Characterization of Microscale Material Behavior with MEMS Resonators
C. D. White, R. Xu, X. Sun and K. Komvopoulos*
Keywords: MEMS resonators, material behavior, fatigue
The reliability of MEMS devices greatly depends on precise characterization of material behavior at the micron scale. This paper presents a novel material characterization device for fatigue testing. The fatigue specimen is subjected to multi-axial loading, which is typical of most MEMS devices. Fatigue devices were fabricated using the MUMPS process with a three-layer mask process: a ground plane, anchor and structural layer of polysilicon. A fatigue device (Fig. 1) consists of two or three beams, attached to a rotating ring and anchored to the substrate on each end. The beams act as the suspension and fatigue specimens, with the suspended ring structure connecting the six comb-drives. When an electrostatic driving force is applied to the comb drives, a bending stress is produced in the specimen. In addition, its axial length extends as the fatigue device rotates and an axial tensile stress is generated. Even at small rotation angles, stiffening of the beam occurs which cannot be neglected in numerical simulations. The comb drives are divided into two groups to provide the driving and sensing capability. Differential driving voltages are applied to one group of the comb drives to cancel the DC and double-frequency components in the driving force. Synchronous detection (modulation) technique is employed for position sensing to avoid possible feedthrough problems (Fig. 4).
To generate a sufficiently high stress, the fatigue devices are tested in resonance to produce a von Mises equivalent stress as high as 1 GPa, which is close to the fracture strength of bulk polysilicon. The maximum stress occurs in the beam-anchor region (Fig. 2), where fillets with radius measured from SEM photos were modeled to avoid unpractical stress concentration effect. High stresses also exist in the beam-ring region due to the geometry constraint. A further increase of the stress in the specimen beam is obtained by introducing a notch with a focused ion beam (Fig. 3). Previously published data by Muhlstein et al. (2001) for pure bending show fatigue lifetimes from 105−1011 cycles for stresses in the range of 2−4 GPa. This notch has a stress concentration factor of about 3.8, generating a Mises equivalent stress of 1−4 GPa.
To fully characterize the material and determine the stresses produced, lateral resonators are used to determine the elastic modulus of the structural layer of polysilicon. The Rayleigh’s method is used to extract the natural frequency of the elastic modulus resonators. Its accuracy was verified in light of results obtained from a finite element analysis, and the difference was found to be less than 2%. Results for the dynamic behavior of the devices are given in Table 1.
This work provides insight into multi-axial fatigue testing under typical MEMS conditions and new insight into micron-scale polysilicon mechanical behavior, which is the current basic building material for MEMS devices.
NSTI Nanotech 2003 Conference Technical Program Abstract