MEMS process error characterization using lateral resonant structures

George C. Johnson; A. Miller Allen

doi:10.1117/12.524236

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23 December 2003 MEMS process error characterization using lateral resonant structures

George C. Johnson, A. Miller Allen

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Proceedings Volume 5343, Reliability, Testing, and Characterization of MEMS/MOEMS III; (2003) https://doi.org/10.1117/12.524236
Event: Micromachining and Microfabrication, 2004, San Jose, California, United States

Abstract

Accurate determination of the as-built geometry of micro-electro-mechanical systems (MEMS)is important given the magnitude of the geometric uncertainty relative to the dimensions of these devices. A method for determining geometric process errors in MEMS fabrication from measurements of the resonant frequencies of simple structures is presented. This method provides a way to determine the process offset (the difference between the design width of a structural element and the as-built width) and, in the ideal case, the average angle of the side-walls of the films involved. An important feature of the approach presented is that by using frequency ratios, neither the elastic modulus nor the mass density of the film need be known a priori. This paper also introduces a robust design technique for MEMS subject to the inherent geometric and material uncertainties discussed previously. Although a range of design tools have been developed for MEMS, little has been done to account for the uncertainties associated with MEMS fabrication. The robust design problem we pose is to minimize the expected variance between the specified target system performance and the actual performance that a particular realization would be expected to exhibit. This robust design problem can be written as a constrained minimization. We consider a subset of these problems and develop an algorithm to minimize rational polynomial functions subject to polynomial inequality constraints. The details of the algorithm are presented and we verify its performance by examining the design of lateral resonators with specified resonant frequency. This example shows that the robust design nominally meets the target performance and is significantly less sensitive to geometric uncertainties than typical designs.

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George C. Johnson and A. Miller Allen "MEMS process error characterization using lateral resonant structures", Proc. SPIE 5343, Reliability, Testing, and Characterization of MEMS/MOEMS III, (23 December 2003); https://doi.org/10.1117/12.524236

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