NEGF%20Method:%20Capabilities%20and%20Challenges

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NEGF MethodCapabilities and Challenges
Molecular Electronics
Supriyo Datta School of Electrical Computer
Engineering Purdue University
CNT Electronics
Molecular Sensor
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Nanodevices A Unified View
Unified Model
Molecular Electronics
CNT Electronics
Molecular Sensor
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Hamiltonian, H
Effective Mass Equation
Finite Difference / Finite Element
Damle, Ren, Venugopal, Lundstrom ---gt nanoMOS
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Hamiltonian, H
Nanowire Electronics
Atomistic sp3d basis
Rahman, Wang, Ghosh, Klimeck, Lundstrom
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Hamiltonian, H
CNT Electronics
Atomistic pz basis
Guo, Lundstrom
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Hamiltonian, H
Nanowire/CNT Electronics
Atomistic non-orthogonal basis
EHT
Siddiqui, Kienle, Ghosh, Klimeck
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Hamiltonian, H
Molecular Electronics
Atomistic basis
Huckel / EHT / Gaussian
Ghosh, Rakshit,Liang, Zahid, Siddiqui, Golizadeh,
Bevan, Kazmi
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Self-energy,
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Self-energy,
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Self-energy,
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Self-energy,
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Self-energy,
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From molecule to QPC
molecule
Damle, Ghosh PRB (2001)
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Bridging Disciplines
Basis mixing Ghosh, Liang, Kienle, Polizzi
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C60 on Silicon
I
II
III
dI/dV
IV
I
IV
II
dI/dV
III
T(E)
STS measurements (a) Dekker, et al., surface
science 2002. (b) (c) Yao, et al, surface
science 1996
V (V)
Theory Liang, Ghosh
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Molecule on silicon
Quantum chemistry
Surface Physics
ExptMark Hersam Nanoletters, 01/04 Cover story
Room temperature
(a) V 0 (b) V lt 0 (c) V gt 0
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NEGF equations
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Matrices lt--gt Numbers
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Minimal Model
U --gt I
Nanowires / Nanotubes / Molecules
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FET Why current saturates ?
Drain current
Drain voltage
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Self-consistent field, U
3D Poisson solver Eric Polizzi
Method of moments Jing Guo
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Self-consistent field, U
3D Poisson solver Eric Polizzi
Method of moments Jing Guo
Correlations
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Self-consistent field, U
Quantum Chemistry Closed System in Equilibrium
U
HU, N
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Self-consistent field, U
Quantum Chemistry Closed System in Equilibrium
U
HU, N
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Self-consistent field, U
Quantum Chemistry Closed System in Equilibrium
U
HU, N
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Which self-consistent field ?
µ
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Which LDA ?
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Which LDA ?
IP E(N) - E(N-1) EA E(N1) - E(N)
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N vs. µ
µ
N - N0
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N vs. µ SCF Theory
µ
U0/2
N - N0
Rakshit
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Self-interaction Correction
µ
U0/2
No general method
N - N0
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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
Works for
Works for
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Two choices
2N many electron levels
Works for
Works for
?
Mott insulator
Band theory
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What is a contact?
Klimeck, Lake et.al. APL (1995)
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What is a contact?
Klimeck, Lake et.al. APL (1995)
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Hot contacts
Energy has to be removed efficiently from the
contacts otherwise --gt hot contacts
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Hot contacts
Venugopal, Lundstrom
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Hot contacts
Venugopal, Lundstrom
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Other contacts
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Other contacts
Hot phonons ?
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Other contacts
Hot phonons ?
Molecular desorption ?
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Hot contacts
Hot phonons ?
Molecular desorption ?
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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
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Summary
Electronics Sensing
Unified Model
www.nanohub.org
Transients? Strong correlations ? Hot contacts ?
Electrical Resistance An Atomistic View,
Nanotechnology 15 , S433 (2004)
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Experiment vs. Theory
Zahid, Paulsson, Ghosh