NEGF Method: Capabilities and Challenges

Gate M SOURCE DRAIN CHANNEL INSULATOR VG VD I NEGF Method:Capabilities and Challenges Supriyo Datta School of Electrical & Computer Engineering Purdue University Molecular Electronics CNT Electronics Molecular Sensor

‘s’ Gate H + U M SOURCE DRAIN CHANNEL INSULATOR VG VD I Nanodevices: A Unified View Unified Model Molecular Electronics CNT Electronics Molecular Sensor

‘s’ H + U -t -t -t -t 2t 2t 2t SOURCE DRAIN CHANNEL INSULATOR VG VD I Hamiltonian, [H] Effective Mass Equation Finite Difference / Finite Element Damle, Ren, Venugopal, Lundstrom ---> nanoMOS

‘s’ H + U , are matrices SOURCE DRAIN CHANNEL INSULATOR VG VD I Hamiltonian, [H] Nanowire Electronics Atomistic sp3d basis Rahman, Wang, Ghosh, Klimeck, Lundstrom

‘s’ Gate H + U , are (2x2) matrices Hamiltonian, [H] CNT Electronics Atomistic pz basis Guo, Lundstrom

‘s’ Gate H + U Hamiltonian, [H] Nanowire/CNT Electronics Atomistic non-orthogonal basis EHT Siddiqui, Kienle, Ghosh, Klimeck

‘s’ H + U Hamiltonian, [H] Molecular Electronics Atomistic basis: Huckel / EHT / Gaussian Ghosh, Rakshit,Liang, Zahid, Siddiqui, Golizadeh, Bevan, Kazmi

‘s’ H + U “Self-energy”,

‘s’ gate H + U “Self-energy”,

‘s’ [H] H + U [H] “Self-energy”,

‘s’ H + U From molecule to QPC “molecule” Damle, Ghosh PRB (2001)

Quantum Chemistry Surface Physics Surface Physics Bridging Disciplines Basis mixing: Ghosh, Liang, Kienle, Polizzi

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

Molecule on silicon Quantum chemistry Surface Physics Expt:Mark Hersam Nanoletters, 01/04 Cover story Room temperature (a) V = 0 (b) V < 0 (c) V > 0

‘s’ H + U NEGF equations

‘s’ H + U µ1 µ2 Matrices <--> Numbers

“Poisson” N --> U Self- Consistent Solution U --> N SOURCE DRAIN CHANNEL INSULATOR VG VD I Minimal Model U --> I Nanowires / Nanotubes / Molecules

µ1 µ2 INSULATOR CHANNEL W L z x E D(E) FET: Why current “saturates” ? Drain current Drain voltage

‘s’ H + U Self-consistent field, U 3D Poisson solver: Eric Polizzi Method of moments: Jing Guo

‘s’ H + U Self-consistent field, U 3D Poisson solver: Eric Polizzi Method of moments: Jing Guo Correlations

‘s’ H + U Self-consistent field, U Quantum Chemistry: Closed System in Equilibrium U H+U, N

‘s’ H + U Which self-consistent field ? µ

‘s’ H + U Which LDA ?

‘s’ H + U Which LDA ? IP = E(N) - E(N-1) EA = E(N+1) - E(N)

N vs. µ µ N - N0

N vs. µ: SCF Theory µ U0/2 N - N0 Rakshit

Self-interaction Correction µ U0/2 No general method N - N0

11 10 01 00 One-electron vs. Many-electron N one-electron levels 2^N many electron levels

‘s’ H + U 11 10 01 00 Two choices 2^N many electron levels Works for Works for

‘s’ H + U 11 10 01 00 Two choices 2^N many electron levels Works for Works for ? Mott insulator Band theory

‘s’ H + U What is a contact? Klimeck, Lake et.al. APL (1995)

‘s’ H + U “Hot” contacts Energy has to be removed efficiently from the contacts: otherwise --> “hot” contacts

‘s’ H + U Source Drain “Hot” contacts Venugopal, Lundstrom

‘s’ H + U Other “contacts”

‘s’ H + U Other “contacts” Hot phonons ?

‘s’ H + U Other “contacts” Hot phonons ? Molecular desorption ?

‘s’ H + U Source Drain Hot “contacts” Hot phonons ? Molecular desorption ?

‘s’ H + U 11 11 10 10 01 01 00 00 Two choices “Contact” State A “Contact” State B Supplement NEGF with separate rate equation for “contact” Rate equation for full system Works for

‘s’ H + U M SOURCE DRAIN CHANNEL INSULATOR VG VD I Summary Unified Model Electronics & Sensing www.nanohub.org Transients? Strong correlations ? “Hot contacts” ? Electrical Resistance: An Atomistic View, Nanotechnology 15 , S433 (2004)

EXPT: Karlsruhe THEORY: Purdue Group (cond-mat/0403401) Experiment vs. Theory Zahid, Paulsson, Ghosh

NEGF Method: Capabilities and Challenges