ECE 802-604: Nanoelectronics

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ECE 802-604Nanoelectronics

• Prof. Virginia Ayres
• Electrical Computer Engineering
• Michigan State University
• ayresv_at_msu.edu

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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 Sol
itons (polarons) Su-Schreiffer-Heeger (SSH) model
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New Bond alteration polyacetylene HAA typesno
formula changes due to long and short bonds
A
B
-a
a
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New Bond alteration polyacetylene HAB types
-a
a
A
B
B
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Two identical bond alterations
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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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Describe as a perturbation on the original. Two
possibilties
less
more
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Original
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Two possibilities
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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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Now repeat with unequal bond lengths
Now have four possibilities for where Carbon B
is
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t0
Example Units of t0 ? Units of a x0
? Units of a ?
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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
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E-k relationship for more realistic polyacetylene
with bond alteration
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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 whats the problem with
the slow transport?
For polyacetylene
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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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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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Polyactylene with bond alterations
Minor problem Egap Not so narrow
Egap 0.4 eV
0.2 eV
- 0.2 eV
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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
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2 identical bond alterationsNomenclature
both are fully isomerized means large
segments of each chain type can form.
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What about this?
Some connection here Can be neutral or charged
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This defect is a soliton.
w
Defect soliton
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A soliton is a defect site that separates the two
phases of polyacetylene W the soliton
wall width
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The minimum energy of the soliton ES is ALWAYS
within the gap Egap!
Egap
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Another way to say this is that there is a
localised electronic state (the soliton) at the
center of the gap
Egap
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Plot of the probability distribution of the
localised electronic state (the soliton) at the
center of the gap
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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 doesnt go into the conduction band it
goes into the creation of a charged soliton
Egap
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PART 01 of problem A and B structures form
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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 doesnt go into the conduction band
it goes into the creation of a charged soliton
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Energy of an electron in the soliton region
solved using a Greens function approach
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Corresponding wavefunction for the electron in
the soliton region
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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 f0(n) 0)
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A neutral soliton has an unpaired electron
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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. Everyones happy
except the experimenter. Pinning results.
Transport tanks.
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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.
Its 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