LETTER pubs.acs.org/JPCL
Chemically Gated Quantum-Interference-Based Molecular Transistor Aleksey A. Kocherzhenko, Laurens D. A. Siebbeles, and Ferdinand C. Grozema* Optoelectronic Materials, Department of Chemical Engineering, Delft University of Technology, Julianalaan 136, 2628BL Delft, The Netherlands
bS Supporting Information ABSTRACT: This Letter proposes a realistic design of a single-molecule quantuminterference-based transistor. The transistor consists of a cross-conjugated donor bridge acceptor molecule and is chemically gated by a functional group that can be charged. Numerical simulations indicate that the device properties can be tuned to desired specifications by the choice of its constituting functional groups. The transistor does not require external contacts to control its operation. However, it can be chemically functionalized for easy integration into molecular electonic circuits, especially because its operation does not involve any conformational changes in the molecule. The upper operational frequency limit of the proposed device is found to be in the terahertz range. SECTION: Electron Transport, Optical and Electronic Devices, Hard Matter
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n this Letter, a concept design of a quantum-interference-based and chemically controlled molecular transistor is proposed. Because Sautet and Joachim suggested that charge transfer through molecules is largely controlled by quantum interference,1 3 a number of interference-based molecular switches have been suggested.4 8 In these devices, charge transfer through a molecule is usually switched on and off by means of either intramolecular structural reorganization or by an external gate electrode. However, in practice, controlled positioning of a single molecule between three electrodes is extremely difficult and has not been achieved so far. Internal structural reorganization may also be undesirable because it inevitably limits the switching rate of a molecular electronic device. Furthermore, atomic reorganization could disrupt the (self-assembling) electronic circuit, into which a molecular switch should ultimately be integrated. The transistor proposed here is based on a single donor bridge acceptor molecule and does not require external electrodes. Switching between the “on” and “off” states of the device involves no atomic reorganization in the transistor channel. The design is highly versatile; it allows tuning both the electrical characteristics and chemical functionality of the device. The chemical structure of the molecular transistor is shown in Chart 1a. The device consists of a donor group D (source) and an acceptor group A (drain), connected by a cross-conjugated bridge (channel). It has recently been demonstrated that charge transfer in donor bridge acceptor systems with cross-conjugated bridges (Chart 1a) is relatively inefficient, as compared with molecules with linearly conjugated bridges (Chart 1b).2,9 12 Here it is shown that charge transfer through a cross-conjugated bridge can be turned “on” and “off” by a functional group G (gate) that is not part of the π-conjugated channel. The choice of the donor, acceptor, and gate groups as well as of the cross-conjugated bridge determines the electrical and chemical characteristics of the molecular transistor. r 2011 American Chemical Society
To prove the validity of this concept, we have performed numerical simulations of charge transfer in static donor bridge acceptor systems. The simulations followed the procedure described in refs 2 and 10. A charge carrier was initially placed on a point-like donor D. The time evolution of its wave function was then described by the time-dependent Schr€odinger equation with a one-electron tight-binding H€uckel Hamiltonian. The pz orbitals of all carbon atoms were included in the charge transfer simulations. The coupling J between pz orbitals on two carbon atoms as a function of the distance l was taken to be J(l) = J0exp( l/l0), with J0 = 16.69 eV, l0 = 0.71 10 10 m.2,10 When the charge carrier reached a point-like acceptor A, it was removed from the system by adding an imaginary term, ip/τ, to the acceptor site energy.2,10 A characteristic time of charge decay τ = 1.3 fs was assumed. This value is small enough that the charge disappears from the acceptor site instantaneously, yet not small enough to cause reflections of the wave function at the acceptor site. Charge transfer from the donor to the acceptor was characterized by the probability of the charge carrier having reached the acceptor as a function of time. The use of the H€uckel Hamiltonian is a simplification and ignores for instance electron correlation effects; however, it has been previously shown that it does account for the essential features of quantum interference effects in conjugated systems.10 The results of simulations for a cross-conjugated bridge (Chart 1a) and a linearly conjugated bridge (Chart 1b) are shown in Figure 1 (solid lines). From the transients, the charge transfer rates are estimated to be kLC = 2.0 1013 s 1 and kCC = 2.5 1011 s 1, respectively (almost two orders of magnitude difference). This can be understood in the following way. In the case of the Received: April 20, 2011 Accepted: June 30, 2011 Published: June 30, 2011 1753
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Chart 1. (a) Proposed Molecular Transistor with a CrossConjugated (3-Methylene-penta-1,4-diyne-1,5-diyl)dibenzene channel; (b) Linearly Conjugated Reference Donor Bridge Acceptor System, (E)-1,6-Diphenylhexa-3-en-1,5-diyne; and (c) Cross-Conjugated Donor Bridge Acceptor System with a Longer Side Chain in the Cross-Conjugated Bridgea
Figure 2. Probability of charge transfer from a donor to an acceptor in the “off” (black) and “on” (red) state of a molecular transistor with a cross-conjugated channel (Chart 1a).
a
Examples of the gate group G are given in Chart 2.
Figure 1. Probability of charge transfer from a donor to an acceptor through: cross-conjugated bridge, Chart 1a (black, solid); linearly conjugated bridge, Chart 1b (red, solid); and cross-conjugated bridge with longer side chains, Chart 1c (dashed line corresponds to n = 2, dotted line corresponds to n = 3). In these simulations, no gating group is present; that is, G = CH2.
linearly conjugated bridge shown in Chart 1b, the charge carrier wave function propagates along the bridge from the donor D to the acceptor A. Once the charge carrier reaches the acceptor, it is trapped there. However, in the case of the cross-conjugated bridge shown in Chart 1a, there is also an alternative pathway for the charge to travel along into the side chain, toward the gate group G. Thus, one component of the charge carrier wave function travels directly from the donor D to the acceptor A, whereas another component enters the π-conjugated side chain and is reflected at its end. The reflected component then also travels toward the acceptor. Both wave function components propagate coherently (i.e., phase information is retained during propagation) and can form an interference pattern.2,10,11 This pattern can be constructive or destructive, depending on the length of the π-conjugated side chain. For a side chain with an odd number of carbon atoms, the phase difference of the wave function components traveling via covalently bound atoms is (N + 1/2)π, where N is integer. Thus, a destructive interference pattern is formed by these wave function components and charge transfer to the acceptor occurs mostly due to the electronic couplings
between pz orbitals on non-nearest carbon atoms.10 (Conduction via the σ-system is comparatively small because of the significant length of the molecule.)13 Because electronic couplings show exponential distance dependence, charge transfer via non-nearest carbon atoms is relatively inefficient. If it is true that charge transfer from the donor D to the acceptor A is influenced by wave function propagation in the π-conjugated side chain, then varying its length should affect the charge transfer rate in the main channel. Charge transfer simulations performed for the molecule shown in Chart 1c confirm this. The results of these simulations are shown in Figure 1 by the dashed (n = 2) and dotted (n = 3) lines. It can be seen that increasing the length of the side chain increases the rate of charge transfer from the donor D to the acceptor A. This may seem counterintuitive at first, but using the reasoning presented above, it can be easily understood. The component of the charge carrier wave function that enters the side chain needs time to reach the end of the chain, be reflected, and travel back. Therefore, if the side chain becomes longer, then the two wave function components form a destructive interference pattern at a later time. Prior to that, direct charge transfer from the donor D to the acceptor A can occur without the effects of interference. Therefore, the results for variation of the length of the side chain directly show that the interference effects play a role here. This result agrees well with previous studies of the effects of side chains on charge transport in molecules using Landauer linear response theory5b and the Green’s function density functional tight-binding method.11 The proposed molecular transistor design is shown in Chart 1a. To control charge transfer from the donor D (source) to the acceptor A (drain), a third terminal, gate G, is introduced. In the “off” state of the transistor, the cross-conjugated channel ensures relatively inefficient charge transfer from the donor D to the acceptor A. However, placing a repulsive charge on the gate group G (for example, by protonation or deprotonation) creates an additional electrostatic potential that can significantly change the energy landscape within the molecular transistor, particularly in the side branch, leading to the gate group G. Consequently, a fully destructive interference pattern is no longer formed by the charge carrier wave function components going in and coming out of the side branch. Simulations show that if a point charge is placed on the gate group G, then charge transfer from the donor D to the acceptor A through a cross-conjugated bridge becomes as efficient as in the case of a linearly conjugated bridge (Figure 2). The molecular transistor is then considered to be in the “on” state. It should be noted that simulations have shown that the sign of the charge, either positive or negative, does not influence 1754
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LETTER
operation of the described chemically gated molecular transistor is predominantly governed by quantum interference effects. In summary, this Letter describes a realistic design of a quantum-interference-based molecular transistor. The transistor is based on a donor bridge acceptor system with a crossconjugated bridge and a gate group that can be charged. The flexibility in the choice of the donor, acceptor, bridge, and gate allows tuning the electronic and chemical properties of the device to desired specifications. Absence of structural reorganization in the transistor channel during operation eases the integration of the device into molecular electronic circuits.
’ ASSOCIATED CONTENT
bS the results markedly. The main effect of the charge on G is to influence the propagation speed in the side chain, and both reducing and increasing the propagation speed can lift the destructive interference. The case of a point-like donor D, point-like acceptor A, and point charge on the gate group G defines the theoretical upper limit for the operational frequency of quantum-interferencebased molecular transistors. From comparison of the charge transfer rate kCC in the “off” state and the charge transfer rate kLC in the “on” state, the upper operational frequency limit is found to be in the terahertz range. It has been shown that for real donor D and acceptor A groups where the initially prepared charge is distributed, the charge transfer rate in the molecular transistor, and thus its operational frequency, are lower.10 The operational frequency can be further limited by the rate of charging the gate group G because the charging of the gate group may require time also. The latter may be even more important, and particular care should be taken in the choice of the gate group. The choice of the donor D, acceptor A, and gate G groups defines the electronic parameters of the molecular transistor. These groups can also be functionalized to promote specific chemical behavior, such as self-assembly. The actual donor and acceptor groups that can be used are very diverse; some examples are given in refs 9 and 14. Chart 2 shows three possible gate groups. The charge is placed on the gate group G by protonation (Chart 2a), deprotonation (Chart 2b), or binding a heavy cation (Chart 2c). The excess charge is positive in the case of gate groups shown in Chart 2a,c and negative in the case of the gate group shown in Chart 2b. The examples for the gate group in Chart 2 all require charging by addition or removal of some ionic species, which is relatively slow and impractical in single-molecule conductance experiments. In such a measurement, other gate groups may be considered, for instance, groups that can be reduced or oxidized by a gating electrode underneath the devices. Such ways of introducing a charge would have the same effect as the “chemical” gate groups considered here. One concern that may be raised with regard to such a molecular device design is whether quantum interference actually survives on the time scale of charge transfer. Vibrations in the molecule and in the molecular environment may lead to decoherence of the wave function components traveling along different “spatial” pathways, thus suppressing interference. However, recent studies have shown that interference effects are more robust than previously believed: they are well-pronounced up to picosecond time scales even for large molecules and supramolecular complexes at room temperature.5b10,11, Therefore, the
Supporting Information. Atomic coordinates for molecular structures used in the simulations. This material is available free of charge via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT This work was financially supported by a VIDI grant from The Netherlands Organisation for Scientific Research (NWO) and by the European Union FP6Marie Curie Research Training Network “THREADMILL” (contract number MRTN-CT-2006036040). ’ REFERENCES (1) Sautet, P.; Joachim, C. The Sixl-Higelin Salicylideneaniline Molecular Switch Revisited. Chem. Phys. 1989, 135, 99. (2) Kocherzhenko, A. A.; Grozema, F. C.; Siebbeles, L. D. A. Single Molecule Charge Transport: From a Quantum Mechanical to a Classical Description . Phys. Chem. Chem. Phys. 2011, 13, 2096. (3) Markussen, T.; Stadler, R.; Thygesen, K. S. The Relation between Structure and Quantum Interference in Single Molecule Junctions. Nano Lett. 2010, 10, 4260. (4) van der Molen, S. J.; Liljeroth, P. Charge Transport through Molecular Switches. J. Phys.: Condens. Matter 2010, 22, 133001. (5) (a) Baer, R.; Neuhauser, D. Phase Coherent Electronics: A Molecular Switch Based on Quantum Interference. J. Am. Chem. Soc. 2002, 124, 4200. (b) Collepardo-Guevara, R.; Walter, D.; Neuhauser, D.; Baer, R. A H€uckel Study of the Effect of a Molecular Resonance Cavity on the Quantum Conductance of an Alkene Wire. Chem. Phys. Lett. 2004, 393, 367. (6) Cardamone, D. M.; Stafford, C. A.; Mazumdar, S. Controlling Quantum Transport through a Single Molecule. Nano Lett. 2006, 6, 2422. (7) Ke, S.-H.; Yang, W.; Baranger, H. U. Quantum-InterferenceControlled Molecular Electronics. Nano Lett. 2008, 8, 3257. (8) van Dijk, E. H.; Myles, D. J. T.; van der Veen, M. H.; Hummelen, J. C. Synthesis and Properties of an Anthraquinone-Based Redox Switch for Molecular Electronics. Org. Lett. 2006, 8, 2333. (9) Ricks, A. B.; Solomon, G. C.; Colvin, M. T.; Scott, A. M.; Chen, K.; Ratner, M. A.; Wasielewski, M. R. Controlling Electron Transfer in Donor Bridge Acceptor Molecules Using Cross-Conjugated Bridges. J. Am. Chem. Soc. 2010, 132, 15427. (10) Kocherzhenko, A. A.; Grozema, F. C.; Siebbeles, L. D. A. Charge Transfer Through Molecules with Multiple Pathways: Quantum Interference and Dephasing. J. Phys. Chem. C 2010, 114, 7973. (11) Solomon, G. C.; Andrews, D. Q.; Van Duyne, R. P.; Ratner, M. A. When Things Are Not as They Seem: Quantum Interference 1755
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Turns Molecular Electron Transfer “Rules” Upside Down. J. Am. Chem. Soc. 2008, 130, 7788. (12) Solomon, G. C.; Andrews, D. Q.; Goldsmith, R. H.; Hansen, T.; Wasielewski, M. R.; Van Duyne, R. P.; Ratner, M. A. Quantum Interference in Acyclic Systems: Conductance of Cross-Conjugated Molecules. J. Am. Chem. Soc. 2008, 130, 17301. (13) Solomon, G. C.; Andrews, D. Q.; Van Duyne, R. P.; Ratner, M. A. Electron Transport through Conjugated Molecules: When the π System Only Tells Part of the Story. ChemPhysChem 2009, 10, 257. (14) Weiss, E. A.; Tauber, M. J.; Kelley, R. F.; Ahrens, M. J.; Ratner, M. A.; Wasielewski, M. R. Conformationally Gated Switching between Superexchange and Hopping within Oligo-p-phenylene-Based Molecular Wires. J. Am. Chem. Soc. 2005, 127, 11842.
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