Wolfram Doetzel

Reduced order modeling of fluid structural interactions in MEMS based on model projection techniques

Reduced order macromodeling (ROM) of electrostatic structural interaction has become state of the art for fast component and system simulations. The following paper presents a new approach to add dissipative effects into existing macromodels for damped harmonic and transient analyses. The models are automatically generated by a modal projection technique based on the harmonic transfer functions of the fluidic domain. The transfer functions are either obtained at the initial position (small signal case) or at various deflection states (large deflection case). This method has been successfully applied to squeeze and slide film problems and holds for nontrivial plate shapes and arbitrary motion.

Silicon mirror arrays fabricated by using bulk and surface micromachining

Recently scanning actuator arrays have developed using metal, e.g. aluminium, or polysilicon as mirror material. Design and technology of micro mirror arrays mad of monocrystalline silicon are discussed in this paper as well as experimental results characterizing the arrays. Micro mirror arrays with up to 1000 simultaneously movable electrostatically operated cells convenient for continuous scanning with frequencies of several hundred Hz up to some kHz will be presented. The technological approaches consist of the use of silicon wet- and dry-etching, wafer bonding and metallization. A novel modified BESOI technology with CMP, wafer bonding with buried refractory metal electrodes and sacrificial layer etching has ben developed and will be discussed. The design process is based on simple analytical calculations of the mechanical behavior, the fluid flow surrounding the movable mirror and the electrostatic field as well as numerical simulations by means of the finite element method and network analysis. Furthermore, some experimental methods to characterize the electro-mechanical behavior of micro mirror arrays are discussed. In order to evaluate theoretical models describing the behavior, the natural frequencies, the damping coefficients and the frequency transfer function are measured. The adaptation of the model parameters leads to more accurate values simulating the behavior.

A novel 24-kHz resonant scanner for high-resolution laser display

This contribution deals with design, fabrication and test of a micromachined resonant scanner usable for horizontal deflection of the laser beam in a projection display. The electrostatically driven plate is separated from the mirror in order to reduce air damping and electrostatic non linearity. The device consists of a circularly shaped mirror which is suspended by torsion beams in the center of an elastically suspended driving plate. A resonator with two rotational degrees of freedom is arranged in this way. The rotation axes of mirror and driving plate are the same. A suitable design of the properties of the two degrees of freedom resonator leads to a significant amplification of the oscillation of the mirror compared to the oscillation of the driving plate. The first resonant mode is a rotation of both plates with nearly the same magnitude at a frequency of approx. 5 kHz. The second mode with paraphase deflection at 24 kHz shows a deflection amplification by a ratio of 53 and is used for scanning operation. A supporting part made of glass carries two electrodes in the region of the driving plate and has a micro sandblasted hole beneath the mirror. Bulk micromachining KOH wet etching of the electrode gap size on the back side of the driving plate, reactive ion etching for contour shaping of the mirror, of the driving plate and of the torsion beams and anodic bonding have been used for fabrication of the mechanical structure. The mirror is evaporated by an aluminum layer. Applying a voltage of 380V results in a mechanical deflection of ± 5.5 degrees at 24 kHz at atmosphere pressure. The device shows very small dynamic warp (<100nm) of the mirror plate even though the relatively large size of 2.2 mm diameter because of the thickness of 280 µm. The measured mechanical Q-factor is 5100.

Low-temperature approaches for fabrication of high-frequency microscanners

Within this paper novel applications of low temperature silicon wafer bonding technologies for the fabrication of high frequency silicon microscanners are presented. Two technological approaches are discussed, both using low temperature bonding as a key technological step. Results of the integration of a special low temperature bonding process within the bulk technology approach are shown. Micromirror arrays fabricated with this technology are presented and show promising results for optical applications.

Parametric model extraction for MEMS based on variational finite element techniques

This article is focused on new finite element technologies which account for parameter variations in a single finite element run. The key idea of the new approach is to compute not only the governing system matrices of the FE problem but also n high order partial derivatives with regard to design parameters by means of automatic differentiation (AD). As result, Taylor vectors of the systems response can be expanded in the vicinity of the initial position capturing dimensions and physical parameter. Essential speed-up can be achieved for shape optimization, sensitivity analyses and data sampling needed for reduced order modeling of MEMS.

Tunable Fabry-Perot-Interferometer for 3-5 μm wavelength with bulk micromachined reflector carrier

This contribution deals with design, fabrication and test of a micromachined first order Fabry-Perot-Interferometer (FPI) usable as tunable infrared filter in a spectrometer. The approach discussed here minimizes mirror curvature by using relative thick (300 μm Si ) mirror carriers for the fixed and the movable mirror of the FPI. We use thermally grown λ/4 thick SiO2 for antireflection layer at the mirror back side and for the first low refractive layer followed by a λ/4 thick polycrystalline silicon high refractive layer. Second and third λ/4 layer pairs of SiO2 and polycrystalline silicon complete the mirrors. The cavity size is electrostically tuned and capacitively detected by a closed loop control.

A derivatives-based method for parameterization of MEMS Reduced Order Models

The paper demonstrates an advanced simulation methodology based on differentiation of the discretized Finite Element (FE) equations for parameterization of MEMS macromodels. The idea of the approach is to compute not only the governing system matrices but also high order derivatives (HOD) with regard to design parameters by means of Automatic Differentiation (AD). As result, Taylor vectors of the model response can be expanded in the vicinity of the initial position with regard to dimensional and physical parameters. The objective of this presentation is to demonstrate the viability of HOD methods to parameterization of the mode superposition based Reduced Order Models (ROM) of the coupled- physics domains.

Application of Higher Order Derivatives Method to Parametric Simulation of MEMS

The paper demonstrates the advanced simulation methodology based on differentiation of the discretized finite element (FE) equations to parametric simulation of micro-electro-mechanical-systems (MEMS). The idea of the approach is to compute not only the governing system matrices but also high order derivatives (HOD) with regard to design parameters by means of automatic differentiation (AD). As result, Taylor vectors of the model response can be expanded in the vicinity of the initial position with regard to dimensional and physical parameters. The objective of this presentation is to demonstrate the viability of HOD methods to parametric simulation of MEMS in the static, modal, frequency response domains on the basis of the structural analysis and macromodeling.

Micromachined pressure gauge for the vacuum range based on damping of a resonator

Vacuum pressure measuring has been a field low permeated by micromachined devices until now. We designed a micromachined resonating system for friction vacuum gauge and tested it with the related electronics. The Silicon resonator is electrostically driven and capacitively sensed. Working at the fundamental resonant frequency (14 kHz), the damping of the oscillation is a measure for the pressure. We use bulk micromaching for the fabrication of the sensor cells. They consist of two fusion bonded silicon layers forming the resonator and two anodically bonded glass layers for caring sensing electrodes. A modified tuning fork design has been used for the resonator. It has a mechanical Q-factor of 33.000 at the low measurement range. The electronic circuit consists of a phase locked loop for driving at resonance and a PI controller to keep a constant vibration magnitude. The sensor has a nearly logarithmic transfer in a vacuum pressure range of 10-3 mbar ... 100 mbar.

Micromirrors and micromirror arrays for scanning applications

The main focus of this contribution will be the description of already realized applications of micromirrors and micromirror arrays and future opportunities. As an example image projection and environmental monitoring will be discussed. The micro scanning elements where fabricated by using monocrystalline silicon and are convenient for continuous scanning with working frequencies between several 100 Hz up to 100 kHz.