(Invited) Effect of Microfabrication Induced Stresses on the Sensing Characteristics of Dynamic MEMS Devices
Authors: Pratap Rudra , Dangi Ajay , Behera Amruta Ranjan 
Published: February 2020

Dynamic MEMS devices such as 1-D and 2-D resonators, microphones, gyroscopes, and ultrasound transducers critically depend on the natural frequency and quality factor of the vibrating micro-mechanical structure for their essential operation. While the role of geometric design and material properties of such structures is well understood and even codified in MEMS design tools, the role and estimation of fabrication induced stresses on the operational characteristics of these structures is still an open area of research. For simpler MEMS structures, such as beams and membranes made of a single layer material, the fabrication induced residual stresses are easy to account for in figuring out natural frequencies and quality factors since they result in fairly simple tensile or compressive in-plane stresses. This analysis becomes a lot more complicated when we start looking at multilayer structures such as those used in piezoelectric MEMS. Even the estimates of stresses in individual layers are typically unavailable and hard to get from experimental measurements. However, these process-induced stresses can not only shift the natural frequencies of the structures but also change their sensitivity significantly. It is, therefore, essential to study the effect of these stresses on the performance of MEMS devices and perhaps get a handle on how to control and exploit the level of such stresses. Here, we present two separate studies on the effect of fabrication induced stresses on the dynamic response of MEMS devices: one on the post-buckling vibrations of SiC beams, and the other on the response of a multi-layer piezoelectric membrane.

Microfabrication induced stresses can be severe enough to cause buckling in suspended structures. Buckling introduces nonlinearity that leads to rich dynamics of the buckled structure. We present analytical and experimental studies to show that odd and even mode frequencies of a buckled fixed-fixed beam behave quite differently with changes in the residual stress. While the odd mode frequencies change with increasing compressive stresses, the even mode frequencies remain invariant. We use this difference in frequency response to decouple the experimental estimation of material properties and residual stresses, thus developing a new technique for easy estimation of residual stresses. We also show how one can design structures with a particular level of residual stress that allows crossover of odd and even frequencies under incremental stresses from, say, adsorbed analytes, thus providing a way to make a very sensitive sensor.

MEMS structures made from PECVD grown material layers can be engineered to have residual stresses that span a large range of compressive to tensile stresses. A fairly good control of this process allows us to induce desired level of residual stress in the final structure. Our study on a multi-layered piezoelectric membrane, meant for a PMUT, shows that by varying the residual stress level one can get the multi-layer stack to transition from a plate-like dynamic behavior to a membrane-like behavior, thus changing the dynamic response significantly. This transition can be exploited in various ways for designing dynamic MEMS sensors including designs that incorporate tunable residual stresses (e.g., with variable electrostatic force) for achieving a large bandwidth.