Scanning Probes

Goals:

• 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 (STM)
Binnig & Rohrer 1982 [1]
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 (AFM)
Binnig 1985, Binnig, Quate, Gerber 1986 [2]
AFM is similar to STM, but a tip-sample force F_ts takes the role of the tunneling current I_t in STM.

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)

Frequency-modulation-AFM (FM-AFM)
Albrecht et al. 1991 [3]

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 = 2π(k/m*)^0.5, k is the spring constant and m* is the effective mass of the cantilever. Forces between tip and sample change the frequency f = 2π(k*/m*)^0.5 with k*=k+k_ts, where the tip-sample force gradient is given by k_ts. When k_ts is small compared to k and essentially constant within the tips trajectory to and from the sample, a frequency change
Δf =f₀ k_ts / 2k (1)
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 and A are chosen correctly.
In 1994, AFM passed an important test - atomic imaging of the silicon (111)-(7×7) surface [4].

Piezoresistive cantilever (M. Tortonese [5])

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 [5] 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 2000 Hamburg 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 k_ts is not constant, Eq. (1) needs to be replaced by

(2)

2. Minimal image noise δz is then proportional to

(3)

where λ is the range of the tip-sample forces. For chemical forces, λ ≈ 0.1 nm. Optimal resolution is expected for A ≈ λ.

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 [6]:

(4)

2. Tip-sample forces are not conservative, i.e. the cantilever loses an amount of energy ΔE_ts 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 ΔE_ts is small to the intrinsic energy loss of the cantilever (given by its Q-factor). Thus, we have an additional (conjectural) stability criterion [10]:

(5)

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 [001]-crystal direction - an unfavorable orientation, see [10].
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' [8]. 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 [9].

Experimental AFM image of a single atom [9]


Explanation: two sp³ orbitals originating at the tip cause two crescents in the image of a single atom [9]




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) [10]

Model of a tip oriented in [111]-see [10]

Markus Herz, preparing a Si surface for dynamic STM and AFM imaging




Measuring lateral forces with atomic resolution [11]

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]

STM	AFM

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. [14]


[1] G. Binnig, H. Rohrer, Ch. Gerber and E. Weibel, Phys. Rev. Lett. 50, 120 (1982)
[2] G. Binnig US Pat. RE 33 387 (1985); G. Binnig, C.F. Quate, Ch. Gerber, Phys. Rev. Lett. 56, 930 (1986)
[3] T. R. Albrecht et al., J. Appl. Phys. 69, 668 (1991)
[4] F. J. Giessibl, Science 267, 68 (1995)
[5] M. Tortonese, R. C. Barrett, C.F. Quate, Appl. Phys. Lett., 62, 834 (1993)
[6] F. J. Giessibl, Phys. Rev. B 56, 16010 (1997)
[7] F. J. Giessibl, S. Hembacher, H. Bielefeldt, J. Mannhart, Appl. Surf. Sci. 140, 352 (1999)
[8] F. J. Giessibl, Appl. Phys. Lett. 73, 3956 (1998) , Appl. Phys. Lett. 76, 1470 (2000)
[9] F. J. Giessibl, S. Hembacher, H. Bielefeldt, J. Mannhart, Science 289, 422 (2000)
[10] F. J. Giessibl, H. Bielefeldt, S. Hembacher, J. Mannhart, Ann. Phys. (Leipzig) 10, 887 (2001)
[11] F. J. Giessibl, M. Herz, J. Mannhart, Proc. Natl. Acad. Sc. (USA) 99, 12006 (2002)
[12] S. Hembacher, F. J. Giessibl, J. Mannhart, Appl. Surf. Sci. 188, 445 (2002)
[13] S. Hembacher, F. J. Giessibl, J. Mannhart, C. F. Quate, PNAS 100 12539-12542 (2003)
[14] S. Hembacher, F. J. Giessibl, J. Mannhart, Science 305 380-383 (2004)

SPM Manufacturers
www.nanosurf.com
www.ntmdt.com
www.omicron.de
www.rhk-tech.com
www.veeco.com
www.vts-createc.com

Other Nano-Links
http://faculty.washington.edu/fain/
www.almaden.ibm.com/vis/stm/hexagone.html
www.chem.ucla.edu/dept/Faculty/gimzewski/
www.cens.de/
www.eng.yale.edu/nanomechanics/
www.nanoanalytik.de/
www.nanoscience.de/group_r/index.shtml
www.nanoscience.unibas.ch/nccr
http://reichling.physik.uos.de
www.stanford.edu/group/.../HomePages/GroupMembers/Quate.html
www.stanford.edu/dept/physics/people/faculty/manoharan_hari.html
www.zurich.ibm.com/st/nanoscience/index.html
www.zyvex.com/nanotech/feynman.html

 

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