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
Nanoprobes, Spectroscopy & Scattering
Lecture 5: Nanoprobes: Frontiers of scanning probe techniques
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,
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Nanoprobes, Spectroscopy & Scattering
Lecture 5: Nanoprobes: Frontiers of scanning probe techniques
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
Nanoprobes, Spectroscopy & Scattering
Lecture 5: Nanoprobes: Frontiers of scanning probe techniques
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:
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Nanoprobes, Spectroscopy & Scattering
Lecture 5: Nanoprobes: Frontiers of scanning probe techniques
Tunneling current
Binnig 1982
φ
χm2
=
Local tunneling barrier height = ‘effective workfunction’
Typical distance:1 nm ~ several atoms!
Nanoprobes, Spectroscopy & Scattering
Lecture 5: Nanoprobes: Frontiers of scanning probe techniques
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):
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Nanoprobes, Spectroscopy & Scattering
Lecture 5: Nanoprobes: Frontiers of scanning probe techniques
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?
Nanoprobes, Spectroscopy & Scattering
Lecture 5: Nanoprobes: Frontiers of scanning probe techniques
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)
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Nanoprobes, Spectroscopy & Scattering
Lecture 5: Nanoprobes: Frontiers of scanning probe techniques
Comparison photoemission – STS
examples
O. Sanchez et al. PRB 52, 7984 (1995)
Nanoprobes, Spectroscopy & Scattering
Lecture 5: Nanoprobes: Frontiers of scanning probe techniques
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):
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Nanoprobes, Spectroscopy & Scattering
Lecture 5: Nanoprobes: Frontiers of scanning probe techniques
SPSTM on Cr(001)
Wiesendanger et al.: PRL 65, 247 (1990)
W tip
CrO2 tip
Nanoprobes, Spectroscopy & Scattering
Lecture 5: Nanoprobes: Frontiers of scanning probe techniques
Technical Design
Piezo effect ~ 109 V/m=> nm precision
Tip/samplestage
Damping system
He-cooling
UHV compatible STM (Omicron)
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Nanoprobes, Spectroscopy & Scattering
Lecture 5: Nanoprobes: Frontiers of scanning probe techniques
STM-Tips
Tip artifactsTip radius < 20 nm
STS:Which atom is at the tip end?
Nanoprobes, Spectroscopy & Scattering
Lecture 5: Nanoprobes: Frontiers of scanning probe techniques
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
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Nanoprobes, Spectroscopy & Scattering
Lecture 5: Nanoprobes: Frontiers of scanning probe techniques
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
Nanoprobes, Spectroscopy & Scattering
Lecture 5: Nanoprobes: Frontiers of scanning probe techniques
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
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Nanoprobes, Spectroscopy & Scattering
Lecture 5: Nanoprobes: Frontiers of scanning probe techniques
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
Nanoprobes, Spectroscopy & Scattering
Lecture 5: Nanoprobes: Frontiers of scanning probe techniques
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
Nanoprobes, Spectroscopy & Scattering
Lecture 5: Nanoprobes: Frontiers of scanning probe techniques
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)
Nanoprobes, Spectroscopy & Scattering
Lecture 5: Nanoprobes: Frontiers of scanning probe techniques
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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Nanoprobes, Spectroscopy & Scattering
Lecture 5: Nanoprobes: Frontiers of scanning probe techniques
k-space: square lattice reconstructions
Real space k-space
Nanoprobes, Spectroscopy & Scattering
Lecture 5: Nanoprobes: Frontiers of scanning probe techniques
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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Nanoprobes, Spectroscopy & Scattering
Lecture 5: Nanoprobes: Frontiers of scanning probe techniques
Brill ouin zones
k = -1 0 1 2 3 4 52D Brillouin zone
3D-BZ
Nanoprobes, Spectroscopy & Scattering
Lecture 5: Nanoprobes: Frontiers of scanning probe techniques
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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Nanoprobes, Spectroscopy & Scattering
Lecture 5: Nanoprobes: Frontiers of scanning probe techniques
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?
Nanoprobes, Spectroscopy & Scattering
Lecture 5: Nanoprobes: Frontiers of scanning probe techniques
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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Nanoprobes, Spectroscopy & Scattering
Lecture 5: Nanoprobes: Frontiers of scanning probe techniques
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
Nanoprobes, Spectroscopy & Scattering
Lecture 5: Nanoprobes: Frontiers of scanning probe techniques
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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Nanoprobes, Spectroscopy & Scattering
Lecture 5: Nanoprobes: Frontiers of scanning probe techniques
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
Nanoprobes, Spectroscopy & Scattering
Lecture 5: Nanoprobes: Frontiers of scanning probe techniques
Growth of thin films
external transport
hom ogeneous nuleationheterogeneous
adsorption-desorption
Cluster-kinetics
surface-diffusion
growth- kinetics
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Nanoprobes, Spectroscopy & Scattering
Lecture 5: Nanoprobes: Frontiers of scanning probe techniques
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:
Nanoprobes, Spectroscopy & Scattering
Lecture 5: Nanoprobes: Frontiers of scanning probe techniques
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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Nanoprobes, Spectroscopy & Scattering
Lecture 5: Nanoprobes: Frontiers of scanning probe techniques
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)
Nanoprobes, Spectroscopy & Scattering
Lecture 5: Nanoprobes: Frontiers of scanning probe techniques
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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Nanoprobes, Spectroscopy & Scattering
Lecture 5: Nanoprobes: Frontiers of scanning probe techniques
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:
Nanoprobes, Spectroscopy & Scattering
Lecture 5: Nanoprobes: Frontiers of scanning probe techniques
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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Nanoprobes, Spectroscopy & Scattering
Lecture 5: Nanoprobes: Frontiers of scanning probe techniques
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
Nanoprobes, Spectroscopy & Scattering
Lecture 5: Nanoprobes: Frontiers of scanning probe techniques
NanotechnologyThe quantum corral reef-
An academic gadget Manipulating the surface by AFM-The data storage future?
Sou
rce:
IB
M
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Nanoprobes, Spectroscopy & Scattering
Lecture 5: Nanoprobes: Frontiers of scanning probe techniques
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)
Nanoprobes, Spectroscopy & Scattering
Lecture 5: Nanoprobes: Frontiers of scanning probe techniques
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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Nanoprobes, Spectroscopy & Scattering
Lecture 5: Nanoprobes: Frontiers of scanning probe techniques
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.