Enhancing the sensitivity and measuring the deflection of MEMS microcantilevers

This thesis investigates how the deflection sensitivity of microcantilever sensors can be increased, and how the deflections of an array of these cantilevers can be measured up to a few micrometers, with sub-nanometric resolution, using a simple optical system. The deflection of microcantilevers for a given stimulus can be increased by increasing the length or by decreasing the thickness of the beam, but these result in lower resonant frequencies. A lower resonant frequency makes the cantilever susceptible to thermal noise and low-frequency vibrations. The sensitivity of cantilevers can be increased by simultaneously increasing the deflection and the resonant frequency. However, a method of achieving this has not been demonstrated in the literature. This thesis shows that the deflection and resonant frequency of cantilevers can be simultaneously increased by creating perforations in a manner that reduces its mass by a larger fraction than the reduction of its spring constant. Analytical models are developed to describe the deflection and the resonant frequency of perforated microcantilevers. Results obtained from these models show good agreement with finite element method simulation results obtained using ANSYS, which validates the models. The variations of the deflections and resonant frequencies of cantilevers with perforation parameters are characterised using these models. Using these results, the cantilever profile that optimises sensitivity is determined. Using the developed analytical models, models from the literature and simulations using ANSYS, it is established that cantilevers with triangular profiles have larger deflection—resonant frequency combinations compared with standard rectangular cantilevers, and are proposed as being more suitable for sensor applications than standard rectangular beams. The reasons for the measurement range of the standard interdigital interferometric method being limited to a quarter of the wavelength ë of the optical source are also investigated. Using a novel mathematical approach, the far-field optical intensity pattern is decomposed into the sum of spatial harmonic functions. The spatial frequencies of these harmonic functions are shown to be determined by the distances between each cantilever of the array, and the phase terms are shown to be dependent on the amount of deflection. It is shown that by making each moving cantilever in the array to have distinct deflections for a given stimulus, and extracting the phase terms of the spatial harmonic functions from the Fourier transformation of the far-field diffraction pattern, the measurement range can be increased independent of the quarter-wavelength limitation. A principle to correct the errors induced by the misalignment of the image sensor is established, as well as principles to determine the width and the locations of individual cantilevers. The requirements of the photo sensor, namely, the maximum allowable pixel spacing, the size of the image sensor and the resolution of the Analog to Digital Converter for a given measurement resolution are also determined. By simulating an example cantilever array, deflections up to 3250 nm are demonstrated to be measurable with a 0.2 nm measurement resolution, compared with the 162.5 nm deflection range of standard interferometric measurement techniques.