Multi-mode noise analysis of cantilevers for scanning probe microscopy

A multi-mode analysis of micro-cantilever dynamics is presented. We derive the power spectral density of the cantilever displacement due to a thermal noise source and predict the cantilevers’s fundamental resonant frequency and higher harmonics. The first mode in the multi-mode model is equivalent to the traditional single-mode model. Experimental results obtained with a silicon nitride cantilever at 300 K are in excellent qualitative agreement with the multi-mode model. The multi-mode model may be used to obtain accurate values of the cantilever properties such as the elastic modulus,effective mass, thickness and moment of inertia

Dynamical Analysis and Control of Microcantilevers

In this paper, we study the dynamical behaviour of a microcantilever-sample system that forms the basis for the operation of atomic force microscopes (AFM). We model the microcantilever by a single mode approximation and the interaction between the sample and cantilever by a van der Waals (vdW) potential. The cantilever is vibrated by a sinusoidal input, and its deflection is detected optically. We analyze the forced dynamics using Melnikov method, which reveals the region in the space of physical parameters where chaotic motion is possible. In addition, using a proportional and derivative controller we compute the Melnikov function in terms of the parameters of the controller. Using this relation it is possible to design controllers that will remove the possibility of chaos. Keywords: Atomic Force Microscopy, Chaotic Behaviour, Melnikov Method, Microcantilevers. 1 Introduction Surfaces at the atomic level can be probed with good accuracy using the atomic force microscope (AFM) which ..

This content has been downloaded from IOPscience. Please scroll down to see the full text. Real-time probe based quantitative determination of material properties at the nanoscale Real-time probe based quantitative determination of material properties at

Abstract Tailoring the properties of a material at the nanoscale holds the promise of achieving hitherto unparalleled specificity of the desired behavior of the material. Key to realizing this potential of tailoring materials at the nanoscale are methods for rapidly estimating physical properties of the material at the nanoscale. In this paper, we report a method for simultaneously determining the topography, stiffness and dissipative properties of materials at the nanoscale in a probe based dynamic mode operation. The method is particularly suited for investigating soft-matter such as polymers and bio-matter. We use perturbation analysis tools for mapping dissipative and stiffness properties of material into parameters of an equivalent linear time-invariant model. Parameters of the equivalent model are adaptively estimated, where, for robust estimation, a multi-frequency excitation of the probe is introduced. We demonstrate that the reported method of simultaneously determining multiple material properties can be implemented in real-time on existing probe based instruments. We further demonstrate the effectiveness of the method by investigating properties of a polymer blend in real-time