Minhang Bao

Energy transfer model for squeeze-film air damping in low vacuum

High quality factors are essential for vibratory microsensors. Therefore, the vibrating structure of the sensors is often encapsulated in a housing where the air is evacuated for reduced air damping. However, the vacuum is usually low and the quality factor is still mainly determined by the energy losses to the surrounding air molecules. Air damping in low vacuum is usually estimated using the free molecular model proposed by Christian (Christian R 1966 Vacuum 16 175–8). The major drawback of the model is that the effect of the nearby objects (e.g. the electrodes for electrostatic driving) and the dimensions of the plate cannot be considered. Therefore, the damping effect is often significantly underestimated for real structures. This paper proposes a new model for air damping of microstructures in low vacuum. In this model, the damping effect is calculated by using an energy transfer mechanism instead of the momentum transfer mechanism in Christians model. For an isolated oscillating plate, the calculated quality factor by the model is the same as that by Christians model. However, for an oscillating plate with a neighboring object, the damping effect by the new model is related to the dimensions of the vibrating plate and the gap between the plate and the nearby object. The quality factors calculated agree with experimental data better than with Christians model by about an order of magnitude.

Future of microelectromechanical systems (MEMS)

Abstract The development of microelectromechanical systems (MEMS) based on micromachining and microelectronics technologies has been significant for almost a decade. However, it is unrealistic to consider micromachining technology as a micro version of conventional machining technology. As a matter of fact, micromachining technology stemmed from the planar technology of silicon and is basically a two-dimensional processing technology. On the other hand, it is obvious that a micromachine cannot compare with a conventional machine in strength and power. For the successful development of MEMS in the future, a simple rule is suggested by the experience gained in the past few years: try to avoid as much as possible mechanical coupling with the outside world while trying hard to improve the MEMS technology to enhance the mechanical power of the devices. In addition to that, the strategy proven to be correct for the development of solid-state sensors also applies: MEMS devices should mainly be developed for new applications with a vast market. Their substitution for traditional applications should not be considered as a main strategy of development. Based on these arguments, the future development of MEMS devices and technologies is further discussed in the paper.

Squeeze-film air damping of thick hole-plate

Abstract The damping effect of air flow in holes is considered based on Poiseuille equation and the damping effect of lateral flow is considered by conventional Reynolds’ equation for infinite thick hole-plate. The expression for damping ratio is obtained and the conditions for minimum damping ratio can be found. A modified Reynolds’ equation is established for thick hole-plate with finite dimensions. The equation is a good approximation for hole-plates in typical MEMS devices. As it is also effective for non-hole-plate as well, it is more general than the conventional Reynolds’ equation. The distribution of damping pressure under a hole-plate can be found by solving the modified Reynolds’ equation with appropriate boundary conditions. As an example, the damping pressure of squeeze-film air damping of a long rectangular hole-plate is considered. Analytical expressions for the damping pressure, damping force and damping ratio are found.

A piezoresistive accelerometer with a novel vertical beam structure

Abstract A micromachined piezoresistive accelerometer sensitive to an acceleration component in the chip plane and vertical to the beam direction has been developed. To sense a lateral acceleration, a beam with a cross section vertical to the (001) wafer surface has been developed by anisotropic etching in aqueous KOH. The vertical beam is along the 〈100〉 direction and has a high aspect ratio. Two n-type piezoresistors instead of p-type ones are positioned on the top edge (wafer top surface) of the beam with one resistor on each side of the neutral line of the beam. The top edge of the beam is widened slightly to make enough room to accommodate the piezoresistors and their interconnections so that, in fact, the beam has a T-shaped cross section. The sensitivity of the device fabricated is about 0.5 mV g−1 5 V1 and the resonance frequency is about 1.2 kHz. As the sensitivity is comparable to and the fabrication process is compatible with the conventional piezoresistive accelerometers for normal acceleration, this design leads the way to developing a monolithic piezoresistive multi-axis accelerometer.

Effects of electrostatic forces generated by the driving signal on capacitive sensing devices

Abstract In measuring the capacitance of a variable mechanical capacitor used in a capacitive mechanical sensor, an electrical driving signal is usually needed. The electrostatic forces caused by the driving signal on the mechanical capacitor may interfere with the measurement and the normal operation of the devices significantly. In this paper, quantitative analyses on the effects of driving signal are made for single-sided driving, double-sided driving and double-sided driving with voltage feedback (i.e., force-balanced measurement schemes). The effects caused by the driving signal are found to be: (1) the zero offset of the sensors for single-sided driving signal, (2) the change of the measurement sensitivity, and (3) the reduction of the critical measurand signal level causing the pull-in effect that hampers the normal operation of the device. The levels of critical measurand signal for specific driving signal levels are found quantitatively. Based on the analyses, the conclusions are: (1) the level of driving signal can be selected by the compromise among the requirements on the sensitivity, the accuracy and the reliability of the sensors devices for a specific configuration, (2) the side effects of the driving signal can be minimized by using the testing scheme of double driving with voltage feedback.

Maskless etching of three-dimensional silicon structures in KOH

Abstract A novel micromechanical technique using maskless etching of three-dimensional anisotropically etched silicon structures is investigated. The structures investigated are convex prismatic edges included by {100} and {111} planes and the convex corners of a rectangular m both formed by a previous masked anisotropic etching in KOH. Experimental results verify that the cutting planes developed at the mesa edges are {311} planes that make the contour change obviously. Analytical relations have been found to predict the evolution of the contour and the undercutting rate at the convex edges and corners based on the fact that the cutting planes at the convex edge are {311} planes while the cutting planes at the convex corner are {411}. The relations have been confirmed by experiments and the etching rate of {311} p found for various KOH concentrations. As an example of application, a symmetric cantilever beam-mass structure with beams horizontally located at the central plane of the wafer has been fabricated for a differential capacitive accelerometer with minimized cross-axis sensitivity.

Squeeze-film air damping of a torsion mirror at a finite tilting angle

This paper proposes an analytical model for calculating the squeeze-film air damping of a rectangular torsion mirror at finite normalized tilting angles. The general Reynolds equation is first modified to a nonlinear equation for the condition. Based on the nonlinear equation, the damping pressure, the damping torque and the coefficient of the damping torque are derived as functions of the tilting angle and the aspect ratio of the mirror plate. To show the relation clearly and for the ease of application, the coefficient of the damping torque is given in curves in addition to complicated analytical expressions. The results show that the damping torque coefficient is a highly nonlinear function of the tilting angle and basically a linear function of the aspect ratio of the mirror. The coupling between the two factors is appreciable but not very strong. When the tilting angle is reduced to zero, the result of this paper agrees perfectly well with those of previous papers, which have been verified by experiments and/or numerical calculation. The analytical results are effective for normalized tilting angles up to 0.7.

Over-range capacity of a piezoresistive microaccelerometer

Over-range capacity is one of the most important parameters for an accelerometer. Over-range protection has been provided for commercially available micromechanical piezoresistive accelerometers to make them practical for applications. Described in this paper is an extensive analysis on the over-range protection capability for a cantilever beam accelerometer. Also analysed in the paper is the acceleration of a laboratory testing system using a drop hammer scheme for shock accelerations. Based on the theoretical analyses and experimental data, the system has been calibrated and used to provide shock accelerations for experimental testing in the laboratory.

Stress concentration structure with front beam for pressure sensor

Abstract The beam-diaphragm structure is a new type of stress concentration structure in which the stress concentration areas are separated for positive and negative stresses. Geometric design considerations for beam-diaphragm structures have been investigated theoretically and experimentally. According to the results of finite-element analysis and experimental measurements, geometric design rules for maximum sensitivity are given. Experimental results of the dependence of the non-linearity on the beam width, W2, are also presented.

Two-dimensional excitation operation mode and phase detection scheme for vibratory gyroscopes

We propose a novel operation mode of two-dimensional excitation and phase detection for vibratory gyroscopes. It has been proven that the angular rate output is both amplitude-modulated and phase-modulated when the structure is driven into vibration in both the x- and y-directions. The output can be converted into a narrow-band phase-modulated signal by an amplitude limiter. Therefore, the angular rate signal of a vibratory gyroscope can be measured by detecting the phase change of the output signal. This operation scheme features high accuracy, high immunity against interference and a low-temperature coefficient. A bulk micromachined gyroscope with piezoresistive sensing elements is tested in the two-dimensional excitation mode with the phase detection scheme and the experimental results are presented.