NEGF Method Capabilities and Challenges NCN INAC Molecular
NEGF Method: Capabilities and Challenges NCN INAC Molecular Electronics Supriyo Datta School of Electrical & Computer Engineering Purdue University Molecular Sensor S O U R CE CNT Electronics M Gate D R A IN CHANNEL INSULATOR VG I VD
Nanodevices: A Unified View NCN INAC Unified Model ‘s’ Molecular Electronics H + U Molecular Sensor S O U R CE CNT Electronics M Gate D R A IN CHANNEL INSULATOR VG I VD
Hamiltonian, [H] NCN INAC ‘s’ S O U R CE D R A IN CHANNEL INSULATOR H + U VG VD I Effective Mass Equation Finite Difference / Finite Element -t 2 t -t Damle, Ren, Venugopal, Lundstrom ---> nano. MOS
Hamiltonian, [H] NCN INAC Nanowire Electronics ‘s’ H + U S O U R CE D R A IN CHANNEL INSULATOR VG VD I Atomistic sp 3 d basis , are matrices Rahman, Wang, Ghosh, Klimeck, Lundstrom
Hamiltonian, [H] NCN INAC ‘s’ CNT Electronics Gate H + U Atomistic pz basis , are (2 x 2) matrices Guo, Lundstrom
Hamiltonian, [H] NCN INAC Nanowire/CNT Electronics ‘s’ Gate H + U Atomistic non-orthogonal basis EHT Siddiqui, Kienle, Ghosh, Klimeck
Hamiltonian, [H] NCN INAC Molecular Electronics ‘s’ H + U Atomistic basis: Huckel / EHT / Gaussian Ghosh, Rakshit, Liang, Zahid, Siddiqui, Golizadeh, Bevan, Kazmi
“Self-energy”, NCN INAC ‘s’ H + U
“Self-energy”, NCN INAC ‘s’ H + U gate
“Self-energy”, NCN INAC ‘s’ H + U gate
“Self-energy”, NCN INAC ‘s’ H + U gate
“Self-energy”, NCN INAC ‘s’ H + U [H]
From molecule to QPC NCN INAC ‘s’ H + U Damle, Ghosh PRB (2001) “molecule”
NCN INAC Bridging Disciplines Surface Physics Quantum Chemistry Surface Physics Basis mixing: Ghosh, Liang, Kienle, Polizzi
NCN INAC C 60 on Silicon I I III IV IV II III T(E) d. I/d. V II STS measurements: (a) Dekker, et al. , surface science 2002. (b)& (c) Yao, et al, surface science 1996 V (V) Theory: Liang, Ghosh
NCN INAC Molecule on silicon Surface Quantum Physics chemistry Expt: Mark Hersam Nanoletters, 01/04 Cover story Room temperature (a) V = 0 (b) V < 0 (c) V > 0
NEGF equations NCN INAC ‘s’ H + U
Matrices <--> Numbers NCN INAC ‘s’ H + U µ 1 µ 2
NCN Minimal Model INAC S O U R CE D R A IN CHANNEL INSULATOR VG N --> U VD I U --> N “Poisson” Self. Consistent Solution U --> I Nanowires / Nanotubes / Molecules
NCN INAC FET: Why current “saturates” ? Drain current E µ 1 µ 2 D(E) Drain voltage INSULATOR z CHANNEL L W x
Self-consistent field, U NCN INAC ‘s’ H + U Method of moments: Jing Guo 3 D Poisson solver: Eric Polizzi
Self-consistent field, U NCN INAC ‘s’ H + U Method of moments: Jing Guo 3 D Poisson solver: Eric Polizzi Correlations
Self-consistent field, U NCN INAC ‘s’ Quantum Chemistry: Closed System H + U in Equilibrium U H+U, N
Self-consistent field, U NCN INAC ‘s’ Quantum Chemistry: Closed System H + U in Equilibrium U H+U, N
Self-consistent field, U NCN INAC ‘s’ Quantum Chemistry: Closed System H + U in Equilibrium U H+U, N
NCN INAC Which self-consistent field ? ‘s’ H + U µ
Which LDA ? NCN INAC ‘s’ H + U
Which LDA ? NCN INAC ‘s’ H + U IP = E(N) - E(N-1) EA = E(N+1) - E(N)
N vs. µ NCN INAC µ N - N 0
N vs. µ: SCF Theory NCN INAC µ U 0/2 N - N 0 Rakshit
NCN INAC Self-interaction Correction µ U 0/2 N - N 0 No general method
NCN INAC One-electron vs. Many-electron N one-electron levels 2^N many electron levels 11 10 01 00
Two choices NCN INAC ‘s’ 2^N many electron levels 11 10 H + U 01 00 Works for
Two choices NCN INAC 2^N many electron levels ‘s’ 11 10 H + U 01 00 Works for Band theory ? Works for Mott insulator
What is a contact? NCN INAC ‘s’ H + U Klimeck, Lake et. al. APL (1995)
What is a contact? NCN INAC ‘s’ H + U Klimeck, Lake et. al. APL (1995)
“Hot” contacts NCN INAC ‘s’ H + U Energy has to be removed efficiently from the contacts: otherwise --> “hot” contacts
“Hot” contacts NCN INAC ‘s’ H + U Source Drain Venugopal, Lundstrom
“Hot” contacts NCN INAC ‘s’ H + U Source Drain Venugopal, Lundstrom
Other “contacts” NCN INAC ‘s’ H + U
Other “contacts” NCN INAC ‘s’ H + U Hot phonons ?
Other “contacts” NCN INAC ‘s’ Hot phonons ? H + U Molecular desorption ?
Hot “contacts” NCN INAC Hot phonons ? ‘s’ H + U Molecular desorption ? Source Drain
Two choices NCN INAC ‘s’ “Contact” State A “Contact” State B 11 11 H + U 10 01 Supplement NEGF with separate equation for “contact” 10 01 00 00 Rate equation for full system Works for
Summary NCN INAC Unified Model Electronics & Sensing ‘s’ H + U M S O U R CE D R A IN CHANNEL INSULATOR VG VD I www. nanohub. org Electrical Resistance: An Atomistic View, Nanotechnology 15 , S 433 (2004) Transients? Strong correlations ? “Hot contacts” ?
NCN INAC Experiment vs. Theory THEORY: Purdue Group (cond-mat/0403401) EXPT: Karlsruhe Zahid, Paulsson, Ghosh
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