Electrostatic micro actuators for mirror and other applications

Micro-electro-mechanical systems (MEMS) based electrostatic micro actuators are becoming important building blocks for innovations in optical signal processing and computing systems due to their inherently small size, high density, high speed and low power consumption. Generally, the principle of operation in these systems can be described as: an electrostatic attractive force causes a mechanical rotation, translation or deformation of a mirror plate, controlling the power, phase or direction of a light beam while it propagates through some medium or through free space. The fast paced, competitive research and development efforts widely being undertaken, both in academia and industry, are demanding simple, fast methods for the design of quasi-static Mirror systems, with a large, stable, analog range of operation. In addition fast prototyping methods are in demand for the proof of concept fabrication of these mirror designs. This dissertation addresses these research topics by presenting 1) a general capacitance-based quasi-static design theory and methodology for electrostatic micro actuators, 2) a study of electrostatic travel range extension methods to minimize the pull in effect, and 3) a fast prototyping approach for electrostatic mirror devices using ultra thin silicon wafer bonding and deep reactive etching technologies. In the first topic, two fundamental capacitance-based differential equations are developed for the quasi-static description of electrostatic micro actuator systems. A structural equation is developed to represent the coupled electromechanical response of the system under applied voltage bias, and a pull in equation is determined to identify the intrinsic collapse point beyond which an actuator system no longer has a stable equilibrium, the so-called pull in point. These equations are applied to various complex electrostatic micro actuator systems to predict specific quasi-static behavior. A unitless equation is introduced for each actuator category, and based on it, a design method is proposed to quickly provide specifications for a particular desired performance of an electrostatically actuated micro-mirror system. In the second topic, and as an application of the proposed design methodology, the travel range extension issue is addressed leading to two new methods to increase travel range by sacrificing driving voltage. Both methods are applied directly in the electrostatic domain. The first method utilizes a series capacitor to modulate the effective actuation voltage across the variable capacitor micro mirror. The second method utilizes negative feedback due to the coulombic repulsive interaction between charge layers inserted between the micro mirror electrodes. An analytical study of representative mirror devices is presented, and verification of the travel range extension models is provided via finite element analysis (FEA) simulation. As a further application of the design methodology developed as part of the first research topic, three state-of-the-art micro actuator systems are designed and studied: 1) a variable optical attenuator (VOA), 2) an optical cross connect device (OXC) and 3) an electrostatically tunable, wavelength selecting device. FEA simulations are used to confirm design specifications. In the third research topic, VOA and electrostatically tunable, wavelength selecting devices are fabricated using fast prototyping via ultra thin wafer bonding and deep reactive etching (DRIIE) technologies. Both silicon wet-etching and SU-8 patterning are investigated for the formation of mirror gaps. Testing in the mechanical domain and partial device characterization in the optical domain is provided for these devices. Finally, as a demonstration that the actuator design approach developed in this thesis can be applied to systems other than micro mirrors, we use the approach to design an innovative true mass flow sensor using an electrostatic resonant beam as the sensing element