The Quantum Interference Effect Transistor David M. Cardamone, Charles A. Stafford, and Sumit Mazumdar
Nano and Giga Challenges in Electronics and Photonics, March 16, 2007
“Controlling Quantum Transport through a Single Molecule”Nano Letters 6, 2422 (2006)
Patent application (in preparation)
Funding: NSF Grant Nos. PHY0210750 and DMR0312028
Fundamental challenges of nanoelectronics(a physicist’s perspective)
1. Switching mechanism:
Raising/lowering energy barrier necessitates dissipation of minimumenergy 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 variationsin device characteristics → environmental sensitivity.
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.
Alternative switching mechanism: Quantum interference
(a) 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 notcancel, allowing current to flow from E to C.
Many-body Hamiltonian
π-electron molecular Hamiltonian (extended Hubbard model):
Molecule coupled to metallic leads (capacitively and via tunneling):
Ohno parametrization:
Theory:
Nonequilibrium Green function approach
Retarded and Keldysh Green functions:
Nonequilibrium current formula (Meir & Wingreen, PRL ’92):
Tunneling widths:
Multi-terminal quantum transport
Mean-field (e.g., Hartree-Fock) self-energies:
Transmission probabilities:
Multi-terminal current formula (M. Büttiker, PRL 57, 1761 (1986)):
Linear response calculation for benzene
Proposed structure for a QuIET:
1
2
3
Tunable Fano anti-resonancedue to vinyl linkage
Real (not decoherence)3
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 morestrongly to benzene, introducing symmetry-breaking scattering.
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).
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.
Example of a class of QuIETs based on [18]-annulene
Interference due to aromatic ring;
Polymeric sidegroups for interconnects/control element(s).
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…
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:
Justin Bergfield & CAS (unpublished)
Full many-body calculation for C6H4S2(Au) including exact intramolecular correlations
Includes:
Transmission nodeat the Fermi energyin meta configuration
Coulomb blockade
Emergence ofMott-Hubbard gap
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