Reconstruction of the Distributed Force on an Atomic Force Microscope Cantilever

R. Wagner National Institute of Standards and Technology, United States

Keywords: AFM, cantilever

Summary:

The shape in which an AFM cantilever vibrates is dependent on the properties of the cantilever, properties of the sample, properties of the environment, and the nature of the cantilever excitation force. This cantilever vibration shape is a fundamental aspect of AFM operation with far reaching consequences for AFM measurements. Here, we take advantage of off-resonance AFM cantilever vibration shape to reconstruct the distribution of force applied to an AFM cantilever. By manipulating Bernoulli Euler beam theory such that the force on the cantilever is approximated as a linear superposition of the cantilever eigenmodes we can reconstruct the force distribution. The experimental inputs to this method are amplitude and phase as a function of axial position along the cantilever. The accuracy of the force reconstruction depends on the measurement frequency, the number of discrete points at which amplitude and phase are measured, and the signal-to-noise ratio of the experiment. Experiential tests were performed on an electrostatically excited cantilever and the expected force distribution for electrostatic theory and a given cantilever-sample geometry is recovered. This force reconstruction technique offers previously unmeasurable information about the distributed force on an AFM cantilever allowing for more accurate AFM measurements in AFM modes such as piezoresponse force microscopy and electrostatic force microscopy where such force distributions are present.