Daniel Forchheimer

Title: Imaging materials with intermodulation : Studies in multifrequency atomic force microscopy

Abstract:

The Atomic Force Microscope (AFM) is a tool for imaging surfaces at the microand nano meter scale. The microscope senses the force acting between a surfaceand a tip positioned at the end of a micro-cantilever, forming an image of the surface topography. Image contrast however, arises not only from surface topography, but also from variation in material composition. Improved material contrast, and improved interpretation of that contrast are two issues central to the further development of AFM.

This thesis studies dynamic AFM where the cantilever is driven at multiple frequencies simultaneously. Due to the nonlinear dependence of the tip-surface force on the tip’s position, the cantilever will oscillate not only at the driven frequencies, but also at harmonics and at mixing frequencies of the drives, so-called intermodulation products. A mode of AFM called Intermodulation AFM (ImAFM) is primarily studied, which aims to make use of intermodulation products centered around the resonance frequency of the cantilever. With proper excitation many intermodulation products are generated near resonance where they can be measured with large signal-to-noise ratio.

ImAFM is performed on samples containing two distinct domains of different material composition and a contrast metric is introduced to quantitatively evaluate images obtained at each response frequency. Although force sensitivity is highest on resonance, we found that weak intermodulation response off resonance can show larger material contrast. This result shows that the intermodulation images can be used to improve discrimination of materials.

We develop a method to obtain material parameters from multifrequency AFM spectra by fitting a tip-surface force model. Together with ImAFM, this method allows high resolution imaging of material parameters. The method is very generalas it is not limited to a specific force model or particular mode of multifrequency AFM. Several models are discussed and applied to different samples. The parameter images have a direct physical interpretation and, if the model is appropriate, they can be used to relate the measurement to material properties such as the Young’s modulus. Force reconstruction is tested with simulations and on measured data. We use the reconstructed force to define the location of the surface so that we can address the issue of separating topographic contrast and material contrast.