Understanding Nanoscale Conduction

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UnderstandingNanoscale Conduction
Molecular Electronics
Supriyo Datta School of Electrical Computer
Engineering Purdue University
CNT Electronics
Nanowire Electronics
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Nanoscale Conductors
Top Down
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NanodevicesBottom-up View
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Band-Diagram
Vacuum Level
LUMO
µ
HOMO
Fermi function
Electrochemical Potential
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Band-Diagram
µ
Fermi function
Electrochemical Potential
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Band-Diagram
µ
Fermi function
Electrochemical Potential
7
What makes electrons flow?
µ1
LUMO (n-type) Conduction
HOMO (p- type) Conduction
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Escape time
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Quantitative model
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Maximum conductance?
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Broadening
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Broadening
Maximum conductance
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Broadening
E
µ1
E
µ2
f1
f2
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Broadening
E
µ1
E
µ2
f1
f2
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Broadening
E
µ1
E
µ2
f1
f2
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Channel potential
U
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Channel potential?
U 1 V, if insulating 0 V, if metallic
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Where is the voltage drop ?
U
Poisson Equation
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Channel potential
U
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Channel potential
U
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Self-consistent calculation
U
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What makes a good transistor ?
E
µ1
µ2
D(E)
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What makes a good transistor ?
U
E
µ1
µ2
U
D(E)
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Minimal model
U
Nanowires / Nanotubes / Molecules
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Matrices lt--gt Numbers
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Experiment vs. Theory
Zahid, Paulsson, Ghosh
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Negative DifferentialResistance (NDR)
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Negative DifferentialResistance (NDR)
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Molecule on p-Silicon (100)
Experiment Hersam et.al.
Theory Rakshit, Liang, Ghosh
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Ohms Law ?
E
µ1
µ2
D(E)
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Where is the heat dissipated ?
Dissipative processes in the contacts maintain
them in equilibrium
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Dissipation lt--gt Contact
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How much poweris needed to switch ?
1 GHz
1 µm x 1 µm
0.4 mW/cm2 x N 100 W/cm2 N
2.5 x 105
Can this be reduced? How much ?
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Representing bitsof information
Charge
Reading the information
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Representing bitsof information
Charge
Spins
Reading the information
?
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How much energy does it take ?
Charge
Spins
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How much energy does it take?
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How much energy does it take?
Heat Dissipated
Work Done
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How much energy does it take?
Heat Dissipated
Work Done
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How much energy does it take?
Heat Dissipated
Work Done
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Thermodynamicvs. Dynamic switching
Heat dissipation necessary
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Thermodynamicvs. Dynamic switching
Heat dissipation NOT necessary

• THERMODYNAMIC --gt IRREVERSIBLE / REVERSIBLE
• DYNAMIC

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Thermodynamicvs. Dynamic switching
Heat dissipation necessary

• THERMODYNAMIC --gt IRREVERSIBLE

Heat dissipation NOT necessary

• THERMODYNAMIC --gt IRREVERSIBLE / REVERSIBLE
• DYNAMIC

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Dynamic switchingPros and cons

• Pros
• No heat
• No limit on speed
• Cons
• Not accurate
• Need ordered
• initial state

No
Yes
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Thermodynamicvs. Dynamic switching
Heat dissipation necessary
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How much poweris needed to switch ?
1 GHz
1 µm x 1 µm
0.4 mW/cm2 x N 100 W/cm2 N
2.5 x 105
Can this be reduced? How much ?
47
Nanoscale conduction A Unified Bottom-up View
Electronics Sensing
Unified model
Electrical Resistance An Atomistic View,
Nanotechnology 15 , S433 (2004)
www.nanohub.org
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Atom to Transistor
Unified model
Electrical Resistance An Atomistic View,
Nanotechnology 15 , S433 (2004)
www.nanohub.org
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Conformational Transistors ?
(Ses)min 2.3(kBT/e) ? 60 mV/dec. (Sconf)min2.3
(kBT/e).(etox/m)
Ghosh, Rakshit (Nanoletters, 2004)
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Bridging Disciplines
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Real (?) Models
Incoherent Scattering,
Open System, Out-of-equilibrium
Closed System
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Self-interaction correction
U
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One-electron vs. Many-electron
N one-electron levels
2N many electron levels
11
10
01
00
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One-electron vs. Many-electron
N one-electron levels
2N many electron levels
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Two choices
2N many electron levels w/o broadening
One-electron picture with broadening
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Two choices
2N many electron levels w/o broadening
One-electron picture with broadening
Band conductor
Mott insulator
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Hot contacts
Hot phonons ?
Hersam, Nanoletters, 01/04
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Two choices
Contact State A
Contact State B
Supplement NEGF with separate rate equation for
contact
Rate equation for full system
Works for