Nanomechanical characterization of materials by enhanced higher harmonics of a tapping cantilever

Abstract

In a tapping-mode atomic force microscope, the periodic interaction of the tip with the sample surface creates a tip-sample interaction force, and the pure sinusoidal motion of the cantilever is disturbed. Hence, the frequency spectrum of the oscillating cantilever contains higher harmonics at integer multiples of the excitation frequency. In this thesis, we utilize one of the higher harmonics of a vibrating cantilever to investigate the material properties at the nanoscale. We show analytically that the amplitudes of the higher harmonics increase monotonically for a range of sample stiffness, if the interaction is dominated by elastic force. We propose a method in which the cantilever is excited at a submultiple of its resonant frequency (w1/n) to enhance the nth harmonic. The numerical simulations are performed to obtain the response of the tip-sample system for the proposed method. The proposed method is modified to eliminate the chaotic system response observed in the very high harmonic distortion case. The experiments are carried out to see if the enhanced higher harmonic can discriminate the material variations in heterogeneous samples and to find how it is related to the topography changes on the homogeneous sample surfaces. We show that the enhanced higher harmonic can be utilized to map material heterogeneity in polymer blends with a very high signal-to-noise ratio. The surface features ca. 100 nm in size are clearly resolved. A comparison is also made to conventional tapping-mode topography and phase imaging