1

Molecular ElectronicsMolecular ElectronicsAviram-Ratner Diode: an acceptor-bridge-donor moleculeAviram-Ratner Diode: an acceptor-bridge-donor moleculeChem.Phys.Lett. (1974) 29, 277.Chem.Phys.Lett. (1974) 29, 277.

1. Electrode charge-injection to donor2. Donor-Acceptor ET3. Acceptor-electrode charge-injection

A molecular rectifier

• What are the electronic states occupied by electrons on complex, many atom molecules?

• How do molecules charge to form ions?

• What makes a “donor” and an “acceptor”?

• How do charges move through a solid molecular material?

• Can a linear molecule make a wire (a ‘molecular wire)?

• How are electrons transferred between metal electrodes and molecules, and how do the energies of available states on molecules align with the Fermi level of metals or semiconductors?

QuestionsQuestions

h

e-

-

Copyright Stuart Lindsay 2008

An artificial photosynthetic unitAn artificial photosynthetic unit

porphyrinporphyrin

fullerenefullerene

e-

+

A long-lived charge-transfer state (from 60ns to a microsecond)!A long-lived charge-transfer state (from 60ns to a microsecond)!

carotenecarotene

τI = 30psτII = 130ps

Molecular wiresMolecular wires

Copyright Stuart Lindsay 2008 4

Carotene: a full conjugated structureCarotene: a full conjugated structure

The gap between π states is so small, that visible light can be absorbed.

Photochromic moleculesPhotochromic molecules

When the central ring is open the molecule absorbs in the UV, relaxing back from the optically excited state into a fully conjugated structure able to absorb in the visible. Excitation in the visible drives a transition back to the open form.

6

Electron transfer in moleculesElectron transfer in molecules

S

S

S

S

CCC

C

C

C N

NN

N

TTFTTF: tetrathiofulvalenetetrathiofulvalene TCNQ: tetracyanoquinodimethane

Reduction potentials

Copyright Stuart Lindsay 2008

Donor Acceptor

1108 molkJnFEG

The reverse reaction would have to overcome a 1.12 eV barrier: a diode-like behaviour.

8

Physics of donor-acceptor electron Physics of donor-acceptor electron transfer: The Marcus Theorytransfer: The Marcus Theory

There is no free energy difference between the reactants and products, but the ET rate is found to be strongly thermally activated. It has a significant kinetic barrier!

Work must be done to transfer polarization!

λ = reorganization energyreorganization energy

Reorganization energyReorganization energy

λ = λ in + λ out

λ in = inner reorganization energydistortion and reorganization of molecular bonds following charge transfer

λ out = outer reorganization energyReorientation of the solvent outer shell following charge transfer. It is on the order of the Born solvation energy:

1

14 0

22

a

ez

For a=1nm, ε=80 and z=1: λ≈1 eV.

10

Marcus ModelMarcus Model• Assume quadratic electronic “energy landscape” and

the same spring constant, i.e. potential curvature, for reactants and products.

2

2

1AR qqkE

2

2

1BP qqkE

Nobel Prize, 1992Nobel Prize, 1992

1. q1. q = reaction coordinate= reaction coordinate

= degree of distortion of a set of coordinates along the Electron Transfer pathway. q = q(r1, r2, r3, r4, rN)

2. λλ is vertical as electrons jump istantaneously

Following B.O. approximation the electron energy is additive to the environmental distortion energy

3. The reaction coordinates shifts the electronic energy quadratically.

For small nuclear distortions the leading term in the expansion of any potential is quadratic.

At q=q* the energies of the reactants and products are degenerate.

The energy degeneracy at this point permits tunneling according to the Fermi’s Golden Rule.When reactants fluctuate into this configuration, the electron may tunnel to the product.

Setting qA=0:

2

*

22

1)(

Bq

kqqG

2

2

1Bkq

4)( ** qqG

Diabatic vs. Adiabatic ETDiabatic vs. Adiabatic ET

weak coupling strong couplingweak coupling strong coupling

ΔΔ = energy gap (avoided crossing) = energy gap (avoided crossing)

ΔΔ<<kT: <<kT: diabatic ETdiabatic ET

The system may move through the transition state many times without ET.

ΔΔ>>kT: adiabatic ET>>kT: adiabatic ET

The system moves to the products as soon as the transition state is attained.

The Transition State (The Transition State (G° G° 0) 0)

2

2

1kqEP

G)qq(kE RR 2

2

1

Products have minimum energy at q=0.Reactants have minimum energy at q=qR.

ΔG° = reaction standard free energy

2

2

11R

R

kqGkq

*q

22

22

2

11

2

1

2

1

R

R

kqGkq

*kq*G

At the intersection point (q=q*): EP=ER

G)q*q(k*kq R 22

2

1

2

1

4

)( 20*

GG

2

2

1Rkq

When:

02

1 2 *GkqG R

2

2

1RkqG

For:

The ET reaction rate decreases when increasing the thermodynamic driving force (Marcus inverted regionMarcus inverted region).

Intramolecular rate constants as a function of free energy change in 2-methyloxacyclopentane solution at 296 K. The electron transfer occurs from biphenyl anions to the eight different acceptor moieties (shown adjacent to the data points).

]4

)(exp[

4

1)(

20

Tk

G

TkP

BB

In the case of adiabatic ET, the probability is:

For the reaction:

λ≈1 eV, kT=0.025eV at 300KeV.G 121

870102504

1121 2

.].

).(exp[)(P

For the reverse reaction:

202

103102504

1121

]

.

).(exp[)(P

Charge Transport in Molecular SolidsCharge Transport in Molecular Solids

Weakly interacting molecular solids: hopping conductancehopping conductance

• Weak overlap between sites

The interaction energy between neighboring molecules (the hopping matrix element, τ) is much smaller than the reorganization energy.

• Strong trapping

Electrons are trapped and can only move by thermally activated hopping over the energy reorganization barrier (λ/4).

In disordered solid the barrier to hopping is randomly distributed, because the local polarization is randomly distributed.

The smallest barrier controls hopping, not the average. The probability of finding small barrier increases with volume.

Armin 34

3

The minimum energy barrier falls with increasing the number of barriers N(λ):

ρ = density of barrier

)rexp( 2

Tunneling rate decreases exponentially with distance:

κ = decay of electronic coupling wavefunction

In the low-bias limit, the overall conductance of the material vary as:

)Tk

exp()rexp(GGB

minmax

2

Electronic coupling decay Reorganization energy barrier

TkArrexpGG

Bmax

34

32

48

9

TkArr

Bc

)Texp(G .250

The conductance varies with temperature as:

The conductance will be maximum for:

Mott variable Mott variable range hoppingrange hopping

Charge transport at the electrode interfaceCharge transport at the electrode interface

Double-layer region: Double-layer region: the surface charge on the metal is balanced by the accumulation of by the accumulation of counter charges ( (red dotsred dots).).Open circlesOpen circles: : neutral molecules; filled circles: reduced molecules.

dx

)x(d Potential gradient through dx

dx

)x(dn Concentration gradient through dx

n(x) = carrier density at x distance from the electrode surface.

Three length scales:

• Debye lengthDebye length

Electric fields do no penetrate the bulk further than the Debye length.

• Tunneling distanceTunneling distance

1)2( t

48

9

TkAr

Bc

• Hopping length (Mott equation) Hopping length (Mott equation)

• The potential Φ(x) changes rapidly over a distance on the order of the Debye length.

• Ion can be created (or neutralized) by a Marcus ET process driven by the electric field close to the electrode.

• Bulk current is driven by carrier concentration gradient:

dx

xdnTk

dx

xdxnxJ nBnn

)()()()(

μn = mobility of the ion carrier

In liquids: diffusive motion

In solids: ET hopping

Polymer wiresPolymer wires

• Motion in 1-D is highly correlated

• In polymers, charge carriers are various kinds of polarons (trapped-charge carriers)BipolaronBipolaron: a dication involving no unpaired electrons (no net spin). Two equivalents of oxidant needed.

• True metallic behavior requires 3D crystallinity (Fermi liquid model breaks down in 1D)

PolypyrrolePolypyrrole

Ox : AsCl5, FeCl3

Single Molecule ElectronicsSingle Molecule Electronics

Cui et al., Science 294 571 (2001)

Copyright Stuart Lindsay 2008

Self-assembled molecular junctions

Insertion of a dithiolated

molecule in an alkanethiol SAM.

AFM conductive tip

Haiss et al., PCCP 6 4330 (2004)

ON OFF

Bond-fluctuations in fixed junctions

Metal-molecule-metal junctionMetal-molecule-metal junction: the current at each voltage is an integer multiple of some fundamental current.

Xu and Tao, Science 301 1221 (2003)

I/V curvesI/V curves

The series of current-voltage curves correspond to integer number of molecules trapped in the gap.

Break junctions

Repeatedly breaking a gold wire in the presence of molecules with reactive ends.

0.000 0.005 0.010 0.015 0.020

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.4 0.8 1.2 1.60

2

4

6

Current (nA

)

G (

10-5X

2e2 /h

)

Time (Second)

Distance (nm)

Jumps in conductivity correspond to integer numbers of molecules spanning the gap.

VTh

eGVI

ijij

222

eVEE)E(f)E(fTe

jijiij

ij

2 2

Tunneling mechanismTunneling mechanism: states with energies closest to the Fermi energy contribute most to conductance,

Density of statesFermi distribution

Tij = overlap integrals connecting initial (left electrode) and final (right electrode) electronic states.

33

Conductance as a function of twist angle between aromatic rings:

Copyright Stuart Lindsay 2008

Dependence of single-molecule junction conductance on molecular conformation, Venkataraman, L., J.E. Klare, C. Nuckolls, M.S. Hybertsen, and M.L. Steigerwald Nature,2006, 442: 905-907.

2cosGG max

Current statusCurrent status

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Before their use DNA is:

An INSULATOR (D. Dunlap et al. PNAS 90, 7652, 1993)

A SEMICONDUCTOR (D. Porath et al, Nature 403, 635, 2000)

A CONDUCTOR (Fink and Schoenberger, Nature 398, 407,1999)

A SUPERCONDUCTOR (A.Y. Kasumov et al. Science 291, 280, 2001)

How reliable are these methods?How reliable are these methods?

For the answer: Xu et al. NanoLetters 4, 1105 (2004)

Copyright Stuart Lindsay 2008

Tunneling vs. hopping conductanceTunneling vs. hopping conductance

xexpGG 0

Tunneling conductance distance dependence:

10

xGG

Hopping conductance distance dependence (Ohm’s law):

temperature independent

thermally activated

Xu et al. Nanoletters 4, 1105 (2004)

TunnelingTunneling

HoppingHopping

Molecular wiresMolecular wires: short molecules show a rapid exponential decay of current with no temperature dependence, whereas longer molecules display a slower decay of a current with a marked temperature dependence.

40

Electrochemical gating: Electrochemical gating: measuring transport as a function of oxidation statemeasuring transport as a function of oxidation state

H NH N

O

H NHN

OH N

H NO

HNHN

O

H NH N

O

H NH N

OH N

H NO

HNHN

O

O

O +-

Es

Vts

LOCAL FIELD

SURFACE FIELD

Insulated probe with small opening

Copyright Stuart Lindsay 2008

Chen, F et al., Nano Letters,2005, 5: 503-506.

Single Molecule Switch made from Oligo AnilineSingle Molecule Switch made from Oligo Aniline

HS

HN

NH

HN

NH

HN

NH

HN

SH

Insulator

Oxidize: Conductor

-2e-

Oxidize: Insulator

-2e-

E°=0.2V

E°=0.6V

-0.2 0 0.2 0.4 0.6 0.8

Electrochem

ical Current

Surface Potential, ES , V vs. Ag

-0.2 0 0.2 0.4 0.6 0.80

1

2

3

4

5

6

7M

olec

ular

Con

duct

ance

(nS

)

-0.2 0 0.2 0.4 0.6 0.8

G=GMAX- a(ES-b)2

Insulator Conductor Insulator

Single molecule conductance measured as a function of the charge state of an oligoaniline molecule in an electrochemical break junction.

Copyright Stuart Lindsay 2008

I II

irr

Single molecule conductance

43

0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.1 0.2 0.3 0.4 0.5 0.6

Neutral molecule

- - - - - -

Cur

rent

(nA

)

Tip-substrate bias (V)

(NO IONS)

FIX EFIX ESS, VARY TIP FIELD, VARY TIP FIELD

Oxidized molecule ES=0.4V(H2SO4)

Copyright Stuart Lindsay 2008

Negative differential resistance