Dynamic behavior of dagger-shaped atomic force microscope cantilevers
K Shen, Donna C. Hurley, J Turner
Experimental techniques based on the atomic force microscope (AFM) have been developed for characterizing mechanical properties at the nanoscale and applied to a variety of materials and structures. Atomic force acoustic microscopy (AFAM) is one such technique that uses spectral information of the AFM cantilever as it vibrates in contact with a sample. In this article, the dynamic behavior of AFM cantilevers that have a dagger shape is investigated using a power series method. Dagger-shaped cantilevers have plan-view geometry consisting of a rectangular section at the clamped end and a triangular section at the tip. Their geometry precludes modeling using closed-form expressions. The convergence of the series is demonstrated and the convergence radius is shown to be related to the given geometry. The accuracy and efficiency of the method are investigated by comparison with finite element results for several different cases. Of particular interest for these cantilevers is their use for AFAM measurements. The experiments for these applications are modeled by including a linear spring at the tip that represents the contact stiffness. The technique developed is shown to be very effective for inversion experimental frequency information into contact stiffness results. In addition, the sensitivities of the frequencies to the contact stiffness are discussed in terms of the various geometric parameters of the problem including the slope, the ratio of the rectangular to triangular section, and the tip location. Calculations of contact stiffness from experimental data using this model are shown to be very good in comparison with other models. It is anticipated that this approach may be useful for other cantilever geometries as well such that AFAM accuracy may be improved.
, Hurley, D.
and Turner, J.
Dynamic behavior of dagger-shaped atomic force microscope cantilevers, Nanotechnol. Lett., [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=50027
(Accessed May 29, 2023)