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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’
P. Grutter
Outline
• Motivation and Intro
• History of tunneling
• STM and STS theory
• Wires
• Molecules
• Chemically and atomically defined contacts
P. Grutter
P. Grutter
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
P. Grutter
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)
P. Grutter
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)
P. Grutter
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
P. Grutter
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 !)
P. Grutter
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)
P. Grutter
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 !
P. Grutter
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)
P. Grutter
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
P. Grutter
1. Chemical nature of the tip1
[1] P. Varga and M. Schmid, Appl. Surf. Sci. 141, 287 (1999)
P. Grutter
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)
P. Grutter
Electronic properties of the tip:non-magnetic tip models
P. Grutter
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
P. Grutter
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
P. Grutter
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
P. Grutter
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
P. Grutter
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)
P. Grutter
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
P. Grutter
Quenching of surface states
Simulation of quenching: distance dependent reduction of the occupationnumber of single Kohn-Sham states of the surface, 2nd order polynomial
P. Grutter
5. Importance of different effects
P. Grutter
Tunneling Spectroscopy (cartoon version)
Elastic: linear I-V Inelastic: non-linear I-V
P. Grutter
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)
P. Grutter
Tunneling Spectroscopy: an example
Hyrogen on SiC surface:goes from insulator -> conductor
Derycke et al., Nature Mater. 2, 253 (2003)
UPS
P. Grutter
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
P. Grutter
Geometric and Electronic Propertiesof Molecules II
J. Mativietsky, S. Burke, Y.Sun, S. Fostner,R. Hoffmann, P. Grutter
C60 on Au(111)
P. Grutter
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)
P. Grutter
Single-Molecule VibrationalSpectroscopy and Microscopy
B.C. Stipe, M.A. Rezaei, W. HoScience 280, 1733 (1998)
C2H2 and C2D2 comparison
P. Grutter
Geometric and Electronic Propertiesof Nanowires I
Whitman et al, PRL 66, 1338 (1991)0.3 ML Cs on GaAs
and InSb (fig. C)
P. Grutter
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?
P. Grutter
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)
P. Grutter
Defined, reproducible, understandableI-V of molecules
Chemically reliable contact
Cui et al. Nanotechnology 13, 5 (2002), Science 294, 571 (2001)
P. Grutter
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.
P. Grutter
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
P. Grutter
STM/STS and conductivity
So
if STM/STS is so powerful
- can we use it to determine the conductivityof molecules???
P. Grutter
‘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
P. Grutter
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
P. Grutter
ab-initio modelling of electronictransport
lead
Hong Guo’s research group, McGill Physics
P. Grutter
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
P. Grutter
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
P. Grutter
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)
P. Grutter
So is SPM useful in molecularelectronics?
P. Grutter
Molecular electronics: the issues
• Contacts
• Structure-functionrelationship betweentransport process andmolecular structure
• Dissipation
• Crosstalk(interconnects)
• Architecture
• I-O with a trillionprocessors
• Fault tolerance
• Manufacturing costs
P. Grutter
Does atomic structure of the contactmatter?
YES !
P. Grutter
Does atomic structure of the contactmatter?
Mehrez, Wlasenko, et al,Phys. Rev. B 65, 195419 (2002)
P. Grutter
Electronic Properties of Molecules:Requirements
R. Reifenberger
P. Grutter
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
P. Grutter
Field IonMicroscopy
(FIM)
E. Muller, 1950’s
P. Grutter
P. Grutter
FIM of W(111) tip
Imaging at 5.0 kV
A. Schirmeisen,
G. Cross,
A. Stalder,
U. Durig
P. Grutter
FIM of W(111) tip
Imaging at 5.0 kV
Manipulating at 6.0 kV
P. Grutter
FIM of W(111) tip
Imaging at 5.0 kV
Manipulating at 6.0 kV
P. Grutter
FIM of W(111) tip
Imaging at 5.0 kV
Manipulating at 6.0 kV
P. Grutter
Single Au atom on W(111) tip
Imaged at 2.1 KV
P. Grutter
Anne-Sophie Lucier
P. Grutter
W(111) tipon Au(111)
Cross et al.
PRL 80, 4685 (1998)
Schirmeisen et al,
NJP 2, 29.1 (2000)
P. Grutter
W(111) trimer tip on Au(111)
Ead = 21 eV
λ = 0.2 nm
P. Grutter
Molecular Dynamics Simulations
U. Landman et al, Science 248, 454 (1990)
P. Grutter
Force and Current vs. Distance
Sun et al,subm. PRL
P. Grutter
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
P. Grutter
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
P. Grutter
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
P. Grutter
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.
P. Grutter
Beware ofPowerPoint Engineering
orCartoon Physics!!!
P. Grutter
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
P. Grutter
Conductance via dissipation imaging?
Stowe et al., APL 75, 2785 (1999)
Denk and Pohl, JAP 59, 2171 (1991)
zyx
stx VCvP
δδδρ
222
=
P. Grutter
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.