Modeling and Simulation of Non-idealities in a Z-axis CMOS-MEMS Gyroscope

摘要

MEMS gyroscopes are extremely difficult to manufacture reliably. The MEMS gyroscope is sensitive to spurious vibrations and other coupling mechanisms. This thesis aims to quantitatively capture 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 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 is also modeled in the gyroscope. Fundamental issues related to the modeling and simulation of MEMS gyroscopes are addressed. Behavioral simulation is used to analyze the gyroscope and system-level design issues. The elastic modeling effort is primarily aimed at a thorough understanding of cross-axis 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. 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. Analytic equations relating gyroscope non-idealities: the Zero Rate Output, acceleration and acceleration-squared sensitivity and cross-axis sensitivity to manufacturing effects are derived. The analysis and simulations result in several insights into gyroscope non-idealities and design pointers to reduce them.