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ECE 802-604: Nanoelectronics

ECE 802-604: Nanoelectronics. Prof. Virginia Ayres Electrical & Computer Engineering Michigan State University ayresv@msu.edu. Lecture 27, 03 Dec 13. Molecular Electronics: Why not polyacetylene? or any conjugated “ene”? Examples of possibilities Actual performance

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ECE 802-604: Nanoelectronics

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  1. ECE 802-604:Nanoelectronics Prof. Virginia Ayres Electrical & Computer Engineering Michigan State University ayresv@msu.edu

  2. Lecture 27, 03 Dec 13 • Molecular Electronics: • Why not polyacetylene? or any conjugated “ene”? • Examples of possibilities • Actual performance • Electronic (p) structure brief review • Mechanical (s) structure brief review • New: bond alteration structure in polyacetylene • Electronic result of bond alteration structure • Qualitative • Quantitative • Solitons (polarons): Su-Schreiffer-Heeger (SSH) model VM Ayres, ECE802-604, F13

  3. H H H H c c c c c c c c c H H H H H New: Bond alteration polyacetylene: HAA types:no formula changes due to long and short bonds “A” “B” -a +a VM Ayres, ECE802-604, F13

  4. H H H H c c c c c c c c c H H H H H New: Bond alteration polyacetylene: HAB types -a +a “A” “B” “B” VM Ayres, ECE802-604, F13

  5. Two “identical” bond alterations VM Ayres, ECE802-604, F13

  6. Describe as: a perturbation of the original.Two chances of it happening A bit less A bit more A bit less A bit more VM Ayres, ECE802-604, F13

  7. Describe as: a perturbation on the original. Two possibilties more less VM Ayres, ECE802-604, F13

  8. Original: VM Ayres, ECE802-604, F13

  9. Two possibilities: VM Ayres, ECE802-604, F13

  10. VM Ayres, ECE802-604, F13

  11. For HW: do the 2nd nearest neighbor “B” atoms N = 2 in the original model Also ask: Where does HAB come form? VM Ayres, ECE802-604, F13

  12. Now repeat with unequal bond lengths: Now have four possibilities for where Carbon “B” is:: VM Ayres, ECE802-604, F13

  13. t0 = Example: Units of t0 = ? Units of a x0 = ? Units of a = ? VM Ayres, ECE802-604, F13

  14. t0 = Answer: Units of t0 = eV Units of a x0 = eV Units of a = eV/ (distance = Ang) a is a phonon coupling coefficient: Converts the extra bit distance into the impact this perturbation has on the energy levels VM Ayres, ECE802-604, F13

  15. E-k relationship for more realistic polyacetylene with bond alteration: VM Ayres, ECE802-604, F13

  16. E-k relationship for more realistic polyacetylene with bond alteration: Solve for E: This bond alteration realism “opened up a gap” but it seems narrow so what’s the problem with the slow transport? For polyacetylene: VM Ayres, ECE802-604, F13

  17. Polyactylene without bond alterations Polyactylene with bond alterations Egap = 0.4 eV +0.2 eV - 0.2 eV Electrons will want to bond using the lowest energy level possible. Bond alteration configurations “lock”. VM Ayres, ECE802-604, F13

  18. Polyactylene without bond alterations Polyactylene with bond alterations Egap = 0.4 eV +0.2 eV - 0.2 eV Electrons will want to bond using the lowest energy level possible. Bond alteration configurations “lock”. The major problem: VM Ayres, ECE802-604, F13

  19. Polyactylene with bond alterations Minor problem: Egap: Not so narrow: Egap = 0.4 eV +0.2 eV - 0.2 eV VM Ayres, ECE802-604, F13

  20. Lecture 27, 03 Dec 13 • Molecular Electronics: • Why not polyacetylene? or any conjugated “ene”? • Examples of possibilities • Actual performance • Electronic (p) structure brief review • Mechanical (s) structure brief review • New: bond alteration structure • Electronic result of bond alteration structure • Qualitative • Quantitative • Solitons (polarons): Su-Schreiffer-Heeger (SSH) model VM Ayres, ECE802-604, F13

  21. 2 “identical” bond alterationsNomenclature: both are = “fully isomerized”: means: large segments of each chain type can form. VM Ayres, ECE802-604, F13

  22. What about this? Some connection here Can be neutral or charged VM Ayres, ECE802-604, F13

  23. This defect is a soliton. w Defect = “soliton” VM Ayres, ECE802-604, F13

  24. A soliton is a defect site that separates the two “phases” of polyacetylene “W” = the soliton “wall width” VM Ayres, ECE802-604, F13

  25. ES( ) VM Ayres, ECE802-604, F13

  26. ES( ) ES( ) The minimum energy of the soliton ES is ALWAYS within the gap Egap! Egap VM Ayres, ECE802-604, F13

  27. ES( ) ES( ) Another way to say this is that there is a localised electronic state (the soliton) at the center of the gap Egap VM Ayres, ECE802-604, F13

  28. ES( ) Plot of the probability distribution of the localised electronic state (the soliton) at the center of the gap VM Ayres, ECE802-604, F13

  29. ES( ) ES( ) Yet another way to say this is that “the soliton formation energy is less than that needed to create a band excitation”. That means an electron doesn’t go into the conduction band – it goes into the creation of a charged soliton Egap VM Ayres, ECE802-604, F13

  30. PART 01 of problem: A and B structures form VM Ayres, ECE802-604, F13

  31. PART 02 of problem: A and B structures are connected by a defect with its own local energy state in the middle of the bandgap. “the soliton formation energy is less than that needed to create a band excitation”. That means an electron doesn’t go into the conduction band – it goes into the creation of a charged soliton VM Ayres, ECE802-604, F13

  32. Energy of an electron in the soliton region solved using a Green’s function approach VM Ayres, ECE802-604, F13

  33. Corresponding wavefunction for the electron in the soliton region VM Ayres, ECE802-604, F13

  34. 2 n = 0, ± 2, 4, 6,….. (for odd n: f0(n) = 0) l is a “stretching parameter” that scales n/l a = 1.22 Angstroms = the x-spacing between CH groups VM Ayres, ECE802-604, F13

  35. A neutral soliton has an unpaired electron: VM Ayres, ECE802-604, F13

  36. Two different transport situations defeated by soliton: Situation 01 on left: This is in a single polyacetylene chain. A dopant added to polyacetylene chain, say a nitrogen atom N. Soliton becomes charged with one dopant-contributed electron. Charged soliton grabs an off-chain impurity = the parent phosphorous N+ ion at a distance of about 2 angstroms and becomes neutral. Everyone’s happy except the experimenter. Pinning results. Transport tanks. VM Ayres, ECE802-604, F13

  37. Two different transport situations defeated by soliton: Situation 02 on right: This is in a self-assembled monolayer of many aligned polyactylene chains. Experimenter liberates an electron from a neutral soliton using a laser. It’s supposed to go into the conduction band of that polyactylene chain. Actually it goes into charging up another soliton on an adjacent chain at distance of about 4 angstroms. The two solitons, the first + charged and the second - charged lock up. End of transport. The experimenter predicts it will take 20 years to finish his/her Ph.D. and tears hair out VM Ayres, ECE802-604, F13

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