11/9/2015 1 06.11.15 10:15-12:00 Introduction - SPM methods 13.11.15 10:15-12:00 STM 20.11.15 10:15-12:00 STS 27.11.15 10:15-12:00 Novel SPM techniques 04.12.15 10:15-12:00 2-dimensional crystallography, LEED, AES Erik Zupanič [email protected]stm.ijs.si Microscopical and Microanalytical Methods (NANO3 ) Summary... ... of previous lecture: Surface – a few topmost atomic layers of material with electronic and crystal structure different than that of a bulk material Surface structure, defects, reconstruction-relaxation... Surface science techniques Ultra-high vacuum Sample preparation Scanning probe microscopy (branch of microscopy that forms images of surfaces using a physical probe that scans the specimen) Atomic force microscopy Scanning near-field optical microscopy next: Scanning tunneling microscopy
Scanning probe microscopy (branch of microscopy that forms images of surfaces using a physical probe that scans the specimen)
Atomic force microscopy
Scanning near-field optical microscopy
next: Scanning tunneling microscopy
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History:
1972 piezoelectric driver (Young et al.)
1978 electron tunneling experiment (Teague)
1981 tunneling between a scanning W tip and Pt
STM (IBM Zürich Research Labs)
G. Binnig, H. Rohrer, Ch. Gerber and E. Weibel
(Phys. Rev. Lett. 49, 57-60 (1982))
Nobel prize in physics 1986
Books:
R. Wiesendanger, Scanning Probe Microscopy and Spectroscopy, Methods and Applications, Cambridge Univ. Press 1994
S. N. Magonov and M.-H. Whangbo, Surface Analysis with STM and AFM, Experimental and Theoretical Aspectst of Image Analysis, VCH Verlagsgesellschaft mbH, Weinheim 1996
Scanning Tunneling Microscopy and Spctroscopy, Theory, Techniques and Applications, Ed. D. A. Bonnell, VCH Verlagsgesellschaft mbH, Weinheim 1993
Scanning Tunneling Microscopy I & II, Eds. R. Wiesendanger and H.-J. Güntherodt, Springer Series in Surface Sciences 20 & 28, Springer Verlag Berlin 1992
E. Meyer et al.,Scanning Probe Microscopy – The Lab in a Tip, Springer 2006
Scanning tunneling microscopy
Scanning tunneling microscopy
The STM operation is based on the concept of quantum tunneling…
STM tip
sample surface
A
Utunneling
Typical values: Utunneling = 10 mV …. 10 VItunneling = 10 pA …. 10 nA
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2k → 20 nm-1
Δd = 0.1 nm
order of magnitude→ difference in the
tunneling probability
„I think I can safely say that nobody understands quantum mechanics.“ Richard Feynman in The Character of Physical Law (1965)
Scanning tunneling microscopy
STM: Bardeen‘s perturbation approach
• gives approximate solutions to the time-dependent Schrödinger equation
• valid in case of weak tunneling (large tip-sample separation and low bias voltage)
• its limits:
a) validity of first-order perturbation approach
b) ortho-normalized tip and sample wave functions
c) electron - electron interactions neglected (not appliable e.g. in case of single-electron tunneling - “Coulomb blocade“)
d) tunneling doesn’t change tip and sample occupation probabilities (tip and sample system are large systems in comparison with the tunneling electrons)
e) tip and sample are each supposed to be in electrochemical equilibrium
In accord with c) single electron Hamiltonian is considered first:
Hψ(r) = -(ħ2/2m)Δψ(r) + V(r) ψ(r) (1)
J. Bardeen, Phys. Rev. Lett. 6(1961), 57-59; A. D. Gottlieb and L. Wesoloski, Nanotechnology 17(2006), R57-R65
STM – Bardeen‘s approach
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Even the single electron problem is not soluble. The current through the tip-sample junction is calculated by considering separately the electronic structures of the tip (plus the barrier) and the sample (plus the barrier), i.e. left and rigt side are considered separately:
Hsψ(r) = -(ħ2/2m)Δψ(r) + Vs(r) ψ(r) (2)
Htψ(r) = -(ħ2/2m)Δψ(r) + Vt(r) ψ(r) (3)
The sample potential Vs(r) is taken as V(r) for any r inside the sample and the barrier and as 0 for any r in the tip region (and vice-versa for Vt(r)).
The tunneling current is a net result of all electron transfers from the tip to the sample and vice-versa under the action of H, as given in (1).
Single electron scattering rate:
For an electron initially in the sample state ψ with energy ε:
Hsψ = εψ (4)
STM – Bardeen‘s approach
The sample state Ψ changes with time into Ψ(t). For small t and for weak tunneling:
Ψ(t)≈ Ψ(0) → Ψ(t) = e-itε/ ħ + ∑kak(t)φk (5)
with the sum over all tip states φk of the tip Hamiltonian:
Htφk = Ek φk (6)
The goal is to find approximate coeficients ak(t) for t>0. Ψ(t) from (5) is inserted into the time-dependent Schrödinger equation:
iħ∂/∂tΨ(r,t)=HΨ(r,t) (7)
and it is assumed (in accord with a) and b)) that the coeficients ak(t) remain small for small t.
It can be shown that the total rate, at which an electron is scattered from a sample state Ψ into a tip states φk , is approximately given by:
d/dtΣk|ak(t)|2=d/dt({4∑k[sin2(t(Ek-ε)/2ħ)/(Ek-ε)
2] x |< φk|H-Hs| ψ>|2 }) (8)
Likewise, the same formula is valid for the oposite process, i.e. the total rate of electron scatteringfrom a tip states φi into a given sample state ψ.
STM – Bardeen‘s approach
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(next steps are again left out): These comprise
first, summing over all sample states, weighted by their occupational probabilities and by the probabilities of the tip states being vacant, giving the total rate at which electrons are scattered into the tip states,
second, multiplying the difference between the two oposite rates by e and finally, approximating the right side in the sum of (8) („Fermi´s golden rule“) as:
∑kPt(Ek- ε)M2(φk,ψ) (9)
with Pt(x)=sin2(tx/2ħ)/x2 (10)
whose integral with respect to x is t/2ħ (11)
and replacing the second part in the sum of (8) with the matrix element defined as: M2(φn,ψ) ≈ - ħ2/2m ∫dS(T*S - ST*) (12)
where the quantity in parenthesis represent the current density jTS , the total tunneling current I is obtained as:
with F the Fermi-Dirac functions, t and s the tip and the sample chemical potential and T the temperature.
STM – Bardeen‘s approach
Tersoff-Hamann Theory
- Since the tip and sample are only weakly coupled, perturbation theory is
appropriate for the junction.
- Predominant tip state in tunneling is s-orbital.
Solve for Matrix Element!
J. Tersoff and D.R. Hamann. Phys. Rev. B. 31, 805 (1985) G.A.D. Briggs and A.J. Fisher. Surf. Sci. Rep. 33, 1 (1999)
Bardeen’s Tunneling Current:
STM – Tersoff-Hamann Theory
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Sdm
M TSST
e
)**(
2
2
Green’s Function for SE: )()(][ 22
oo rrrrG
)(4
)( oT rrGC
r
Tip: S-state from Spherical Potential Well
Green’s Theorem
drrGrrG
m
CoSSo
e
)]()([2 22
2
Schroedinger Equation (SE) in Vacuum:
mrr
2);()( 22
drrrrGrrG
m
CooSSo
e
))]()(()([2 22
2
2|)(|S
oS rI
)(2
)()(2 22
oS
e
ooS
e
rm
Cdrrr
m
C
Substitute Eq. (2) Substitute Eq. (3)
SdrrGrrGm
CM oSSo
e
)]()([
2 2
Introduction to Scanning Tunneling Microscopy. C.J. Chen. (Oxford University Press, New York, 1993).
No Tip Contributions
STM – Tersoff-Hamann Theory
Limitations of Tersoff-Hamann
• Experimental verification of T-H theory: Au(110) surface
• Most STM tips are transition metals → dominant d-orbital character
• Tip-sample forces modification of sample wavefunctions
• Poor understanding of tip structure
Tersoff-Hamann Theory:Simple model for fundamental understanding of STM images
STM – Tersoff-Hamann Theory
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Chen (1990): s-wave tip approach is too simple major contribution from d-orbitals:
the angular dependance of the tip wave functions is given by the „derivative rule“: e.g. pz ∂/∂z or dxy ∂2/∂x∂y
wave functions for different tip states given as:
STM – s,p states
assuming similar atomic-like states at the sample surface conductance distribution (r) can be evaluated: except for st and ss states, coductance depends on cos = z/r:
reciprocity principle:
lateral atomic resolution requires other than s-states in either the tip or the sample !
STM – s,p states
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STM imaging
Scanning tunneling microscopy
Scanning Tunneling Spectroscopy (STS)
Different spectroscopy modes:
I-d
V-d
I-V
IETS
Scanning tunneling microscopy
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single atom / molecule manipulation
Lateral manipulation:Vertical manipulation:
Scanning tunneling microscopy
0.255 nm
15 m
m
150 000 000 X
Lateral resolution: < 100 pm
Vertical resolution: < 10 pm
> 2
000
km
Lateral resolution: < 15 mm
Vertical resolution: < 1.5 mm
40 mm
Scanning tunneling microscopy
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Experimental set-up
LT-STM RT-STM LHe cryostat Omicron LEED / AES ion gun / annealing load lock
Besocke-type STMT ≈ 7 Kp < 1· 10-10 mbarScan range: 1µm x 1µm x 0.2µm @ 6K
The cryostat The LT-STM head
LHe temperature: 4.2 K
LN2 temperature: 77 K
Experimental set-up
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LT-STM under construction:Laser-assisted STM and RF-STM
Joule-Thomson LT-STMworking temperature T < 1 K
Experimental set-up
Typical temperatures:
- below 5K without the Joule-Thomson stage operation
- 1.0K in 4He JT mode, <500 mK in 3He JT mode
- variable temperature 1 - 100 K
Measuring times:
- LHe hold time (9.5l) over 6 days
- LN2 hold time (18l) over 4 days
Specifications:
- X & Z coarse positioning
- in-situ tip and sample exchange
- scan range @ 1K: 1 x 1 µm
- drift rate < 100 pm/h
- sample dimensions: 10 x 10 mm
Joule – Thomson STM
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4 ports for in-situ evaporation
2 ports (optical access) for laser assisted STM
Joule – Thomson STM
Joule – Thomson STM
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Why low (cryogenic) temperatures?
- Better mechanical (temperature) stability
- Lower electrical noise
- Low temperatures stabilizes surface and surface adsorbates
- Observe low-temperature effects
- Improved energy resolution in spectroscopy measurements
- ...
STM variants:
- ambient / ultra-high vacuum STM
- high- / room- / low- temperature STM
- high-speed STM
- magnetic field
Experimental set-up
W tip preparation Sample preparation
- ion gun sputtering
- annealing
- repeat …
Tip and sample preparation
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STM tips
STS measurements
Best tips for STS: clean, slightly blunt
6.3 x 6.3 nm2
9.5 x 9.5 nm2
0 pm
8 pm
Examples
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8 x 8 nm2
Cu(111)
500 x 500 nm2
step height 0.21 nm
Examples
STM does not probe the position of the atomicnucleus, but rather its electron density. Thus, STMimages do not always show exact atomic positionsand the images depend on the nature of the surfaceand the magnitude and sign of the tunnelingcurrent.
Cu(111) – surface-state electrons standing waves
9.5 x 9.5 nm2 19 x 19 nm2
150 x 150 nm2
Wavelenght λF of 1.4 nm was measured for surface state electrons at EF.
Examples
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Impurities on Cu(111) – CO molecules @ 25 K
150 x 150 nm2
clean STM tip
150 x 150 nm2
STM tip terminated by a CO molecule
Examples
Controlled tip – sample interaction (tip crashing)
50 x 30 nm2
200 x 120 nm2
120 x 120 nm2
Examples – tip-sample interaction
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Lateral (pull mode) manipulation
18 x 15 nm2
Examples - manipulation
M.F. Crommie, C.P. Lutz, D.M. Eigler, E.J. Heller. Waves on a metal surface and quantum corrals. Surface Review and Letters 2 (1), 127-137 (1995). S. Fölsch et al., Quantum Confinement in
Monatomic Cu Chains on Cu(111), Phys. Rev. Lett. 92, 056803 (2004)
Examples – quantum confinement
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Lagoute et al., Link between Adatom Resonances and the Cu(111) Shockley Surface State, Phys. Rev. Lett. 95, 136801(2005)
Examples – quantum confinement
When a magnetic cobalt atom is placed at a focus point of an elliptical corral (upper right), some of its properties also appearat the other focus (lower left), where no atoms exists. In this case, a change in the surface electrons due to the cobalt'smangetism -- the Kondo resonance -- appears as a bright spot at each focus.When the cobalt atom is placed elsewhere within the ellipse but not at a focus point, the mirage disappears, and the Kondo effect is detected only at the cobalt atom itself.
This projection of information from an atom to another place where there is no atom was named the "quantum mirage" effectby the three IBM Research - Almaden (San Jose, Calif.) physicists who discovered it: Hari Manoharan, Christopher Lutz andDonald Eigler.Because the quantum mirage effect projects information using the wave nature of electrons rather than a wire, it has thepotential to enable data transfer within future nanoscale electronic circuits so small that conventional wires do not work. Manybarriers must be overcome to make this scientific discovery useful in this way. But if it can be developed, the quantum miragecould enable the miniaturization of electronic circuits far beyond that envisioned today.
In this case, the corral is made of 36 cobalt atoms positioned on a copper (111) surface. The discovery was first described inthe cover article of the February 3, 2000, issue of Nature, a prestigious technical journal.
Examples – quantum mirage
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Examples – inducing chemical reaction
Dislocations – one-dimensional defects
Primer vijačne dislokacije:
Examples – dislocations
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Alloy PtRh (100) – engine catalytic converter
Composition 50-50, but on surface 31 % Rh (bright) and 69% Pt (dark).
Examples – alloys
Quasicrystal - a structure that is ordered but not periodic
Examples – quasicrystal
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Superconductors
Images are usually obtained by mapping the tunneling conductance in real space at a
particular bias voltage.
Conductivity (dI/dV) map at zero bias showing location of vortices in NbSe2
superconductor acquired at 400 mK and field of 0.5 T. Image size 250 nm x 250 nm.
Examples – superconductors
Examples – adatom diffusion
Study of surface diffusion of “trapped” and “free” Co adatoms
Co adatom tracking during sample heating (from 8.2 to 9.5 K, 10 mK/min), 110 positions in 120 sec interval
Free Co adatom: - stable up to 8.2 K
- from 8.2 to 8.8 K jumping between adjacent binding sites (n.n. of 0.255 nm)
- T > 8.8 K longer displacements between consecutive images
Trapped Co adatom: - stable up to 12.7 K
- T > 12.7 K becomes free
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STM and AFM imaging of pentacene on Cu(111):(A) Ball-and-stick model of the pentacene molecule. (B) Constant-current STM and (C and D) constant-height
AFM images of pentacene acquired with a CO-modifiedtip.
The asymmetry in the molecular imaging in (D) (showinga “shadow” only on the left side of the molecules) isprobably caused by asymmetric adsorption geometry of theCO molecule at the tip apex.
STM images of a pentacene molecule on a two-atomic-layer-thick NaCl film on Cu(111). The STM images wereacquired with a metal and a pentacene tip. Whereas theSTM images for bias voltages in the HOMO-LUMO bandgap are relatively featureless (center), the images at biasvoltages exceeding the HOMO (left) or LUMO (right)exhibit very pronounced features, resembling theelectron density of the HOMO (left) and LUMO (right)of the free molecule. The geometry of the free pentacenemolecule is displayed in the lower center image togetherwith calculated contours of constant orbital probabilitydistribution of the free molecule
Examples – STM/AFM
Conclusions
STM is a powerful nanotechnological tool, used for atomic resolution imaging, singleatom and molecule manipulation and high energy resolution spectroscopymeasurements.
Advantage:
- very versatile method
- high spatial and energy resolution (local measurements)
Drawbacks:
- tip shape and chemistry influences the STM/STS results
- sometimes complicated interpretation of results due to topography/electronicstructure contributions
- generally a difficult technique to perform (time consuming), requires very stableand clean surfaces, excellent vibration control and sharp tips
