Mechanical design for tailoring the resonance harmonics of an atomic force microscope cantilever during tip-surface contact

We describe an atomic force microscope cantilever design for which the second flexural mode frequency can be tailored relative to the first mode frequency, for operation in contact with a substrate. A freely resonating paddle internal to the cantilever reduces the stiffness of the second flexural mode relative to the first while nearly maintaining the mass of the original cantilever. Finite element analysis is used to predict the performance of various cantilever designs and several cantilevers are fabricated and tested. This strategy allows the ratio of the first two resonant modes f(2)/f(1) to be controlled over the range 1.6-4.5. The ability to vary f(2)/f(1) could improve a variety of dynamic contact-mode measurements.