Teaching Nanoelectronics Paolo Lugli Institute for Nanoelectronics Munich, Germany.
ECE 802-604: Nanoelectronics
description
Transcript of ECE 802-604: Nanoelectronics
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ECE 802-604:Nanoelectronics
Prof. Virginia AyresElectrical & Computer EngineeringMichigan State [email protected]
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VM Ayres, ECE802-604, F13
Lecture 27, 03 Dec 13
Molecular Electronics:
Why not polyacetylene? or any conjugated “ene”?Examples of possibilitiesActual performance
Electronic () structure brief reviewMechanical () structure brief review
New: bond alteration structure in polyacetyleneElectronic result of bond alteration structureQualitativeQuantitative
Solitons (polarons): Su-Schreiffer-Heeger (SSH) model
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VM Ayres, ECE802-604, F13
New: Bond alteration polyacetylene: HAA types:no formula changes due to long and short bonds
“A”c
H
c
H
c
H
c
H
c
H
“B”c
H
c
H
-a +a
c
H
c
H
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VM Ayres, ECE802-604, F13
New: Bond alteration polyacetylene: HAB types
“A”c
H
c
H
c
H
c
H
c
H
“B”c
H
c
H
-a +a
c
H
c
H
“B”
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VM Ayres, ECE802-604, F13
Two “identical” bond alterations
“A”c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
“B”c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
“B”
“A”c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
“B”c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
“B”
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VM Ayres, ECE802-604, F13
Describe as: a perturbation of the original.Two chances of it happening
“A”c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
“B”c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
“B”
“A”c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
“B”c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
“B”
A bit more
A bit moreA bit less
A bit less
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VM Ayres, ECE802-604, F13
Describe as: a perturbation on the original. Two possibilties
“A”c c c c c
H
H
H
H
H
“B”c
H
c
H
-a/2 +a/2
lessmore
“A”c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
“B”c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
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VM Ayres, ECE802-604, F13
Original:
“A”c c c c c
H
H
H
H
H
“B”
a
c
H
c
H
a
-a/2 +a/2
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VM Ayres, ECE802-604, F13
Two possibilities:
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VM Ayres, ECE802-604, F13
For HW: do the 2nd nearest neighbor “B” atoms N = 2 in the original model
“A”c c c c c
H
H
H
H
H
“B”
a
c
H
c
H
a
-a/2 +a/2
Also ask: Where does HAB come form?
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VM Ayres, ECE802-604, F13
“A”c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
“B”c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
“B”
A bit more
Now repeat with unequal bond lengths:
“A”c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
“B”c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
“B”
A bit moreA bit less
Now have four possibilities for where Carbon “B” is::
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t0 =
Example:
Units of t0 = ?
Units of x0 = ?
Units of = ?
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VM Ayres, ECE802-604, F13
t0 =
Answer:
Units of t0 = eV
Units of x0 = eV
Units of = eV/ (distance = Ang)
is a phonon coupling coefficient:Converts the extra bit distance into the impact this perturbation has on the energy levels
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VM Ayres, ECE802-604, F13
E-k relationship for more realistic polyacetylene with bond alteration:
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VM Ayres, ECE802-604, F13
E-k relationship for more realistic polyacetylene with bond alteration:
Solve for E:
For polyacetylene:This bond alteration realism “opened up a gap” but it seems narrow so what’s the problem with the slow transport?
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VM Ayres, ECE802-604, F13
+0.2 eV
- 0.2 eV
Polyactylene without bond alterations Polyactylene with bond alterations
Egap = 0.4 eV
Electrons will want to bond using the lowest energy level possible.Bond alteration configurations “lock”.
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VM Ayres, ECE802-604, F13
+0.2 eV
- 0.2 eV
Polyactylene without bond alterations Polyactylene with bond alterations
Egap = 0.4 eV
Electrons will want to bond using the lowest energy level possible.Bond alteration configurations “lock”.The major problem:
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VM Ayres, ECE802-604, F13
+0.2 eV
- 0.2 eV
Polyactylene with bond alterations
Egap = 0.4 eV
Minor problem:Egap: Not so narrow:
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VM Ayres, ECE802-604, F13
Lecture 27, 03 Dec 13
Molecular Electronics:
Why not polyacetylene? or any conjugated “ene”?Examples of possibilitiesActual performance
Electronic () structure brief reviewMechanical () structure brief review
New: bond alteration structureElectronic result of bond alteration structureQualitativeQuantitative
Solitons (polarons): Su-Schreiffer-Heeger (SSH) model
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VM Ayres, ECE802-604, F13
“A”c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
“B”c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
“B”
“A”c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
“B”c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
“B”
2 “identical” bond alterations
Nomenclature: both are = “fully isomerized”: means: large segments of each chain type can form.
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VM Ayres, ECE802-604, F13
“A”c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
“B”c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
“B”
“A”c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
“B”c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
“B”
What about this?
Some connection hereCan be neutral or charged
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VM Ayres, ECE802-604, F13
This defect is a soliton.
Defect = “soliton”
“A”c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
“B”c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
“B”
“A”c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
“B”c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
“B”
w
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VM Ayres, ECE802-604, F13
Neutral defect = “soliton”
w
A soliton is a defect site that separates the two “phases” of polyacetylene
“W” = the soliton “wall width”
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VM Ayres, ECE802-604, F13
ES(
)
Neutral defect = “soliton”
w
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The minimum energy of the soliton ES is ALWAYS within the gap Egap!
ES(
)
Eg
ap
ES( )
Neutral defect = “soliton”
w
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VM Ayres, ECE802-604, F13
Another way to say this is that there is a localised electronic state (the soliton) at the center of the gapE
S(
)
Eg
ap
ES( )
Neutral defect = “soliton”
w
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VM Ayres, ECE802-604, F13
Plot of the probability distribution of the localised electronic state (the soliton) at the center of the gapE
S(
)
Neutral defect = “soliton”
w
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VM Ayres, ECE802-604, F13
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(
)
Eg
ap
ES( )
Neutral defect = “soliton”
w
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VM Ayres, ECE802-604, F13
PART 01 of problem:A and B structures form
“A”c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
“B”c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
“B”
“A”c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
“B”c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
“B”
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VM Ayres, ECE802-604, F13
“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
Neutral defect = “soliton”
w
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.
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VM Ayres, ECE802-604, F13
“A”c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
“B”c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
“B”
“A”c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
“B”c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
“B”
Energy of an electron in the soliton region solved using a Green’s function approach
ES(
)E
S(
)
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VM Ayres, ECE802-604, F13
“A”c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
“B”c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
“B”
“A”c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
“B”c
H
c
H
c
H
c
H
c
H
c
H
c
H
c
H
“B”
Corresponding wavefunction for the electron in the soliton region
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VM Ayres, ECE802-604, F13
a = 1.22 Angstroms = the x-spacing between CH groups
l is a “stretching parameter” that scales n/l
n = 0, ± 2, 4, 6,…..
(for odd n:0(n) = 0)
2
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VM Ayres, ECE802-604, F13
A neutral soliton has an unpaired electron:
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VM Ayres, ECE802-604, F13
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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VM Ayres, ECE802-604, F13
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
Two different transport situations defeated by soliton: