Jan Mehner

Computer-aided generation of nonlinear reduced-order dynamic macromodels. I. Non-stress-stiffened case

Reduced-order dynamic macromodels are an effective way to capture device behavior for rapid circuit and system simulation. In this paper, we report the successful implementation of a methodology for automatically generating reduced-order nonlinear dynamic macromodels from three-dimensional (3-D) physical simulations for the conservative-energy-domain behavior of electrostatically actuated microelectromechanical systems (MEMS) devices. These models are created with a syntax that is directly usable in circuit- and system-level simulators for complete MEMS system design. This method has been applied to several examples of electrostatically actuated microstructures: a suspended clamped beam, with and without residual stress, using both symmetric and asymmetric positions of the actuation electrode, and an elastically supported plate with an eccentric electrode and unequal springs, producing tilting when actuated. When compared to 3-D simulations, this method proves to be accurate for non-stress-stiffened motions, displacements for which the gradient of the strain energy due to bending is much larger than the corresponding gradient of the strain energy due to stretching of the neutral surface. In typical MEMS structures, this corresponds to displacements less than the element thickness, At larger displacements, the method must be modified to account for stress stiffening, which is the subject of part two of this paper.

Silicon mirrors and micromirror arrays for spatial laser beam modulation

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.

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.

Simulation of gas damping in microstructures with nontrivial geometries

Methods to calculate the fluid depending forces in movable micromechanical structures will be shown in this paper. In most cases fluid flow within narrow air gaps can be simply described by the Reynolds gas film equation. Analytical solutions are known for simple plate shapes. New ways to describe the damping and squeeze film effect for nontrivial plate shapes using analogy relations are discussed. Reynolds equation fails in the case of large air gaps between plates or if free outstream conditions are not valid. In these cases the general Navier-Stokes-Equation must be used. FE-tools with fluidmechanical capabilities are able to solve this partial differential equation and allow a damping analysis. Phase shift between plates velocity and reaction forces can be interpreted as additional inertial or squeeze forces. Results of simulation and experimental analysis are verified on a gyroscope and a micromirror array.

The substrate matters in the Raman spectroscopy analysis of cells

Raman spectroscopy is a powerful analytical method that allows deposited and/or immobilized cells to be evaluated without complex sample preparation or labeling. However, a main limitation of Raman spectroscopy in cell analysis is the extremely weak Raman intensity that results in low signal to noise ratios. Therefore, it is important to seize any opportunity that increases the intensity of the Raman signal and to understand whether and how the signal enhancement changes with respect to the substrate used. Our experimental results show clear differences in the spectroscopic response from cells on different surfaces. This result is partly due to the difference in spatial distribution of electric field at the substrate/cell interface as shown by numerical simulations. We found that the substrate also changes the spatial location of maximum field enhancement around the cells. Moreover, beyond conventional flat surfaces, we introduce an efficient nanostructured silver substrate that largely enhances the Raman signal intensity from a single yeast cell. This work contributes to the field of vibrational spectroscopy analysis by providing a fresh look at the significance of the substrate for Raman investigations in cell research.

Computational Methods for Reduced Order Modeling of Coupled Domain Simulations

This paper deals with computer aided generation of reduced-order models for fast static and dynamic simulations of micro electromechanical systems. Following previous work, we present improved methods to reduce the computational effort of parameter extraction techniques, to consider multiple electrodes and the extension of analysing capabilities. A micromirror example will be used to demonstrate the practical suitability of reduced-order models for system simulations and feedback controller design.

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.

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.

SYSTEM LEVEL SIMULATIONS OF MEMS BASED ON REDUCED ORDER FINITE ELEMENT MODELS

Reduced Order Modeling (ROM) of MEMS has become state of the art for fast component and system level simulations. Based on the well known modal decomposition technique, the automatic generated macromodel is no longer simplified to rigid body and lumped parameter approximations. It retains the true flexible characteristics of electromechanical structures and is able to capture mechanical nonlinearities (Stress-Stiffening), electrostatic fringing fields and large signal behavior with the same order of accuracy as the corresponding FE-model. After a brief description of the ROM approach, the following paper is focused on a new capability of the macromodel which couples nodal degree of freedoms of the FE-model and modal degrees of freedom used for the internal governing equations of the ROM. The new interface is necessary to model temporary displacement constrains, to couple several ROMs together and to analyze system with mechanical contact.

Homogeneous catheter for esophagus high-resolution manometry using fiber Bragg gratings

The high resolution manometry of the upper gastrointestinal tract is moving from research into clinical practice [1], [2]. Hence, there is a need for easy to use and patient friendly diagnosis devices for high resolution esophagus manometry. Besides established methods like perfusion manometry and solid state sensor manometry the use of optical fiber sensor catheters based on fiber Bragg gratings (FBGs) is gaining interest among physicians and medical equipment manufacturers [3], [4]. This paper presents design, prototyping and characterization of a fiber Bragg grating pressure sensor catheter. It uses a two layer polymer coating for the transformation of radial forces into axial strain of the optical fiber. The sensitivity with respect to pressure is in the range of 1 mmHg, the spatial resolution is provided by 32 sensors with a pitch of 10 mm. The coating technique is scalable to smaller diameters down to 0.5 mm and the flexibility is homogeneous over the whole length and can be adjusted by the choice of the coating materials.