The fabrication of microelectromechanical systems (MEMS) devices comprises many steps, each of which adds to the tolerance, resulting in device performances that may fall outside the defined limits in the design process. Hence, it is important to know local thin film properties most accurately, directly affecting the performance of the MEMS device. Furthermore, the capability of monitoring and mapping the thin film thickness and stress across a wafer enables device statistics and the strengthening of scientific statements. Within this study, we used standard MEMS structures consisting of a cantilever and a step profile to perform automated and contactless characterization of the local thin film thickness and stress across six 4-inch (100 mm) wafers. For this purpose, we constructed a measurement setup combining white light interferometry (WLI) to measure the static deflection of the cantilevered beams and plates and the thickness of the thin film through a step profile etched into the thin film. Even more, an XYZ-stage positions hundreds of devices below the objective lens of the WLI. This leads to precise maps of the local thin film thickness and to the extraction of a mean stress and a gradient stress from the static deflection of slender beams. The beams are oriented parallel and perpendicular to the wafer flat so that the measurement of orientation-dependent stress values is possible.

Accurately modeling viscous fluid-structure interaction in MEMS remains a significant challenge in fluidic sensing and BioMEMS. We present a numerical method that couples the Kirchhoff plate equation with an efficient numerical integration of the unsteady Stokeslet, enabling fast and accurate simulation of MEMS resonators immersed in viscous fluids. The framework supports both 2D and full 3D Stokes flow formulations, incorporating GPU and PETSc acceleration for large-scale problems. Experimental validation using piezoelectrically actuated resonators demonstrates excellent agreement with the 3D model at frequencies below 500 kHz, revealing the frequency- and mode-dependent limits of conventional viscous-flow approximations at higher frequencies.

Several intrinsic and extrinsic contributing loss mechanisms make the estimation of the total Q-factor Q of MEMS resonators challenging, as it is influenced by many parameters. Experimentally, however, only the total Q-factor of a vibrational mode can be measured; so for the study of environmental conditions, pressure and temperature sweeps are typically performed to provide knowledge about fluidic and thermo-elastic dissipation. However, the contributing amounts of intrinsic damping mechanisms cannot be split into their individual components. In this study, we explore the dynamics of many non-slender MEMS resonators while varying the width. We call this technique design-dependent Q-factor spectroscopy (DDQS). The use of hundreds of devices with several out-of-plane resonance modes within DDQS allows the separation of the total Q-factor into the different dissipation mechanisms in thin films and MEMS resonators. Experimental results discussed alongside theoretical predictions indicate how the variation of a geometrical parameter of the resonator allows access to frequency regions with different dominant dissipation mechanisms. Furthermore, we evaluate the impact of surface-related losses and fluidic damping, showing a two-fold improvement in Q by removing the native grown silicon dioxide layer under high vacuum conditions. Our results highlight the advantages of optimizing the design of MEMS resonators within DDQS to understand the contributions to energy dissipation and lead to a new MEMS design approach.

This paper reports on the impact of grain size on the quality factor of poly-crystalline-diamond (PCD) MEMS resonators. For this purpose, the grain size of each PCD thin film is tuned from tens of nm to several mu m via the methane flow rate during the chemical vapor deposition process on silicon substrates. In addition, a PCD stack, where the growth regime is changed during the deposition run, is studied. From these thin films purely mechanical plate-type resonators were fabricated and photo thermally actuated. The resonance characteristics are studied with Laser-Doppler vibrometry. Measurements are performed in a regime where material losses are the dominant dissipation mechanism and others like gas damping and thermo-elastic damping can be neglected. Furthermore, the resonator devices are assumed to have similar anchor losses across all thin films. It is shown, that quality factors of PCD MEMS-resonators can be increased by more than one order of magnitude when increasing the grain size in the investigated range.

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We present a semi-numerical method for determining the dynamics of non-slender structures in viscous fluids. An investigation of the quality factor ( Q-factor) of the vibrational modes of non-slender structures in gases and liquids reveals that, in gases, the conventional Euler-Bernoulli (EB) modes exhibit the lowest Q-factors, while non-EB modes exhibit the highest Q-factors. In liquids, the opposite occurs. EB modes exhibit the highest Q-factors, and non-EB modes the lowest. This opposite Q-factor pattern in gases and liquids is the modal quality factor inversion. We expect the modal quality factor inversion of non-slender resonator geometries to enable novel MEMS fluid sensors.

Anchor losses are one of the dominant dissipation mechanisms for MEMS resonators in vacuum. For slender beam resonators, the underlying mechanism is modeled by approximating the anchor region as a single point source of elastic waves. Here, we discuss that this approximation is not valid for plate resonators where the anchor region effectively becomes a line distribution of point sources. We use finite element simulations to show that the flux of mechanical energy in the substrate strongly depends on the mode in which the resonators vibrates. We utilize this effect to modulate the anchor loss quality factor in simulations and experiments over two orders of magnitude by changing the resonator’s width.

We present a semi-numerical method for solving the dynamics of microplates in viscous fluids. The method is based on the Kirchhoff plate equation with a hydrodynamic force deduced from the Stokes equations. The equation of motion is solved with the Galerkin mode decomposition (GMD) using the vacuum vibrational modes of cantilevered microplates as the basis functions. We investigate the Q-factor of the vibrational modes of microplate-resonators in gases and liquids. In gases, the Euler–Bernoulli (EB) modes (modes with nodal lines only along the plate’s width) exhibit the lowest Q-factors, while non-EB modes exhibit the highest Q-factors. In liquids, the opposite is found. EB modes exhibit the highest Q-factors, and non-EB modes lower Q-factors. We name this opposite Q-factor pattern in gases and liquids the gas-liquid-Q-inversion (GL-Q-inversion). Experiments in water and air showed a Q-factor agreement with the GL-Q-inversion, and differences in Q-factor between simulation and experiments were below 25%. Further numerical analysis reveals the physical mechanism underlying the GL-Q-inversion in terms of the system’s stored and dissipated energy. The results and methods shown here will pave the way to efficiently exploit the two-dimensional vibrational modes of microplate-resonators to improve their performance in gaseous and liquid environments.

In this paper, we present a semi-numerical method for determining the dynamics of micro-resonators with finite width immersed in incompressible viscous fluids. The micro-resonator is modeled using Kirchhoff plate theory, and the hydrodynamic force acting on the plate is determined from a boundary integral formulation of the Stokes equations. The resulting equation of motion is solved with a continuous/discontinuous finite element method in which an interior penalty term imposes C-1-continuity to the plate's deflection. Numerical investigations show the method to be convergent with an exponent of the convergence rate equals 2. Examples demonstrate that the proposed method overcomes the limitations of existing semi-analytic methods, only applicable to beam geometries, considering arbitrary plate modes in the structure's dynamics and their effects on the fluid flow. Different resonator geometries are investigated for which displacement spectrum, mode shapes, and quality factors are not determinable with existent semi-analytic methods. Moreover, we find excellent agreement between simulated and experimental data, which has not been achieved even with purely numerical methods. The present method will allow the understanding of high quality factors of wide micro-resonators in viscous fluids and facilitate new applications in liquid atomic force microscopy and gas sensing in ambient and low-pressure conditions. (C) 2021 The Authors. Published by Elsevier Ltd.

We numerically investigate the fluid–structure interaction of thin elastic cantilever micro-structures in viscous fluids. The Kirchhoff plate equation describes the dynamics of the structure, and a boundary integral formulation represents the fluid flow. We show how the displacement spectrum of the structures changes as the geometry is altered from a narrow beam to a wide plate in a liquid. For narrow beams, the displacement spectrum exhibits only a few resonance frequencies, which correspond to the vibrational modes described by the Euler–Bernoulli equation (Euler–Bernoulli modes). The spectrum of wide plates exhibits several additional resonance frequencies associated with the plate’s torsional and higher-order vibrational modes. Wide plates in Euler–Bernoulli modes exhibit higher damping coefficients, but due to an increased added-mass effect, also higher Q-factors than slender beams. An investigation into the fluid flow reveals that for the Euler–Bernoulli modes of wider plates, the fluid flow and energy dissipation near the plate’s edges increase, resulting in increased damping coefficients. Concomitantly, a region of minimal viscous dissipation near the plate’s center appears for wider plates, resulting in an increased added-mass effect. Higher-order modes of wider plates exhibit lower Q-factor than the Euler–Bernoulli modes due to a decreased fluid flow at the plate’s edges caused by the appearance of circulation zones on both sides of the plate. This decreased flow at the edge reduces the damping and the added-mass effect, yielding lower Q-factors. We anticipate that the results presented here will play a vital role in conceiving novel MEMS resonators for operation in viscous fluids.

Understanding of the fluid-structure interaction between a MEMS resonator and a surrounding fluid is key for understanding and predicting the dynamics of MEMS resonators in fluids. Here, we present a numerical method for modelling the fluid-structure interaction between a viscous fluid and vibrational eigenmodes of a plate-like MEMS resonator. The dynamics of the MEMS resonator is determined using a finite element method while the fluid flow is obtained from a boundary integral formulation. With this method we compute the spectral response of MEMS plate resonators in fluids.

The prediction of quality factors of MEMS plate resonators immersed in fluids requires new methods since most existing methods are based on Euler-Bernoulli beam theory. Here, we present a novel numerical method for computing the spectral response of MEMS plate resonators in fluids. We model the plate as a thin Kirchhoff plate and use a non-conformal finite element method to solve the equation of motion which includes the fluid-structure interaction with a viscous fluid. We investigate the convergence behavior of the proposed method and present numerical examples for MEMS beam and plate resonators in water.

Totally implantable hearing devices have been proposed as a solution to mitigate limitations associated with external elements in traditional hearing devices. However, requirements for an implantable sensor are difficult to be achieved concurrently, and therefore, no sensor developed fulfills them entirely. In this paper, we investigate how various geometries of MEMS piezoelectric accelerometers, optimized via different optimization techniques, behave in terms of the equivalent input noise (EIN) in sound pressure level (SPL) when coupled to the middle ear ossicular chain. An alternative optimization goal based on the minimization of the EIN is proposed in contrast to the traditional charge sensitivity maximization, and this alteration rendered near 20-dB improvement in EIN in low frequencies. Prototypes are fabricated through a multi-user batch process featuring a 500-nm aluminum nitride piezoelectric layer and experimentally characterized for the validation of the finite-element analysis and analytic modeling of spectral noise. Despite limitations imposed by the current batch fabrication process, we are able to design a highly competitive implantable sensor in the form of a 2 x 2 mm(2) footprint cantilever accelerometer, which should be able to detect 60-dB SPL between 250 Hz and 8 kHz. These promising results establish piezoelectric sensors as a viable alternative for totally implantable hearing devices and put an implantable sensor, which fulfills all requirements concurrently within our grasp.

Totally implantable hearing devices have been proposed as a solution to mitigate the constraints related to the presence of external elements in traditional hearing devices. This work reports on a novel approach for the development of a MEMS piezoelectric accelerometer as an implantable sensor for hearing devices. Traditionally these sensors are designed for maximum sensitivity; however, the primary bottleneck for this type of transducer is the internal noise level. Two differential evolution optimization routines were developed. The first used sensitivity maximization whereas the second seeks minimization of the equivalent input noise (EIN). Both methods were applied to different designs of Lead Zirconate Titanate (PZT) MEMS piezoelectric accelerometer in the frequency range of 250 Hz to 8 kHz with layer thickness varying from 0.1 μm to 1 μm. In the latter approach, the sensor's acceleration noise was estimated analytically, considering capacitance and charge response acquired through finite element modeling (FEM) previously validated. Acceleration noise was converted to EIN, in sound pressure level (SPL), through an FE-model of the middle ear considering the sensor coupled at the umbo. Preliminary results indicate that using EIN as optimization goal, opposed to sensitivity, leads to a higher performance over a broader bandwidth.

Most commercially available cochlear implants and hearing aids use microphones as sensors for capturing the external sound field. These microphones are in general located in an external element, which is also responsible for processing the sound signal. However, the presence of the external element is the cause of several problems such as discomfort, impossibility of being used during physical activities and sleeping, and social stigma. These limitations have driven studies with the goal of developing totally implantable hearing devices, and the design of an implantable sensor has been one of the main challenges to be overcome. Different designs of implantable sensors can be found in the literature and in some commercial implantable hearing aids, including different transduction mechanisms (capacitive, piezoelectric, electromagnetic, etc), configurations microphones, accelerometers, force sensor, etc) and locations (subcutaneous or middle ear). In this work, a detailed technical review of such designs is presented and a general classification is proposed. The technical characteristics of each sensors are presented and discussed in view of the main requirements for an implantable sensor for hearing devices, including sensitivity, internal noise, frequency bandwidth and energy consumption. The feasibility of implantation of each sensor is also evaluated and compared.

The presence of external elements is a major limitation of current hearing aids and cochlear implants, as they lead to discomfort and inconvenience. Totally implantable hearing devices have been proposed as a solution to mitigate these constraints, which has led to challenges in designing implantable sensors. This work presents a feasibility analysis of a MEMS piezoelectric accelerometer coupled to the ossicular chain as an alternative sensor. The main requirements of the sensor include small size, low internal noise, low power consumption, and large bandwidth. Different designs of MEMS piezoelectric accelerometers were modeled using Finite Element (FE) method, as well as optimized for high net charge sensitivity. The best design, a 2 × 2 mm2 annular configuration with a 500 nm thick Aluminum Nitride (AlN) layer was selected for fabrication. The prototype was characterized, and its charge sensitivity and spectral acceleration noise were found to be with good agreement to the FE model predictions. Weak coupling between a middle ear FE model and the prototype was considered, resulting in equivalent input noise (EIN) lower than 60 dB sound pressure level between 600 Hz and 10 kHz. These results are an encouraging proof of concept for the development of MEMS piezoelectric accelerometers as implantable sensors for hearing devices.

Dissertacao (mestrado) Universidade Federal de Santa Catarina, Centro Tecnologico, Programa de Pos-Graduacao em Engenharia Mecânica, Florianopolis, 2017.

The presence of an external element is still a major limitation of current hearing devices such as hearing aids and cochlear implants. The main problems associated with the external element are discomfort, inconvenience and social stigma, which can be overcome by totally implantable hearing devices. A fundamental requirement of such systems is a totally implantable sensor. In this sense, an accelerometer coupled to the ossicular chain of the middle ear may be used as an alternative sensor to the traditional external microphone. Although micro machined accelerometers are used in a variety of applications, there are no commercially available accelerometers that fulfill the requirements. This paper presents a review on implantable sensors for hearing devices, and requirements for this transducers are summarized. The Finite Element Method (FEM) is used to verify the feasibility of an implantable piezoelectric accelerometer. Design was made considering limitations and characteristics of microelectromechanical systems (MEMS) fabrication techniques. Different designs for the accelerometer are considered, and the results for the sensor response at different points of the ossicular chain are presented and analyzed in view of the defined requirements.