Nonlinear Behavior of Contact Resonance Atomic Force Microscopy Due to Stick-Slip Phenomena

摘要

Contact-resonance atomic force microscopy (CR-AFM) has emerged as an advanced scanning probe microscopy technique for characterizing materials with lateral resolutions down to 5 nm. In CR-AFM the AFM cantilever may be excited either by an ultrasonic transducer beneath the sample (AFAM mode) or by the piezoelement on the cantilever chip (UAFM mode). The contact-resonance frequency can be used to derive the tip-sample contact stiffness and in-turn the elastic modulus of the material under examination after proper calibration. The width of the resonance curve can be used to measure the damping of the tip-sample contact. In addition to the internal friction in the material and the air damping, partial slip or sliding of the tip at the surface also contributes significantly to the measured contact damping. The CR curves become nonlinear at high excitation amplitudes while under relatively low contact forces. The transition from linear to nonlinear behavior indicates the onset of mechanical yielding of the contact from sticking to sliding. The sliding depends on the friction coefficient of the tip material, usually Si, against the material examined. The present study aims at understanding the influence of excitation amplitude (causing the tangential force) and applied load (normal force) on the appearance of nonlinearities in the CR curves. The softening behavior of the CRs is analyzed in terms of a Duffing oscillator.