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A. Nitzan ( [email protected] ; http://atto.tau.ac.il/~nitzan/nitzan.html ). PART B : Molecular conduction: Main results and phenomenology. Introduction to electron transport in molecular systems. PART A : Introduction: electron transfer in molecular systems.

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Part b molecular conduction main results and phenomenology l.jpg

A. Nitzan ([email protected]; http://atto.tau.ac.il/~nitzan/nitzan.html)

PART B: Molecular conduction: Main results and phenomenology

Introduction to electron transport in molecular systems

PART A: Introduction: electron transfer in molecular systems

PART C: Inelastic effects in molecular conduction

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

© A. Nitzan, TAU


Landauer formula l.jpg
Landauer formula

For a single “channel”:

(maximum=1)

Maximum conductance per channel

© A. Nitzan, TAU



General case l.jpg
General case

Unit matrix in the bridge space

Bridge Hamiltonian

B(R) + B(L) -- Self energy

Wide band approximation

© A. Nitzan, TAU


Barrier dynamics effects on electron transmission through molecular wires and layers l.jpg
BARRIER DYNAMICS EFFECTS ON ELECTRON TRANSMISSION THROUGH MOLECULAR WIRES AND LAYERS

  • ?Using frozen configurations in transmission calculations?

  • Relevant timescales

  • Inelastic contributions to the tunneling current

  • Dephasing and activation - transition from coherent transmission to activated hopping

  • Heating of current carrying molecular wires

  • Inelastic tunneling spectroscopy

© A. Nitzan, TAU


Electron transfer transmission l.jpg

Bridge MOLECULAR WIRES AND LAYERS

A

D

Electron transfer/transmission

© A. Nitzan, TAU


Barrier dynamics effects on electron transmission through molecular wires and layers7 l.jpg
BARRIER DYNAMICS EFFECTS ON ELECTRON TRANSMISSION THROUGH MOLECULAR WIRES AND LAYERS

  • ?Using frozen configurations in transmission calculations?

  • Relevant timescales

  • Inelastic contributions to the tunneling current

  • Dephasing and activation - transition from coherent transmission to activated hopping

  • Heating of current carrying molecular wires

  • Inelastic tunneling spectroscopy

© A. Nitzan, TAU


Slide8 l.jpg

ENERGY PARAMETERS: MOLECULAR WIRES AND LAYERS

ΔE(energy gap) ; VB (intersite coupling, bandwidth) ; Γ (coupling of edge sites to leads); U(charging energy); λ (reorganization energy - interaction with environment); kBT(thermal energy), eΦ (voltage drop)

TIME SCALES:

Traversal time

energy relaxation time

dephasing time

environmental correlation time

hopping time

lifetime of electron on edge site

© A. Nitzan, TAU


Traversal time for tunneling l.jpg
Traversal time for tunneling? MOLECULAR WIRES AND LAYERS

1

2

B

A

© A. Nitzan, TAU


Traversal time l.jpg
Traversal Time MOLECULAR WIRES AND LAYERS

© A. Nitzan, TAU


Tunnelling times l.jpg
"Tunnelling Times" MOLECULAR WIRES AND LAYERS

© A. Nitzan, TAU


Estimates l.jpg

For: MOLECULAR WIRES AND LAYERS

D=10A (N=2-3)

UB-E = E~1eV

m=me

  • Notes:

  • Both time estimates are considerably shorter than vibrational period

  • Potential problem: Near resonance these times become longer

Estimates

For resonance transmission same expression applies except that DE becomes the bandwidth

© A. Nitzan, TAU


Transmission through several water configurations equilibrium 300k l.jpg
Transmission through several water configurations (equilibrium, 300K)

Galperin, AN & Benjamin, J. Phys. Chem., 106, 10790-96 (2002)

Vacuum barrier

1. A compilation of numerical results for the transmission probability as a function of incident electron energy, obtained for 20 water configurations sampled from an equilibrium trajectory (300K) of water between two planar parallel Pt(100) planes separated by 10Å. The vacuum is 5eV and the resonance structure seen in the range of 1eV below it varies strongly between any two configurations. Image potential effects are disregarded in this calculation.

© A. Nitzan, TAU


Barrier dynamics effects on electron transmission through molecular wires and layers14 l.jpg
BARRIER DYNAMICS EFFECTS ON ELECTRON TRANSMISSION THROUGH MOLECULAR WIRES AND LAYERS

  • ?Using frozen configurations in transmission calculations?

  • Relevant timescales

  • Inelastic contributions to the tunneling current

  • Dephasing and activation - transition from coherent transmission to activated hopping

  • Heating of current carrying molecular wires

  • Inelastic tunneling spectroscopy

© A. Nitzan, TAU


Water tunneling time and transmission probability l.jpg
Water: Tunneling time and MOLECULAR WIRES AND LAYERS transmission probability

Galperin, AN, Peskin J. Chem. Phys. 114, 9205-08 (2001)

© A. Nitzan, TAU

Vacuum barrier


Fig 5 l.jpg
Fig. 5 MOLECULAR WIRES AND LAYERS

The ratio between the inelastic (integrated over all transmitted energies) and elastic components of

Vacuum barrier

the transmission probability calculated for different instantaneous structures of a water layer consisting of 3 monolayers of water molecules confined between two Pt(100) surfaces.

Galperin & AN, J. Chem. Phys. 115, 2681 (2001)

© A. Nitzan, TAU


Barrier dynamics effects on electron transmission through molecular wires and layers17 l.jpg
BARRIER DYNAMICS EFFECTS ON ELECTRON TRANSMISSION THROUGH MOLECULAR WIRES AND LAYERS

  • ?Using frozen configurations in transmission calculations?

  • Relevant timescales

  • Inelastic contributions to the tunneling current

  • Dephasing and activation - transition from coherent transmission to activated hopping

  • Heating of current carrying molecular wires

  • Inelastic tunneling spectroscopy

© A. Nitzan, TAU


Coupling to thermal environment l.jpg
Coupling to thermal environment MOLECULAR WIRES AND LAYERS

E1

activated

coherent

E0

Molecule

Lead

  • Energy resolved transmission:

© A. Nitzan, TAU


Dependence on temperature l.jpg
Dependence on temperature MOLECULAR WIRES AND LAYERS

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.

© A. Nitzan, TAU


The photosythetic reaction center l.jpg
The photosythetic reaction center MOLECULAR WIRES AND LAYERS

© A. Nitzan, TAU


Slide21 l.jpg

Selzer et al, JACS (2003) MOLECULAR WIRES AND LAYERS

© A. Nitzan, TAU


Dependence on bridge length l.jpg
Dependence on bridge length MOLECULAR WIRES AND LAYERS

© A. Nitzan, TAU


Dna giese et al 2001 l.jpg
DNA (Giese et al 2001) MOLECULAR WIRES AND LAYERS

© A. Nitzan, TAU


Tunneling through n hexane l.jpg
Tunneling through n-hexane MOLECULAR WIRES AND LAYERS

L.G. Caron et. al. (L. Sanche) Phys. Rev. B 33, 3027 (1986)

© A. Nitzan, TAU


Barrier dynamics effects on electron transmission through molecular wires and layers25 l.jpg
BARRIER DYNAMICS EFFECTS ON ELECTRON TRANSMISSION THROUGH MOLECULAR WIRES AND LAYERS

  • ?Using frozen configurations in transmission calculations?

  • Relevant timescales

  • Inelastic contributions to the tunneling current

  • Dephasing and activation - transition from coherent transmission to activated hopping

  • Heating of current carrying molecular wires

  • Inelastic tunneling spectroscopy

© A. Nitzan, TAU


Slide26 l.jpg

Elastic transmission vs. maximum heat generation: MOLECULAR WIRES AND LAYERS



© A. Nitzan, TAU


Heating l.jpg
Heating MOLECULAR WIRES AND LAYERS

© A. Nitzan, TAU


The quantum heat flux l.jpg
The quantum heat flux MOLECULAR WIRES AND LAYERS

Transmission coefficient at frequency w

Bose Einstein

populations for left

and right baths.

J. Chem. Phys. 119, 6840-6855 (2003)

© A. Nitzan, TAU


Slide29 l.jpg

Anharmonicity effects MOLECULAR WIRES AND LAYERS

Heat current vs. chain length from classical simulations. Full line: harmonic chain; dashed line: anharmonic chain using the alkane force field parameters; dash-dotted line: anharmonic chain with unphysically large (x 30) anharmonicity

© A. Nitzan, TAU


Heat conduction in alkanes of different chain length l.jpg
Heat conduction in alkanes of different chain length MOLECULAR WIRES AND LAYERS

The thermal conductance vs. the chain length for Alkanes, c=400 cm-1 , VL=VR=50 cm-2. Black: T=50K; Red: T=300K; Blue: T=1000K

c=400 cm-1 , VL=VR=200 cm-2. Black: T=50K; Red: T=300K; Blue: T=1000K.

© A. Nitzan, TAU


Density of normal modes in alkanes l.jpg
Density of normal modes in alkanes MOLECULAR WIRES AND LAYERS

Low frequency group: 0-600cm-1; Intermediate frequency group: 700-1500cm-1 High frequency group: 2900-3200cm-1

© A. Nitzan, TAU


Heat conduction by the lower frequency groups l.jpg
Heat conduction by the lower frequency groups MOLECULAR WIRES AND LAYERS

© A. Nitzan, TAU


Thermal conduction vs alkane chain length l.jpg
Thermal conduction vs. alkane chain length MOLECULAR WIRES AND LAYERS

Dashed line: T=0.1K; Blue dotted line: T=1K; Full line: T=10K; Red- dotted line: T=100K; Line with circles: T=1000K. c=400 cm-1 ,VL=VR=50 cm-2.

© A. Nitzan, TAU


Slide34 l.jpg

D.Schwarzer, P.Kutne, C.Schroeder and J.Troe, J. Chem. Phys., 2004

Intramolecular vibrational energy redistribution in bridged azulene-anthracene compounds:Ballistic energy transport through molecular chains

© A. Nitzan, TAU


Barrier dynamics effects on electron transmission through molecular wires and layers35 l.jpg
BARRIER DYNAMICS EFFECTS ON ELECTRON TRANSMISSION THROUGH MOLECULAR WIRES AND LAYERS

  • ?Using frozen configurations in transmission calculations?

  • Relevant timescales

  • Inelastic contributions to the tunneling current

  • Dephasing and activation - transition from coherent transmission to activated hopping

  • Heating of current carrying molecular wires

  • Inelastic tunneling spectroscopy

© A. Nitzan, TAU


Slide36 l.jpg

Light Scattering MOLECULAR WIRES AND LAYERS

incident

scattered

© A. Nitzan, TAU


Slide37 l.jpg

INELSTIC ELECTRON TUNNELING SPECTROSCOPY MOLECULAR WIRES AND LAYERS

© A. Nitzan, TAU


Slide38 l.jpg

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

Recall: van Ruitenbeek et al (Pt/H2)- dips

© A. Nitzan, TAU


Slide39 l.jpg
Electronic Resonance and Symmetry in Single-Molecule Inelastic Electron TunnelingJ.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 -Ag

stretch vibration.

© A. Nitzan, TAU


Slide40 l.jpg

Inelastic Electron Tunneling Spectroscopy of Inelastic Electron TunnelingAlkanedithiol Self-Assembled MonolayersW. Wang, T. Lee, I. Kretzschmar and M. A. Reed(Yale, 2004)

Inelastic electron tunneling spectra of C8 dithiol SAM obtained from lock-in

second 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

© A. Nitzan, TAU

Nano letters, in press


Slide41 l.jpg

Nanomechanical oscillations in a single C Inelastic Electron Tunneling60 transistorH. Park, J. Park, A.K.L. Lim, E.H. Anderson, A. P. Alivisatos and P. L. McEuen [NATURE, 407, 57 (2000)]

Vsd(mV)

Two-dimensional differential conductance (I/V)plots as a function of the bias voltage (V) and the gate voltage (Vg ). The dark triangular regions correspond to the conductance gap, and the bright lines represent peaks in the differential conductance.

Vg(Volt)

© A. Nitzan, TAU


Conductance of small molecular junctions n b zhitenev h meng and z bao prl 88 226801 2002 l.jpg
Conductance of Small Molecular Junctions Inelastic Electron TunnelingN.B.Zhitenev, H.Meng and Z.BaoPRL 88, 226801 (2002)

38mV

22

125

35,45,24

Conductance of the T3 sample as a function of source-drain bias at T =4.2 K. The steps in conductance are spaced by 22 mV.

Left inset: conductance vs source-drain bias curves taken at different temperatures for the T3 sample (the room temperature curve is not shown because of large switching noise).

Right inset: differential conductance vs source-drain bias measured for two different T3 samples at T = 4.2 K.

© A. Nitzan, TAU


Slide43 l.jpg

MODEL Inelastic Electron Tunneling

© A. Nitzan, TAU


Parameters l.jpg

V Inelastic Electron Tunneling

Parameters

Constant in the wide band approximation

GL

GR

electrons

e1

M

Molecular vibrations

w0

U

Thermal environment

M – from reorganization energy (~M2/w0)

U – from vibrational relaxation rates

© A. Nitzan, TAU


Slide45 l.jpg

NEGF Inelastic Electron Tunneling

({ }=anticommutator)

© A. Nitzan, TAU


Slide46 l.jpg

electrons Inelastic Electron Tunneling

M

vibrations

A1

A2M

A3M2

elastic

inelastic

elastic

© A. Nitzan, TAU


Slide47 l.jpg

© A. Nitzan, TAU Inelastic Electron Tunneling


Slide48 l.jpg

© A. Nitzan, TAU Inelastic Electron Tunneling


Slide49 l.jpg

Changing position of molecular resonance: Inelastic Electron Tunneling

© A. Nitzan, TAU


Slide50 l.jpg

Changing tip-molecule distance Inelastic Electron Tunneling

© A. Nitzan, TAU


Iets intrinsic linewidth l.jpg

V Inelastic Electron Tunneling

IETS (intrinsic?) linewidth

GL

GR

electrons

e1

M

Molecular vibrations

w0

U

Thermal environment

M – from reorganization energy (~M2/w0)

U – from vibrational relaxation rates

© A. Nitzan, TAU


Slide52 l.jpg

IETS linewidth Inelastic Electron Tunneling

e1=1eV

GL=0.5eV

GR=0.05eV

w0=0.13eV

M2/w0=0.7eV

© A. Nitzan, TAU


Slide53 l.jpg

© A. Nitzan, TAU Inelastic Electron Tunneling


Barrier dynamics effects on electron transmission through molecular wires and layers54 l.jpg
BARRIER DYNAMICS EFFECTS ON ELECTRON TRANSMISSION THROUGH MOLECULAR WIRES AND LAYERS

  • ?Using frozen configurations in transmission calculations?

  • Relevant timescales

  • Inelastic contributions to the tunneling current

  • Dephasing and activation - transition from coherent transmission to activated hopping

  • Heating of current carrying molecular wires

  • Inelastic tunneling spectroscopy

© A. Nitzan, TAU


Part b molecular conduction main results and phenomenology55 l.jpg

A. Nitzan MOLECULAR WIRES AND LAYERS([email protected])

PART B: Molecular conduction: Main results and phenomenology

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

Introduction to electron transport in molecular systems

PART A: Introduction: electron transfer in molecular systems

PART C: Inelastic effects in molecular conduction

THANK YOU !

© A. Nitzan, TAU


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