© a. nitzan, tau part b: main results and phenomenology a. nitzan
Post on 22-Dec-2015
226 views
TRANSCRIPT
© A. Nitzan, TAU
PART B: Main results and PART B: Main results and phenomenologyphenomenology
A. Nitzan
© A. Nitzan, TAU
Electron transfer in DNAElectron transfer in DNA
© A. Nitzan, TAU
Weber et al, Chem. Phys. 2002
© A. Nitzan, TAU
q = 1q = 0 q = 1q = 0
Electron transfer
Electron transition takes place in unstable nuclear configurations obtained via thermal fluctuations
Nuclear motion
Nuclear motion
q= 0q = 1q = 1q = 0
© A. Nitzan, TAU
Bridge assisted ET ratesBridge assisted ET rates
2
2 (1
2)1 ( )
|
)2
| ( )
(
2
BD
DA
D
D A AD
N ANA D
V
V
E
GV E
k
E
F
F
2/ 4
( )4
BE k T
B
eE
k T
F
Bridge Green’s Function
Donor-to-Bridge/ Acceptor-to-bridge
Franck-Condon-weighted DOS
Reorganization energy
Effective donor-acceptor coupling
Golden-rule-like equation
© A. Nitzan, TAU
Electron transferElectron transfer
E aE A
E b
E
e ne r g y
ab
0 tr 1
VAD
© A. Nitzan, TAU
Bridge mediated ET rateBridge mediated ET rate
~ ( , )exp( ' )ET AD DAk E T RF
’ (Å-1) =
0.2-0.6 for highly conjugated chains
0.9-1.2 for saturated hydrocarbons
~ 2 for vacuum
© A. Nitzan, TAU
ET rate from steady state ET rate from steady state hoppinghopping
/
1,0
1
1
B BE k T
D A N
N A D
kek k
k kN
k k
Bridge length
Activation to bridge
Constant (k=rate on bridge)
© A. Nitzan, TAU
A level interacting with a A level interacting with a continnumcontinnum
{ }l0
V0l
Starting from state 0 at t=0:
P0 = exp(-t)
= 2|Vsl|2L (Golden Rule)
l
0 0
0 0
(1 / 2)
exp ( / ) ) exp ( / ) ) (1 / 2)
E E i
i E t i E t t
01 12 , 10, 1
1 10
1 1 1 1ˆ ( ) ...B N NN
N N
G E V V VE E E E E EE E
0 0
1
1
2 LE E i
1 1,
1
1
2N N RE E i
SELF ENERGY
© A. Nitzan, TAU
Resonant Transmission – 3dResonant Transmission – 3d
|1 >
|0 >
x
V (x )
RL
. . . .
. . . .
. . . .
. . . .
. . . . . . . .
(a )
(b)
( c)
R
L
120 0 0( ) exp ( ) / 1Bc f E E k T
1 0 1 0
0 2 20 1 1 0
1 1 1
( ) ( )( )
( ) / 2
L R
R L
E EE
E E E
T
1d
0
21 0 1 002 2
0 1 1 0
( ) ( ) ( )1| |
2 ( ) / 2
L R L R
E E
dJ E E Ec
dE E E E
3d: Total flux from L to R at energy E0:
If the continua are associated with a metal electrode at thermal equilibrium than
(Fermi-Dirac distribution)
l
1
V1r
r
V1lE0
21 (1 / 2)E E i
© A. Nitzan, TAU
CONDUCTIONCONDUCTION
0
0 0
( ) 1( ) ( )
2L R
LE E
dJ EE f E
dE
T
( ))2
( ) (L Rf Ee
I d fE EE
T
1 1
2 21 1
( ) ( )( )
( ) / 2
L RE EE
E E E
T
0( ) ( ) ( )f E e f E e E 2
( )2
eI E
T
2 spin states
2
( )e
g E
T
Zero bias conduction ( 0)g
L R
LRe|
RL
© A. Nitzan, TAU
Landauer formulaLandauer formula2
( 0) ( ) ; Fermi energye
g E
T
( ) ( ) ( )L R
eI dE f E f E E
T ( )
dIg
d
1 1
2 21 1
( ) ( )( )
( ) / 2
L RE EE
E E E
T
(maximum=1)
2
112.9
eg K
Maximum conductance per channel
For a single “channel”:
© A. Nitzan, TAU
Molecular level structure Molecular level structure between electrodesbetween electrodes
en erg y
LUMO
HOMO
© A. Nitzan, TAU
“The resistance of a single octanedithiol molecule was 900 50 megaohms, based on measurements on more than 1000 single molecules. In contrast, nonbonded contacts to octanethiol monolayers were at least four orders of magnitude more resistive, less reproducible, and had a different voltage dependence, demonstrating that the measurement of intrinsic molecular properties requires chemically
bonded contacts”.
Cui et al (Lindsay), Science 294, 571 (2001)
© A. Nitzan, TAU
General caseGeneral case
( )† ( )B
ˆ ˆˆ ˆ(E)=Tr ( ) ( ) ( ) ( )B BE G E E G E T
( ) ( )
( ), , ', '
( ) (1 / 2)
2
R R
Rn r r n Rn n
B E i
H H
1( ) ( ) ( )ˆ( ) IB B BG E E H
( ), ' , ', '
Bn n n nn nH H B
Unit matrix in the bridge space
Bridge Hamiltonian
B(R) + B(L) -- Self energy
Wide band approximation
( ) ( ) ( )L R
eI dE f E f E E
T
© A. Nitzan, TAU
The N-level bridge (n.n. The N-level bridge (n.n. interactions)interactions)
0
{ r }{ l}
RL
1 . . . . N + 1
2
( )e
g E
T
( ) ( )20, 1 0 1( ) | ( ) | ( ) ( )L R
N NE G E E E T
( ) ( ) ( )L R
eI dE f E f E E
T
01 12 , 10, 1
1 10
1 1 1 1ˆ ( ) ...B N NN
N N
G E V V VE E E E E EE E
0 0
1
1
2 LE E i
1 1,
1
1
2N N RE E i
G1N(E)
© A. Nitzan, TAU
ET vs ConductionET vs Conduction
2
01 ,(11
2
2)
2| |
2
(
(( )
)
)
AD
NB
D A
D A DA
N N DV V
E
G E
k
E
V
F
F
01 , 1
( ) ( )0
( ) ( )
1
0 1
( ) ( )0
2
2
( )
1
1
2
1
0,
2
2
| ( ( ) ( )
( )1 1
)
)
2
(
2
( )
|
N N
L RD
L RN
L RNN
A
B
N
N
eg
e V V
E E i E
E E
E
G
G
E
EE
E
i
........
0 = D
1 2 N
N + 1 = A
E
© A. Nitzan, TAU
A relation between g and A relation between g and kk
2
2 ( ) ( )
8D AL R
D A
eg k
F
conduction Electron transfer rate
MarcusDecay into electrodes
Electron charge
© A. Nitzan, TAU
A relation between g and A relation between g and kk
2
2 ( ) ( )
8D AL R
D A
eg k
F
1
4 exp / 4B Bk T k T
F
eV ( ) ( ) 0.5L RD A eV
2 13 1
17 1 1
~ / 10 ( )
10 ( )
D A
D A
g e k s
k s
© A. Nitzan, TAU
Comparing conduction Comparing conduction to ratesto rates
(M. Newton, 2003)(M. Newton, 2003)
© A. Nitzan, TAU
2-level bridge (local 2-level bridge (local representation)representation)
( ) ( ) 22
1,21 2
2( ) ( ) 2
1 2 1,21 2
( ) ( ) | |( )
(1 / 2) ( ) (1 / 2) ( ) | |
L R
L R
E E Veg E
E E i E E E i E V
1
{ r }{ l}
RL
2
V 1 2
•Dependence on:
•Molecule-electrode coupling L
, R
•Molecular energetics E1, E2
•Intramolecular coupling V1,2
© A. Nitzan, TAU© A. Nitzan, TAU
-1
0
1
2
3
4
5
6
-1 -0.5 0 0.5 1
I /
arb
. u
nit
s
0.0 - 0.5
0.5
I
V (V)
Ratner and Troisi, 2004
© A. Nitzan, TAU
““Switching”Switching”
© A. Nitzan, TAU
Reasons for switchingReasons for switching Conformational changesConformational changes
STM under waterSTM under waterS.Boussaad et. al. S.Boussaad et. al. JCP (2003)JCP (2003)
Tsai et. al. PRL 1992: RTS in Me-SiO2-Si junctions
Transient Transient chargingcharging
© A. Nitzan, TAU
Temperature and chain Temperature and chain length dependencelength dependence
Giese et al, 2002
Michel-Beyerle et al
Selzer et al 2004
Xue and Ratner 2003
© A. Nitzan, TAU
Where does the potential Where does the potential bias falls, and how?bias falls, and how?
•Image effect
•Electron-electron interaction (on the Hartree level)Vacuu
mExcess electron density
Potential profile
Xue, Ratner (2003)
Galperin et al 2003
L
Galperin et al JCP 2003
© A. Nitzan, TAU
Why is it important?Why is it important?D. Segal, AN, JCP 2002 Heat Release on junction
Tian et al JCP 1998
© A. Nitzan, TAU
ExperimentExperiment Theoretical Model
© A. Nitzan, TAU
Experimental i/V behaviorExperimental i/V behavior
© A. Nitzan, TAU
Potential distributionPotential distribution
© A. Nitzan, TAU
NEGF - HF calculationNEGF - HF calculation
© A. Nitzan, TAU
HS - CHHS - CH22CHCH22CHCH22CHCH22CHCH22CHCH33 . . . CH . . . CH33CHCH22 - SH- SH
MO Segment Orbital
© A. Nitzan, TAU
Electron and Phonon Electron and Phonon Transport in molecular wiresTransport in molecular wires
•Inelastic tunneling spectroscopy
•Relevant timescales
•Heating of current carrying molecular wires
•Inelastic contributions to the tunneling current
•Dephasing and activation - transition from coherent transmission to activated hoppinga
(1) dissipation of electronic energy (2) Heat conduction away from junction
© A. Nitzan, TAU
Elastic transmission vs. maximum heat generation:
© A. Nitzan, TAU
The quantum heat The quantum heat fluxflux
( ) ( ) ( )h L RI n n d T
Bose Einstein populations for left
and right baths.
Transmission coefficient at
frequency
With Dvira Segal and Peter Hanggi
© A. Nitzan, TAU
Inelastic tunneling Inelastic tunneling spectroscopy: Peaks and spectroscopy: Peaks and
dipsdips
With Michael Galperin and Mark Ratner
© A. Nitzan, TAU
h0h0
incident scattered
Light Scattering
o utin-0in
o utin-0in
o utin-0in
© A. Nitzan, TAU
h
h
INELSTIC ELECTRON TUNNELING SPECTROSCOPY
V
h
© A. Nitzan, TAU
Localization of Inelastic Tunneling and the Determination of Atomic-Scale Structure with Chemical Specificity
B.C.Stipe, M.A.Rezaei and W. Ho, PRL, 82, 1724 (1999)
STM image (a) and single-molecule vibrational spectra (b) of three acetylene isotopes on Cu(100) at 8 K. The vibrational spectra on Ni(100)are shown in (c). The imaged area in (a), 56Å x 56Å, was scanned at 50 mV sample bias and 1nA tunneling current
© A. Nitzan, TAU
Electronic Resonance and Symmetry in Electronic Resonance and Symmetry in Single-Molecule Inelastic Electron Single-Molecule Inelastic Electron
TunnelingTunnelingJ.R.Hahn,H.J.Lee,and W.Ho, PRL 85, 1914 (2000)J.R.Hahn,H.J.Lee,and W.Ho, PRL 85, 1914 (2000)
Single molecule vibrational spectra obtained by STM-IETS for 16O2 (curve a),18O2 (curve b), and the clean Ag(110)surface (curve c).The O2 spectra were taken over a position 1.6 Å from the molecular center along the [001] axis.
The feature at 82.0 (76.6)meV for 16O2 (18O2) is assigned to the O-O stretch vibration, in close agreement with the values of 80 meV for 16O2 obtained by EELS.The symmetric O2 -Ag stretch (30 meV for 16O2) was not observed.The vibrational feature at 38.3 (35.8)meV for 16O2 (18O2)is attributed to the antisymmetric O2 -Agstretch vibration.
© A. Nitzan, TAU
Inelastic Electron Tunneling Spectroscopy ofInelastic Electron Tunneling Spectroscopy of
Alkanedithiol Self-Assembled MonolayersAlkanedithiol Self-Assembled Monolayers W. Wang, T. Lee, I. Kretzschmar and M. A. Reed (Yale, W. Wang, T. Lee, I. Kretzschmar and M. A. Reed (Yale,
2004)2004)
Inelastic electron tunneling spectra of C8 dithiol SAM obtained from lock-insecond harmonic measurements with an AC modulation of 8.7 mV (RMS value) at a frequency of 503 Hz (T =4.2 K).Peaks labeled *are most probably background due to the encasing Si3N4
Nano letters
© A. Nitzan, TAU
ParametersParameters
electrons
Molecular vibrations
Thermal environment
M
U
L R
0
V
M – from reorganization energy (~M2/0)
U – from vibrational relaxation rates
© A. Nitzan, TAU
electrons
vibrationsM
A1A2M
A3M2
2 2
2 2 2 213 31
21A AA MA M AA AM
elastic inelastic elastic
© A. Nitzan, TAU
Changing position of molecular resonance:
© A. Nitzan, TAU
Changing tip-molecule distance
© A. Nitzan, TAU
Challenges and prospectsChallenges and prospects Characterization of the temperature dependence of conductance. Characterization geometry and its evolution during transport. Measurements with differing junction subunits (molecular conjugation, interface bonding “alligator clip” functional groups, electrodes). Use of semi-conductor electrodes More extensive work on gating of molecular junctions. Finding other controls. Elucidating the change in behavior from a single molecule conductance through junctions comprising a few molecules to molecular film conductors. Effects of changing chemistry and doping on the bridge – can mechanisms be altered by chemical change, as in conducting polymers, and can we predict and control such behavior? Characterizing transport junctions behavior in the presence of radiation. Understanding noiseUnderstanding heating , heat conduction and current induced chemical changes