A New Approach to the Realization and Control of Negative

Department of Physics, Simon Fraser University, Burnaby, British Columbia, .... states for the Pd/AT4/Rh molecular junction are plotted vs bias voltag...
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NANO LETTERS

A New Approach to the Realization and Control of Negative Differential Resistance in Single-Molecule Nanoelectronic Devices: Designer Transition Metal−Thiol Interface States

2006 Vol. 6, No. 6 1274-1278

Hugh Dalgleish* and George Kirczenow Department of Physics, Simon Fraser UniVersity, Burnaby, British Columbia, Canada V5A 1S6 Received January 8, 2006

ABSTRACT On the basis of ab initio and semiempirical calculations, we predict single alkane dithiolate molecules bridging transition metal nanoelectrodes (including Pd/Rh, Pt/Rh, and Pt/Pt) to exhibit negative differential resistance (NDR). The mechanism is resonant conduction via interface states arising from hybridization between molecular thiol groups and transition metal d orbitals. We show how the NDR realized in this new way can be controlled by tailoring interface state properties through appropriate choice of nanoelectrode transition metals and surface structures.

Negative differential resistance (NDR) is a decrease in current occurring in response to an increase in the bias voltage applied across an electronic circuit element. It has important device applications including high-frequency oscillators,1 analog-to-digital converters,2 and logic.3 Recent experimental observations of NDR in nanoscale molecular junctions in which a molecular monolayer connects a pair of metal electrodes4-8 have raised the exciting prospect that the ultimate nanoelectronic technology may be based on single-molecule devices exhibiting NDR. A number of possible explanations of NDR in molecular junctions have been proposed4-20 including: current-induced charging or conformational changes in the molecules,4,6,8-13 metal filaments,15 or impurities16,17 within the molecular layer, bond fluctuation,7 vibronic mediation,18,19 and polaron formation.20 However the proposed mechanisms are controversial, and the NDR has been difficult, at best, to control experimentally. In this Letter we present calculations of electron transport through nanoscale molecular junctions where a single thiolated organic molecule bridges a pair of transition metal nanocontacts. We predict that for appropriate choices of the transition metals these systems should exhibit pronounced NDR, even for such simple bridging molecules as alkane dithiols. This prediction is far from obvious a priori since, due to their large HOMO-LUMO gaps, alkane dithiols are insulators and thus for simple metal contacts such as gold they display featureless, monotonic current-voltage char* Corresponding author. Email: [email protected]. 10.1021/nl060040m CCC: $33.50 Published on Web 05/04/2006

© 2006 American Chemical Society

acteristics. The new NDR mechanism that we propose differs from those studied previously in that here the NDR is due to electronic states at the transition metal/molecule interfaces that arise from the strong chemical bonding between molecular thiol end groups and transition metal d orbitals. Because these interface states are located mainly within the transition metal contacts and have strong transition metal d orbital character, their physics is relatively simple (the complex and poorly understood atomic or molecular rearrangements and/or molecular charging effects that are thought to give rise to hysteresis as well as NDR in other molecular systems are not involved here) and thus it is reasonable to expect theoretical predictions of their properties and associated NDR to be inherently more reliable. For example, because of their predominantly transition metal d-orbital nature, the crucial interface states have energies pinned to the vicinities of maxima of the transition metal d-orbital densities of states. Also, because the interface states are located mainly within the metal contacts, their energies track the electrochemical potentials of the metal electrodes as the bias applied across the junction is varied. As we demonstrate below, this simple bias dependence of the energies of the states that are responsible for the NDR, together with the strong dependence of the interface state energies on the d-orbital electronic structure of the contacts (that depends strongly on which particular transition metals are used for the contacts), makes it feasible for the first time to design the nonlinear current-voltage characteristics (NDR) of single

molecule nanoelectronic devices by appropriate choice of the specific transition metals used for the contacts and their crystallographic orientations. In the remainder of this paper we show how the above principles apply to some specific systems: We consider a single butyl dithiolate (4-alkane dithiolate, hereafter denoted AT4) molecule bridging the gap between palladium and rhodium (Pd/AT4/Rh), platinum and rhodium (Pt/AT4/Rh), and platinum and platinum (Pt/AT4/Pt) nanocontacts. We predict NDR in all of these systems,21 and we explain how the pronounced differences between the NDR characteristics of the three systems arise from the different electronic structures of the metal contacts. Thus we demonstrate how the NDR of single-molecule nanoelectronic devices can be tailored by appropriate choice of transition metal contacts. For a detailed discussion of our theoretical approach, we refer the reader to refs 22 and 23; a brief summary now follows: The metal-thiol bonding geometries of the systems that we consider were calculated by means of ab initio relaxations within density functional theory.24 The electronic structures of the metal/molecule/metal junctions were calculated using tight-binding models based on the results of ab initio calculations as well semiempirical considerations from quantum chemistry: The tight binding parameters for the transition metal contacts were obtained from ab initio calculations.25 Those describing the molecule and metalmolecule coupling were based and on the semiempirical extended-Hu¨ckel tight-binding model, optimized for the specific system being studied.26 Ab initio calculations have shown28 that well chosen models for the electrostatic potential profiles that develop in metal/molecule/metal junctions under applied bias can yield accurate calculated results for the current. We adopted this approach here,29 assuming the majority of the applied bias to drop over the metal-molecule interfaces.28,30,31 However, we found our results not to depend qualitatively on the details of the model potential profile. We use standard Lippmann-Schwinger and Green’s function techniques, and Landauer transport theory32 to calculate the current-voltage characteristics of the metal/molecule/metal junctions with the above electronic structures. Similar models have successfully explained experimental current-voltage characteristics of molecules connecting gold electrodes33-35 and of molecular wires between silicon and tungsten contacts.36 Theoretical studies have suggested that they can also provide an adequate description of nanostructures involving other transition metals, including Fe atomic contacts,22 Fe/molecule/Fe junctions,23 and Pt atomic contacts.37 Figure 1a shows the calculated electron transmission probability at zero bias through a Pd/AT4/Rh molecular junction. The inset shows the “extended molecule” consisting of the AT4 molecule and adjacent clusters of Pd and Rh atoms38 to which arrays of ideal leads representing source and drain electron reservoirs are coupled in our transport calculation. Here the Pd and Rh contacts both have a (111) crystallographic orientation and the molecular thiol groups are bonded over hexagonal close packed (hcp) type hollow sites. Nano Lett., Vol. 6, No. 6, 2006

Figure 1. Transmission probabilities, T(E,V), for different bias applied across the Pd/AT4/Rh molecular junction. (a) Transmission probability vs energy at zero bias. Fermi energy ) 0 eV. The Pd/ AT4/Rh extended molecule is shown in the inset. (b) Interface state on the Pd source electrode corresponding to the transmission resonance below the Fermi energy in Figure 1a. Only three Pd atoms and three Rh atoms are shown. (c) Interface state on the Rh drain electrode. (d) Transmission probability at 0.6 V bias. (e) 1.3 V. (f) 1.8 V. The labels Pd and Rh in (b), (c), (d), and (f) indicate the electrodes at which the labeled interface state resonances originate. Note the changes of scale between (e) and (d) and (f).

The molecular HOMO (highest occupied molecular orbital) gives rise to the broad transmission peaks 1-2 eV below the Fermi energy (EF ) 0 eV) in Figure 1a; the lowest unoccupied molecular orbital (LUMO) lies outside the plotted energy range due to the large molecular HOMO-LUMO gap of AT4. More important, however, as they determine the current at lower bias, are resonant states within the HOMO-LUMO gap arising from strong hybridization between the molecular sulfur and metal d-electron orbitals. In Figure 1a these states give rise to the sharp transmission features peaked near 0.4 eV below and 0.8 eV above the Fermi energy. A representative molecular orbital (shown only on the molecule and a few surrounding metal atoms) for a state with energy within the sharp transmission peak below 1275

the Fermi energy is displayed in Figure 1b. This electronic state is clearly an interface state, being located mainly on the Pd (left) electrode (85%) and extending onto the sulfur atom (10%) bonded to it; its amplitude on the rest of the molecule and on the Rh contact is small. Figure 1c shows a representative state with energy in the range of the transmission peak aboVe the Fermi energy. This is also clearly an interface state, but located mainly on the Rh (right) electrode (70%) and adjacent sulfur atom (10%). These interface states allow electrons to transmit efficiently between the metal and molecule and thus mediate moderately strong resonant electron transmission through the molecular junction. We now consider electron transport through this junction under applied bias with the Rh contact at a positiVe electrostatic potential relative to the Pd, i.e., with the net electron flux in the direction from the Pd electron source to the Rh drain electrode.39 As the magnitude of the bias increases, the electrostatic potential energy of electrons on the Rh electrode decreases while that of electrons on the Pd electrode increases. Therefore, since the interface state responsible for the transmission resonance that is above the Fermi level in Figure 1a is located predominantly at the Rh electrode (Figure 1c), the energy of that resonance decreases with increasing bias. Similarly the energy of the interface state transmission resonance that is below the Fermi level in Figure 1a increases with increasing bias because that state is located at the Pd electrode (Figure 1b). Thus with increasing bias the two interface state transmission resonances move closer together in energy. At an applied bias of 0.6 V (Figure 1d), their separation has been reduced to approximately 0.6 eV. At a bias of 1.3 V (Figure 1e) the two resonances merge and the resonant transmission is greatly enhanced because the interface states at the two contacts have become degenerate and thus the resonantly transmitting state has strong contributions at both of the metal-molecule interfaces, as is seen in the inset of Figure 1e. (Note the change in vertical scale between parts d and e of Figure 1.) At still higher bias the energy of the interface state on the Pd electrode continues to rise while that on the Rh electrode continues to fall. Thus transmission resonances associated with the two interface states separate and weaken as shown for a bias of 1.8 V in Figure 1f. (Note again the change of scale.) The electric current I passing through through the molecular junction is related to the transmission T discussed above by the Landauer expression32 I(V) )

2e h

∫ dE T(E,V)[f(E,µS) - f (E,µD)]

(1)

where T(E,V) is the electron transmission probability through the junction at bias voltage V and electron energy E, f(E,µ) is the equilibrium Fermi distribution, and µS,D ) EF ( eV/2 represents the electrochemical potentials of the source (S) and drain (D) electrodes in terms of the common Fermi energy, EF. The energies of the interface states for the Pd/AT4/Rh molecular junction are plotted vs bias voltage in Figure 2a, 1276

Figure 2. Energies of interface states (solid lines) and electrode electrochemical potentials (dashed) labeled according to the respective electrode vs bias applied across some metal/molecule/metal junctions. (a) The same Pd/AT4/Rh system as in Figures 1 and 3a. (b) Pt/AT4/Pt junction. S(D) stands for the electron source (drain) electrode.

together with the electrochemical potentials µS,D of the two contacts. It can be seen that the energies of the interface states track the electrochemical potentials of their respective contacts. As the Pd and Rh interface state transmission resonances approach and enter the energy window between the electrochemical potentials of the contacts (near V ) 0.4 and 0.9 V, respectively, in Figure 2a), they contribute increasingly to the integral in eq 1 and hence to the current I through the Pd/AT4/Rh junction, which is plotted in Figure 3a. The strongly enhanced transmission T (seen in Figure 1e) that results from the crossing of the interface state energies at bias V ∼ 1.3 V gives rise to further enhancement of the current through the junction near this value of the bias. Indeed, as is seen in Figure 3a, this enhanced transmission results in a peak in the calculated current through the Pd/AT4/Rh molecular junction at a bias of 1.3 V. The decrease in current with increasing voltage (i.e., negative differential resistance or NDR) seen above 1.3 V in Figure 3a is due to the overall weakening of the resonant transmission T as the energies of the transmitting interface states separate with further increase of the bias, as can be seen in Figure 1f. It is reasonable to expect our qualitatiVe prediction that NDR should occur in the Pd/AT4/Rh system to be model independent for the following reasons: The Pd electrode has its d-orbital density of states maxima below the zero bias Fermi energy (both surface and bulk DOS are relevant), while the Rh electrode has its d-orbital density of states maxima aboVe the Fermi energy.25 Since the interface states are located primarily in the contacts and have transition metal d-orbital character there, their energies are pinned to the maxima of the Rh and Pd d-orbital densities of states. Nano Lett., Vol. 6, No. 6, 2006

Figure 3. Calculated current-voltage characteristics displaying negative differential resistance. Metal contacts have the (111) orientation. (a) The same Pd/AT4/Rh molecular junction with hollow hcp site bonding as in Figures 1 and 2a. Pronounced NDR is visible above 1.3 V. (b) Pd/AT4/Rh junction with fcc site bonding. (c) Pt/AT4/Rh junction with hcp site bonding. (d) Pt/AT4/ Pt junction with hcp site bonding.

Therefore the strong difference between the d-electronic structures of Rh and Pd must result in the interface states on the Rh and Pd electrodes occurring at well-separated energies at zero bias. Furthermore since these interface states are each confined mainly to one electrode as in parts b and c of Figure 1, when a bias is applied across the junction, the energies of these interface states must follow the electrochemical potentials of their respective electrodes. Therefore if the bias is increased sufficiently (with the appropriate sign) the interface state energies must cross resulting in enhancement followed by weakening of the transmission and hence NDR.40 These qualitative considerations should hold for any realistic model of this system, and therefore our prediction that NDR should occur in this system is expected to be robust. Consistent with this, our calculations also predict Pd/AT4/ Rh molecular junctions with thiol groups bonded over hollow face-centered cubic (fcc) Pd and Rh sites to exhibit NDR as is shown in Figure 3b, although in this geometry the currentvoltage characteristic differs quantitatively from that for hcp site bonding (Figure 3a). In addition to the above bonding geometries for (111) oriented contacts, we have carried out calculations for Pd/AT4/Rh with (100) oriented Pd and Rh electrodes and also found NDR, whose onset is, however, at a lower bias (∼0.9 V). This indicates that NDR in such devices can be tailored by choosing the crystallographic Nano Lett., Vol. 6, No. 6, 2006

orientations of the transition metal contacts. The NDR can also be tailored by choosing different transition metals for the contacts, for example, our calculations predict that if the Pd electrode is replaced with Pt the onset of NDR occurs at higher bias ∼1.7 V, as in Figure 3c. We also predict NDR due to interface states to occur in some cases if the same transtion metal is used for both contacts, as shown in Figure 3d where a weaker NDR is visible beginning already at a bias ∼0.7 V for a Pt/AT4/Pt junction.42 In this case at zero bias the interface states on the two contacts have the same energy because the contacts are identical. Because of this the crossing of the energies of the interface states (and the resonant enhancement of the transmission associated with this) occurs at zero bias (see Figure 2b). Thus the amplitudes of the transmission peaks associated with the interface states decrease with increasing bias. However, the current through the molecular junction increases with bias at low bias in Figure 3d because (as shown in Figure 2b) the transmission peak due to the interface state on the source (S) electrode is approaching the energy window between the source and drain electrochemical potentials (µS,D) in which (according to eq 1) electron transmission contributes the most effectively to the current. Once the source interface state resonance has fully entered this window, the current begins to decrease due to the decreasing amplitude of the resonance with increasing bias mentioned above. This results in the NDR visible in Figure 3d. As the bias increases further, the current begins to increase again because of the increasing width of the window between µS and µD and the decreasing importance of the interface state transmission resonance relative to the background transmission due to nonresonant tunneling through the AT4 molecule. In Summary. We predict that single molecules thiolbonded between transition metal contacts should exhibit negative differential resistance due to resonant transport mediated by interface states that result from hybridization between the molecular sulfur p orbitals and transition metal d orbitals. We find the current-voltage characteristics, including the strength of the NDR and the range of bias voltage in which it occurs, to depend strongly on both the specific transition metals used as electrodes and their crystallographic orientations. These findings raise the prospect of tailoring the NDR of single-molecule junctions for nanoelectronic device applications by appropriate choice of transition metal electrodes and their surface structures. Acknowledgment. This work was supported by NSERC and the Canadian Institute for Advanced Research. References (1) Brown, E. R.; So¨derstro¨m, J. R.; Parker, C. D.; Mahoney, L. J.; Molvar, K. M.; McGill, T. C. Appl. Phys. Lett. 1991, 58, 22912293. (2) Broekaert, T. P. E.; Brar, B.; van der Wagt, J. P. A.; Seabaugh, A. C.; Morris, F. J.; Moise, T. S.; Beam, E. A., III; Frazier, G. A. IEEE J. Solid State Circuits 1998, 33, 1342-1349. (3) Mathews, R. H.; Sage, J. P.; Sollner, T. C. L. G.; Calawa, S. D.; Chen, C.-L.; Mahoney, L. J.; Maki, P. A.; Molvar, K. M. Proc. IEEE 1999, 87, 596-605. 1277

(4) Chen, J.; Reed, M. A.; Rawlett, A. M.; Tour, J. M. Science 1999, 286, 1550-1552. Chen, J.; Wang, W.; Reed, M. A.; Rawlett, A. M.; Price, D. W.; Tour, J. M. Appl. Phys. Lett. 2000, 77, 12241226. (5) Xue, Y.; Datta, S.; Hong, S.; Reifenberger, R.; Henderson, J. I.; Kubiak, C. K. Phys. ReV. B 1999, 59, R7852-R7855. (6) Rawlett, A. M.; Hopson, T. J.; Nagahara, L. A.; Tsui, R. K.; Ramachandran, G. K.; Lindsay, S. M. Appl. Phys. Lett. 2002, 81, 3043-3045. (7) Khondaker, S. I.; Yao, Z.; Cheng, L.; Henderson, J. C.; Yao, Y.; Tour, J. M. Appl. Phys. Lett. 2004, 85, 645-647. (8) Gergel, N.; Majumdar, N.; Keyvanfar, K.; Swami, N.; Harriott, L. R.; Bean, J. C.; Pattanaik, G.; Zangari, G.; Yao, Y.; Tour, J. M. J. Vac. Sci. Technol., A 2005, 23, 880-885. (9) Seminario, J. M.; Zacarias, A. G.; Tour, J. M. J. Am. Chem. Soc. 1998, 120, 3970-3974. Seminario, J. M.; Zacarias, A. G.; Tour, J. M. J. Am. Chem. Soc. 2000, 122, 3015-3020. Seminario, J. M.; Zacarias, A. G.; Derosa, P. D. J. Phys. Chem. A 2001, 105, 791795. (10) Emberly, E. G.; Kirczenow, G. Phys. ReV. B 2001, 64, 125318. (11) Di Ventra, M.; Pantelides, S. T.; Lang, N. D. Phys. ReV. Lett. 2002, 88, 046801. (12) Cornil, J.; Karzazi, Y.; Bre´das, J. L. J. Am. Chem. Soc. 2002, 124, 3516-3517. (13) Taylor, J.; Brandbyge, M.; Stokbro, K. Phys. ReV. B 2003, 68, 121101(R). (14) Rakshit, T.; Liang, G.-C.; Ghosh, A. W.; Datta, S. Nano Lett. 2004, 4, 1803. (15) Lau C. N.; Stewart D. R.; Williams R. S.; Bockrath M. Nano Lett. 2004, 4, 569. (16) Yu, L. H.; Natelson, D. Nanotechnology 2004, 15, S517-S524. (17) Larade, B.; Bratkovsky, A. M. Phys. ReV. B 2005, 72, 035440. (18) Gaudioso, J.; Lauhon, L. J.; Ho, W. Phys. ReV. Lett. 2000, 85, 19181921. (19) Lakshmi, S.; Pati, S. K. J. Chem. Phys. 2004, 121, 11998-12004. (20) Galperin M.; Ratner M. A.; Nitzan A. Nano Lett. 2005, 5, 125130. (21) Our calculated transmissions and currents scale with the alkane chain length. Thus we predict NDR to also occur also for other alkane dithiol molecules bridging the same pairs of metal contacts. (22) Dalgleish, H.; Kirczenow, G. Phys. ReV. B 2005, 72, 155429. (23) Dalgleish, H.; Kirczenow, G. Phys. ReV. B 2005, 72, 184407. (24) The Gaussian 03 package (Rev. B.05) was used with the B3PW91 density functional and the Lanl2DZ basis set. (25) Papaconstantopoulos, D. A. Handbook of the Band Structure of Elemental Solids; Plenum Press: New York, 1986. (26) The extended Hu¨ckel parameters are based on atomic ionization energies while the electronic parameters from ref 25 describing the metal clusters are defined up to an arbitrary additive constant. We

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(27) (28) (29)

(30) (31) (32) (33) (34) (35) (36) (37) (38) (39) (40)

(41) (42)

adjust this constant to align the Fermi energy of the contacts relative to the HOMO of the AT4 molecule, according to the difference between the work function of the metals and the HOMO energy of the isolated molecule obtained from density functional theory,24 a method that has been used successfully for gold/benzene dithiolate junctions.27 However, since the interface states (that are responsible for the transport penomena discussed here) are pinned to maxima of the transition metal densities of states, our qualitative predictions regarding NDR are independent of the precise value of the above constant, i.e., of the exact location of the molecular HOMO level relative to the zero bias Fermi level of the metal electrodes. Derosa, P. A.; Seminario, J. M. J. Phys. Chem. B 2001, 105, 471481. Ke, S.-H.; Baranger, H. U.; Yang, W. T. Phys. ReV. B 2004, 70, 085410-085421. We assume that one-third of the applied bias drops at each interface and the remaining one-third drops linearly over the length the molecule. Mujica, V.; Roitberg, A. E.; Ratner, M. J. Chem. Phys. 2000, 112, 6834-6839. Damle, P. S.; Ghosh, A. W.; Datta, S. Phys. ReV. B 2001, 64, 201403-201406. For a review see: Datta, S. Electronic Transport in Mesoscopic Systems; Cambridge University Press: Cambridge, 1995. Datta, S.; Tian, W.; Hong, S.; Reifenberger, R.; Henderson, J. I.; Kubiak, C. P. Phys. ReV. Lett. 1997, 79, 2530-2533. Emberly, E.; Kirczenow, G. Phys. ReV. Lett. 2001, 87, 269701; Phys. ReV. B 2001, 64, 235412-235419. Kushmerick, J. G.; Holt, D. B.; Yang, J. C.; Naciri, J.; Moore, M. H.; Shashidhar, R. Phys. ReV. Lett. 2002, 89, 086802. Kirczenow, G.; Piva, P. G.; Wolkow, R. A. Phys. ReV. B 2005, 72, 245306. Cuevas, J. C.; Heurich, J.; Pauly, F.; Wenzel, W.; Scho¨n, G. Nanotechnology 2003, 14, R29-R38. Each Pd and Rh cluster of the extended molecule is built from 70 atoms arranged in bulk FCC geometries. Because the Pd/AT4/Rh molecular junction is asymmetric, it should also exhibit rectification. NDR due to enhanced transmission arising from a crossing of resonant levels in a different system (a pair of Al atoms between ideal metal electrodes) has previously been proposed by Lang.41 Lang, N. D. Phys. ReV. B 1997, 55, 9364. We also predict a similar weak NDR for certain Pd/AT4/Pd junction geometries.

NL060040M

Nano Lett., Vol. 6, No. 6, 2006