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

2. Molecular Electronics:
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, ECE , F13

3. c c c c “A” c c c c c “B” -a +a H H H H H H H H H
New: Bond alteration polyacetylene: HAA types: no formula changes due to long and short bonds c H c H c H c H
“A” c H c H c H c H c H
“B” -a +a
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4. New: Bond alteration polyacetylene: HAB types
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5. Two “identical” bond alterations
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6. Describe as: a perturbation of the original
Describe as: a perturbation of the original. Two chances of it happening
A bit less
A bit more
A bit less
A bit more
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7. Describe as: a perturbation on the original. Two possibilties
more
less
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8. Original:
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9. Two possibilities:
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10. VM Ayres, ECE , F13

11. Also ask: Where does HAB come form?
For HW: do the 2nd nearest neighbor “B” atoms N = 2 in the original model
Also ask: Where does HAB come form?
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12. Now repeat with unequal bond lengths:
Now have four possibilities for where Carbon “B” is::
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13. t0 = Example: Units of t0 = ? Units of a x0 = ? Units of a = ?
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14. Units of a = eV/ (distance = Ang)
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
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15. E-k relationship for more realistic polyacetylene with bond alteration:
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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:
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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”.
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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:
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19. Minor problem: Egap: Not so narrow: Polyactylene with bond alterations
Egap = 0.4 eV
+0.2 eV
- 0.2 eV
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20. Molecular Electronics:
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, ECE , F13

21. 2 “identical” bond alterations Nomenclature: both are = “fully isomerized”: means: large segments of each chain type can form.
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22. Can be neutral or charged
What about this?
Some connection here
Can be neutral or charged
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23. This defect is a soliton.w
Defect = “soliton”
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24. “W” = the soliton “wall width”
A soliton is a defect site that separates the two “phases” of polyacetylene
“W” = the soliton “wall width”
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25. ES( )
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26. The minimum energy of the soliton ES is ALWAYS within the gap Egap!
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27. Another way to say this is that there is a localised electronic state (the soliton) at the center of the gap
ES( )
Egap
ES( )
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28. Plot of the probability distribution of the localised electronic state (the soliton) at the center of the gap
ES( )
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29. 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
ES( )
Egap
ES( )
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30. PART 01 of problem:
A and B structures form
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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
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32. Energy of an electron in the soliton region solved using a Green’s function approach
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33. Corresponding wavefunction for the electron in the soliton region
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34. l is a “stretching parameter” that scales n/l 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
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35. A neutral soliton has an unpaired electron:
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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.
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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, ECE , F13