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Molecular Rectification Based on Asymmetrical Molecule-Electrode Contact Jianwei Zhao,* Cui Yu, Nan Wang, and Hongmei Liu Key Laboratory of Analytical Chemistry for Life Science (Ministry of Education), School of Chemistry and Chemical Engineering, Nanjing UniVersity, Nanjing 210008, P. R. China ReceiVed: June 17, 2009; ReVised Manuscript ReceiVed: January 19, 2010
Instead of asymmetric molecular substitution, we investigate the molecular rectification originating from asymmetrical electrode-molecule contacts using density functional theory combined with the nonequilibrium Green’s function method. In the porphyrin-based molecular junction, we employ an additional thiol group on the left side to enhance the electronic coupling. The transportation of these contact-asymmetrical junctions shows obvious rectification, implying that the asymmetrical interface modification is feasible in the design of molecular diodes. The theoretical calculations show that the rectification ratio is about 2.6 in the large bias range from 0.6 to 1.2 V. We give an interpretation using the alignment of the molecular orbital levels to the biased electrodes in the metal-molecule-metal junction. This highlights the fact that contact asymmetry is a significant factor to be considered when evaluating nanoelectrical junctions incorporating single molecules. 1. Introduction
{
D(Ex) ) exp -
Molecular-level rectification plays an important role in molecular electronics.1-4 The asymmetric feature of electron transport is sensitive to the structure of a molecular junction. Molecular bridges5 and interfaces6,7 are the most important factors determining the junction transportation. Since the first proposal by Aviram and Ratner5 that the asymmetric molecular bridge may function as a molecular rectifier, the study of the asymmetric substitution with electron-donating and electron-withdrawing groups has attracted increasing attention.8-12 This junction structure is the analogue of the semiconductor p-n junction, where the electron-donating group serves as the n-dope, and the electron-withdrawing group the p-dope. Unfortunately, more recent theoretical studies have failed to observe a discernible rectification in the A-R-type architecture,10-15 but single molecular rectification has been shown in several experiments.2,3,10,11,13,16,17 The failure has led to the proposition that the experimental observations of the unidirectional current in the A-R architecture is a result of asymmetric coupling between the molecule and the electrodes. Several theoretical regimes can be used for interpreting the lack of the asymmetric electron transportation in the A-R-type junction. Mujica et al. have analyzed the voltage profiles for forward and reverse biases of an extended molecular junction from the theoretical framework of Green’s function for the coherent electron tunneling and concluded that the junction can not rectify.18 The semiclassic theoretical model also strengthened the conclusion that the simple A-R molecule can not present a strong rectification. According to the analysis of electron tunneling across a molecule, the organic medium can be treated as a continuum barrier, as originally proposed by Simmons.19 The probability D(Ex) that an electron can penetrate a potential barrier of height V(x) is given by the well-known WKB approximation: * To whom correspondence should be addressed. E-mail: zhaojw@ nju.edu.cn.
4π h
∫ss [2m(V(x) - Ex)]1/2 dx} 1
2
(1)
where Ex ) mVx2/2 is the energy component of the incident electron in the x direction, and S1 and S2 denote the barrier length from S1 to S2 on the x axis. When a positive bias, V, is applied, the Fermi level of the left electrode reduces by V/2, and the right electrode increases by V/2. Conversely, a negative bias decreases the Fermi level of the right electrode, and increases that of the left. However, the mean potential barrier obtained from the integral between S1 and S2 is an even function and remains the same no matter whether under positive or negative bias, indicating that the simple A-R molecule will have no obvious rectification. Despite the lack of an applicable theoretical explanation, a lot of evidence has emerged suggesting that the molecular rectification may originate from the interface.6,19-24 This fact stimulates us to consider another type of semiconductor diode, the Schottky diode, which is formed from the contact between a metal and a semiconductor rather than by a p-n junction. In contrast to the sandwiched organic molecule, the metallic electrode is sufficiently large that it is appropriate to use the free electron gas model. In addition to the difference in size, the electrode and molecule are essentially different in nature, resulting in a unique molecule-electrode contact.7,20,21 The rectification of contact asymmetry has been demonstrated for molecules sandwiched in the metal-molecule-metal junctions in electrical junctions;22 for example, by controlling the nature of the metal-molecule connection and through the choice of the metal electrode materials and scale.23-25 In the metal-molecule connection studies, thiol featured one terminus of the molecule, whereas the other end employed the nitro,22 nonbonded,6,22 carboxylate,26 or isocyanide.27 The rectification was also reported for dithiocarbamate28 and dithiocarboxylate29 that have two thiols connected to one electrode while the other electrode remained connected to a thiol group or nitrogen atom. Furthermore, the rectification effect could also be achieved by adjusting the molecule-electrode length, as was suggested theoretically,30,31 but it is difficult to realize this kind of rectification in a controllable way. Thus, the molecular level elucidation of the
10.1021/jp905713a 2010 American Chemical Society Published on Web 02/10/2010
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Figure 1. Schematic illustration of the theoretical models and the device background. All the model molecules connect to two Au (111) surfaces via thiolate bonds.
interfacial electronic structure forms the basis for understanding and improving the performance of molecular devices.32 In this study, we propose a theoretical explanation for the interface rectification based on the asymmetrical electrodemolecular coupling that causes the unequal shift of the Fermi levels of the electrodes. This proposal can be seen as the analogue of the Schottky diode and has been verified by the molecular simulation. We focused on the first principles theoretical investigation of the transport behavior of the porphyrin with different interfacial anchors. The most popular anchoring group used to connect with the gold electrodes is still the thiol group.33-36 We have designed the interface with different numbers of thiols, as anchors shown in Figure 1. Due to the specific connection with two thiol groups, this side of the molecular junction may have a better electronic coupling to the electrode. Therefore, the alignment of the metallic Fermi level to the molecular orbital is stronger than the opposite side, which has only one thiol connection. Since the alignment of the metallic Fermi level to the molecular orbital directly reflects the electron transport barrier, we have obtained an asymmetric electron transport in this junction configuration. 2. Methodology 2.1. The Model Systems. Figure 1 shows the schematic models of the molecular junctions. All the models are based on the porphyrin ring with one thiol anchored to the electrode on the right hand, with different numbers of thiols connected to the electrode on the left. Model A has the symmetrical structure with one thiol on each side. Models B and C have two thiol groups anchored on the left, having one more charge injection route than model A. The two thiols in model B are adjacent; in model C, they are far apart. 2.2. Calculation Method. Before the transportation calculations, all model molecules were optimized primarily at B3LYP level with a LANL2DZ basis set by using the Gaussian03 software.37 On the basis of the results, each of them was then sandwiched between two triangle gold planes with a Au-Au bond length of 2.88 Å.10,11 The model molecules were set perpendicular to the Au plane, and each sulfur atom was chemisorbed in the local energy minimum, that is, the hollow site on the Au clusters.11,38-42 The relative positions of the Au atoms were frozen in each triangle cluster, but the distance between the two Au clusters was relaxed during the subsequent geometric optimization at the B3LYP level with a LANL2DZ basis set. The theoretical calculations of electron transport were carried out using the Atomistix Toolkit (ATK) software,43-46 which is
Zhao et al. based on first-principles DFT combined with the nonequilibrium Green’sfunction(NEGF)formalism.Thistheoreticalframework47,48 has been demonstrated to be highly reliable in predicting transportation properties,49,50 providing a powerful tool for exploring new molecular rectifiers. The ATK package is capable of modeling the electronic properties of nanostructured systems coupled to semiinfinite electrodes. The dynamic current calculation followed two main processes. (1) Structural relaxation: To simulate the molecular junction, each optimized molecule except the two Au clusters was translated into the Au junction with the Au(111) surface as a common treatment in the software. The Au(111) facet was simulated using a 4 × 4 cell with periodic boundary conditions, and the supercell consisted of two layers of Au atoms to the left and three layers to the right with 16 atoms for each layer in the scattering region. The molecule-electrode contact distance was initially set as 2.0 Å10,11,38 and then optimized. A double-ζ plus polarization basis set was used for all atoms in the organic molecule, and a single-ζ plus polarization basis set was used for gold atoms with a local density approximation in the calculation. All atoms were relaxed until the force on each was less than 0.1 eV/Å. (2) Electron transport between Au electrodes: On the basis of the results of the first process, a bias from -2.0 to 2.0 V was applied between the two metal leads, and the electric current was generated using the NEGF method. 3. Results and Discussion The original A-R-type molecular junction is based on the p-n analogue diode of the semiconductor. However, in this architecture, it is difficult for the electron-donating group to fully give an electron to the electron-withdrawing group; therefore, no depletion region can be formed in this junction. Many theoretical prediction12,15and experimental measurements16 have demonstrated that an A-R-type molecular junction cannot achieve obvious rectification. In the present study, we propose the interface coupling that is most likely the analogue of Schottky diodes. Schottky diodes are constructed from a metalto-semiconductor contact. They have different densities of state at both sides; therefore, the shifts of the Fermi levels are unequal under either forward or backward biases. At such a molecular level, the strong chemical bonds may fix the energy levels of a molecular orbital with respect to the Fermi level of the electrode. Therefore, the tunneling barrier might be different between the forward and backward baises. The theoretical work on molecular electronic devices focuses on either static or dynamic study. The first is concerned with the molecular geometric and electronic structures, from which we can predict junction properties, such as interfacial electronic coupling and thermal stability. The latter reveals the dynamic transport behavior by means of simulating the I-V curves and analyzing the transmission spectra of the junctions. Therefore, we first show the static molecular properties, such as the frontier molecular orbitals, the distributions of HOMO and LUMO, and the potential distribution. 3.1. Energy Levels and Spatial Distributions of the Frontier Molecular Orbitals. The shift of molecular orbitals with repect to the Fermi level is an important factor dominating the junction transportation.6,51,52 Figure 2 gives the energy levels of molecular orbitals, while the Fermi level of the gold electrode is set to be zero. From Figure 2a, we can see that both the HOMO and LUMO of model A drop down with the increase in bias. Models B and C have trends similar to model A, but HOMOs under the positive bias are higher than that under the negative bias, leading to an asymmetrical shift of the HOMO-LUMO gap (HLG).
Molecular Rectification
Figure 2. (a) HOMO and LUMO energy levels as functions of the applied bias and (b) the HOMO-LUMO gap evolution with the bias of the model junctions.
Figure 2b shows the HLG of the three models. Without the applied bias, the HLG values follow the order of model C (1.68 eV) > model A (1.61 eV) > model B (1.49 eV). After the application of bias, model A shows a symmetric variation with respect to the zero bias due to its symmetric structure. Despite the bias direction, HLG increases almost linearly. This variation appears to be opposite with other linear conjugated molecules, such as polyacene, which showed a decrease in the HLG with the bias.53 For model C, the HLG variation is not significant. The maximum variation is only 0.10 eV in the bias range concerned. On the contrary, the HLG value of model B is nearly constant at the negative bias from 0 to -1.4 V, but linearly decreases by 0.22 eV on the positive side. Since the barrier of electron transfer is approximately proportional to the HLG,54 model B might rectify. As demonstrated by us10,11 and others,55 the spatial distribution of the frontier molecular orbitals is a good indicator of molecular electron transfer, which not only qualitatively shows whether these orbitals form the transport channels but also describes the coupling between the molecule and the electrode. Figure 3 displays the spatial distribution of HOMO and LUMO at different biases. It can been seen that both the HOMO and LUMO of model A spread over the whole molecule, and they have no change in the concerned bias region. This feature is quite different from other linear conjugated molecular wires, such as polyacetylene, polythiophene, and tolane,56,57 in which HOMO moves to the low potential end and LUMO moves toward the high potential end with increasing bias. Although the LUMO of model B looks less sensitive to the bias, HOMO has some change at different bias that it is more delocalized at higher bias. Therefore, it may have some influence on the energy level distribution, as shown in Figure 2b. Model C displays
J. Phys. Chem. C, Vol. 114, No. 9, 2010 4137 significant change in the spatial distribution. The HOMO spreads over the conjugation ring in the bias region from -1.2 to 0.6 V. It then becomes localized on the thiol anchor at higer bias. Most of the LUMO is localized on the left half of porphyrin, but the right side gradually makes a contribution at high positive bias. In a word, a very small change in the frontier molecular orbitals are obtained for models B and C at high bias. The HOMO/LUMO frontier orbitals do not always provide the actual tendency of the electron flow,58 and the spatial distribution is very sensitive to the anchor groups; therefore, we have performed additional electronic calculations of the molecular orbital distribution for the Au-model-Au to elucidate the interfacial coupling effect (see Supporting Information). For models B and C, the orbitals tend to be localized on the one thiol anchoring (two-thiol anchoring) for HOMO (LUMO). Since the HOMO resonance forms the main electron transport channel, a strong coupling deduces the orbital spreading. In summary, due to the circular conjugation structure, the spatial distribution is very sensitive to the anchor groups, i.e., the electronic coupling to the electrode. A strong coupling may deduce the orbital spreading and therefore decrease the electron transfer probability. 3.2. Potential Distribution Analysis. To a certain extent, the electrostatic potential distribution at a plane above the molecular bridge reflects the potential drop across the junction. It may also give atomic-level information about the electron transfer barrier. We analyzed the potential distribution by calculating the contribution from each atomic Mulliken charge in the molecule superposed with the external electric field. Asymmetric electrode coupling may cause the asymmetric potential distribution along the molecular junction, as shown in Figure 4. Without application of bias, the four nitrogen atoms in model A are negatively charged (-0.147, -0.147, -0.338, and -0.338 e), whereas the two sulfurs are positively charged (0.138 and 0.136 e), and they play a major role in the potential distribution. Because of the symmetrical connection of the anchor groups, the potential gradient is also symmetric at positive and negative biases. But for models B and C, the potential gradient at zero bias shows asymmetric features. For model B, the adjacent sulfur atoms are negatively charged (-0.02 and -0.01e), whereas the sole sulfur on the right side has 0.145e. For model C, the two sulfur atoms on the left side are positively charged (0.125 and 0.210e), and the opposite lone sulfur also has a positive change of 0.191e. Obviously, these charged states make the potential gradient asymmetric in these two models. The application of bias greatly changes the potential distribution because of the superposition with the external electric field. For model A, the potential distribution is always symmetric at corresponding positive and negative biases; however, the potential gradient for models B and C is dependent on the bias direction. For example, at -1.0 V, the potential gradient is uniform for model B, but it becomes very steep at the left side at 1.0 V. Since the potential gradient may partially reflect the slope of the electron transfer barrier, this asymmetric feature indicates that models B and C may rectify. 3.3. Current-Voltage Curves. The above analysis of the static characteristics of the junctions infers an asymmetric transportation for models B and C. Then, we discuss the dynamic current-voltage (I-V) response.
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Figure 3. Spatial distribution of HOMO and LUMO of the model molecules under different biases.
Figure 4. Potential distribution above the model molecules at different biases.
The calculated current as a function of bias is presented in Figure 5a. Under the lower bias, the current increases almost linearly with the increase in bias, showing an Ohmic signature. However, the nonlinearity is found at the higher bias, especially for models B and C. The current in model A is larger than in the others, implying the electron transport in model A is more efficient. Figure 5b gives the differential conductance of the models. The differential conductance at zero bias follows the order of model A > model B > model C. In general, the differential conductance of model A rises dramatically when the bias ranges from 0 to +0.6 V and then decreases However, both models B and C show different trends under positive and negative bias. For model B at negative bias, the differential conductance rises first, then decreases sharply. This character is similar to model A, whereas for model C, the conductance rises all through the
negative bias investigated. The conductance of the positive bias has a similar tendency, but it is smaller than that under the negative high bias for models B and C. To fully evaluate the molecular rectification, we defined a rectification ratio as
R(V) )
|
I(+V) I(-V)
|
(2)
Figure 5c shows the dependence of R on the applied bias for the model molecules. Clearly, the R values of models B and C are over the unit 1 in the bias range. Furthermore, model B shows a rectification ratio of 2.6 at a wide range between 0.8 and 1.2 V. Since model B is more conductive under positive bias, the favored direction of electron transport is from the one-
Molecular Rectification
J. Phys. Chem. C, Vol. 114, No. 9, 2010 4139 The current through a single molecule that bridges two metal electrodes is given by the Landauer-Bu¨ttiker formula,48,59-61
I)
Figure 5. (a) The I-V curves of the model junctions, (b) the differential conductance of the model molecules under various bias, and (c) the rectification ratio as a function of the applied bias.
thiol electrode to the two-thiol electrode. In other words, the electron favors transport from the weak coupling side to the strong coupling side. Model C shows a similar rectification, but with a reduced R value of 1.6 at 1.0 V. The R value is below unit 1 at high bias because it may have deviated from practical research. We have compared the present results with the other molecular rectifiers in the revised manuscript. Stadler et al.15 used a first-principle method with nonequilibrium Green’s function approach to study the substitution effects in unimolecular rectifiers. The results show the rectification ratio is below 2. By using the same method, we have studied a donor-(πbridge)-acceptor molecule asymmetrically substituted by various functional groups and found very slight rectification.10 Therefore, the Schottky-like molecular diode might be promising.
2e h
∫µµ
L
R
dE (fR(E, Vb) - fL(E, Vb)) T(E, Vb)
(3)
where fR(E, Vb), and fL(E, Vb) are the Fermi-Dirac functions for the left and right electrodes at energy level E under the bias voltage, Vb; T(E, Vb) is the transmission coefficient, which is the function of the energy level E as well as bias; µL and µR are the chemical potentials of the left and right electrodes; and [µL(Vb), µR(Vb)] denotes the energy region that contributes to the current integral and is referred to as the bias window. The bias window is given by µL ) EF - eVb/2 and µR ) EF + eVb/ 2, and EF is the Fermi energy that can be set to zero. From the expression, it can be expected that only electrons with energies around the Fermi level contribute to the total current. Thus, only a finite range of transmission coefficient needs to be analyzed. Since the current is the integral of the transmission coefficient in the bias window, analysis of the transmission spectra may give us a clear understanding of the electron transport behavior. Figure 6 plots the transmission spectra of these junctions at different biases. There are two main peaks in the vicinity of the average electrode Fermi energy. Their heights and locations are different from each other. The first peak below the average electrode Fermi energy is the HOMO resonance, whereas above the average is the LUMO resonance. In the case of model A in Figure 6a, the HOMO is located in the bias window, whereas LUMO is out and contributes less to the current in this bias range. Furthermore, the HOMO shift is symmetric to zero bias; therefore, no rectification was observed in this junction. For models B and C in Figure 6b and c, the HOMO resonance also forms the main electron transport channel. The positive bias drives the HOMO transmission wave near the Fermi level and into the bias window. The integral of the transmission coefficient in the positive bias window is larger than that at the negative bias. Therefore, the clear rectification was observed for them. 3.4. Energy Band Diagram. On the basis of the results presented above, we propose a conceptual model, as shown in Figure 7. The molecular rectification of the porphyrin-based junction can be understood from the asymmetric shift of the Fermi level. Since two different interfaces are applied on each side, their electronic coupling strengths are also different: the more connections, the stronger the coupling. In particular, the electronic coupling at the left side is stronger than that at the right side for models B and C (Figure 7a). Now, we discuss the shift of the energy levels around the molecule-electrode interface. Although the strong coupling is established, the molecular level just at the surface should shift together with the Fermi level of the electrode when a bias is applied. Intuitively, the electrode and the molecular species at the surface can be viewed as a whole system due to the strong electronic coupling. Therefore, their Fermi levels are very much pinned together, as shown in Figure 7b. In contrast, the weak interfacial connection, like the single S-Au bond, also shows weak electronic coupling. Then the Fermi level shift of the metal electrode can not bring the molecular energy level along at this side. Therefore, the barrier height, that is, the relative distance between the molecular LUMO and the Fermi level of the right side of the junction, is reduced due to the positive bias applied. When we apply a negative bias, the Fermi level of the left electrode rises, whereas it decreases for the right electrode. We can then find that the barrier height is almost constant, if we
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Zhao et al. positive or negative biases. As a result, we may observe the asymmetric transport behavior caused by the interfacial coupling. 4. Conclusion In conclusion, we have designed contact-asymmetrical junctions based on the porphyrin molecule and have investigated the transport behavior using DFT combined with the NEGF formalism. The contact-asymmetrical porphyrins resulted in asymmetric electron transport when the bias in different directions was applied. It is possible to introduce the asymmetry into the molecular junction so that asymmetric electronic transportation can be achieved. We show the rectification ratio is close to 2.6 and can be maintained in a large bias range from 0.6 to 1.2 V. The preferential direction for the current is from two-thiol anchoring to the one-thiol anchoring side. Acknowledgment. This work was supported by the National Natural Science Foundation of China (NSFC) (20821063 and 20873063) and the National Basic Research Program of China (973 Program, 2007CB936302 and 2010CB732400). Supporting Information Available: Transmission spectra for the model molecules, PDOS for the model molecules, spatial distributions of the frontier molecular orbitals connected with the Au clusters, and I-V curves and the rectification ratio as a function of the applied bias. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes
Figure 6. Transmission spectra for models (a) A, (b) B, and (c) C.
Figure 7. Schematic energy level diagrams for models B and C: (a) energy levels without applied bias, (b) energy levels under positive bias, and (c) energy levels under negative bias. EFL and EFR represent the left and right Fermi levels of the metal electrodes, respectively. φ represents the energy barrier needed to align the Fermi level of the electrode with HOMO under the positive or the negative bias.
assume a very strong coupling at the left side of the junction. Therefore, the barrier height depends on whether we apply
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