Enormously Enhanced Rectifying Performances by Modification of

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Enormously Enhanced Rectifying Performances by Modification of Carbon Chains for D−σ−A Molecular Devices C. Guo, Z. H. Zhang,* G. Kwong, J. B. Pan, X. Q. Deng, and J. J. Zhang Institute of Nanomaterial & Nanostructure, Changsha University of Science and Technology, Changsha 410114, China ABSTRACT: By using the carbon chain as the end group attached to either the left or right side or both sides of the D−σ−A molecule, we investigate theoretically its rectifying performance. Interestingly, the currently reported highest rectification ratio, 408, with the density functional calculations for a unimolecule device with metal electrodes can be obtained when both carbon chains are symmetrically attached to both sides of the D−σ−A molecule. Our finding implies that to greatly promote rectifying characteristics of the D−σ−A molecule the suitable end-group engineering might be a key issue, and increasing geometrical asymmetries of a molecule may not be the only effective way. insulating groups.13 So far, such a rectification mechanism has been investigated extensively.17−19 Nevertheless, two crucial issues naturally arise: (1) an insulating end group is very resistive, and its larger length would lead to current unobservable small rectifying efficiency and make a molecular rectifier application unpractical; thus its rectification ratio is severely limited; and (2) whether increasing the geometrical asymmetry of a molecule is a necessary condition for improving a rectifying efficiency. The other structures for a unimolecule rectification have also been explored deeply in the past years. For example, Stadler et al.1,2 devoted their study to the molecular rectification based on systems1 where the donor and acceptor parts of the molecules are taken from charge-transfer salt components, zwitterionic systems, tour wires with nitro substituents, and systems2 where the carboxylic group acts as a bridge between the acceptor and donor segments. They particularly emphasized the mechanism analysis for recification. More recently, few works have also touched on rectifying behaviors of a functionalized graphene, such as rectifications upon a heterostructure of graphene20,21 and in N doping a graphene nanoribbon device.22 However, how to greatly enhance the rectification ratio of molecular nanorectifiers still needs to be addressed intensively because the rectification ratio is a crucial parameter for the technical usefulness. In our previous work,15,16 we predicted theoretically that donor−acceptor molecules have a strikingly inverse rectification, disagreeing completely with the classic prediction by Aviram and Ratner,7 due to an always-existing asymmetrical coupling of molecular orbitals to both electrodes, which has recently been confirmed experimentally by Yee et al.23 In this

1. INTRODUCTION Molecular nanostructures have been investigated actively in last few decades due to their promising potential for developing molecular devices.1−6 One of the most important molecular devices is the molecular rectifier. The concept of a modern molecular rectifier, the so-called A−R diode, was proposed first by Aviram and Ratner in 1974.7 Such a unimolecule with a unique donor (D)−σ bridge−acceptor (A) structure is the analogue of the semiconductor p−n junction. The study on this architecture has attracted increasing attention.8−16 Unfortunately, the rectification efficiency of the original A−R diode is generally extremely low. For example, Stokbro et al.9demonsdemonstrated theoretically that the simple A−R molecule has only negligible rectifying, and Staykov et al.10 presented that the conductance ratio 7 could be obtained for the donor−π bridge−acceptor system. Therefore, how to enhance the rectification efficiency of the A−R molecule has been a focus of study in molecular electronics. Metzger et al.11 experimentally presented the results of a better rectifying behavior for an A−R molecular junction formed from a Langmuir−Blodgett multi- or monolayer of C16H33Q−3CNQ. However, Krzeminski et al.12confirmed theoretically that the C16H33 tail plays an important role in such a junction due to the asymmetrical electrostatic potential profile across the system. Thus, it seems to be likely for the increasing geometrical asymmetry of a molecule to promote a rectifying behavior. This idea was further verified by Kornilovitch et al.13 through tight-binding calculations for molecular rectifiers HS−(CH2)m−C6H4−(CH2)n−SH, and a rectification ratio as high as 500 was achieved (this value was downscaled to 35 when cross-checked with DFT (density functional theory) calculations by the same group14). It was concluded that for creating a significant asymmetrical potential profile for achieving a large rectification ratio the active part of the molecule must be connected to electrodes by asymmetrical © 2012 American Chemical Society

Received: March 8, 2012 Revised: May 22, 2012 Published: May 23, 2012 12900

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until all residual forces on each atom are smaller than 0.05 eV/ Å. The electronic transport calculations for our two-probe systems are performed using the density functional theory (DFT) combined with the nonequilibrium Green’s function (NEGF) method as implemented in the latest version of Atomistix ToolKit (ATK).35−40 For a given Hamiltonian matrix H in the device region, overlap matrix S, and left and right electrode self-energies ΣL,R with corresponding broadening functions ΓL,R = i(∑L,R − Γ+L,R), the energy levels are given by the poles of the Green’s function G

present paper, we further enhance and extend our work to consider how to promote rectifying behaviors for donor− acceptor molecules. As is well-known, a linearly monatomic carbon chain is an important chemical structure. After a linear chain containing up to 20 carbon atoms connected to metal atoms at its two ends had been synthesized,24 various carbon chains with different lengths were subsequently observed in different experiments as well.25−27 So far, there have also been extensively theoretical investigations on carbon chains with the saturated cumulene or polyyne bond pattern, and it has been found that they have unique electronic structures.28−34 Here, we consider using a carbon chain to attach to the D−σ−A molecule. It should be possible to boost rectifying efficiency because exceptional electronics characteristics of a carbon chain might greatly modify the electronic structure of such a molecule. Indeed, the currently reported highest rectification ratio, 408, with our DFT calculations for a unimolecule with metal electrodes can be predicted when both carbon chains C7 are symmetrically attached to both sides of the D−σ−A molecule. Our findings highlight that increasing the geometrical asymmetry of a molecule may not be the only effective way to enhance a rectification behavior, and the suitable end-group engineering might be more important for greatly promoting rectifying characteristics.

G(E) = (E +S − H − Σ L − Σ R )−1

(1)

where E = E + iη. In the DFT, the density matrix ρ plays a crucial role, which can be calculated by +

∞

ρ = (1/2π )

∫−∞ dE(fL GΓLG+ + fR GΓRG+)

(2)

where f L,R is the Fermi function for left and right electrodes. Using the density matrix ρ, the Hamiltonian matrix H in eq 1 can be determined. Self-consistent calculations are conducted until convergence, and the current through a molecular junction as a function of the applied external bias can be obtained by the Landauer-like formula41

2. MODEL AND METHOD The molecular rectifiers under study, as illustrated schematically in Figure 1, are formed by the D−σ−A molecule adsorbing

I = (2e/h)

∫μ

μL R

dET (E , V )[fL (E) − fR (E)]

(3)

where the transmission T is given by T(E,V) = trace(ΓLGΓRG+). For computing the Hamiltonian matrix H in the DFT, we employ Troullier−Martins norm-conserving pseudopotentials to represent the atom core and linear combinations of local atomic orbitals to expand the valence states of electrons. The Perdew-Burke-Ernzerhof (PBE) formulation of the generalized gradient approximation (GGA) is used as the exchangecorrelation functional. The single-ζ plus polarization (SZP) basis set for Au and H atoms and double-ζ plus polarization (DZP) basis set for other atoms are adopted.

3. RESULTS AND DISCUSSION In Figure 2, we present the I−V characteristics for all four models. The currents in M1 and M3 sustain small values in the

Figure 1. Structures of molecular devices in our simulation.

onto two semi-infinite 3 × 3 Au electrode surfaces through different end groups. The phenylamine and the nitrobenzene serve as electron-donor (D) and electron-acceptor (A) moieties, respectively, and they are connected via an insulating alkane (ethane). Systems only with thiol anchoring groups or with the carbon chain C7 attached on the left side, right side, and both sides of the D−σ−A molecule via thiol−Au contact to electrodes are referred to as models M1 or M2, M3, and M4, respectively. Model M1 is the simplest original A−R diode model. The purpose of forming four such different devices is to demonstrate carbon-chain-modified effects on rectifying. To construct these molecular devices, each optimized molecular core by a separate calculation based on DFT is positioned between two Au(111) electrodes and is initially chosen to sit upright on the Au surface, where S atoms locate at the hollow site of the Au triangle with a typical Au−S distance of 2.45 Å. Each model is composed of the left electrode, the scattering region (the device region), and the right electrode. The scattering region contains three layers of Au surfaces (27 atoms) on each side of molecule. Its geometries are optimized

Figure 2. I−V curves for all models. The I−V curve for M4 shows a highly asymmetric characteristic.

low bias region and increase slowly at high bias. For M2, the current rises rapidly under very small bias and then drops dramatically in the 0.4−0.8 V region under positive bias, and almost similar changes in current can been seen under reverse bias. Very interestingly, the I−V curve for M4 shows a highly asymmetric characteristic: the current rises rapidly from 0.6 to 1.0 V under positive bias and is almost quenched to zero in the 12901

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whole region of negative bias, which is very analogous to the I− V curve for a traditional diode, and thus a rather large rectification ratio can be expected. Figure 3 shows the rectification ratio which is defined as R(V) = I(V)/|I(−V)|. Obviously, M4 presents the best

region (the nitrobenzene), respectively, for M3 and at the same region (left carbon chain) for M4. Therefore, different rectifying behaviors, especially for a low bias, in various models can be expected due to different spatial distributions of molecular states.42−44 We plot transmission spectra of all models at various biases in steps of 0.2 V, as shown in Figure 4, where the Fermi level is set to zero. For M1(M3), the tunneling peak(s) always stays inside (run into) the bias window (BW) (beyond a certain bias) under positive bias and stays outside the BW under negative bias, thus a forward rectification occurs. For M2, the tunneling peak is involved in the BW under lower and higher positive bias and at the moderate and high negative bias, leading thus to a reverse rectification in the region of a medium-sized bias. M4 is special because the tunneling peak shifts into the BW after exceeding around 0.4 V under positive bias and moves far away from the BW under negative bias, and a large forward rectification therefore shows up. Here, modified effects on electronic structures by two carbon chains can be clearly observed. It is worth noting that Table 1 is only related to zero-bias molecular states. When the bias is applied, a system is driven out of the equilibrium, and molecular levels should shift due to complicated reasons, such as the enhancement of molecular polarization and variations of the electrode potential, potential drop profile in the whole device region, and the bias-dependent coupling strength between a molecule and electrodes. Therefore, we give an evolution of the molecular orbitals (MOs) with applied bias for all models, as shown in Figure 5. For simplicity, only MOs in the proximity of the Fermi level are displayed, which can enter into or go close to the BW. The HOMO (LUMO) is defined as the level with a lower (higher) energy position than the Fermi level at zero bias. As is well-known, the MO provides the transmission channel for electronic transport, and the delocalized degree of its spatial distribution directly determines the size of the transmission peaks. In Figure 5, the MOs denoted by lines with open circle symbols, namely, the HOMO for M1, the LUMO+1 for M2, the LUMO+1 and LUMO for M3, and the LUMO+1 and HOMO−1 for M4, feature a higher delocalization as compared with other MOs which tend to be much more localized, which can be clearly identified just looking at the MPSH states plotted as upper and lower panels for each MO in each model. Highly delocalized MOs should make a large contribution to the electronic tunneling through a molecule and thus result in obvious transmission peaks at a transmission spectrum curve, while for those highly localized MOs their tunneling ability is strongly suppressed so that no or relatively small transmission peaks pop up in the transmission spectrum curves. Obviously, all of these are in agreement with those observed in Figure 4 for transmission spectra. To understand the rectifying performance with more details, the device density of states (DOS) and the projected density of states (PDOS) are calculated, as depicted in Figure 6, for all models at zero bias and several typical nonzero biases, corresponding to maximum values of rectification ratios. For narrative convenience, PDOS here is the density of states projected on three parts: sulfur and carbon-chain C7, molecular core (D−σ−A molecule), and the screening layers. They are obtained by summing their individual orbital PDOS contributions for each atom in the respective part. The orbital PDOS here is the density of states projected on the ith atomic basis orbital |χi⟩, namely, PDOS = ∑nkRe[ci*(Enk)⟨χi|ψ(Enk)⟩]δ(E −

Figure 3. Rectification ratios change with bias for all models.

rectifying effect as compared with models M1, M2, and M3, in which maximum values of rectification ratios are 2.49, 3.69, and 4.44, respectively, and are far less than that for M4, 408, which is a currently reported highest rectification ratio with DFT calculations for a unimolecule device with metal electrodes and 170 times higher than M1, an original A−R diode. Other merits for M4 are its lower threshold bias, larger forward current, and wider bias range for rectification. Such a result for M1 is basically similar to previous investigations for the A−R diode.9,10,15,16 Interestingly, though M4 has much higher symmetric characteristics than M2 and M3, the highest rectification ratio is obtained. Therefore, it is reasonable to conclude that increasing geometrical asymmetry of a molecule may not be a necessary condition to promote rectifying performance. Table 1 illustrates the spatial distribution of the molecular projected self-consistent Hamiltonian eigenstates (MPSH)16 Table 1. Spatial Distribution of Molecular States for All Models at Zero Bias

for the HOMO and LUMO levels at zero bias, which gives a visual description of the electronic structure. For M1 and M2, the HOMO (LUMO) state is localized at the left (right) area of the molecular device. However, M3 and M4 are significantly different because the HOMO and LUMO states locate at the right region (right carbon chain) and almost entirely middle 12902

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Figure 4. Transmission spectra of all models at various biases in steps of 0.2 V. The middle region of both red dotted lines denotes the bias window (BW). The blue transmission spectrum curve corresponds to the bias for a maximum value of rectification ratio.

Figure 5. Evolution of the molecular orbitals (MOs) with applied bias for all models. The MOs denoted by lines with open circle symbols feature a higher delocalization. The MPSH states are plotted as upper and lower panels for each MO at certain biases.

Enk), where |ψ(E)⟩ is a wave function for the device scattering state and could be presented as a linear combination of the pseudoatomic basis orbitals |χi⟩, |ψ⟩ = ∑ici|χi. Enk are energies of incident states of electrodes. At positive and negative biases, the DOS or PDOS in each part for M1 has a very small difference except a little separation of the peak positions. M2 or M3 is similar to M1 except that a higher DOS peak with a negative energy near the Fermi level appears at negative bias; however, it

originates from the screening layers, not from the sulfur and carbon chain C7 and molecular core, thus there is no contribution to the electronic tunneling through a molecule. In other words, a weak rectification in M1, M2, and M3 can be expected. Nevertheless, M4 is entirely different; the PDOS peaks on the sulfur and carbon chain C7 and molecular core at positive bias can line up to form a large DOS peak at positive energy position near the Fermi level, which can greatly facilitate 12903

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Figure 6. Device DOS, PDOS, or all models at zero bias and several typical nonzero biases.

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the electronic tunneling. As a result, it has a best forward rectification. Such a large DOS peak can be explained by the hybridization behaviors of the sulfur and carbon chain C7 and molecular core states, as stated in ref 3; namely, the levels corresponding the PDOS peaks at positive energy position near the Fermi level for both the sulfur and carbon chain C7 and molecular core are hybridized due to the interaction of molecular components to form a degenerate level with the same energy position for the whole molecule.

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4. CONCLUSIONS Applying the first-principles calculations, we obtain a rectification ratio as high as 408 with a lower threshold bias, larger forward current, and wider bias range for rectification when carbon chains C7 are symmetrically attached to both sides of the D−σ−A molecule. This is an interesting result. Such a high rectification ratio originates from its unique electronic structures and transmission features. Our finding implies that to greatly promote rectifying characteristics of the D-σ-A molecule the suitable end-group engineering might be a key issue, and increasing geometrical asymmetrics of a molecule may not be the only effective way.

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*Tel./Fax: +86073185040376. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (Grant Nos. 61071015 and 61101009), the Hunan Provincial Innovation Foundation for Postgraduate (Grant No. CX2011B367), and the Construct Program of the Key Discipline in Hunan Province 12904

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