CMU MEMS Laboratory Publication Abstract

 

in Ph.D. Thesis, April 2003, Carnegie Mellon University, Pittsburgh, PA.
Modeling and Simulation of Non-idealities in a Z-axis CMOS-MEMS Gyroscope
S. V. Iyer
ABSTRACT:
MEMS gyroscopes have proved to be extremely difficult to manufacture reliably. The MEMS gyroscope is required to sense picometer-scale displacements, making it sensitive to spurious vibrations and other coupling mechanisms. This thesis aims to quantitatively capture, through models and simulations, the sensitivity of a MEMS gyroscope to manufacturing variations in the widths of suspension beams and gaps between fingers in electrostatic actuation and capacitive sensing combs. The gyroscope considered in this thesis is manufactured in a CMOS-MEMS process. The suspended MEMS structures are composed of the multi-layer stack of interconnect metals and dielectrics in a CMOS process. The effect of misalignment between the metal layers in the suspended microstructures is also modeled in the gyroscope. A number of fundamental issues related to the modeling and simulation of MEMS gyroscopes are addressed. Models in elastic and electrostatic domains are developed. Numerical tools such as finite element analysis or boundary element analysis are used for model verification. Behavioral simulation is used throughout this thesis to analyze the gyroscope and system-level design issues.

The elastic modeling effort is primarily aimed at a thorough understanding of crossaxis coupling in micromechanical springs and at multi-dimensional curvature in the multilayer suspended structures in the CMOS-MEMS process. Cross-axis stiffness constants are derived for basic spring topologies such as crab-leg, u-spring and serpentine springs. Techniques to reduce, and even completely eliminate, elastic cross-axis coupling are discussed. In the electrostatic domain, a methodology which combines analytical equations with numerically obtained data is developed to model CMOS-MEMS combs. Particular attention is paid in this methodology to make the resultant behavioral model energy conserving. Convergence problems found in behavioral simulations of gyroscopes lead to a detailed comparison of different Analog Hardware Description Language (AHDL) model implementation of mechanical second-order systems, such as the resonating structure in a gyroscope. AHDL model implementation guidelines for improved convergence in behavioral simulations are deduced from the comparisons.

Using the elastic and electrostatic models as the basis, analytical equations relating gyroscope non-idealities: the Zero Rate Output, acceleration and acceleration-squared sensitivity and cross-axis sensitivity to manufacturing effects are derived. The equations are compared with results of behavioral simulation. Monte Carlo simulations using the behavioral models are run in order to verify the trends predicted by the analytical equations. The analysis and simulations result in several insights into gyroscope non-idealities and design pointers to reduce them.
© 2003 Carnegie Mellon University, Department of Electrical and Computer Engineering.
Full paper (PDF) (opens in new window).


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