- Reaching the physical resolution limit of STM and AFM
- sensors with optimized physical properties
- low temperatures
- tips with defined chemical composition and structure
- Improve understanding of tip-sample interaction
- Simplifying STM and AFM operation for
- applications in difficult environment
(UHV, low temperatures)
- tool to study insulators
- big hairy audacious goal: atomic manipulation on insulating substrates
Principle of the Scanning Tunneling Microscope
Binnig & Rohrer 1982 
How does the spatial resolution come about?
|1. Ultra-precise electromechanical instrumentation (piezoelectric scanner, precise electromechanic components for sample positioning)|
|2. Quantummechanical tunneling-effect: When approaching two biased conductors, the current increases exponentially by a factor of 10 for each 0.1nm reduction in distance before they finally make contact. |
|Cross-section through tip and sample in STM (contour-lines indicate constant charge density)|
|Because of the sharp increase in tunneling current with decreasing distance, even tips with moderate sharpness yield atomic resolution easily, because the front atom carries the lion´s share of the tunneling current! |
Principle of the atomic force microscope
Binnig 1985, Binnig, Quate, Gerber 1986 
AFM is similar to STM, but a tip-sample force Fts
takes the role of the tunneling current It
|AFM faces four additional challenges:|
1. Attractive forces may cause an instability ('jump-to-contact')
2. Potentially large long-range background forces add to weak short-range forces
3. Force-versus-distance relation is not monotonic, making distance control difficult
4. Measurement of weak forces (nano-Newton) is more prone to experimental noise than measurement of weak currents (nano-Ampere)
Albrecht et al. 1991 
A cantilever with a sharp tip is excited in resonance by positive feedback, controling a constant amplitude A
. For the free cantilever, the eigenfrequency is given by f0
is the spring constant and m*
is the effective mass of the cantilever. Forces between tip and sample change the frequency f
, where the tip-sample force gradient is given by kts
. When kts
is small compared to k
and essentially constant within the tips trajectory to and from the sample, a frequency change
results. Forces cause a frequency shift, and with a feedback circuit adjusting the sample height such that Δf
remains constant, an image is created.
Frequency-modulation-AFM provides a solution to three of the four challenges faced by AFM, if k
are chosen correctly.
In 1994, AFM passed an important test - atomic imaging of the silicon (111)-(7×7) surface .
|Piezoresistive cantilever |
(M. Tortonese )
The atoms appear clearly as individual bumps, albeit slightly noisy. A piezoresistive cantilever with k
= 17 N/m, f0
= 114 kHz and a quality factor Q
= 28000 made by M. Tortonese  was chosen in this experiment. The amplitude was set to A
= 34 nm and the setpoint of the frequency shift was Δf
= -70 Hz.
Today, frequency-modulation-AFM is a standard method for atomic imaging of semiconductors, metals, insulators and organic films and used by many scientists, see e.g.
|International Conference on Non-contact Atomic Force Microscopy (NCAFM)
1998 Osaka, Japan
1999 Pontresina, Schweiz
2001 Kyoto, Japan
2002 Montréal, Canada
2003 Dingle, Irland
2004 Seattle, USA
2005 Osnabrück, Germany
'Classic' frequency-modulation-AFM with k
≈ 20 N/m and A
≈ 10 nm enables routine-imaging at atomic resolution, however:
Theory of relation between noise and imaging parameters (k,A) shows that resolution enhancement is possible by using sub-nm amplitudes with stiff cantilevers.
1. If kts
is not constant, Eq. (1) needs to be replaced by
2. Minimal image noise δz
is then proportional to
where λ is the range of the tip-sample forces. For chemical forces, λ ≈ 0.1 nm. Optimal resolution is expected for A
Q: Why didn‘t people use small amplitudes from the beginning?
A: It was not for lack of trying, but
1. The tip-sample forces disturb the cantilever´s oscillation. Jump-to-contact, e.g., is avoided if the restoring force that the cantilever exerts on the tip when it is deflected at amplitude A
is larger than the sample force trying to pull the tip towards the sample :
2. Tip-sample forces are not conservative, i.e. the cantilever loses an amount of energy ΔEts
on its way to the sample and back. This energy has to be supplied by the amplitude controller. The amplitude controller‘s task - keeping A
constant - is easier if ΔEts
is small to the intrinsic energy loss of the cantilever (given by its Q
-factor). Thus, we have an additional (conjectural) stability criterion :
Operation with sub-nm amplitudes is thus only possible using very stiff cantilevers (k
≈ 1 kN/m). Traditional silicon cantilevers with such a large stiffness are usually not available, moreover they suffer from two additional disadvantages:
1. The tips of microfabricated Si cantilevers point in a -crystal direction - an unfavorable orientation, see .
2. The eigenfrequency of Si-cantilevers varies strongly with temperature (-58 ppm/K). Oscillators with low temperature drift are important in watch technology. Today, most watches utilize quartz tuning forks as time-keeping elements.
Quartz tuning forks for watches are two coupled oscillators, housed in an evacuated metal case. Most of them come with an eigenfrequency f0
= 32 768 = 215
Hz. We build cantilevers from these tuning forks by attaching one prong to a large-mass substrate and mounting a tip to the free prong, creating the 'qPlus-Sensor' . Its eigenfrequency is approximately 20 kHz (depending on the mass of the tip), and the spring constant of our favorite tuning forks (taken from Swatch-watches) is k
= 1800 N/m.
The advantages offered by high-stiffness, small-amplitude FM AFM have been demonstrated by
experimental imaging of single atoms with "subatomic" resolution, i.e. structures within a single atom related
to the orbital charge density have been resolved .
Experimental AFM image of a single atom 
Explanation: two sp3
orbitals originating at the tip cause two crescents in the image of a single atom 
Manufacturing tips with defined crystallographic orientation: Christian Schiller operating a scanning electron microscope
AFM image of Si, imaged with a Si tip oriented with z || (111) 
|Model of a tip oriented in -see ||
Markus Herz, preparing a Si surface for dynamic STM and AFM imaging
Measuring lateral forces with atomic resolution 
|qPlus lateral force sensor - the tip oscillates in parallel to the surface||Image of a Si surface imaged with a lateral force sensor. In the left half of the image, the cantilever does not oscillate, in the right half, it oscillates with an amplitude of 0.09 nm, yielding a double image of every atom.
Topography, lateral stiffness and dissipation energy atomically resolved
Sample bias voltage -0.8 V, average tunneling current 400 pA, cantilever amplitude A
= 0.3 nm
Stefan Hembacher and the 5 K UHV AFM/STM [12,13,14]
AFM-image with 77 pm resolution. Subatomic structures are visible within single tungsten atoms. The
simultaneously recorded STM image shows the atomic positions.
Image size 500 × 500 pm2
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