absence of Backscattering in the Quantum Hall Effect in Multiprobe Conductors. Phys. Rev. B 1988, 38, 9375−9389. (52) Yaghobi, M.; Yuonesi, M. Electronic Transport through a C60−nXn (X = N and B) Molecular Bridge. Mol. Phys. 2011, 109, 1821−1829. (53) Yuan, S.; Wang, S.; Mei, Q.; Ling, Q.; Wang, L.; Huang, W. First-Principles Study of Rectification in Bis-2-(5-ethynylthienyl)ethyne Molecular Junctions. J. Phys. Chem. A 2011, 115, 9033−9042. (54) Zhao, J.; Yu, C.; Wang, N.; Liu, H. Molecular Rectification Based on Asymmetrical Molecule-Electrode Contact. J. Phys. Chem. C 2010, 114, 4135−4141. (55) Yuan, S.; Dai, C.; Weng, J.; Mei, Q.; Ling, Q.; Wang, L.; Huang, W. Theoretical Studies of Electronic Transport in Thiophene Dimer: Effects of the Substituent Group and the Heteroatom. J. Phys. Chem. A 2011, 115, 4535−4546. (56) Shi, X.; Zheng, X.; Dai, Z.; Wang, Y.; Zeng, Z. Changes of Coupling between the Electrodes and the Molecule under External Bias Bring Negative Differential Resistance. J. Phys. Chem. B 2005, 109, 3334−3339. (57) Long, M.; Chen, K.; Wang, L.; Zou, B. S.; Shuai, Z. Negative Differential Resistance Induced by Intermolecular Interaction in a Bimolecular Device. Appl. Phys. Lett. 2007, 91, 233512. (58) Smeu, M.; Wolkow, R. A.; DiLabio, G. A. Theoretical Investigation of Electron Transport Modulation through Benzenedithiol by Substituent Groups. J. Chem. Phys. 2008, 129, 034707.

626


Effects of Electrodes and Nitrogen-Atom Locations on Electron

Recommend Documents