© a. nitzan, tau part b: main results and phenomenology a. nitzan

PART B: Main results and PART B: Main results and phenomenologyphenomenology

A. Nitzan

Electron transfer in DNAElectron transfer in DNA

Weber et al, Chem. Phys. 2002

q = 1q = 0 q = 1q = 0

Electron transfer

Electron transition takes place in unstable nuclear configurations obtained via thermal fluctuations

Nuclear motion

q= 0q = 1q = 1q = 0

Bridge assisted ET ratesBridge assisted ET rates

2)1 ( )

D A AD

N ANA D

BE k T

Bridge Green’s Function

Donor-to-Bridge/ Acceptor-to-bridge

Franck-Condon-weighted DOS

Reorganization energy

Effective donor-acceptor coupling

Golden-rule-like equation

Electron transferElectron transfer

E aE A

e ne r g y

0 tr 1

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

ET rate from steady state ET rate from steady state hoppinghopping

B BE k T

Bridge length

Activation to bridge

Constant (k=rate on bridge)

A level interacting with a A level interacting with a continnumcontinnum

Starting from state 0 at t=0:

P0 = exp(-t)

= 2|Vsl|2L (Golden Rule)

(1 / 2)

exp ( / ) ) exp ( / ) ) (1 / 2)

i E t i E t t

01 12 , 10, 1

1 1 1 1ˆ ( ) ...B N NN

G E V V VE E E E E EE E

2 LE E i

2N N RE E i

SELF ENERGY

Resonant Transmission – 3dResonant Transmission – 3d

V (x )

. . . .

. . . . . . . .

120 0 0( ) exp ( ) / 1Bc f E E k T

1 0 1 0

0 2 20 1 1 0

( ) ( )( )

( ) / 2

21 0 1 002 2

0 1 1 0

( ) ( ) ( )1| |

2 ( ) / 2

L R L R

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)

21 (1 / 2)E E i

CONDUCTIONCONDUCTION

( ) 1( ) ( )

dJ EE f E

( ) (L Rf Ee

I d fE EE

2 21 1

( ) ( )( )

( ) / 2

L RE EE

0( ) ( ) ( )f E e f E e E 2

2 spin states

Zero bias conduction ( 0)g

Landauer formulaLandauer formula2

( 0) ( ) ; Fermi energye

( ) ( ) ( )L R

eI dE f E f E E

2 21 1

( ) ( )( )

( ) / 2

L RE EE

(maximum=1)

Maximum conductance per channel

For a single “channel”:

Molecular level structure Molecular level structure between electrodesbetween electrodes

en erg y

“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)

General caseGeneral case

( )† ( )B

ˆ ˆˆ ˆ(E)=Tr ( ) ( ) ( ) ( )B BE G E E G E T

( ) ( )

( ), , ', '

( ) (1 / 2)

Rn r r n Rn n

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

The N-level bridge (n.n. The N-level bridge (n.n. interactions)interactions)

{ r }{ l}

1 . . . . N + 1

( ) ( )20, 1 0 1( ) | ( ) | ( ) ( )L R

N NE G E E E T

( ) ( ) ( )L R

eI dE f E f E E

01 12 , 10, 1

1 1 1 1ˆ ( ) ...B N NN

G E V V VE E E E E EE E

2 LE E i

2N N RE E i

G1N(E)

ET vs ConductionET vs Conduction

01 ,(11

D A DA

N N DV V

01 , 1

( ) ( )0

( ) ( )

( ) ( )0

| ( ( ) ( )

( )1 1

E E i E

........

N + 1 = A

A relation between g and A relation between g and kk

2 ( ) ( )

8D AL R

conduction Electron transfer rate

MarcusDecay into electrodes

Electron charge

A relation between g and A relation between g and kk

2 ( ) ( )

8D AL R

4 exp / 4B Bk T k T

eV ( ) ( ) 0.5L RD A eV

2 13 1

17 1 1

~ / 10 ( )

10 ( )

g e k s

Comparing conduction Comparing conduction to ratesto rates

(M. Newton, 2003)(M. Newton, 2003)

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) ( ) | |

E E Veg E

E E i E E E i E V

{ r }{ l}

•Dependence on:

•Molecule-electrode coupling L

•Molecular energetics E1, E2

•Intramolecular coupling V1,2

-1 -0.5 0 0.5 1

0.0 - 0.5

Ratner and Troisi, 2004

““Switching”Switching”

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

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

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

Galperin et al JCP 2003

Why is it important?Why is it important?D. Segal, AN, JCP 2002 Heat Release on junction

Tian et al JCP 1998

ExperimentExperiment Theoretical Model

Experimental i/V behaviorExperimental i/V behavior

Potential distributionPotential distribution

NEGF - HF calculationNEGF - HF calculation

HS - CHHS - CH22CHCH22CHCH22CHCH22CHCH22CHCH33 . . . CH . . . CH33CHCH22 - SH- SH

MO Segment Orbital

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

Elastic transmission vs. maximum heat generation:

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

Inelastic tunneling Inelastic tunneling spectroscopy: Peaks and spectroscopy: Peaks and

dipsdips

With Michael Galperin and Mark Ratner

incident scattered

Light Scattering

o utin-0in

INELSTIC ELECTRON TUNNELING SPECTROSCOPY

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

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.

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

ParametersParameters

electrons

Molecular vibrations

Thermal environment

M – from reorganization energy (~M2/0)

U – from vibrational relaxation rates

electrons

vibrationsM

2 2 2 213 31

21A AA MA M AA AM

elastic inelastic elastic

Changing position of molecular resonance:

Changing tip-molecule distance

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

© a. nitzan, tau part b: main results and phenomenology a. nitzan

nitzan slide

bridge slide

tau conduction

dna slide

e0e0 slide

vacuum slide

equation slide

ev slide

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