This paper presents a generalized model for the pull-in phenomenon in electrostatic actuators with a single input, either charge or voltage. The pull-in phenomenon of a general electrostatic actuator with a single input is represented by an algebraic equation referred to as the pull-in equation. This equation directly yields the pull-in parameters, namely, the pull-in voltage or pull-in charge and the pull-in displacement. The model presented here permits the analysis of a wide range of cases, including nonlinear mechanical effects as well as various nonlinear, nonideal, and parasitic electrical effects. In some of the cases, an analytic solution is derived, which provides physical insight into how the pull-in parameters depend upon the design and properties of the actuator. The pull-in equation can also yield rapid numerical solutions, allowing interactive and optimal design. The model is then utilized to analyze analytically the case of a Duffing spring, previously analyzed numerically by Hung and Senturia, and captures the variations of the pull-in parameters in the continuum between a perfectly linear spring and a cubic spring. Several other case studies are described and analyzed using the pull-in equation, including parallel-plate and tilted-plate (torsion) actuators taking into account the fringing field capacitance, feedback and parasitic capacitance, trapped charges, an external force, and large displacements.

A methodology and model for the pull-in parameters of electrostatic actuators

Electrostatically actuated, 500micrometers diameter, Si surface micromachined 2-axis tilting micromirrors were designed and fabricated in a 2 structural + 1 interconnect layer polysilicon process. The mirrors are capable of large, continuous, controlled, DC tilt in any direction at moderate actuation voltages. The lowest-mode resonance frequency is sufficiently high to decouple from the ambient vibration noise and allow setting times of less than a few milliseconds. The Au- coated reflectors, suspended in gimbal mounts via torsional springs and bearings, are tilted by applying voltage to four electrically independent sets of fixed electrodes on the substrate. The electrodes and the springs are designed to optimize actuation voltages, resonance frequencies and the deflection range. To achieve the range, the mounts are lifted and fixed fifty microns above the substrate surface during the release process by a self-assembly mechanism powered by tailored residual stress in a separate metalization layer. Square arrays with 1 mm pitch containing independently addressable identical 16, 64 and 256 mirrors were fabricated and hermetically packaged. Based on these devices, fully functional, bitrate and wavelength independent, single stage, low insertion loss, single mode fiber optical crossconnect system are built.

Lucent Microstar micromirror array technology for large optical crossconnects

This contribution deals with the design, technology and experimental investigations of mirrors and micromirror arrays made of monocrystalline silicon Electrostatically operated two-directionally deflecting mirrors and mirror arrays for continuous scanning with working frequencies between several 100 Hz and 200 kHz are presented The modified BESOI technology used and the experimental-data-based method to improve the accuracy of model parameters for simulations and to determine the cross-coupling between array cells are new in the field of micromechanics Furthermore, results of application-related experiments of laser projection are given

Silicon mirrors and micromirror arrays for spatial laser beam modulation

The aim of this paper is to provide a review of micromirror array (MMA) technologies (2631 MMA research papers and patents were reviewed for this effort). The performance capabilities of 277 MMA designs from 49 companies and 23 academic research groups are categorized and compared. The designs are categorized according to (i) their array’s dimension (e.g., 2D arrays consisting of mirrors that cover a surface, 1D arrays consisting of mirrors in a row, and 0D arrays consisting of only a single mirror), (ii) the nature of the surface of their mirrors (e.g., continuous or discrete), (iii) what combination of tip, tilt, and/or piston degrees of freedom (DOFs) they achieve, and (iv) how they are actuated. Standardized performance metrics that can be systematically applied to every MMA design (e.g., mirror area, fill factor, pitch, range of motion, maximum acceleration, actuator energy density, and number of uncontrolled DOFs) are defined and plotted for existing designs to enable their fair comparison. Theoretical bounds on what is physically possible for MMAs to achieve are also derived and depicted in these plots to highlight the amount of performance improvement that remains to be achieved by future designs and guidelines are provided to aid in the development of these future designs.

A review of micromirror arrays

In a semiconductor device having a MEMS according to this invention, a plurality of units having movable portions for constituting a MEMS are monolithically mounted on a semiconductor substrate on which an integrated circuit including a driving circuit, sensor circuit, memory, and processor is formed. Each unit has a processor, memory, driving circuit, and sensor circuit.

Semiconductor device having MEMS

The paper presents a technological study for the realization of micromirrors which have both, a large pixel size (100 /spl mu/m/spl times/100 /spl mu/m) and a large mirror deflection angle (/spl plusmn/15/spl deg/). This specification requires a 13 /spl mu/m gap for electrostatic actuation. A metal surface micromachining process has been developed using thick resist UV-lithography, multiple electroplating, a copper sacrificial layer and a polishing process step. Using nonplanar electrodes the driving voltage of electrostatic actuators can be reduced by factors. Two different technologies to realize tapered electrodes are presented.

K. Riemer

Papers

Infrared micromirror array with large pixel size and large deflection angle