Tip-sample interactions

Many groups are now trying to fit frequency shift curves in order to understand the imaging mechanism, calculate the minimum tip-sample separation and obtain some chemical sensitivity (quantitative infonuation on the tip-sample interaction). The most conunon methods appear to be perturbation theory for considering the lever dynamics [103], and quantum mechanical simulations to characterize the tip-surface interactions [104]. Results indicate that the... 

Gotsmann B, Anczykowski B, Seidel C and Fuchs H 1999 Determination of tip-sample interaction forces from measured dynamic force spectroscopy curves Appl. Surf. Sc/. 140 314... 

Tamayo, J. and Garcia, R., Relationship between phase shift and energy dissipation in tapping-mode scanning force microscopy. Appl Phys. Lett., 73(20), 2926-2928 (1998). Gotsmann, B., Seidel, C., Anezykowski, B. and Fuchs, H., Conservative and dissipative tip-sample interaction forces probed with dynamic AFM. Phys. Rev. B Condens. Matter, 60, 11051-11061 (1999). 

Ebenstein, Y., Nahum, E., and Banin, U., Tapping mode atomic force microscopy for nanoparticle sizing Tip-sample interaction effects, Nano Lett., 2, 945, 2002. 

The magnitude of the pull-off force depends on the natnre of the tip-sample interaction during contact. Adhesion depends on the deformation of the tip and the sample, because attractive forces are proportional to the contact area. Quantifying the work of adhesion is difficult. The measured magnitude of A7 is strongly dependent on environment, surface roughness, the rate of pull-off, and inelastic deformation surrounding the contact. 

Landman, U., and W. D. Luedtke, Consequences of tip-sample interactions, in Scanning Tunneling Microscopy III, R. Wiesendanger and H. J. Guntherodt Eds., Springer-Verlag, Berlin, 1993. Lorentz, W. J., and W. Plieth, Eds., Electrochemical Nanotechnology, Wiley-VCH, New York, 1996. 

The actual achievement of STM greatly exceeds this expectation. Details of surface electronic structures with a spatial resolution of 2 A are now routinely observed. Based on the obtained electronic structure, the atomic structures of surfaces and adsorbates of a large number of systems are revealed. Furthermore, the active role of the STM tip through the tip-sample interactions enables real-space manipulation and control of individual atoms. An era of experimenting and working on an atomic scale arises. 

The atomic resolution in STM can be understood in terms of tip electronic states and tip-sample interactions. We will discuss the effect of tip electronic states in this section, and the tip-sample interactions in the next section. 

In order to achieve atomic resolution, even with p and d tip states, the tip-sample distance should be very short. At such short distances, the tip-sample interactions arc strong. There are two kinds of interaction effects... 

Ciraci, S., Baratoff, A., and Batra, I. P. (1990). Tip-sample interaction effects in scanning-tunneling and atomic-force microscopy. Phys. Rev. B 41, 2763-2775. 

Tip-sample interactions 36, 195—210 force and deformation 37 local modification of sample wavefunctions 195 uncertainty principle, and 197 wavefunction modification 37 Topografiner 44—47 Topographic images 122, 125 Transient response 261, 262 Transition probability 67 Transmission electron microscopy 43... 

Fig. 13.20. Optical heterodyne force microscopy (OHFM) and its application to a copper strip of width 500 nm, thickness 350 nm, on a silicon substrate, with subsequent chemical vapour deposition (CVD) of a silicon oxide layer followed by polishing and evaporation of a chromium layer of uniform thickness 100 nm and flatness better than 10 nm (a) amplitude (b) phase 2.5 [im x 2.5 m. Ultrasonic vibration at fi = 4.190 MHz was applied to the cantilever light of wavelength 830 nm was chopped at fo = 4.193 MHz and focused through the tip to a spot of diameter 2 im with incident mean power 0.5 mW the cantilever resonant frequency was 38 kHz. The non-linear tip-sample interaction generates vibrations of the cantilever at the difference frequency f2 — f = 3 kHz (Tomoda et al. 2003).

The diagrams in Fig. 1 lb can be obtained by the so-called frequency-sweep method, where the lateral position and the distance Zc are fixed, while the frequency is varied around (O0. The Zc value corresponds to a given set-point ratio of the amplitude in contact to the free amplitude, rsp=Asp/Af. Depending on the tip-sample interaction, both the amplitude and the phase curve shifts in a certain direction. When the overall force is repulsive, the resonance frequency moves to higher values and results in a positive phase shift A(p=90 °-(p>0, where the phase shift of 90 ° corresponds to the free cantilever oscillations at ks=0 in Eq. 12. When the force is attractive the resonance frequency decreases compared to the free cantilever and Acp becomes negative. The situation in Fig. lib corre-... 

In spite of the apparent sensitivity to the material properties, the direct assignment of the phase contrast to variation in the chemical composition or a specific property of the surface is hardly possible. Considerable difficulties for theoretical examination of the tapping mode result from several factors (i) the abrupt transition from an attractive force regime to strong repulsion which acts for a short moment of the oscillation period, (ii) localisation of the tip-sample interaction in a nanoscopic contact area, (iii) the non-linear variation of both attractive forces and mechanical compliance in the repulsive regime, and (iv) the interdependence of the material properties (viscoelasticity, adhesion, friction) and scanning parameters (amplitude, frequency, cantilever position). The interpretation of the phase and amplitude images becomes especially intricate for viscoelastic polymers. 

The one exception in which phase contrast is not due to the dissipation arises when the tip jumps between attraction phases (>90°) and repulsion phases (<90°). Since sine is a symmetric function about 90°, the phase changes symmetric even if there are no losses in the tip-sample interaction. The relative contribution of the repulsive and attractive forces can be estimated experimentally from the frequency-sweep curves in Fig. lib by measuring the effective quality factor as Qe=co0/Ao)1/2, where Ago1/2 is the half-width of the amplitude curve. The relative contribution of the attractive forces was shown to increase with increasing the set-point ratio rsp=As/Af. Eventually, this may lead to the inversion of the phase contrast when the overall force becomes attractive [110,112]. The effect of the attractive forces becomes especially prominent for dull tips due to the larger contact area [147]. 

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