© a. nitzan, tau introduction to electron transport in molecular systems i. benjamin, a. burin, b....

Introduction to electron Introduction to electron transport in molecular systemstransport in molecular systems

I. Benjamin, A. Burin, B. Davis, S. Datta, D. Evans, M. Galperin, A. Ghosh, H. Grabert, P. Hänggi, G. Ingold, J. Jortner, S. Kohler, R. Kosloff, J. Lehmann, M. Majda, A. Mosyak, V. Mujica, R. Naaman, U. Peskin, M. Ratner, D. Segal, T. Seideman, H. Tal-Ezer

Thanks

Reviews: Annu. Rev. Phys. Chem. 52, 681– 750 (2001) [http://atto.tau.ac.il/~nitzan/nitzanabs.html/#213]

Science, 300, 1384-1389 (2003); MRS Bulletin, 29, 391-395 (2004); Bulletin of the

Israel Chemical Society, Issue 14, p. 3-13 (Dec 2003) (Hebrew)

PART BPART B: Molecular : Molecular conduction: Main results and conduction: Main results and phenomenologyphenomenology

A. Nitzan (nitzan@post.tau.ac.il;

http://atto.tau.ac.il/~nitzan/nitzan.html)

PART APART A: Introduction: electron : Introduction: electron transfer in molecular systemstransfer in molecular systems

PART CPART C: Inelastic effects in : Inelastic effects in molecular conductionmolecular conduction

Introduction to electron transport in molecular systems

http://atto.tau.ac.il/~nitzan/tu04-X.ppt (X=A,B,C)

Molecules as conductorsMolecules as conductors

m o lecule

Aviram Ratner

Abstract

The construction of a very simple electronic device, a rectifier, based on the use of a single organic molecule is discussed. The molecular rectifier consists of a donor pi system and an acceptor pi system, separated by a sigma-bonded (methylene) tunnelling bridge. The response of such a molecule to an applied field is calculated, and rectifier properties indeed appear.

Molecular Rectifiers

Arieh Aviram and Mark A. RatnerIBM Thomas J. Watson Research Center, Yorktown Heights, New

York 10598, USADepartment of Chemistry, New York New York University, New

York 10003, USA

Received 10 June 1974

Xe on Ni(110)

Feynman

Chad Mirkin (DPN)

Moore’s “Law”

Moore’s 2nd law

Molecules get wired

Science, Vol 302, Issue 5645, 556-559 , 24 October 2003MOLECULAR ELECTRONICS:

Next-Generation Technology Hits an Early Midlife CrisisRobert F. Service

Researchers had hoped that a new revolution in ultraminiaturized electronic gadgetry lay almost within reach. But now some are saying the future must wait

Two years ago, the nascent field of molecular electronics was riding high. A handful of research groups had wired molecules to serve as diodes, transistors, and other devices at the heart of computer chips. Some had even linked them together to form rudimentary circuits, earning accolades as Science's 2001 Breakthrough of the Year (Science, 21 December 2001, p. 2442). The future was so bright, proponents predicted that molecular electronics-based computer chips vastly superior to current versions would hit store shelves in 2005

Now, critics say the field is undergoing a much-needed reality check. This summer, two of its most prominent research groups revealed that some of their devices don't work as previously

thought and may not even qualify as molecular

electronics. And skeptics are questioning whether

labs will muster commercial products within the next

decade, if at all

IEEE TRANSACTIONS ON ELECTRON DEVICES VOL.43OCTOBER 1996 1637

Need for Critical AssessmentRolf Landauer,Life Fellow,IEEE

AbstractAdventurous technological proposals are subject to inadequate critical assessment. It is the proponents who organize meetings and special issues. Optical logic, mesoscopic switching devices and quantum parallelism are used to illustrate this problem.

This editorial,disguised as a scientific paper, is obviously a plan for more honesty. We do not, in the long run, build effective public support for science and technology by promising more than we can deliver.

Feynman

• For a successful Technology, reality must take precedence over public relations, for nature cannot be fooled

First Transport Measurements through Single Molecules

Single-wall carbon nanotube on Pt

Dekker et al. Nature 386(97)

Nanopore

Reed et al. APL 71 (97)

Break junction: dithiols between gold

Molecule lying on a surface Molecule between

two electrodes

Dorogi et al. PRB 52 (95) @ Purdue

Au(111)

Pt/Ir Tip

SAM1 nm

~1-2 nm

Self-assembled monolayers

Adsorbed molecule addressed by STM tip

C60 on gold

Joachim et al. PRL 74 (95)

STMtip

Reed et al. Science 278 (97) @ Yale

Nanotube on Au

Lieber et al. Nature 391 (98)

Park et. al. Nature 417,722-725 (2002)

Datta et al

Weber et al, Chem. Phys. 2002

Electron transfer in DNA

loge of GCGC(AT)mGCGC conductance vs length (total number of base pairs). The solid line is a linear fit that reflects the exponential dependence of the conductance on length. The decay constant, , is determined from the slope of the linear fit. (b) Conductance of (GC)n vs 1/length (in total base pairs).

Xu et al (Tao), NanoLet (2004)

=0.43Å-1

Electron transmission Electron transmission processes in molecular processes in molecular

systemssystems Electron transferElectron transfer Electron transmissionElectron transmission ConductionConduction Parameters that affect molecular Parameters that affect molecular

conductionconduction Eleastic and inelastic transmissionEleastic and inelastic transmission Coherent and incoherent conductionCoherent and incoherent conduction Heating and heat conductionHeating and heat conduction

Activated rate processesActivated rate processes

- frictio nr e ac t i o nc o o r di nate

KRAMERS THEORY:

Low friction limit

High friction limit

Transition State theory

TSTE k Tk e

2B Bo B B

TSTE k Tk e k

B BE k TB

k J ek T

(action)

Diffusion controlled

The physics of transition The physics of transition state ratesstate rates

( ,TST B f BP xk d P x

v v v v)

( )2exp ( )

B EB E

E mP x e

dx V x

Assume:

(1) Equilibrium in the well

(2) Every trajectory on the barrier that goes out makes it

r e ac t i o nc o o r di nate

Theory of Electron TransferTheory of Electron Transfer

Activation energyActivation energy Transition probabilityTransition probability Rate – Transition state theory or Rate – Transition state theory or

solvent controlledsolvent controlled

Electron transfer in polar Electron transfer in polar mediamedia

•Electron are much faster than nuclei

Electronic transitions take place in fixed nuclear configurations

Electronic energy needs to be conserved during the change in electronic charge density

q = + e

Electronic transition

Nuclear relaxation

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

Electron transferElectron transfer

E aE A

e ne r g y

X a X tr X b

Transition state theoryTransition state theory of of electron transferelectron transfer

Adiabatic and non-adiabatic ET processesE

E a(R )

E b(R )

E 1(R )

E 2(R )

Landau-Zener problem

( , ) ( )b ak dRR P R R P R

2 | |( ) 1 exp a b

2Aa b E

Alternatively – solvent control

Electron transfer – Marcus Electron transfer – Marcus theorytheory

(0) (0) (1) (1)B BA Aq q q q (0) (0) (1) (1)

B BA Aq q q q

E D 4 P 1

4sP E E

They have the following characteristics:(1) Pn fluctuates because of thermal motion of solvent nuclei.(2) Pe , as a fast variable, satisfies the equilibrium relationship (3) D = constant (depends on only)Note that the relations E = D-4P; P=Pn + Pe are always satisfied per definition, however D sE. (the latter equality holds only at equilibrium).

We are interested in changes in solvent configuration that take place at constant solute charge distribution

The Marcus parabolasThe Marcus parabolas

0 1 0( ) Use as a reaction coordinate. It defines the state of the medium that will be in equilibrium with the charge distribution . Marcus calculated the free energy (as function of ) of the solvent when it reaches this state in the systems =0 and =1.

20 0( )W E 2

1 1( ) 1W E

21 1 1 1 1

2 2e s A B AB

qR R R

Electron transfer: Electron transfer: Activation energyActivation energy

2[( ) ]

21 1 1 1 1

2 2e s A B AB

qR R R

E aE A

e ne r g y

a tr b

20 0( )W E

21 1( ) 1W E

Electron transfer: Effect of Electron transfer: Effect of Driving (=energy gap)Driving (=energy gap)

Experimental confirmation of the inverted regime

Miller et al, JACS(1984)

Marcus Nobel Prize: 1992

Electron transfer – the Electron transfer – the couplingcoupling

• From Quantum Chemical Calculations

•The Mulliken-Hush formula

max 12| |DADA

• Bridge mediated electron transfer

Bridge assisted electron Bridge assisted electron transfertransfer

B 1 B 2 B 3

3V D 1

V 1 2 V 2 3

, 1 , 11

D j Aj

D D AN NA

j j j jj

H E D D E j j E A A

V D V D V A N V N A

V j j V j j

, 1 /,j B j j B D AE E V E E

1 1 12 1

21 2 23 2

NA A A

E E V c

V E E V c

1 12 1

21 2 23 2

DV cE E V cV E E V c

cV E E V c

A A AN N

E E c V c

ˆ I c uB B BH E

( )ˆc uBB G

1( )ˆ ˆIBB BG E H

D D A A j jjc c c

Effective donor-acceptor Effective donor-acceptor couplingcoupling

( ) ( )1 111

ˆ ˆ;B BD D D D A A AN NN NAE E V G V E E V G V

( ) ( ) *1 11 1

ˆ ˆ;B BDA D NA AD AN D DAN NV V G V V V G V V

12 23 1,1

/ 1 / 2 / 1 /

1 1 1 1ˆ ...B N NN

D A D A D A N D A N

G V V VE E E E E E E E

(1/ 2) '1

NbD NA BDA

B D A B

V V VV V e

2' ln B

0 0 0 0 0 0 ...G G G VG G VG VG

Marcus expresions for non-Marcus expresions for non-adiabatic ET ratesadiabatic 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

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

Incoherent hoppingIncoherent hopping

........

N + 1 = A

k 1 0 = k 0 1 e x p (-E 1 0 ) k N ,N + 1 = k N + 1 ,N e x p (-E 1 0 )

0 1,0 0 0,1 1

1 0,1 2,1 1 1,0 0 1,2 2

1, 1, , 1 1 , 1 1

1 , 1 1 1,

( )N N N N N N N N N N N N

N N N N N N N

P k P k P

P k k P k P k P

P k P k P

constant STEADY STATE SOLUTION

ET rate from steady state ET rate from steady state hoppinghopping

0,1 2,1 1 1,0 0 1,2 2

1, 1, ,

0 ( )N N N N N N N

N N N N

k k P k P k P

k k P k P

B BE k T

0D Ak P

Dependence on Dependence on temperaturetemperature

The integrated elastic (dotted line) and activated (dashed line) components of the transmission, and the total transmission probability (full line) displayed as function of inverse temperature.

Parameters are as in Fig. 3.

The photosythetic reaction The photosythetic reaction centercenter

Michel - Beyerle et al

Dependence on bridge Dependence on bridge lengthlength

11 1up diffk k N

DNA (Giese et al 2001)DNA (Giese et al 2001)

Steady state evaluation Steady state evaluation of ratesof rates

Rate of water flow depends linearly on water height in the cylinder

Two ways to get the rate of water flowing out:

(1)Measure h(t) and get the rate coefficient from k=(1/h)dh/dt

(2)Keep h constant and measure the steady state outwards water flux J. Get the rate from k=J/h -- Steady state rate

Steady state quantum Steady state quantum mechanicsmechanics

{ }l l0

Starting from state 0 at t=0:

P0 = exp(-t)

= 2|V0l|2L (Golden Rule)

Steady state derivation:

0 0 0 sl ll

dC iE C i V C

0( ) ( ) 0 ( )ll

t C t C t l 0( / )

0 0i E tC c e

0 0 ; alll l l ld

C iE C iV C ldt

0( / )0 0

i E tC c e

0 0 ; alll l l ld

C iE C iV C ldt

(1 / 2) lC

0( / ) 0

( ) ;/ 2

i E t lsl l l

V cC t c e c

2 2 20 0 2 2

2 200 0 0

l ll l l

J C C VE E

C V E E

2 20 0 0 02

l l l LE El

Jk V E E V

pumping damping

Resonance scatteringResonance scattering

0H H V

0 0 10

0 0 1 1 l rl r

H E E E l l E r r

0,1 1,0 ,1 1, ,1 1,0 1 1 0 1 1 1 1l l r r

V V V V l V l V r V r

Resonance scatteringResonance scattering0

1 1 1 1,0 0 1, 1,

( / 2)

l l r rl r

r r r r

l ll l

C iE C iV C i V C i V C

C iE C iV C

0( ) exp ( / )j jC t c i E t j = 0, 1, {l}, {r}

0 / 2r

0 / 2l

For each r and l

0 / 2r

1, 1 0 1( )r r RrV c iB E c

( ) (1 / 2) ( )

( ) 2 | | ( )

| |( )

R r R r

r R rR

E EE i E

PP dEE E

1 0 1 1,0 0 1, 1,0 l l r rl ri E E c iV c i V c i V c

wide ban

d approximatio

1/ 2R RB E i

( ) rR

ENERGY

0 ,1 10 ( / 2)r r r ri E E c iV c c

1,0 01

0 1 1 0( / 2) ( )

E E i E

1 0 1 0 1 0( ) ( ) ( )L RE E E

2 2 2,1 1,0 02 22 2 2 2

0 0 1 1 0

| | | | | || | | |

( ) ( / 2) ( ) / 2

V V cc C

E E E E E

22 1,00 21 0

0 02 20 1 1 0

| | ( )/ | |

( ) / 2

V EJ c c

21 02 r rV E E

Resonant tunnelingResonant tunneling

21,0 21

0 02 20 1 1

| || |

V (x )

. . . .

. . . . . . . .

Resonant TunnelingResonant Tunneling|1 >

V (x )

. . . .

. . . . . . . .

21,0 21

0 02 20 1 1

| || |

2 00 0 0 0incident flux ( ) | | ( )R

pJ E c E

mL T TTransmission Coefficient

102 ( )L E

1 0 1 0

0 2 20 1 1 0

( ) ( )( )

( ) / 2

Resonant Transmission – 3dResonant Transmission – 3d

V (x )

. . . .

. . . . . . . .

L 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 12

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

(Fermi-Dirac distribution)

CONDUCTIONCONDUCTION

( ) 1( ) | |

dJ EE c

( ) (L Rf Ee

I d fE EE

2 21 1

( ) ( )( )

( ) / 2

L RE EE

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

2 spin states

Zero bias conduction ( 0)g

f(E0) (Fermi function)

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”:

© a. nitzan, tau introduction to electron transport in molecular systems i. benjamin, a. burin, b....

tau introduction

tau molecules

tau science

tau moores law slide

c slide

wired slide

tau xe

tau cornell group slide

Documents

galperin stylistics

light and current ss presentation.pdf · a. nitzan, tel...

michael galperin, mark a. ratner and abraham nitzan- raman...

7 mabel burin

ron galperin controller - clkrep.lacity.org

numerical simulations of solvation dynamics in electrolyte...

(dissertaÇÃo burin)

1 marcos galperin company overview 1

the passion according to berruguete - galperin

innovative environmental solutions in our new world ·...

alexander j. white and michael galperin

nitzan yoel avidor at achva college

guide renovation thermique par travauxlib - matthieu burin

abraham nitzan -...

nitzan -new imp or new capitalism

heat conduction in molecular transport...

michael galperin and abraham nitzan- negf-hf method in...

parallel edge detection daniel dobkin asaf nitzan

galperin text kak obekt lingv issled

galperin: implicaÇÕes educacionais da teoria de …