P. Grutter

STM as a Tool to Understand theElectronic Properties of Molecules

Peter Grutter

Physics Department

McGill University

Part of SPM lecture series in 534A‘Nanoscience and Nanotechnology’

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Outline

• Motivation and Intro

• History of tunneling

• STM and STS theory

• Wires

• Molecules

• Chemically and atomically defined contacts

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History

Binnig and Rohrerobtained the Nobel prizein 1986 for the discoveryof the STM

First STM

But: 1972!

Topografiner

System very similar totoday’s STM, but atomicresolution was not achieved

30 A vertical, 4000 A lateralresolution

How does it work?

Tunneling current between tip and sample

I ~ (V/s) exp (- Av ö *s)

Tunneling current

• Exponential dependence on distance

I ~ (V/s) exp (- Aö 1/2s)

“Proof of concept”

March 18th, 1981

Binnig et al, APL 1982

Very sensitive to gapsize!

First STM image

• Binnig et al. 1982, PRL• First atomic resolution image of the Si (111) 7x7

reconstruction

Tip preparation

• Tip must be as sharp and narrow as possible

Chemicallyetched ormechanicallycut.

Tip effects

The shape of the tip mayaffect the image

-More than one tip

-“flat” or irregular shape

-Structure change duringscan

Scan resolution

STM Large Range

Comparable (or better)to most techniques

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Operation of an STM1,2

[1] C. Julian Chen, Introduction to Scanning Tunnelling Microscopy, Oxford (1993)[2] G.A.D. Briggs and A. J. Fisher, Surf. Sci. Rep. 33, 1 (1999)

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Current theoretical modelsTheoretical methods:

Landauer formula or Keldysh non-equilibrium Green’s functions 1-4

Transfer Hamiltonian methods5

Methods based on the properties of the sample surface alone6

[1] R. Landauer, Philos. Mag. 21, 863 (1970)

M. Buettiker et. al. Phys. Rev. B 31, 6207 (1985)

[2] L. V. Keldysh, Zh. Eksp. Theor. Fiz. 47, 1515 (1964)

[3] C. Caroli et al. J. Phys. C 4, 916 (1971)

[4] T. E. Feuchtwang, Phys. Rev. B 10, 4121 (1974)

[5] J. Bardeen, Phys. Rev. Lett. 6, 57 (1961)

[6] J. Tersoff and D. R. Hamann, Phys. Rev. B 31, 805 (1985)

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Landauer formula for the STM1,2

[1] Y. Meir and N. S. Wingreen, Phys. Rev. Lett. 68, 2512 (1992)[2] A.A. Abrikosov, L.P. Gorkov and I.E. Dzyaloshinski, Methods of Quantum Field Theory in Statistical Physics, Dover, NY (1975)[3] M. Buettiker et al. Phys. Rev. B 31, 6207 (1985)

The tunnel current for non-interacting electrons3:

)],(),([),(2

)( 00 eVEfEfVETdEh

eVI RRLL +=−== ∫

∞

∞−

µµµµ

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Transfer Hamiltonian method1,2

[1] J. Pendry et al. J. Phys. Condens Matter 3, 4313 (1991)[2] J. Julian Chen, Introduction to Scanning Tunneling Microscopy Oxford (1993) pp. 65 - 69

( ) ( )

∇−∇−=

++−=

∫∫

**

2

4

2

0

2

νµµν

χψψχ

ρρπ

rrrh

h

S

eV

FTFs

Sdm

M

MEEEeVEdEe

I

M…overlap of wavefunctions (--> resolution!)

ρ…. DOS ( --> spectroscopy !)

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Bardeen approach1,2

( )( )νµ

νµνµµν

δ

π

EE

dSm

eI

s

−×

Χ∇Ψ−Ψ∇Χ= ∑ ∫2

,

**2

2

4 h

h

( )tipνΧ

( )sampleµΨ

[1] C.J. Chen, Introduction to Scanning Tunneling Microscopy, Oxford Univ. Press (1993)[2] W.A. Hofer and J. Redinger, Surf. Sci. 447, 51 (2000)

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Tunneling Current

)exp( zAVI ⋅Θ⋅−⋅∝

Θ…. Workfunction, typically 3-5 eV

z….. Tip-sample separation, typically 4-10 A

∆ z = 1 A --> ∆ I one order of magnitude !

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Small V approximation!

Simmon’s equation (Simmon, 1963)

Fowler-Nordheim regime (V>> θ)

)exp( zAVI ⋅Θ⋅−⋅∝

⋅−⋅∝ )/exp(2 VconstVIMeasure log I vs log V -> resonances!

Resolution due to exp dependence! (not so on metals -> later)

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Unknown/Challenges:

1. Chemical nature of STM tip (problem for spectroscopy, corrugation)

2. Relaxation of tip/surface atoms (tip sample separation not equal to piezo scale)

3. Effect of tip potential on electronic

surface structure (quenching of surface states)

4. Influence of magnetic properties

on tunnelling current/surface corrugation (is spin-STM possible?)

5. Relative importance of the effects

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1. Chemical nature of the tip1

[1] P. Varga and M. Schmid, Appl. Surf. Sci. 141, 287 (1999)

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Model of the STM tip1,2,3

Number of layers: 7Free standing film

Numerical method: DFT Relaxations: VASP [1]Electronic structure: FLEUR [2]

Lattice constant: 6.016 au (GGA)Exchange/correlation: PW91[3]

Brillouin-zone sampling: 10 k-pointsConvergence parameter: < 0.01 e/au3

[1] G. Kresse and J. Hafner, Phys. Rev. B 47, R558 (1993)[2] Ph. Kurz et al. J. Appl. Phys. 87, 6101 (2000)[3] J. P. Perdew et al. Phys. Rev. B 46, 6671 (1992)

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Electronic properties of the tip:non-magnetic tip models

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Chemical contrast on PtRh(100)1,2

[1] P.T. Wouda et al. Surf. Sci. 359, 17 (1996)[2] P. Varga and M. Schmid Appl. Surf. Sci. 141, 287 (1999)

Experiments: 22 pm contrastSimulations: interval EF +/- 80 meV

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2. The influence of forces in STM scans1

[1] W.A. Hofer, A.J. Fisher, R.A. Wolkow, and P. Grutter, Phys. Rev. Lett 87, 236104 (2001)[2] G. Cross, A. Schirmeisen, P. Grutter, U. Durig, Phys. Rev. Lett. 80, 4685 (1998)

Force measurement on Au(111)2 Simulation of forces:

Simulation: VASPGGA: PW914x4x1 k-points

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Tip relaxation effects

W tip on Au(111) surfaceThe force on the apex atom isone order of magnitude higherthan forces in the second layer

Substantial Relaxations occur only in a distance range below 5A

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Tip relaxation effects

Hofer, Fisher, Wolkow and GrutterPhys. Rev. Lett. 87, 236104 (2001)W tip on Au(111) surface

The real distance is at variance with the piezoscale by as much as 2AThe surplus current due to relaxations is about 100% per A

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Corrugation enhancement

STM simulation: bSCAN Bias voltage: - 100mVEnergy interval: +/- 100meVCurrent contour: 5.1 nA

Due to relaxation effects in the low distance regime thecorrugation of the Au(111) surface is enhanced by about 10-15 pm1

[1] V. M. Hallmark et al., Phys. Rev. Lett. 59, 2879 (1987)

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3. Change of electronic surface properties1

[1] W.A. Hofer, J. Redinger, A. Biedermann, and P. Varga, Surf. Sci. Lett. 466, L795 (2000)[2] V. L. Moruzzi et al. Phys. Rev. B 15, 6671 (1977)

System: Fe(100) bcc latticeDFT calculation: FLEURLattice constant: 2.78 A

LDA: Moruzzi et al [2]No of k-points: 36

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Quenching of surface states

Simulation of quenching: distance dependent reduction of the occupationnumber of single Kohn-Sham states of the surface, 2nd order polynomial

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5. Importance of different effects

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Tunneling Spectroscopy (cartoon version)

Elastic: linear I-V Inelastic: non-linear I-V

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Tunneling Spectroscopies

• I(V) at constant z or variable z

• dI/dV at constant z or constant average I

• d (log I)/dz (barrier height measurement)

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Tunneling Spectroscopy: an example

Hyrogen on SiC surface:goes from insulator -> conductor

Derycke et al., Nature Mater. 2, 253 (2003)

UPS

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Geometric and Electronic Propertiesof Molecules I

P. Weiss et al., Science 271, 1705 (1996)

Y. Sun, H. Mortensen, F.Mathieu, P. Grutter (McGill)

Porphrin on Au(111)

Alkane thiols

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Geometric and Electronic Propertiesof Molecules II

J. Mativietsky, S. Burke, Y.Sun, S. Fostner,R. Hoffmann, P. Grutter

C60 on Au(111)

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Single-Molecule VibrationalSpectroscopy and Microscopy

B.C. Stipe, M.A. Rezaei, W. HoScience 280, 1733 (1998)

25 averages,2 minutes per spectrum

∆σ/σ= 4.2% (1-2)

∆σ/σ= 3.3% (3, different molecule)

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Single-Molecule VibrationalSpectroscopy and Microscopy

B.C. Stipe, M.A. Rezaei, W. HoScience 280, 1733 (1998)

C2H2 and C2D2 comparison

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Geometric and Electronic Propertiesof Nanowires I

Whitman et al, PRL 66, 1338 (1991)0.3 ML Cs on GaAs

and InSb (fig. C)

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Geometric and Electronic Propertiesof Nanowires II

Ohbuchi and Nogami, PRB 66, 165323 (2003)

0.36 ML Ho on Si, 400 nm image

Anisotropic lattice mismatch -->wires. Are they conductive?

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Geometric and Electronic Propertiesof Nanowires III

Evans and Nogami, PRB 59, 7644 (1999)

0.04 ML In on Si(001), 14 nm image

However: In wires are NOTconductive !

Nogami, Surf. Rev. & Letters, 6,1067 (1999)

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Defined, reproducible, understandableI-V of molecules

Chemically reliable contact

Cui et al. Nanotechnology 13, 5 (2002), Science 294, 571 (2001)

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Other spectroscopies of molecules:may the force be with you

Ch. Joachim and J. Gimzewski, Chem. Phys. Lett 265, 353 (1997)

Experimental variation o f the conductance of C60 modulated by Vin (t). The timevariation o f the voltage Vz piezo applied to the piezoelectric actuator is shown as adashed line and the experimental C60(t) conductance response as a solid line.

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Interpretation of C60 amplifier

Ch. Joachim and J. Gimzewski, Proc. IEEE 86, 184 (1998)

Calculated variations of surface resistance ofC60 on Au(110) as a function of applied force

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STM/STS and conductivity

So

if STM/STS is so powerful

- can we use it to determine the conductivityof molecules???

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‘Traditional’: infinite, structureless leads ->periodic boundary conditions.

but:

- result depends on lead size!

- bias not possible due to periodic boundarycondition!

Calculating Conductance

Jellium lead Jellium leadmolecule

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Calculation of electrical transport

)],(),([),(2

)( 00 eVEfEfVETdEh

eVI RRLL +=−== ∫

∞

∞−

µµµµ

Often one assumes that T is not a function of V, i.e.:

)(),( ETVET =

and sticks all the V dependence into the Fermifunction f

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ab-initio modelling of electronictransport

lead

Hong Guo’s research group, McGill Physics

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DFT plus non-equilibrium Green’sFunctions

J. Taylor, H. Guo , J. Wang, PRB 63, R121104 (2001)

1. Calculate long, perfect lead.

Apply external potential V by shifting energy levels

-> create electrode data base and get potential ρ right

lead

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2. Solve Poisson equation for middle part

(device plus a bit of leads); match wavefunctions

ψ and potential as a function of V to leads

(use data base) in real space.

3. ρ calculated with non-equilibrium Green’sfunctions (necessary as this is an opensystem). This automatically takes care ofbound states

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STM/STS and conductivity• STM measures DOS(EFermi)

• DOS related to conductivity

• BUT: how does the tunneling current coupleto molecular conductivity?– Very indirect:

• function of– DOS, E (where does potential drop off?)

– symmetry/coupling (electrode vs. complex molecule)

– k vector (lateral vs. perpendicular conductivity)

– internal transport mechanism (tunneling, hopping, ballistic)

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So is SPM useful in molecularelectronics?

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Molecular electronics: the issues

• Contacts

• Structure-functionrelationship betweentransport process andmolecular structure

• Dissipation

• Crosstalk(interconnects)

• Architecture

• I-O with a trillionprocessors

• Fault tolerance

• Manufacturing costs

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Does atomic structure of the contactmatter?

YES !

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Does atomic structure of the contactmatter?

Mehrez, Wlasenko, et al,Phys. Rev. B 65, 195419 (2002)

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Electronic Properties of Molecules:Requirements

R. Reifenberger

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Low-T UHVSTM/AFM/FIM

140K,

10-11mbar

quick change between

FIM - AFM/STM mode

Stalder, Ph.D. Thesis 1995

Cross et al. PRL 80, 4685 (1998)

Schirmeisen et al. NJP 2, 29.1(2000)

Sun, Lucier, Mortensen, Schaer

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Field IonMicroscopy

(FIM)

E. Muller, 1950’s

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FIM of W(111) tip

Imaging at 5.0 kV

A. Schirmeisen,

G. Cross,

A. Stalder,

U. Durig

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FIM of W(111) tip

Imaging at 5.0 kV

Manipulating at 6.0 kV

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FIM of W(111) tip

Imaging at 5.0 kV

Manipulating at 6.0 kV

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FIM of W(111) tip

Imaging at 5.0 kV

Manipulating at 6.0 kV

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Single Au atom on W(111) tip

Imaged at 2.1 KV

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Anne-Sophie Lucier

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W(111) tipon Au(111)

Cross et al.

PRL 80, 4685 (1998)

Schirmeisen et al,

NJP 2, 29.1 (2000)

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W(111) trimer tip on Au(111)

Ead = 21 eV

λ = 0.2 nm

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Molecular Dynamics Simulations

U. Landman et al, Science 248, 454 (1990)

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Force and Current vs. Distance

Sun et al,subm. PRL

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Making contact

2.0 1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5-7

-6

-5

-4

-3

-2

-1

0

Fo

rce

[nN

]

Tip-Sample Separation [Å]

10

100

1000

Cu

rren

t [n

A]

elastic

C2

~±0.2Å

~±0.2Å

C1

~0.1G0,50mVbias

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8.0 7.0 6.0 5.0 4.0 3.0 2.0 1.0 0.0 -1.0 -2.010-4

10-3

10-2

10-1

100

101

102

103

104

Cu

rren

t [n

A]

Tip-Sample Separation [Å]

Work Function vs. Apparent Barrier Height

Hofer, Fisher, Wolkow, Grutter,Phys.Rev. Lett., 87, 2001, 236104

Zeφ~ 0.4eV

φ~ 4.5eV

φ~9.4eV

ÅW tip-Au surface

dlnI/dz=-(2m)1/2/h φ1/2

φ=0.95(dlnI/dz)2

I[nA] and Z[Å]

Vbias=0.05V

Vbias=0.1V

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Atomic Structure Matters

-10 -9 -8 -7 -6 -5 -4 -30

2

4

6

8

10

12

14

Without relaxation

Atop site

Hollow site

W(111) tip, Au(111) surface

Ap

pa

ren

t B

arr

ier

He

igh

t [e

V]

Tip-sample Separation [Å]

W.A. Hofer, U. of Liverpool, unpublished

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Major Conclusions:• Forces cannot be neglected!

– Different decay lengths -> non-local, non-uniform!

– Substantial (nN)

– Major relaxation effects

• Point of contact determined both electronicallyand mechanically: they are identical to withinmeasurement error.

• W an atomically very robust electrodematerial.

• In tunneling regime: modeling in quantitativeagreement with experiment.

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Beware ofPowerPoint Engineering

orCartoon Physics!!!

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Storing information atom by atom

• Ultra high density(library of congress ona pin head)

• Ultra slow (needs life time ofuniverse to write)

• Huge footprint (UHV 4K STM)

D. Eigler, IBM Almaden

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Conductance via dissipation imaging?

Stowe et al., APL 75, 2785 (1999)

Denk and Pohl, JAP 59, 2171 (1991)

zyx

stx VCvP

δδδρ

222

=

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Summary

• Tools, both experimental and theoretical,drive our capabilities to understand thenanoworld!

• STM spectroscopy very powerful, but bigchallenge to extract conductivity.

• STM and AFM have only started to makean impact in the field of nanoelectronics.