MEMS metrology and materials characterization using resonant structures

A method for determining geometric process errors in MEMS devices from the resonant frequencies of simple structures is presented. The ability to accurately determine the as-built geometry of MEMS devices is important given the magnitude of the geometric uncertainty relative to the dimensions of these devices. The method presented here provides a way to determine the process offset (the difference between the design width of a planar feature and the as-built width) and the average angle of the side-walls of the beam flexures of lateral electrostatic comb drive resonators. 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. As MEMS become smaller, the need for reliable metrology becomes even more important. This method is scale independent and can be applied to either smaller or larger devices provided similar fabrication assumptions apply. The material studied in this work is polycrystalline silicon fabricated at the Cronos Integrated Microsystems Multi-User MEMS Processes (MUMPS) foundry.; The approach used to measure the process offset and wall angle constitutes a novel metrology tool. In contrast to conventional metrology tools, this tool is in situ, inexpensive, and highly accessible to the average MEMS designer.; An analytical model of the ratio of the first laterally resonant mode of two electrostatic comb drive resonators is used in concert with the experimentally measured resonant frequencies of an array of twenty-five electrostatic comb drive resonators. The process offset is determined through a single parameter nonlinear fit of the analytical model to the experimental data. A multi-parameter nonlinear fit to an analytical model of the first laterally resonant mode of an electrostatic comb drive resonator is also used to determine simultaneously the process offset and the ratio of elastic modulus to mass density. Dual mass structures with two resonant frequency modes are also investigated.