Modal interactions in contact-mode atomic force microscopes

Atomic force microscopes (AFM) are used to estimate material and surface properties. When using contact-mode AFM, the sample or the probe is excited near a natural frequency of the system to estimate the linear coefficient of the contact stiffness. Because higher modes offer lower thermal noise, higher quality factors, and higher sensitivity to stiff samples, their use in this procedure is more desirable. However, these modes are candidates for internal resonances, where the energy being fed into one mode may be channeled to another mode. Ignoring such interactions could distort or affect the accuracy of measurements. The method of multiple scales is used to derive an approximate analytical expression to the probe response in the presence of two-to-one autoparametric resonance between the second and third modes. We examine characteristics of this solution in relation to a single-mode response and consider its implications in AFM measurements. We find that the influence of this interaction extends over a considerable range of the tip-sample contact stiffness.