Lee, Kin Wei; (2003) Electromechanical modelling of trapezoidal microstructures. Doctoral thesis (Ph.D.), University College London (United Kingdom).

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Abstract

This thesis is concerned with the assessment of the effects of non conformity of shape when using low cost fabrication methods. The use of deep reactive ion etching and synchrotron sources (LIGA process) allows for almost vertical side walls in an etched or exposed material. However a standard micro-electromechanical systems (MEMS) fabrication process, which uses basic UV lithography and anisotropic wet etching, creates sloping sidewalls thus leaving us with structures that are no longer square or rectangular in cross section, but trapezoidal. This affects the electrostatic actuation of comb electrodes, since they are now asymmetrical and also support beams that may experience twisting or bending. In this case the assumption that structures have simple square or rectangular cross-section is no longer valid and the sloping side wall has to be taken into account. Standard scientific techniques have been employed into the investigation of trapezoidal microstructures namely an analytical process, followed by computer simulation and then comparisons with the fabricated structures. A variational method has been used to calculate the torsional behaviour of trapezoidal beams, while a conformal transformation approach has been used to model the electrostatic behaviour of the comb electrodes. On the computer simulation side ANSYS was used for the finite elment modelling, while MATLAB was used for symbolic mathematical calculations of the variational method. As a comparison to the variational method and the FEM results, electrostatic and mechanical trapezoidal structures were made using nickel electroforming and silicon bulk etching.

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