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Molecular transistors based on quantum interference
Harnessing quantum interference enables single aromatic annulene molecules to function as transistors.
15 February 2007, SPIE Newsroom. DOI: 10.1117/2.1200702.0587
As electronic device complexity increases, industry requires ever smaller transistors packed ever more tightly, a phenomenon quantified by Moore's law. The ubiquitous field effect transistor (FET), however, has reached a fundamental limit.1 FETs, like all conventional transistors, raise and lower an energy barrier to stop and allow current flow. Each time a transistor switches, it dissipates the energy of the barrier as heat. If a microchip consisting of billions of such devices is to be cooled cheaply, therefore, the transistors cannot be packed much more densely than they already are.
The most promising approach to overcome this dilemma is to exploit the quantum-mechanical, wave nature of the electron.2–4 We have proposed such a device, the quantum interference effect transistor (QuIET), based on a single aromatic molecule such as benzene (see Figure 1).5 When the QuIET is off, destructive interference between the various paths an electron can take through the ring totally blocks current. A third lead can break this effect, allowing current flow. With this approach, no energy barrier need be raised or lowered, and power dissipation can be minimal.
Figure 1. Artist's conception of a Quantum-Interference Effect Transistor or QuIET, based on a single sulfonated vinylbenzene molecule. Carbon atoms are green, hydrogen purple, and sulfur yellow. Voltage applied to the red-colored gold contact on the left modulates the current flowing between the other two. Image courtesy of Helen Giesel.5
Figure 2 shows a schematic diagram of a QuIET. Leads 1 and 2 play a role similar to the source and drain electrodes of a FET. In linear response, in the absence of charge transfer, electrons entering from lead 1 have Fermi momentum kF=p2d, where d=1.397Å is the carbon–carbon bond length of benzene. The two most direct paths from lead 1 to lead 2 around the ring have a phase difference of kF2d=p, and interfere destructively. Similarly, all of the paths through the ring cancel pairwise. The net result is zero conductance.
Figure 2. Schematic diagram of a QuIET based on benzene. Lead 3 may be a macroscopic lead or a locally gated side molecule.
The role of the third lead is to permit current flow by controllably adding extra paths that are not phase-related to those within the ring. This lead may have a continuous density of states, such as that of a scanning tunneling microscope (STM) tip, or a discrete one, as a molecular side group would. The distance of the STM tip or the electrostatic gating of the side group modulates current flow.
We have performed quantitative calculations to verify this simple argument. The p-orbitals of the molecule are treated in a tight-binding model, with same-site, intersite, and lead-site Coulomb interactions included in the Hartree–Fock mean field. We solve for the Hamiltonian and Green functions self-consistently. From these, the Landauer–Büttiker formalism6 yields the conductance of the device and the current in each lead.
Figure 3 shows results of these calculations for the device of Figure 1. The coherent suppression of the current is removed by a combination of decoherence from the third lead and elastic scattering from the phenyl linkage. Both of these effects are tuned by electrostatic gating from the third lead. The QuIET's broad current peak contrasts strikingly with single-electron devices, which are in general extremely sensitive to small changes in the electromagnetic environment. Its transconductance, meanwhile, is comparable to or even larger than that of a single-electron transistor.
Figure 3. IV (current-voltage) characteristics of the QuIET shown in Figure 1 at room temperature. Leads 1 and 2 have coupling strengths of 1eV, while the third lead is weakly coupled at 0.0024eV. The curve for I3 is for bias 1V. Other biases have similar curves.5
Skilled experimentalists now routinely attach two leads to single molecules, so the most significant experimental challenge to fabricating a molecular transistor is attaching the third lead. A QuIET such as that in Figure 1, however, requires only local electrostatic gating of a molecule, which has already been achieved.7 Furthermore, use of a larger molecule may ameliorate the problem. For example, the third lead can be attached to an alkene chain that has substituted the phenyl group's hydrogen atom. Additionally, QuIETs can be made not only from benzene but from any stable aromatic annulene.
Single-molecule devices such as the QuIET possess the inherent advantages of chemical fabrication: each device so produced is identical, and therefore the technology is uniquely scalable. Furthermore, such devices have the potential to work in solution, opening the door to in vivo applications. Finally, molecular transistors are the ultimate foreseeable limit of electronics miniaturization.
The authors acknowledge funding for this research from US National Science Foundation grants PHY0210750, DMR0312028, DMR0406604, and PHY0244389.
David M. Cardamone
Department of Physics, Simon Fraser University
Burnaby, BC, Canada
David M. Cardamone is a postdoctoral fellow in the Physics Department of Simon Fraser University, Canada. His interest is the theoretical modeling of mesoscopic systems. Current research includes electron transport through single molecules and the decay-out of superdeformed nuclei.
Charles A. Stafford, Sumit Mazumdar
Department of Physics, Department of Optical Sciences, University of Arizona
Charles A. Stafford is associate professor of physics at the University of Arizona. His current research focuses on quantum effects in metal nanostructures and single-molecule devices.
Sumit Mazumdar is a professor of physics and optical sciences at the University of Arizona. He is interested in the fundamental and device physics of organic molecules, conjugated polymers and carbon nanotubes, and organic charge-transfer solids.
7. P. G. Piva, G. A. DiLabio, J. L. Pitters, J. Zikovsky, M. Rezeq, S. Dogel, W. A. Hofer, R. A. Wolkow, Field regulation of single-molecule conductivity by a charged surface atom,
Nature 435, pp. 658-661, 2005.