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Nano and Giga Challenges in Electronics and Photonics, March 16, 2007

The Quantum Interference Effect Transistor David M. Cardamone, Charles A. Stafford , and Sumit Mazumdar. “Controlling Quantum Transport through a Single Molecule” Nano Letters 6 , 2422 (2006) Patent application (in preparation) Funding: NSF Grant Nos. PHY0210750 and DMR0312028.

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Nano and Giga Challenges in Electronics and Photonics, March 16, 2007

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  1. The Quantum Interference Effect TransistorDavid M. Cardamone, Charles A. Stafford, and Sumit Mazumdar “Controlling Quantum Transport through a Single Molecule” Nano Letters 6, 2422(2006) Patent application (in preparation) Funding:NSF Grant Nos. PHY0210750 and DMR0312028 Nano and Giga Challenges in Electronics and Photonics, March 16, 2007

  2. Fundamental challenges of nanoelectronics (a physicist’s perspective) 1. Switching mechanism: Raising/lowering energy barrier necessitates dissipation of minimum energy kBT per cycle → extreme power dissipation at ultrahigh device densities. Tunneling & barrier fluctuations in nanoscale devices. 2. Fabrication: For ultrasmall devices, even single-atom variations from device to device (or in device packaging) could lead to unacceptable variations in device characteristics → environmental sensitivity.

  3. The molecular electronics solution Fabrication: large numbers of identical “devices” can be readily synthesized with atomic precision. But does not (necessarilly) solve fundamental problem of switching mechanism.

  4. Alternative switching mechanism: Quantum interference • Phase difference of paths 1 and 2: kF 2d = π → destructive interference • blocks flow of current from E to C. • All possible Feynman paths cancel exactly in pairs. • (b) Increasing coupling to third terminal introduces new paths that do not • cancel, allowing current to flow from E to C.

  5. Theory: Many-body Hamiltonian π-electron molecular Hamiltonian (extended Hubbard model): Ohno parametrization: Molecule coupled to metallic leads (capacitively and via tunneling):

  6. Nonequilibrium Green function approach Retarded and Keldysh Green functions: Nonequilibrium current formula (Meir & Wingreen, PRL ’92): Tunneling widths:

  7. Multi-terminal quantum transport Mean-field (e.g., Hartree-Fock) self-energies: Transmission probabilities: Multi-terminal current formula (M. Büttiker, PRL 57, 1761 (1986)):

  8. Linear response calculation for benzene

  9. Proposed structure for a QuIET: 3 2 Tunable Fano anti-resonance due to vinyl linkage 1 Real  (not decoherence) 3

  10. I-V Characteristic of a QuIET based on sulfonated vinylbenzene Despite the unique quantum mechanical switching mechanism, the QuIET mimics the functionality of a macroscopic transistor on the scale of a single molecule! Increasing gate voltage causes electronic states of vinyl linkage to couple more strongly to benzene, introducing symmetry-breaking scattering.

  11. General schematic of a QuIET Source, drain, and gate nodes of QuIET can be functionalized with “alligator clips” e.g., thiol groups, for self-assembly onto pre-patterned metal/semiconducting electrodes (cf. Aviram, US Patent No. 6,989,290).

  12. Example of a class of QuIETs based on benzene Conducting polymers (e.g., polythiophene, polyaniline) connect to source and drain; semiconducting polymer (e.g., alkene chain) connects to gate electrode. Lengths of polymeric sidegroups can be tailored to facilitate fabrication and fine-tune electrical properties.

  13. Example of a class of QuIETs based on [18]-annulene Interference due to aromatic ring; Polymeric sidegroups for interconnects/control element(s).

  14. Conclusions • Transport through single molecules can be controlled • by exploiting quantum interference due to molecular • symmetry. • Alternative to modulating energy barriers could • overcome fundamental problems of power dissipation • and tunneling. • Mechanism operates in the energy gap of molecule; • does not require fine tuning! • Open questions: • Interactions beyond mean-field (Hartree-Fock, DFT)? • Fabrication, fabrication, fabrication…

  15. Many-body Green function calculation Exact many-body Green function of isolated molecule: Retarded self-energy including lead-molecule coupling to 2nd order: Broad-band limit:

  16. Full many-body calculation for C6H4S2(Au) including exact intramolecular correlations Includes: Transmission node at the Fermi energy in meta configuration Coulomb blockade Emergence of Mott-Hubbard gap Justin Bergfield & CAS (unpublished)

  17. Acknowledgements Coauthors: David Cardamone (Ph.D. 2005) & Sumit Mazumdar Current students: Justin Bergfield, Nate Riordan Postdoc: Jérôme Bürki Funding: NSF Grant Nos. PHY0210750 and DMR0312028 Image: Helen Giesel

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