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Explorations in quantum transport – phenomena and methods

Explorations in quantum transport – phenomena and methods Sokrates T. Pantelides Department of Physics and astronomy , Vanderbilt University, Nashville, TN and Oak Ridge National Laboratory, Oak Ridge, TN Collaborators: Yoshihiro Gohda Zhong-yi Lu

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Explorations in quantum transport – phenomena and methods

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  1. Explorations in quantum transport – phenomena and methods Sokrates T. Pantelides Department of Physics and astronomy, Vanderbilt University, Nashville, TN and Oak Ridge National Laboratory, Oak Ridge, TN Collaborators: Yoshihiro Gohda Zhong-yi Lu Kalman Varga Supported in part by Department of Energy

  2. MOORE’S LAW

  3. Phenomena (using the Lippmann-Schwinger method) • Charging of molecules during transport (Gohda) • Transport through ultra-thin films (Lu) • New method (Varga)

  4. t r The Lippmann-Schwinger method • Norton Lang, 1981 – • Di Ventra, Lang, and Pantelides, 2000-2002

  5. Theory 0° 90° 0° 90° Experiment: Reed et al (2000) T=190 K T=300 K

  6. Nature 417, 72 (2002) “The current is strongly suppressed up to a threshold V, then it increases in steps”

  7. Coulomb blockade in a quantum dot GaAs-AlGaAs-InGaAs-AlGaAs-GaAs

  8. Barner and Ruggiero, 1987

  9. LUMO LUMO V=2.4V

  10. V=3.6[V] V=1.2[V]

  11. LUMO LUMO AFTER SELF-CONSISTENCY, MOLECULE IS NEUTRAL! ELECTRODES ARE NEUTRAL! EXCITED STATE?

  12. C6H4(NO2)S ELIMINATE CONTACT ON LEFT C6H5S

  13. -3 -2 -1 0 1 -6 -4 -2 0 2 Energy (eV) Energy (eV) C6H5-S C6H4(NO2)-S

  14. 4.2V 1 e 1.8V 1 e 0.6V 0 e

  15. 0.8 1.2 0.3 dQ=0 Using a gate voltage Vsd = 0.1 V

  16. Fowler-Nordheim tunneling M O S J E Ec Ev n-Si EF Metal SiO2 J/E2 = Aexp(-B/E)

  17. J/E2 = Aexp(-B/E) ln(J/E2) 1/E Fowler-Nordheim I I=V/R V Ohmic

  18. 8-layer Si(001) Ohmic

  19. Effective potential 8 layers Si(001) V=0.1v EF EF J V=1.0v V=5.0v The dash-dot lines are boundary

  20. Current vs thickness [Si(001)] Bias=1.0V

  21. I-V curve through SiO2 nano-film • Three regions: • 0.0 to 0.5V quasi-linear; • 0.5 to 4.0V non-linear; • Over 4.0V quasi-linear

  22. Fowler-Nordheim I-V plot

  23. Effective potential nano-film SiO2 J EF V=0.5v V= 4.0v The dash-dot lines are boundary

  24. 1.2 n m (SiO2) 1.5 n m (SiO2) 0.9 n m (vacuum) 1.2 n m (vacuum) 1.5 n m (vacuum) 0 1 2 3 4 5 G. Timp et al (Bell Lab) 1998 calculation

  25. t r EVERYWHERE The Lippmann-Schwinger method

  26. Static external potential DENSITY FUNCTIONAL THEORY FOR STEADY-STATE TRANSPORT (CURRENT-DENSITY FUNCTIONAL) + B.C.

  27. Sink Source Schrödinger equation with imaginary potential: MAP TRANSPORT ONTO AN EIGENVALUE PROBLEM Battery!

  28. Na wire Real-space DFT calculation Jellium electrodes Bias Voltage

  29. Benzene ring -- IV characteristics Experiment (Reed et al.)

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