Noncontact Atomic Force Microscopy - Yale School of Engineering ...

P.I-33
Experimental Study of Dissipation Mechanisms in AFM Cantilevers
Fredy Zypman
Department of Physics, Yeshiva University, New York, USA.
The presence of energy dissipation in an oscillating AFM cantilever is a fact that must be
included in any force reconstruction algorithm. Although commonly low quality factor
(Q) cantilevers get on the way of high accuracy non-contact measurements, some times
they can be used purposely. A case in point is the study of the measurement of fluids
viscosity by monitoring changes in Q [1]. In this work we study theoretically the
mechanisms of energy dissipation in AFM, and validate the corresponding models
experimentally. This understanding of the origins of energy dissipation is not only
interesting for its own sake, but it is also relevant with an eye on practical applications.
We have done extensive work on cantilevers of various shapes but, to fix ideas we
consider a rectangular cantilever in this abstract. In that case, the beam model is
commonly used to obtain the corresponding frequency spectrum via the steady state
4
2
EI ∂ u(
x,
t)
∂ u(
x,
t)
solution of + = 0 , where u( x,
t)
is the deflection of the cantilever
4
2
Aρ
∂x
∂t
at location x and time t , E is the Young's modulus, I the cross sectional moment of
inertia, A the cross sectional area, and ρ the mass density. In the beam model, a
∂u dissipation term proportional to is usually introduced. The proportionality factor is a
∂t
difficult problem in itself that involves the interaction of the cantilever with the
surrounding fluid [2]. The complete equation describes quite well the central frequency
and width of multiple peaks. However, a detailed analysis shows that the peak shape is
not in full agreement with experiment if fine details are included. We will show that this
is improved by introducing explicit dissipation terms based on basic physical principles
that represent cantilever-fluid interaction and internal viscoelasticity. The model is
solved and compared with experimental data obtained on a Veeco AFM. We will also
argue that this improvement is necessary to produce reconstruction algorithms consistent
with the resolutions necessary today to measure objects at the subnanometer scale, like
charges in biological molecules.
[1] A. Schilowitz, D. Yablon, E. Lansey, and F. Zypman, Measurement 41, 1169 (2008).
[2] J.E. Sader, J. Appl. Phys. 84, 64 (1998)
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