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The electrical and mechanical response of multilayered structures involving a piezoelectric layer and bull’s eye shaped electrodes is investigated. A boundary element method is employed based on spectral domain Green’s functions. With this method, the electric field distribution is determined first, and the local mechanical displacement in a second step. As will be shown, this allows us to exploit cylindrical symmetry for the electric surface charge distribution, but not for the vertical surface displacements. The effect of substrate bending due to in plane-stress, introduced by the piezoelectric constant d31, and the benefits of using bull’s eye electrode geometries with thick metallic backplates intended to reduce this effect are studied. A rigorous analysis and a largely simplified, but accurate approximation are compared. The application of this technique is demonstrated on a practical example for highly efficient and accurate determination of selected piezoelectric coefficients from surface topography measurements on such structures. Linz Center of Mechatronics COMET-K2 Osterreichische Forschungsforderungsgesellschaft (DE-588)10108858-9 H-iSlice Version of record

Small-scale and distortion-free measurement of electric fields is crucial for applications such as surveying atmospheric electrostatic fields, lightning research and safeguarding areas close to high-voltage power lines. A variety of measurement systems exist, the most common of which are field mills, which work by picking up the differential voltage of the measurement electrodes while periodically shielding them with a grounded electrode. However, all current approaches are bulky, suffer from a strong temperature dependency or severely distort the electric field, and thus require a well-defined surrounding and complex calibration procedures. Here we show that microelectromechanical system (MEMS) devices can be used to measure electric field strength without significant field distortion. The purely passive MEMS devices exploit the effect of electrostatic induction, which is used to generate internal forces that are converted into an optically tracked mechanical displacement of a spring-suspended seismic mass. The devices exhibit resolutions on the order of 100 V m−1 Hz−1/2 with a measurement range of up to tens of kilovolts per metre in the quasi-static regime ≲300 Hz). We also show that it should be possible to achieve resolutions of around 1 V m−1 Hz−1/2 by fine-tuning the sensor embodiment. These MEMS devices are compact and could be mass produced easily for wide application. The detection of force-induced displacements within compact MEMS (microelectromechanical system) devices can be used to measure electric field strength without significant field distortion.

This paper reports on a design and simulation study aiming at high-accuracy 2D micromachined thermal flow transducers. The scope is restricted to micromachined devices featuring a square-shaped membrane incorporating central symmetric thin-film devices. A microthermistor array probed spatial excess temperature variations while the main heat supply was alternatively established by optional heating resistors or by pronounced self-heating of the thermistor devices. Proper device designs enable leading edge transducer performance without sophisticated signal conditioning schemes. We found that a high azimuthal uniformity of flow magnitude transduction is tantamount to a precise azimuthal accuracy. The most advanced result gave a maximum azimuthal aberration of 0.17 and 1.7 degrees for 1 m/s and 10 m/s, respectively, while the corresponding magnitude uniformity amounted to 0.07% and 0.5%. Such excellent specifications exceed the need of ordinary meteorological applications by far. However, they are essential for, e.g., precise non-contact measurements of 2D relative movements of two quasi-planar surfaces via the related Couette flow in intermediate air gaps. The simulations predicted significantly better device characteristics than achieved by us in first experiments. However, this gap could be attributed to imperfect control of the flow velocity field by the measurement setup.

We investigate a differential sensor setup utilizing acoustic pressure waves, which aims at the determination of the acoustic viscosity (or the second coefficient of viscosity) of highly viscous liquids with shear viscosities in the range of several 100 mPa $\cdot $ s and above. The whole setup is modeled in PSPICE and investigated experimentally. The presented approach is suitable for further miniaturization and is based on a differential configuration, such that spurious effects associated with the parameter spread of the used lead-zirconate-titanate transducers ideally cancel out. We demonstrate the operation in time domain (avoiding spurious interference effects), present an according calibration procedure with a known reference liquid, and discuss the effects of diffraction. Finally, the experimental results demonstrate the applicability of the setup.

We present a novel transient measurement method to characterize effective values of the thermal conductivity, thermal diffusivity, and emissivity of a thin-film membrane implemented in a micromachined multiparameter wind sensor. Accurate values for these parameters are mandatory as they considerably influence the thermal heat shunt induced by the membrane, which is the main limiting factor for reliable sensor operation in gases with low thermal admittance and thus determines the ultimate device sensitivity. Compared with commonly used measurement techniques for these thermal thin-film parameters, our method does not require custom-built specimens, i.e., the results can directly be obtained from transient excess temperature measurements on the wind sensor device utilizing the embedded thin-film heater and thermistors. The presented method as such is universal and can easily be applied to other configurations of heating and temperature sensing elements placed on a circular thin-film membrane. In this contribution, we describe the theoretical background of this method, provide an efficient semianalytical model for the data evaluation including its validation by computer numerical simulations, and showcase sample measurements on multilayer Si x N y –SiO2 thin films.

This paper addresses the development of flow sensors optimized for heating, ventilating, and air conditioning systems. The sensors are based on the printed circuit board technology facilitating robust, flexible (in terms of layout), and cost-effective devices. Two approaches for measuring fluid quantities like flow velocity over the whole cross section are investigated in this context. The first one relies on hot-film transduction and stands out for its simplicity, but also shows some severe limitations, which can be circumvented by the second approach based on calorimetric transduction. Supported by extensive numerical simulations, several sensor embodiments were investigated and fabricated. After experimental characterization, measurement and simulation results were compared, which turned out to be in good agreement.

The performance of a recently introduced method to estimate the resonance parameters from complex spectral data and the error propagation for viscosity and density parameters of liquids are examined. The method is known to produce excellent results when used for piezoelectric and Lorentz force actuated sensors for single port or two-port devices. The method is also suited for very low quality factors (< 10) which extends the usable measurement range of many sensor concepts, especially for fluid sensing applications. Generally valid expressions for the measurement accuracy are stated and compared to measurement results obtained with a piezoelectric tuning fork and a Lorentz force actuated and inductively read out platelet sensor.

The response to extensional deformation of aqueous polymeric solutions depends strongly on the molecular weight and concentration of the solute. The molecular weight of hyaluronic acid in the synovial fluid is a critical parameter for its physiological condition. We propose a novel method for the characterization of these kinds of fluids using a fluidic two-phase system where a dispensed droplet is elongated by electrostatic forces from a voltage source of up to two kilovolts. This way a filament is formed comparable to laboratory capillary breakup extensional rheometers. High-speed imaging is used to investigate the rapid deformation process. Using a mathematical model for the dynamics of the filament evolution, the fluid parameters like the shear viscosity and elastic modulus are derived. The deformation rate can be controlled over a wide range by the magnitude and slope of the applied voltage.

We present a sensor setup based on acoustic pressure waves allowing the determination of the acoustic viscosity and sound velocity of liquids. Compared to previously presented planar transducer based approaches, the proposed setup does not require the correction of spurious diffraction effects. Beside the basic sensor setup, a 1D-model and experimental data obtained with a first prototype device are discussed.

A method for the fast calculation of vertical displacement fields, observed on thin piezoelectric layers of aluminium nitride (AlN) type deposited on n-doped silicon wafers, is shown. The basic findings are that the surface bending effect due to d 31 , d 32 is very strong but is largely compensated by d33 in the demonstrated case. The displacements are very sensitive on the piezoelectric properties and therefore the field computation must be very accurate in this respect. Furthermore, the anisotropy of the silicon wafer results in noticeable deviations when assuming a rotational symmetry for material properties. The demonstrated approach is based on an electromechanical Green's function (GF) and the assumption of a uniform charge distribution at the electrodes, which is shown to be acceptable when the thickness of the piezoelectric layer is much smaller than the lateral electrode dimensions. The infinite integral encountered in the rigorous field computations is approximated by a truncated series that can be calculated efficiently. The validity of the applied approximations is demonstrated by a comparison with results of a rigorous field calculation and with measurement results obtained with a laser Doppler vibrometer.

We present a two transducer setup suited for the determination of the second coefficient of viscosity, sometimes also termed acoustic viscosity. We present the basic sensor setup and according models in frequency and time domain allowing to extract the acoustic viscosity from the measurement data. We illustrate the approach using experimental data obtained with a demonstrator device. The setup, which has potential for further miniaturization, is operated in the time domain. Unwanted spurious effects and imperfections, such as diffraction, acoustic matching losses, and transducer losses, are discussed and according calibration and correction strategies are presented.

A smart system for flow measurement is presented, consisting of a micromachined thermal flow sensor combined with a smart front-end electronic interface. The flow sensor is based on a novel thermal transduction method, which combines the hot-film and calorimetric sensing principles. The sensor consists of four germanium thermistors embedded in a thin membrane and connected to form a Wheatstone bridge supplied with a constant DC current. In this configuration, both the bridge unbalance voltage and the voltage at the bridge supply terminals are functions of the flow offering high initial sensitivity, i.e., near zero flow and wide measurement range, respectively. The front-end interface is based on a CMOS relaxation oscillator circuit where the frequency and the duty cycle of a rectangular-wave output signal are related to the bridge unbalance voltage and the voltage at the bridge supply terminals, respectively. Furthermore, the amplitude of the output signal is a linear function of the operating temperature. In this way, a single output signal advantageously carries two pieces of information related to the flow velocity and provides an additional measurement of the sensor operating temperature, which enables the correction of the temperature dependence of the sensor readouts. The system has been experimentally characterized for the measurement of nitrogen gas flow velocity at different sensor temperatures. The initial sensitivities at room temperature result 13.7 kHz/(m/s) and 23.5%/(m/s), in agreement with FEM simulations, for frequency and duty cycle readouts, respectively, with an equivalent velocity resolution of about 0.5 and 1.3 cm/s.

In diaphragm-based micromachined calorimetric flow sensors, convective heat transfer through the test fluid competes with the spurious heat shunt induced by the thin-film diaphragm where heating and temperature sensing elements are embedded. Consequently, accurate knowledge of thermal conductivity, thermal diffusivity, and emissivity of the diaphragm is mandatory for design, simulation, optimization, and characterization of such devices. However, these parameters can differ considerably from those stated for bulk material and they typically depend on the production process. We developed a novel technique to extract the thermal thin-film properties directly from measurements carried out on calorimetric flow sensors. Here, the heat transfer frequency response from the heater to the spatially separated temperature sensors is measured and compared to a theoretically obtained relationship arising from an extensive two-dimensional analytical model. The model covers the heat generation by the resistive heater, the heat conduction within the diaphragm, the radiation loss at the diaphragm’s surface, and the heat sink caused by the supporting silicon frame. This contribution summarizes the analytical heat transfer analysis in the microstructure and its verification by a computer numerical model, the measurement setup, and the associated thermal parameter extraction procedure. Furthermore, we report on measurement results for the thermal conductivity, thermal diffusivity, and effective emissivity obtained from calorimetric flow sensor specimens featuring dielectric thin-film diaphragms made of plasma enhanced chemical vapor deposition silicon nitride.

Ultrasonic sensors can be used to determine physical fluid parameters like viscosity, density, and speed of sound. In this contribution, we present the concept for an integrated sensor utilizing pressure waves to sense the bulk of the fluid. Longitudinal viscosity and speed of sound can be determined using interference effects whereas the acoustic impedance of the liquid can be sensed if interference is suppressed by introducing a wedge reflector in the setup.

A novel sensor design comprising four high resolution germanium thermistors and one heating resistor offers three different operating modes. Measurements confirmed very high sensitivity for conventional calorimetric transduction (modes 1 and 2). In a mixed calorimetric-anemometric mode (mode 3), based on the self heating effect of the employed thermistors, the sensor combines extremely low power consumption with high flow sensitivity. Additionally, an unambiguous transduction characteristic over a wide flow range is available. As output quantities, we analyze the temperature difference of the thermistors, the bridge unbalanced voltage and the voltage across the supply terminals. The simulation results are in good agreement with corresponding measurement data confirming the basic assumptions and the modelling approach.

This paper reviews our recent work on vibrating sensors for the physical properties of fluids, particularly viscosity and density. Several device designs and the associated properties, specifically with respect to the sensed rheological domain and the onset of non-Newtonian behavior, are discussed.

A novel thermal flow sensor is presented featuring three spatially separated micromachined silicon-nitride membranes. A thin-film heater is embedded in the central one, while the others carry thermistors. This advanced sensor structure enables two different transduction modes. The electrocalorimetric mode exhibits high resolution and quick response at the expense of high power consumption. For slowly varying flows, the Time-of-Flight mode with low duty-cycles allows for power-saving operation but suffers from less sensitivity and slower response.

A novel thermal flow sensor transduction method is presented combining advantages of the calorimetric and the hot-film transduction principle. Four thin-film germanium thermistors are embedded in the silicon-nitride membrane acting as heat sources and as temperature sensors simultaneously. These devices operate in a Wheatstone bridge. The voltage across the bridge as well as the total dissipated power serves as output quantities. Two sensor configurations with different arrangement of the membrane thermistors were examined experimentally. Moreover, we investigated the influence of different layouts on the rise time, the sensitivity, and the usable flow range by means of two-dimensional finite element simulations.

A performance estimation method for resonant viscosity and density sensors is described. The ultimate sensor precision and the separability of density and viscosity from measured frequency spectra are estimated. The approach relies on using recently introduced models which are flexible enough to describe a large class of sensors. It is therefore not required to develop a specific sensor model and a parameter extraction method for each newly devised sensor. With the method introduced in this contribution, it is sufficient to adjust and validate a general model using at least three test liquids. Then, the error propagation and the error bounds for viscosity and density can be estimated and consequently the required signal-to-noise ratio (SNR) or the amount of required data points can be determined. This method enables direct comparison of different sensor setups as will be demonstrated for piezoelectric tuning fork sensors, electrodynamic platelet sensors and steel tuning forks.

In this article we investigate the spurious excitation of compressional waves by thickness-shear-mode resonators, which are commonly used for chemical sensing and viscosity sensing. In particular, we consider the excitation mechanism due to the nonuniform shear displacement present at the sensitive surface of the resonator. To illustrate the basic mechanism we analytically develop a general solution for a two-dimensional model describing the displacement and the pressure distribution in the liquid obtained in terms of Fourier integrals. We discuss these solutions and derive a useful approximation for the far field representing said compressional modes. We finally illustrate the results considering a practical example and associated numerical results.

This paper addresses the development of a flow sensor optimized for heating ventilating and air conditioning systems. The sensor is based on the printed circuit board technology facilitating robust, flexible (in design layout), and cost-effective devices. Two approaches for measuring fluid quantities like flow velocity and flow rate are investigated in this context. The first one relying on hot-film transduction shows severe limitations while the second one based on calorimetric transduction is able to overcome these drawbacks. Guided by extensive computer numerical simulations, two sensor embodiments were investigated, optimized, and fabricated. Afterwards, the sample devices are characterized by measurements and compared to simulation results which both turned out to be in good agreement.