This paper is going to emphasize on the air squeeze film damping effect on micro-mechanical resonant beam in MEMS. In general, the low energy density of electrode force will cause high-voltage power supply to drive the electro- micro resonators; reducing the distance between the electrode and resonant beam can be the most efficient way to solve this problem. But bringing different exciting frequency of system and environmental pressure to the air squeeze film effect might cause it changes form similarly to the damping qualities, and this will also change the dynamic characteristics of micro resonator. The dynamic model for double clamped micro-mechanical resonant beam is proposed by using Lagrange¡¦s equation in this study. The corresponding eigenvalue problems of resonant beam are formulated and solved by employing the hypothetical mode method. Under the presumption of viscous damping model, we may obtain a damping factor which includes the parameters of size, temperature and air pressure when energy transfer model is employed to simulate the squeeze film damping effect of two immediate objects. Eventually, the damping ratio and the dynamic characteristics of resonant microbeam are derived by means of exploring the frequency response function of system. Besides, the frequency change of micro-mechanical resonant beam due to an axial force is also considered in the thesis.

Fluid damping arising from squeeze film flow of air or some inert gas trapped between an oscillating micro mechanical structure, such as a beam or a plate, and a fixed substrate often dominates the other energy dissipation mechanisms in silicon based MEM devices. As a consequence, it has maximum effect on the resonant response or dynamic response of the device. Unfortunately, modelling of the squeeze film flow in most MEMS devices is quite complex because of several factors unique to MEMS structures. In this thesis, we set out to study the effect of these factors on squeeze film flow. First we list these factors and study each of them in the context of a particular application, using experimental measurements, extensive numerical simulations, and analytical modelling for all chosen factors. We consider five important factors. The most important factor perhaps is the effect of rarefaction that is dominant when a device is vacuum packed with low to moderate vacuum, typical for MEMS packaging. The second problem is to investigate and model the effect of perforations which are usually provided for efficient etching of the sacrificial layer during fabrication of the suspended structures. The third problem is to consider the effect of non-uniform deflection of the structure such as those in MEMS cantilever beams and model its effect on the squeeze film. The fourth effect studied is the influence of different boundary conditions such as simple, fully open and partially closed boundaries around the vibrating structure on the characteristics of the squeeze film flow. The fifth problem undertaken is to analyze the effect of high operating frequencies on the squeeze film damping. In the first problem, the rarefaction effect is studied by performing experiments under varying pressures. Depending on the ambient pressure or the size of the gap between the vibrating and the fixed structure, the fluid flow may fall in any of the flow regimes, ranging from continuum flow to molecular flow, and giving a wide range of dissipation. The relevant fluid flow characteristics are determined by the Knudsen number, which is the ratio of the mean free path of the gas molecule to the characteristic flow length of the device. This number is very small for continuum flow and reasonably big for molecular flow. Here, we study the effect of fluid pressure on the squeeze film damping by carrying out experiments on a MEMS device that consists of a double gimbaled torsional resonator. Such devices are commonly used in optical cross-connects and switches. We vary fluid pressure to make the Knudsen number go through the entire range of continuum flow, slip flow, transition flow, and molecular flow. We experimentally determine the quality factor of the torsional resonator at different air pressures ranging from 760 torr to 0.001 torr. The variation of this pressure over six orders of magnitude ensures the required rarefaction to range over all flow conditions. Finally, we get the variation of the quality factor with pressure. The result indicates that the quality factor, Q, follows a power law, Q P-r, with different values of the exponent r in different flow regimes. To numerically model the effect of rarefaction, we propose the use of effective viscosity in Navier-Stokes equation. This concept is validated with analytical results for a simple case. It is then compared with the experimental results presented in this thesis. The study shows that the effective viscosity concept can be used effectively even for the molecular regime if the air-gap to length ratio is sufficiently small (h0/L < 0.01). However, as this ratio increases, the range of validity decreases. Next, a semianalytical approach is presented to model the rarefaction effect in double-gimballed MEMS torsion mirror. In this device, the air gap thickness is 80 µm which is comparable to the lateral dimension 400 µm of the oscillating plate and thus giving the air-gap to length ratio of 0.2. As the ratio 0.2 is much greater than 0.01, the conventional Reynolds equation cannot be used to compute the squeeze film damping. Consequently, we find the effective length of an equivalent simple mirror corresponding to the motion about the two axes of the mirror such that the Reynolds equation still holds. After finding the effective length, we model the rarefaction effect by incorporating effective viscosity which is based on different models including the one proposed in this paper. Then we compare the analytical solution with the experimental result and find that the proposed model not only captures the rarefaction effect in the slip, transition and molecular regimes but also couples well with the non-fluid damping in the intrinsic regime. For the second problem, several analytical models exist for evaluating squeeze film damping in rigid rectangular perforated MEMS structures. These models vary in their treatment of losses through perforations and squeezed film, in their assumptions of compressibility, rarefaction and inertia, and their treatment of various second order corrections. We present a model that improves upon previously reported models by incorporating more accurate losses through holes proposed by Veijola and treating boundary cells and interior cells differently as proposed by Mohite et al. The proposed model is governed by a modified Reynolds equation that includes compressibility and rarefaction effect. This equation is linearized and transformed to the standard two-dimensional diffusion equation using a simple mapping function. The analytical solution is then obtained using Green’s function. The solution thus obtained adds an additional term Γ to the damping and spring force expressions derived by Blech for compressible squeeze flow through non-perforated plates. This additional term contains several parameters related to perforations and rarefaction. Setting Γ = 0, one recovers Blech’s formulas. We benchmark all the models against experimental results obtained for a typical perforated MEMS structure with geometric parameters (e.g., perforation geometry, air gap, plate thickness) that fall well within the acceptable range of parameters for these models (with the sole exception of Blech’s model that does not include perforations but is included for historical reasons). We compare the results and discuss the sources of errors. We show that the proposed model gives the best result by predicting the damping constant within 10% of the experimental value. The approximate limit of maximum frequencies under which the formulas give reasonable results is also discussed. In the third problem, we study the effect of elastic modeshape during vibration on the squeeze film flow. We present an analytical model that gives the values of squeeze film damping and spring coefficients for MEMS cantilever resonators taking into account the effect of flexural modes of the resonator. We use the exact modeshapes of a 2D cantilever plate to solve for pressure in the squeeze film and then derive the equivalent damping and spring coefficient relations from the back force calculations. The relations thus obtained can be used for any flexural mode of vibration of the resonators. We validate the analytical formulas by comparing the results with numerical simulations carried out using coupled finite element analysis in ANSYS, as well as experimentally measured values from MEMS cantilever resonators of various sizes and vibrating in different modes. The analytically predicted values of damping are, in the worst case, within less than 10% of the values obtained experimentally or numerically. We also compare the results with previously reported analytical formulas based on approximate flexural modeshapes and show that the proposed model gives much better estimates of the squeeze film damping. From the analytical model presented here, we find that the squeeze film damping drops by 84% from the first mode to the second mode in a cantilever resonator, thus improving the quality factor by a factor of six to seven. This result has significant implications in using cantilever resonators for mass detection where a significant increase in quality factor is obtained only by using vacuum. In the fourth and fifth problem, the effects of partially blocked boundary condition and high operating frequencies on squeeze films are studied in a MEMS torsion mirror with different boundary conditions. For the structures with narrow air-gap, Reynolds equation is used for calculating squeeze film damping, generally with zero pressure boundary conditions on the side walls. This procedure, however, fails to give satisfactory results for structures under two important conditions: (a) for an air-gap thickness comparable to the lateral dimensions of the micro structure, and (b) for non-trivial pressure boundary conditions such as fully open boundaries on an extended substrate or partially blocked boundaries that provide side clearance to the fluid flow. Several formulas exist to account for simple boundary conditions. In practice, however, there are many micromechanical structures, such as torsional MEMS structures, that have non-trivial boundary conditions arising from partially blocked boundaries. The most common example is the double-gimballed MEMS torsion mirror of rectangular, circular, or hexagonal shape. Such boundaries usually have clearance parameters that can vary due to fabrication. These parameters, however, can also be used as design parameters if we understand their role on the dynamics of the structure. We take a MEMS torsion mirror as an example device that has large air-gap and partially blocked boundaries due to static frames. Next we model the same structure in ANSYS and carry out CFD (computational fluid dynamics) analysis to evaluate the stiffness constant K, the damping constant C, as well as the quality factor Q due to the squeeze film. We compare the computational results with experimental results and show that without taking care of the partially blocked boundaries properly in the computational model, we get unacceptably large errors. Subsequently, we use the CFD calculations to study the effect of two important boundary parameters, the side clearance c, and the flow length s, that specify the partial blocking. We show the sensitivity of K and C on these boundary design parameters. The results clearly show that the effect of these parameters on K and C is substantial, especially when the frequency of excitation becomes close to resonant frequency of the oscillating fluid and high enough for inertial and compressibility effects to be significant. Later, we present a compact model to capture the effect of side boundaries on the squeeze film damping in a simple rectangular torsional structure with two sides open and two sides closed. The analytical model matches well with the numerical results. However, the proposed analytical model is limited to low operating frequencies such that the inertial effect is negligible. The emphasis of this work has been towards developing a comprehensive understanding of different significant factors on the squeeze film damping in MEMS devices. We have proposed various ways of modelling these effects, both numerically as well as analytically, and shown the efficacy of these models by comparing their predictive results with experimental results. In particular, we think that the proposed analytical models can help MEMS device designers by providing quick estimates of damping while incorporating complex effects in the squeeze film flow. The contents of the thesis may also be of interest to researchers working in the area of microfluidics and nanofluidics.

There are various energy dissipation mechanisms that affect the dynamic response of microstructures used in MEMS devices. A cumulative effect of such losses is captured by an important characteristic of the structure called Quality factor or Q-factor. Estimating Q-factor at the design stage is crucial in all applications that use dynamics as their principle mode of operation. A high Q-factor indicates sharp resonance that, in turn, can indicate a broad flat response region of the structure. In addition, a high Q-factor typically indicates a high sensitivity. Microstructures used in MEMS are generally required to have much higher Q-factors than their macro counterparts. However some damping mechanisms present in microstructures can reduce the Q-factor of the structure significantly. In the present work, we investigate the dependence of Q-factor on the squeeze film damping an energy dissipation mechanism that dominates by a couple of orders of magnitude over other losses when a fluid (e.g., air) is squeezed through gaps due to vibrations of a microstructure. In particular, we show the effect of nonlinear terms in the analysis of squeeze film damping on the Q-factor of a structure. We also show the effect of rarefaction, surface roughness along with their coupled effect and with different boundary conditions such as open border effect, blocked boundary effect on the squeeze film damping. Finally, we develop similitude laws for calculating squeeze film damping force in up-scaled structures. We illustrate the effects by studying various type of microstructures including parallel plates, beams, plate and beam assemblies such as MEMS microphone, vibratory gyroscope etc. We view the contributions of this work as a significant in investigating and integrating all important effects altogether on the squeeze film damping, which is a significant factor in the design and analysis of MEMS devices.

The first objective of this dissertation is to present hybrid numerical-analytical approaches and reduced-order models to simulate microelectromechanical systems (MEMS) in multi-physics fields. These include electric actuation (AC and DC), squeeze-film damping, thermoelastic damping, and structural forces. The second objective is to investigate MEMS phenomena, such as squeeze-film damping and dynamic pull-in, and use the latter to design a novel RF-MEMS switch. In the first part of the dissertation, we introduce a new approach to the modeling and simulation of flexible microstructures under the coupled effects of squeeze-film damping, electrostatic actuation, and mechanical forces. The new approach utilizes the compressible Reynolds equation coupled with the equation governing the plate deflection. The model accounts for the slip condition of the flow at very low pressures. Perturbation methods are used to derive an analytical expression for the pressure distribution in terms of the structural mode shapes. This expression is substituted into the plate equation, which is solved in turn using a finite-element method for the structural mode shapes, the pressure distributions, the natural frequencies, and the quality factors. We apply the new approach to a variety of rectangular and circular plates and present the final expressions for the pressure distributions and quality factors. We extend the approach to microplates actuated by large electrostatic forces. For this case, we present a low-order model, which reduces significantly the cost of simulation. The model utilizes the nonlinear Euler-Bernoulli beam equation, the von K´arm´an plate equations, and the compressible Reynolds equation. The second topic of the dissertation is thermoelastic damping. We present a model and analytical expressions for thermoelastic damping in microplates. We solve the heat equation for the thermal flux across the microplate, in terms of the structural mode shapes, and hence decouple the thermal equation from the plate equation. We utilize a perturbation method to derive an analytical expression for the quality factor of a microplate with general boundary conditions under electrostatic loading and residual stresses in terms of its structural mode shapes. We present results for microplates with various boundary conditions. In the final part of the dissertation, we present a dynamic analysis and simulation of MEMS resonators and novel RF MEMS switches employing resonant microbeams. We first study microbeams excited near their fundamental natural frequencies (primary-resonance excitation). We investigate the dynamic pull-in instability and formulate safety criteria for the design of MEMS sensors and RF filters. We also utilize this phenomenon to design a low-voltage RF MEMS switch actuated with a combined DC and AC loading. Then, we simulate the dynamics of microbeams excited near half their fundamental natural frequencies (superharmonic excitation) and twice their fundamental natural frequencies (subharmonic excitation). For the superharmonic case, we present results showing the effect of varying the DC bias, the damping, and the AC excitation amplitude on the frequency-response curves. For the subharmonic case, we show that if the magnitude of the AC forcing exceeds the threshold activating the subharmonic resonance, all frequency-response curves will reach pull-in. / Ph. D.

MEMS microphones have been a research topic for the last two and half decades. The state-of-the-art comprises surface mount MEMS microphones in laptops, mobile phones and tablets, etc. The popularity and the commercial success of MEMS microphones is largely due to the steep cost reduction in manufacturing afforded by the mass scale production with microfabrication technology. The current MEMS microphones are de-signed along the lines of traditional microphones that use capacitive transduction with or without permanent charge (electret type microphones use permanent charge of their sensor element). These microphones offer high sensitivity, stability and reasonably at frequency response while reducing the overall size and energy consumption by exploiting MEMS technology. Conceptually, microphones are simple transducers that use a membrane or diaphragm as a mechanical structure which deflects elastically in response to the incident acoustic pressure. This dynamic deflection is converted into an electrical signal using an appropriate transduction technique. The most popular transduction technique used for this application is capacitive, where an elastic diaphragm forms one of the two parallel plates of a capacitor, the fixed substrate or the base plate being the other one. Thus, there are basically two main elements in a microphone { the elastic membrane as a mechanical element, and the transduction technique as the electrical element. In this thesis, we propose and study novel design for both these elements. In the mechanical element, we propose a simple topological change by introducing slits in the membrane along its periphery to enhance the mechanical sensitivity. This simple change, however, has significant impact on the microphone design, performance and its eventual cost. Introduction of slits in the membrane makes the geometry of the structural element non-trivial for response analysis. We devote considerable effort in devising appropriate modeling techniques for deriving lumped parameters that are then used for simulating the system response. For transduction, we propose and study an FET (Field Effect Transistor) coupled micro-phone design where the elastic diaphragm is used as the moving (suspended) gate of an FET and the gate deflection modulated drain current is used in the subthreshold regime of operation as the output signal of the microphone. This design is explored in detail with respect to various design parameters in order to enhance the electrical sensitivity. Both proposed changes in the microphone design are motivated by the possibilities that the microfabrication technology offers. In fact, the design proposed here requires further developments in MEMS technology for reliably creating gaps of 50-100 nm between the substrate and a large 2D structure of the order of a few hundred microns in diameter. In the First part of the thesis, we present detailed simulations of acoustic and squeeze lm domain to understand the effect slits could bring upon the behaviour of the device as a microphone. Since the geometry is nontrivial, we resort to Finite element simulations using commercial packages such as COMSOL Multiphysics and ANSYS in the structural, acoustic and Fluid-structure domains to analyze the behaviour of a microphone which has top plate with nontrivial geometry. On the simulated Finite element data, we conduct low and high frequency limit analysis to extract expressions for the lumped parameters. This technique is well known in acoustics. We borrow this technique of curve Fitting from the acoustics domain and apply it in modified form into the squeeze lm domain. The dynamic behaviour of the entire device is then simulated using the extracted parameters. This helps to simulate the microphone behaviour either as a receiver or as a transmitter. The designed device is fabricated using MEMSCAP PolyMUMPS process (a foundry Polysilicon surface micromachining process). We conduct vibrometer (electrostatic ex-citation) and acoustic characterization. We also study the feasibility of a microphone with slits and the issues involved. The effect of the two dissipation modes (acoustic and squeeze lm ) are quantified with the experimentally determined quality factor. The experimentally measured values are: Resonance is 488 kHz (experimentally determined), low frequency roll-off is 796 Hz (theoretical value) and is 780 Hz as obtained by electrical characterization. The first part of this thesis focusses on developing a comprehensive understanding of the effect of slits on the performance of a MEMS microphone. The presence of slits near the circumference of the clamped plate cause reduction in its rigidity. This leads to an increase in the sensitivity of the device. Slits also cause pressure equalization between the top and bottom of the diaphragm if the incoming sound is at relatively low frequencies. At this frequency, also known as the lower cutoff frequency, the microphone's response starts dropping. The presence of slits also changes the radiation impedance of the plate as well as the squeeze lm damping below the plate. The useful bandwidth of the microphone changes as a consequence. The cavity formed between the top plate and the bottom fixed substrate increases the stiffness of the device significantly due to compression of the trapped air. This effect is more pronounced here because unlike the existing capacitive MEMS microphones, there is no backchamber in the device fabricated here. In the second part of the thesis, we present a novel subthreshold biased FET based MEMS microphone. This biasing of the transistor in the subthreshold region (also called as the OFF-region) offers higher sensitivity as compared to the above threshold region (also called as the ON-region) biasing. This is due to the exponentially varying current with change in the bias voltage in the OFF-region as compared to the quadratic variation in the ON-region. Detailed simulations are done to predict the behaviour of the device. A lumped parameter model of the mechanical domain is coupled with the drain current equations to predict the device behaviour in response to the deflection of the moving gate. From the simulations, we predict that the proposed biasing offers a device sensitive to even sub-nanometer deflection of the flexible gate. As a proof of concept, we fabricate fixed-fixed beams which utilize CMOS-MEMS fabrication. The process involves six lithography steps which involve two CMOS and the remaining MEMS fabrication. The fabricated beams are mechanically characterized for resonance. Further, we carry out electrical characterization for I-V (current-voltage) characteristics. The second part of the thesis focusses on a novel biasing method which circumvents the need of signal conditioning circuitry needed in a capacitive based transduction due to inbuilt amplification. Extensive simulations with equivalent circuit has been carried out to determine the increased sensitivity and the role of various design variables.

There are many ways in which the surrounding media, such as air between an oscillating MEMS structure and a fixed substrate, can affect the dynamic response of a MEMS transducer. Some of these effects involve dissipation while others involve energy transfer. Transverse oscillations of a planar structure can cause a lateral air flow in small gaps that results in pressure gradients. The forces due to the built–up pressure are always against the vibration of the structure and have characteristics of damper and stiffener. In this work, we study the squeeze film phenomenon due to the interaction between the air–film and the structure in the presence of restrictive flow boundary conditions. It is known that the squeeze film damping due to the air trapped between the oscillating MEMS structure and the fixed substrate often contributes to maximum energy dissipation. We carry out an analysis to estimate damping and stiffness in cases with restrictive flow boundaries in dynamic MEMS devices. While the studies reported in the present work address fluid flow damping with restrictive flow boundaries, the analysis of air-flow shows another important phenomenon of enhanced air-spring stiffness. This study is discussed separately in the context of spring stiffening behavior in MEMS devices exhibiting squeeze film phenomenon. First a theoretical framework for modeling squeeze film flow is established and this is followed with analytical and numerical solutions of problems involving squeeze film phenomenon. Modeling of squeeze film effects under different flow conditions is carried out using Reynold’s equation. The problem of squeeze film damping in MEMS transducers is more involved due to the complexities arising from different boundary conditions of the fluid flow. In particular, we focus our attention on estimation of damping in restricted flow boundaries such as only one side vented and no side vented passive boundary conditions. Damping coefficient for these cases are extracted when the fluid is subjected to an input velocity profile according to a specific mode shape at a given frequency of oscillation. We also explain the squeeze film flow in restricted boundaries by introducing the concept of passive and active boundary conditions and analyzing the pressure gradients which are related to the compressibility of the air in the cavity. Passive boundary conditions is imposed by specifying the free flow or no flow along one of the edges of the cavity, whereas, active boundary condition is imposed by the velocity profile being specified at the interface of the cavity with the oscillating structure. Some micromechanical structures, such as pressure sensors and ultrasound transducers use fully restricted or closed boundaries where the damping for such cases, even if small, is very important for the determination of the Q–factor of these devices. Our goal here is to understand damping due to flow in such constrained spaces. Using computational fluid dynamics (ANSYS–FLOTRAN), the case of fully restricted boundaries is studied in detail to study the effect of important parameters which determines the fluid damping, such as flow length of the cavity, air–gap height, frequency of oscillations and the operating pressure in the cavity. A simulation strategy is developed using macros programming which overcomes some of the limitations of the existing techniques and proves useful in imposing a non–uniform velocity and the extraction of damping coefficient corresponding to the flexibility of the structure in specific oscillation modes. Rarefaction effects are also accounted for in the FEM model by introducing the flow rate coefficient, or, alternatively using the concept of effective viscosity. The analysis carried out for the fully restricted case is motivated by the analytical modeling of squeeze film phenomenon for a wide range of different restricted boundaries, and analyzing the resulting pressure gradient patterns. We show that significant damping exists even in fully restricted boundaries due to lateral viscous flow. This is contrary to known reported results, which neglect damping in such cases. The result indicates that in fully restrictive fluid flow boundaries or in a closed cavity, air damping cannot be neglected at lower oscillation frequencies and large flow length to air-gap ratio if the active boundary has a non-uniform velocity profile. Analysis of air-flow in the case of restricted flow boundaries shows another important phenomenon of enhanced air-spring stiffness. It is found that fluid film stiffness has a nonlinear dependence on various parameters such as air-gap to length ratio, fluid flow boundary conditions and the frequency of oscillation. We carry out analysis to obtain the dynamic response of MEMS devices where it is significantly affected by the frequency dependent stiffness component of the squeeze film. We show these effects by introducing frequency dependent stiffness in the equation of motion, and taking examples of fluid boundary conditions with varying restriction on flow conditions. The stiffness interaction between the fluid and the structure is shown to depend critically on stiffness ratios, and the cut-off frequency. It is also inferred that for a given air–gap to flow length ratio, the spring behaviour of the air is independent of the flow boundary conditions at very high oscillation frequencies. Hence, we limit our focus on studying the effect of fluid stiffness in the regime where it is not fully compressible. For non-resonant devices, this study finds its utility in tuning the operating frequency range while for resonant devices it can be useful to predict the exact response. We show that it is possible to design or tune the operating frequency range or shift the resonance of the system by appropriate selection of the fluid flow boundary conditions. The emphasis of the present work has been toward studying the effect of squeeze film flow on dynamic response of MEMS structures with restrictive flow boundary conditions. Estimation of energy dissipation due to viscous flow cannot be ignored in the design of MEMS which comprise of restricted flow boundaries. We also remark that modeling of a system with squeeze film flow of the trapped air in terms of frequency independent parameters, viz. damping and stiffness coefficient, is unlikely to be very accurate and may be of limited utility in specific cases. Although the central interest in studying squeeze film phenomenon is on the damping characteristics because of their direct bearing on energy dissipation or Q–factor of a MEMS device, the elastic behaviour of the film also deserves attention while considering restrictive flow boundary conditions.

Im Fokus dieser Arbeit stehen Dämpfungseffekte schwingfähiger Mikroelektromechanischer Systeme (MEMS), die nach dem kapazitiven Wirkprinzip arbeiten. Die verschiedenen Dissipationsprozesse und die zugehörigen analytischen Modelle sowie numerischen Berechnungsmöglichkeiten auf physikalischer Ebene werden vorgestellt und mit eigenen experimentellen Ergebnissen verglichen. Der Schwerpunkt liegt dabei auf der fluidischen Dämpfung im Kontinuum und bei leichter Verdünnung, was bei den meisten kapazitiven MEMS den dominierenden Verlusteffekt darstellt.:1 Überblick 2 Grundlagen zur Beschreibung von Mikrosystemen 3 Herstellung und Charakterisierung 4 Fluidische Dämpfung 5 Weitere dissipative Effekte mikromechanischer Systeme 6 Zusammenfassung und Ausblick / This thesis focuses on damping effects of vibrational micro-electromechanical systems (MEMS) with capacitive working principle. The different dissipation processes and the associated analytical models as well as numerical calculation possibilities on a physical level are presented and compared to own experimental results. The main emphasis is on fluidic damping in the continuum regime and with slight rarefaction, which is the dominant loss effect in most capacitive MEMS.:1 Überblick 2 Grundlagen zur Beschreibung von Mikrosystemen 3 Herstellung und Charakterisierung 4 Fluidische Dämpfung 5 Weitere dissipative Effekte mikromechanischer Systeme 6 Zusammenfassung und Ausblick