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

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

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

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

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

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

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

8. “Self-energy”,
H U
‘s’

9. “Self-energy”,
gate
H U
‘s’

10. “Self-energy”,
gate
H U
‘s’

11. “Self-energy”,
gate
H U
‘s’

12. “Self-energy”,
H U
‘s’
[H]
[H]

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

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

15. C60 on Silicon Theory: Liang, Ghosh dI/dV dI/dV T(E) V (V)II
III
dI/dV IV I II IV
dI/dV
III
T(E)
STS measurements: (a) Dekker, et al., surface science (b)& (c) Yao, et al, surface science 1996
V (V)
Theory: Liang, Ghosh

16. (a) V = 0 (b) V < 0 (c) V > 0
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

17. NEGF equations
H U
‘s’

18. Matrices <--> Numbers
H U
‘s’ µ1 µ2

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

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

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

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

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

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

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

26. Which self-consistent field ?
H U
‘s’

27. Which LDA ?
H U
‘s’

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

29. N vs. µ
N - N0

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

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

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

33. 2^N many electron levels
Two choices
2^N many electron levels
H U
‘s’ 00 11 01 10
Works for
Works for

34. 2^N many electron levels
Two choices
2^N many electron levels
H U
‘s’ 00 11 01 10
Works for
Works for ?
Mott insulator
Band theory

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

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

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

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

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

40. Other “contacts”
H U
‘s’

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

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

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

44. Two choices Works for “Contact” State A “Contact” State B H + U ‘s’ 0011 01 10 00 11 01 10
Supplement NEGF with
separate rate equation
for “contact”
Rate equation for full system
Works for

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

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