A major concern in the development of microelectromechanical systems (MEMS) is the presence of residual stress. This
stress, which is produced during the fabrication of multi-layer thin-film structures, can significantly affect the
performance of micro-scale devices. Though experimental measurement techniques are accurate, actual stress
measurements can vary dramatically from run to run and wafer to wafer. For this reason, the modeling of this stress can
be a challenging task. Past work has often focused on experimental, static techniques for determining residual-stress
levels in single-layer and bi-layer structures. In addition, in prior studies, the focus has primarily been on residual-stress
measurements in thin films as they are being deposited and prior to the release of a particular device. In this effort,
residual stresses in MEMS resonators are characterized pre- and post-micro-machining and release of the structures.
This is accomplished by applying three residual-stress identification techniques. The first technique, which is based on
wafer-bow measurements and Stoney's formula, is suited for determining the residual stresses in thin film layers as they
are being deposited and before the occurrence of a micro-machining or release process. In the second technique, a static
parametric identification technique, device deflection data is made use of to approximate individual device residual
stress immediately after release of a structure. The third technique, a dynamic parametric identification technique, which
can be based on linear or nonlinear frequency response data can be used to estimate device residual stress immediately
after release and after the device has been polarized. The results obtained by using these techniques are used to develop
an understanding of how geometry, fabrication, release and polarization of resonators affect the stress state in a
piezoelectric device. The results, which show that the stress levels can be quite different after a device has been released
and poled, point to the importance of considering parameter identification schemes such as those described in this effort
for identifying residual stresses in multi-layer, micro-structures.
Nonlinear phenomena such as mode localization have been studied for a number of years in the solid-state physics literature. Energy can become localized at a specific location in a discrete system as a result of the nonlinearity of the system and not due to any defects or impurities within the considered systems. Intrinsic Localized Modes (ILMs), which are defined as localization due to strong intrinsic nonlinearity within an array of perfect, periodically repeating oscillators, are of interest to the present work. Here, such localization is studied in the context of micro-cantilever arrays and micro-resonator arrays, and it is explored if an ILM can be realized as a nonlinear normal mode or nonlinear vibration mode. The method of multiple scales and methods to determine nonlinear normal modes are used to study the nonlinear vibrations of the resonator arrays. Preliminary investigations reported in this article suggest that it is possible to realize an ILM as a nonlinear vibration mode. These results are believed to be important for future designs of microresonator arrays intended for signal processing, communication, and sensor applications.