the nano-world - universiteit van amsterdam fnwi2 nanoprobes, spectroscopy & scattering lecture...

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Nanoprobes, Spectroscopy & Scattering

Lecture 5: Nanoprobes: Frontiers of scanning probe techniques

The Nano-worldA. Borgschulte, VU Amsterdam 2003



Table of contents

1. Theory of Scanning Probe Microscopy:

• General Principles

• Electron Tunneling: theoretical background

• SPMs: setups and techniques

2. SPMs: Applications

• Fundamentals of Surface Science: Atomic structure of surfaces, growth studies, gas-solid interaction

• Special appli cations in condensed matter physics, electro-chemistry, life science,

2



Scanning Probe Microscopy

• Measuring physical interaction Ω(z)•Use it as a control parameter to map the surface

•Force (AFM)•Tunneling current (STM)•Capacity (SCAM)•Light (SNOM)•Thermal properties



U I

surface tip

vacuumm etal m e tal

Φ

dE F

Electron tunneling

0 s z

V

Ψ1

Ψ2

Ψ3

One-dimensional rectangular potential barrier with height V and width s

2

2112

122

2,,

2

mE

kAeeEdz

d

m

ikzikz

=+=ΨΨ=Ψ−

22

22222

22)(2

,,2

EVm

CeBeEVdz

d

m

zz −=+=ΨΨ=Ψ+Ψ−−−

χχχ

ikzDeE

dz

d

m=ΨΨ=Ψ− 332

322

,2

z2222

222

i

t Ce)k(

k16D

j

jT χ−

χ+χ≈==

233

33t D

m

k

dz

d)z(

dz

d)z(

m2

ij

=

ΨΨ−ΨΨ−−=∗

∗

m

kji

=

)2exp( sI χ−∝Distance dependence:

3



Tunneling current

Binnig 1982

φ

χm2

=

Local tunneling barrier height = ‘effective workfunction’

Typical distance:1 nm ~ several atoms!



Tunneling current in STM

∑ −⋅−=νµ

µννµ δδπ,

2,

2

)()(||2

FF EEEEMUe

I

∑ −Ψ⋅⋅⋅∝ν

νν δχ )(|)(|)2exp()( 20 FFt EErREnUI

)exp()( znz t χµ ±∝Ψ

)](2exp[|)(| 20 Rsr +−∝Ψ χν

)2exp( sUI χ−∝

s

R

Ψυ

Ψµ

Atomic resolution of |Ψ|2 (no atoms!)

)(2

2

,∗∗ Ψ∇Ψ−Ψ∇Ψ⋅−= ∫ µννµνµ Sd

mM

1st images of Si (111): Binnig and Rohrer 1982

Tersoff-Hamann-simplification (1 atom tip):

4



Mapping electronic states

Imaging the electronic states of the semiconductorSiC(0001) (3x3)

U=-1V (occupied states) U= 1V (unoccupied states)

Can we quantify the process?



Scanning Tunneling Spectroscopy

∫ ⋅⋅±∝eU

tt dEeUETrEnEeUnI0

0 ),(),(),(

dEdU

eUEdTrEnEeUn

eUTeUnendU

dI

eU

st

st

),(),(),(

)()()0(

0

0 ⋅⋅±+

⋅⋅∝

∫

spectroscopy

∑ −⋅−=νµ

µννµ δδπ,

2,

2

)()(||2

FF EEEEMUe

I

PES IPES

SDOS of Si (111)

5



Comparison photoemission – STS

examples

O. Sanchez et al. PRB 52, 7984 (1995)



Spin dependent tunneling

∫ ⋅⋅±∝eU

tt dEeUETrEnEeUnI0

0 ),(),(),(

∑ ∫=

⋅⋅±∝', 0

0 ),(),(),(σσi

eUiii dEeUETrEnEeUnI

tt

Polarisation

↓↑

↓↑

+−=

II

IIP

• Zeeman-split density of states of a superconductor

• Ferromagnetic semiconductors/insulators (e.g. EuS)

• Opticall y pumped semiconductors

• Half-metalli c ferromagnets (e.g. CrO2)

• ‘classical’ ferromagnets (Fe, Ni, Co)

Special requirements for the tip (=> ni or Ti):

6



SPSTM on Cr(001)

Wiesendanger et al.: PRL 65, 247 (1990)

W tip

CrO2 tip



Technical Design

Piezo effect ~ 109 V/m=> nm precision

Tip/samplestage

Damping system

He-cooling

UHV compatible STM (Omicron)

7



STM-Tips

Tip artifactsTip radius < 20 nm

STS:Which atom is at the tip end?



Force microscopy

Single atom at a wall :

3d

1

6

CU ⋅

πρ−=

Two half spheres:

d

1

6

AR

d

1

)RR(6

RARU

21

21 ⋅−→⋅+

−=

k20 =ω

''Uf;kf2f =+=ω

Shift of the resonance frequency of the cantilever is a mass for the tip-sample force interaction

One commonly measures in the tapping mode,i.e. with an oscill ating tip

8



Atomic Force Microscopy (AFM)

AFM on SrTiO3 (001) surface structures

Monoatomic steps => ‘atomic’ resolution

3 nm high Pd clusters??

STM image

atomic resolution of a NaCl(001) surface



Magnetic Force microscopy (MFM)

Magnetic tip feelsstrayfield

M.R

. Kob

lisc

hka

and

U. H

artm

ann,

Ult

ram

icro

sco

py9

7 (2

003)

103

–112

9



Scanning Near Field Microscopy SNOM

Far-field optics: Abbé-limit

=> Raster method

4−∝ sI

Can be surrounded by using evanescent li ght

•Resolution ~ 50 nm (tip!)•(Magneto-) optical effects•Can be combined with STM….

Source: Omicron



Table of contents

1. Theory of Scanning Probe Microscopy:

• General Principles

• Electron Tunneling: theoretical background

• SPMs: setups and techniques

2. SPMs: Applications

• Fundamentals of Surface Science: Atomic structure of surfaces, growth studies, gas-solid interaction

• Special appli cations in condensed matter physics, electro-chemistry, life science,

10



Atomic structure of surfaces

Indexing by Mil ler indices of the corresponding bulk planes

a2

a1

b1

b2

Deviations from bulk planes (reconstructions)

=

2

1

2221

1211

2

1

a

add

dd

b

b

0)22( R×

(001)

(110)(111)



Real vs. reciprocal space

k-Space (i.e. spacing of diff raction spots in nm–1)

Real Space (i.e. spacing of surface atoms in nm)

larger real-space smaller k-space

2G

a

π=

aSTM

e.g.LEED

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k-space: square lattice reconstructions

Real space k-space



k-space and electronic structure

Important property is d/a

)/2()( akk π+Ψ=Ψ

Largest wavelength => infinity (k=0), smallest => a (k=π/a), because

k-vector = 2π/a

Can be understood as a wave with wave length a

kidadi eeadd ⋅=∝Ψ⇒+Ψ=Ψ /2)()( π

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Brill ouin zones

k = -1 0 1 2 3 4 52D Brillouin zone

3D-BZ



Structures of real surfaces

Missing row reconstruction of (110) metal surfaces

2/22 a⋅

a

Rh(110) (1x2)

Reconstruction and relaxation of metal surfaceshcp(0001) Re(-5%), Sc (-2%), Ti (-2%), Zr (-1%)

fcc(111) Al (+1%), Ag (0%), Cu (0.7%), Pt (+1%), Rh (0%)

fcc(100) Al (0%), Cu (-%), Rh (0%)

fcc(110) Al (-8.5%), Ag (-8%), Cu (-8.5%), Rh (-3%)

bcc(110) Fe (+0.5%), V (-0.3%), W (0%)

bcc(100) Fe (-5%), Mo (-9.5%), W (-8%)

d s

d 0

E. Vesselli et al., J. chem. Phys. 114, 4221 (2001)

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Surface structure of Si (111)

LEED: (7x7) reconstruction, real space unknown for years

Power spectrum

STM image

DAS-model

Why does nature behave so crazy?



Electronic structure of surfaces

)z(ue)az(),z(U)az(U

)z(E)z()z(Udz

d

m2

kikz

k

2

22

νν

ννν

=+Ψ=+

Ψ=Ψ

+−

K22

2

KiKz

K

KKK2

22

Em2

K,Km2

E,eL

1)z(

)z(E)z(dz

d

m2

±===Φ

Φ=Φ

−

γ+=Γ+= ikq,iKQ

Schrödinger-equation for bulk states

=> Bloch waves with a

ka

π≤≤π−

Schrödinger-equation for vacuum

K is real (normalisation), while complex solutions are posssible at the surface:

)0z(dz

d)0z(

dz

d),0()0( =Ψ==ΦΨ=Φ

)z(uCe)z(uBe)z(

,Ae)z(

kikz

kikz

z

∗

Γ

+=Ψ

=Φ

Energy E<0 l ies in a band:

Surface state

)z(ueCe)z(

,Ae)z(

kzikz

z

∗γ

Γ

=Ψ

=Φ

)0z(dz

d)0z(

dz

d),0()0( =Ψ==ΦΨ=Φ

Energy E<0 l ies in a bandgap:

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Surface band structure

-1 0

-5

5

1 5

1 0

E F

Γ L

ener

gy (

eV)

-1 0

-5

E F

Γ- K-

ener

gy (

eV)

Schockley-state

Tamm-state



Surface states and morphology

A. B

end

ou

nan

et a

l., P

hys

. Rev

. B 6

7 , 1

6541

2 (2

003)

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Macroscopic morphology of surfaces

Pd cluster on Al2O3

Hansen et al., Phys. Rev. Lett. 83, 4120 (1999)

∫ → .)( MindAhklγ

Definition of surface energy: dAdW pTs γ=),(

γ = γ(hkl) increases with index number

=> stepped surfaces



Growth of thin films

external transport

hom ogeneous nuleationheterogeneous

adsorption-desorption

Cluster-kinetics

surface-diffusion

growth- kinetics

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Growth modesIsland growth

Layer-by layer growth

Step-flow growth

Stranski-Krastanov mode

B. V

oigt

länd

er e

t al.,

PR

L 78

, 216

4 (1

997)

http://www.fz-juelich.de/zam/CompServ/software/video/voigtlaender/http://www.ep4-of.ruhr-uni-bochum.de/methods/movies.shtml

Links:



Growth modesPhenomenological description (thermodynamic)

Island growth Layer-by layer growth Stranski-Krastanov mode

γ

γ

γ SV

EV

SE θ

SVSEEV γγγ +> SVSEEV γγγ +<

Wetting layer:Step-flow growth?kinetics, nucleation

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1st Nucleation

Ag on Si(111) (7x7)

Fil ling factor of the layers:=> 2D / 3D nucleation

Interaction between evaporant and substrate

SEγ⇒

Fe on Si(111) (7x7)D.W. McComb et al., PRB 49, 17139 (1994)

S. H

ajja

ret

al.,

PR

B 6

8, 0

3330

2 (2

003)



TLK-model

Ehrlich-Schwoebel-barrier:Reflection and adsorption at ledges

Al2O3 (0001)

Rh onAl2O3 (0001)

J. F

reun

d, S

urf.

Sci

. 500

,271

–299

(200

2)

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Growth kinetics

diffusional step-flow L2R << Dconvective step-flow L2R ~ Dlayer-by-layer L2R > Dstatistical growth L2R >> D

Terasse length L, rate R and diffusion constant D determine the growth mode:



Birth and death model

k e x k a t

1/τM L

)()(

)()(

)(

1111

121

11

nnnexnnnex

nnnexnnnex

natnatnML

nnn

kk

kk

kk

θθαθθα

θθαθθα

ηηατ

θθα

−−−−

−−−−

+−−

=

−+−

−−+

−−−

−+

+−

−−

nnatnatnnkk ηαηαθ 1+

−+ +=

nn

nnnucn

k θθ

ηαη

−

−=1

2

Mobile adatom coverage:

immobile adatom coverage:

Number of nuclei:

0 1 2 3 40.0

0.2

0.4

0.6

0.8

1.0

0.0

0.2

0.4

0.6

0.8

1.0

t/τML

θ (M

L)in

tens

ity (

1)

Electrochemical deposition of Ni on Au (PRB 56, 12 506 (1997))

=> RHEED-oscill ations

See also J. Y. Tsao, Materials Fundamentals of Molecular Beam epitaxy, Academic Press NY (1993)

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Molecular Beam Epitaxy (MBE)

MBE is the mono-crystalli ne condensation of a vapor on a mono-crystalline substrate

F ilm

Subs trate

in co h ere n t p se u d o m o rp hic se m ico h e re n t

Growth modes, roughness (e.g. misfit dislocations) etc. by SPM

Orientation/strain by diffraction methods (Lecture by W. Lohstroh)

Semiconductor technology



NanotechnologyThe quantum corral reef-

An academic gadget Manipulating the surface by AFM-The data storage future?

Sou

rce:

IB

M

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SPM in Life Sciences

SNOM images of chromsomes

STM image of an unwrapped DNA

STM image of the double-helix structure

Winkler et al. Journal of Microscopy, 209, 23, (2003)



Combining Condensed Matter Physics and Cell Biology

Neuron from rat brain on a linear array of f ield-effect transistors. The ionic current in the cell interacts with the electronic current in the sil icon. Source: MPI Martiensried

The future….?

Main problem:

The interfaces!!!!!

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Literature

• R. Wiesendanger, Scanning Probe Microscopy and Spectroscopy, Cambridge Univesity Press 1993

• J. Y. Tsao, Materials Fundamentals of Molecular Beam epitaxy, Academic Press NY, 1993

• W. Moench, Semiconductor surfaces and interfaces, Springer Verlag, Berlin, 1995

• J. M. Howe, Interfaces in materials, Wiley, New York, 1997.

the nano-world - universiteit van amsterdam fnwi2 nanoprobes, spectroscopy & scattering lecture...

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