Boldys_seminar_AFM
Download
Report
Transcript Boldys_seminar_AFM
Atomic force microscopy
Jiří Boldyš
Outline
Motivation
Minisurvey of scanning probe microscopies
Imaging principles
Ideas about application of moment invariants
Alternative reconstruction approach
Image artifacts
Classification of blur kernel
symmetries
n-fold circular symmetry (Cn symmetry)
Dihedral symmetry (Dn)
Radial symmetry
Common blurs
Atmospheric – radial symmetry
Out-of-focus – radial, cyclic or dihedral symmetry
Motion – central symmetry
What invariants we have
Model: g = f * h
I(f)=I(g)
Invariance x discriminability
Invariants to kernels with Cn and Dn symmetry
Potentially we can, we have not done that - arbitrary symmetry,
arbitrary dimension
Other potential applications
Electron microscopy? – N-fold symmetrical correction elements
Atomic force microscopy (AFM)?
…
But – Is there a convolution???
Scanning probe microscopy classification
Scanning tunneling microscopy - STM
Atomic force microscopy - AFM
Electric force microscopy - EFM
Magnetic force microscopy - MFM
Scanning near-field optical microscopy - SNOM
...
Scanning tunneling microscopy
Mironov: Fundamentals of scanning probe microscopy, 2004
Scanning tunneling microscopy
1981 – Swiss scientists Gerd Binnig
and Heinrich Rohrer
Atomic resolution, simple
1986 – Nobel prize
Chen: Introduction to scanning tunneling microscopy, 1993
Scanning tunneling microscopy
The first demonstration of the atomic-resolution capability of
STM – Si(111)-7x7, Binnig, Rohrer, Gerber, Weibel, 1983
Chen: Introduction to scanning tunneling microscopy, 1993
Scanning tunneling microscopy
Chen: Introduction to scanning tunneling microscopy, 1993
Atomic force microscopy
1986, Binnig, Quate, Gerber
1989 – the first commercially available AFM
Mironov: Fundamentals of scanning probe microscopy, 2004
Magnetic force microscopy
Local magnetic properties
AFM + tip covered by a layer of ferromagnetic material with
specific magnetization
Mironov: Fundamentals of scanning probe microscopy, 2004
Atomic force microscopy in detail
Forces can be explained by e.g. van der Waals forces –
approximated by Lennard-Jones potential
Mironov: Fundamentals of scanning probe microscopy, 2004
Tip – sample force
Energy of interaction
Force – normal + lateral component
Corresponds to deflections of an elastic cantilever
Mironov: Fundamentals of scanning probe microscopy, 2004
STM vs. AFM
STM
Tunneling current drops off exponentially spatially
confined to the frontmost atom of the tip and surface
Distance dependence is monotonic simple feedback
scheme
Modest experimental means, excellent SNR
AFM
Force – short range + long range – less tractable as a
feedback signal
Not monotonic with distance
Giessibl, Quate: Physics Today, 2006
Beam-bounce technique
Mironov: Fundamentals of scanning probe microscopy, 2004
Feedback system
Mironov: Fundamentals of scanning probe microscopy, 2004
Examples of cantilevers
Si3N4, Si
Different spring constants and resonant frequencies
Images: Mironov, Fundamentals of scanning probe microscopy, 2004
Methods used to acquire images
Contact vs. non-contact modes
Contact modes
attractive or repulsive
Balance between atomic and elastic forces
Small stiffness – high sensitivity, gentle to the sample
Tip breakage, surface damages
Not suitable for soft samples (biological)
Constant force
Constant average distance
Mironov: Fundamentals of scanning probe microscopy, 2004
AFM image acquisition at constant
force
Mironov: Fundamentals of scanning probe microscopy, 2004
AFM image acquisition at average
distance
Mironov: Fundamentals of scanning probe microscopy, 2004
Force-distance curves – elastic
interaction
Mironov: Fundamentals of scanning probe microscopy, 2004
Force-distance curves – plastic
interaction
Mironov: Fundamentals of scanning probe microscopy, 2004
Forced oscillations of a cantilever
Better for soft samples
Reduce mechanical influence of the tip on the surface
Possible to investigate more surface properties
Piezo-vibrator
Motion equation
Mironov: Fundamentals of scanning probe microscopy, 2004
Forced oscillations of a cantilever
Mironov: Fundamentals of scanning probe microscopy, 2004
Contactless mode of AFM cantilever
oscillations
Small forced oscillations amplitude – 1nm
Close to surface – additional force
Small oscillation around z0
Presence of a gradient in the tip-surface interaction force
Additional shift of the amplitude and phase response curves
Additional phase shift
phase contrast AFM image
Mironov: Fundamentals of scanning probe microscopy, 2004
Contactless mode of AFM cantilever
oscillations
Mironov: Fundamentals of scanning probe microscopy, 2004
Semi-contact mode of AFM
cantilever oscillations
Before – high sensitivity and stability feedback required
In practice often semi-contact mode
Excited near resonance frequency, amplitude 10-100nm
Working point:
Mironov: Fundamentals of scanning probe microscopy, 2004
Semi-contact mode of AFM
cantilever oscillations
Mironov: Fundamentals of scanning probe microscopy, 2004
Frequency modulation AFM
Si(111) Reactive surface →
Dynamic mode
Ultrahigh vacuum
FM-AFM – frequency modulation – introduced in 1991
First with commercial cantilevers with a limited range of
spring constants
Strong bonding energy Si-Si large amplitude of vibrations
34nm no atomic resolution
small amplitudes stiff cantilevers dramatic
improvement in spatial resolution
Giessibl, Quate: Physics Today, 2006
From static to dynamic mode
Static approach still in use
Materials in liquids
Tip subject to wear
Large lateral forces
Absolute force measurements are noisy
Amplitude modulation AFM
Driven near fundamental resonance frequency
Less noise
Sensing variations in amplitude
Lateral forces minimized – broken contacts
Giessibl, Quate: Physics Today, 2006
From static to dynamic mode
Frequency modulation AFM
Even less noisy
Fixed amplitude
Frequency as a feedback signal
Lateral forces minimized – broken contacts
Average tip-sample force gradient
Frequency shift
Further improvement – exploiting signal proportional to higher-order
derivative – better spatial resolution
And next – reconstruction using the frequency shift and higher-harmonic
components of the cantilever vibrations
Higher harm. can be viewed as a convolution of the nth-order derivative
of the force with some weight function
Giessibl, Quate: Physics Today, 2006
Revealing angular symmetry of
chemical bonds
Combined STM and FM AFM
Angular dependence of chemical bonding forces between
CO on copper surface Cu(111) and the terminal atom of
metallic tip
Forces depend also on angles between atoms
Other opinions: feedback artifact or multiple-atom tips
3D force spectroscopy used
Welker, Giessibl, Science, 2012
Revealing angular symmetry …
Welker, Giessibl, Science, 2012
Silicon (111)-(7x7) surface
Giessibl, Hembacher, Bielefeldt, Mannhart, Science, 2000
Non-expert ideas in the field of AFM
Two ways of imaging
–
Tip imaging
–
Surface imaging
Surface symmetry
Tip symmetry
Do we need to register (align) two blurred images, or one sharp
and one blurred?
Images with different class of blur – generates new
mathematical task for us
Registration of images blurred by
kernels with different symmetry
Example:
–
Tip imaging by surface with 4-fold (C4) symmetry …
–
Followed by tip imaging (the same one) by surface with
3-fold symmetry
–
Both kill different frequencies – together we might
reconstruct them more easily and precisely
Another example:
–
Scanning the same surface with 4-fold symmetrical and
3-fold symmetrical tip (due to crystallic structure)
Is there any convolution?
We are not sensing surface height (z-coordinate) - we are
sensing force / potential energy
Can potential energy be calculated as a 3D convolution?
What we measure is a 2D surface in the 3D potential map
Probe influences atom distribution
We are sensing force through approx. linear dependence F(z)
What if we do not measure pure force but rather frequency shift
or higher order force derivatives?
Mathematical morphology based
reconstruction
Intuitively degradation corresponds to the dilation operation in
mathematical morphology
Why not if the region where the forces are significant is << tip
size
Villarrubia, J. Res. Natl. Inst. Stand. Technol., 1997
Critical dimension AFM
Higher throughput during quality control
Not so ambitious resolution
Dahlen et al., Veeco
AFM imaging artifacts
West, Starostina, Pacific Nanotechnology, Inc.
AFM imaging artifacts
West, Starostina, Pacific Nanotechnology, Inc.
AFM imaging artifacts
West, Starostina, Pacific Nanotechnology, Inc.
AFM imaging artifacts
West, Starostina, Pacific Nanotechnology, Inc.
AFM imaging artifacts
Mates, Summer school of SPM microscopy, 2007
Thank you!
Recommended reading: Giessibl, Quate: Physics Today, Exploring
the nanoworld with atomic force microscopy, 2006