I know that the DA is the amplitude of the voltage applied to the piezo system that
drives the cantilever vibration and I assume that the higher the DA is the higher the force applied is but is there an equation to know exactly this force?
Dear Jordi,
There are some works that may be useful concerning your question:
Anczykowski, B. (1999). How to measure energy dissipation in dynamic mode atomic force microscopy. Applied Surface Science, 376–382.
Cleveland, J. P., Anczykowski, B., Schmid, a. E., & Elings, V. B. (1998). Energy dissipation in tapping-mode atomic force microscopy. Applied Physics Letters, 72(20), 2613–2615. doi:10.1063/1.121434
Paulo, S., & Garc, R. (2001). Tip-surface forces, amplitude, and energy dissipation in amplitude-modulation „tapping mode…force microscopy ´. Physical Review, 64, 1–4. doi:10.1103/PhysRevB.64.193411
I hope you got some insight in the papers mentioned above. Rather than equations I just wanted to give you an experimental point of view. What matter the most for not having too much force when doing tapping is the difference between the amplitude of the cantilever not approach and the one approach. To perform tapping on a fragile samples you can set the approach to an amplitude of ~80% of the free amplitude and, once it is approach, increase the setpoint to about 90%. I encourage you to read the following paper to get a good theory approach:
1. H. Holscher and U. D. Schwarz. Theory of amplitude modulation atomic force microscopy with and without Q-Control. Int. J. Nonlinear Mech. 42, 608–625 (2007).
I agree with Nicolas, however, if the oscillation amplitude of the cantilever is too large, even high value of the setpoint may not prevent the surface modification or elastic deformation causing the lateral resolution decrease. Additionally, when the setpoint 80-90% is applied, you may experience the insufficient dynamics of the system response in terms of the surface tracking when the tip approaches downhill slope. You will be able to identify such an issue by observing trace and retrace profiles while scanning (should be the same). So you need to be very careful then.
Hi, there is an approximation formula for your purposes:
F = k / (2Q) · sqrt(sqr(A0) - sqr(A))
A0 — amplitude of free vibrations of cantilever
A — amplitude of vibrations while scanning
k — cantilever stiffness factor
Q — cantilever vibrations Q-factor
http://latex.codecogs.com/gif.latex?%3CF%3E%20=%20\frac{k}{2Q}\sqrt{A_0^2-A^2}
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