Dynamic behavior of micro-diaphragms and its characterized description

Abstract

Diaphragm structures with micron scale play a significant role in microtransducers and micro-nano devices, and the performance of these devices depends mainly on the dynamic behaviour of diaphragms. Micro-diaphragms are treated commonly as membranes and in some cases as plates or plates in tension (called TD plates for short), but they also show in many cases the behaviour of plates in tension and supported by air spring (called TDK plates for short). Therefore, it is necessary to perform systematic research on the dynamic behaviour of micro-diaphragms, and establish a characterized mathematical description. This paper focuses on the TDK plates since they possess universality, gives the corresponding basic equations, and then derives analytical solutions of TDK circular plates under clamped and simply supported boundary conditions. This paper also gives a 3D plot representation of characteristic curved surfaces, revealing the transition from the TDK and TD plate to the pure plate or pure membrane behaviour; and further uses the value φ to determine the property of diaphragms. Its two extreme cases, i.e. φ = 0 and φ = ∞ , correspond to pure plate or pure membrane, respectively. Thus, membrane, plate and TD plate can be treated as special cases of TDK plate. In addition, this paper reveals that the presence of air-spring not only enhances the restoring force of diaphragm such that increases its natural frequencies, but also results in the resonance of a dynamic system consisting of diaphragm and air-spring. These analytical and computational results are significant for the understanding of the operation mechanism of capacitive microtransducers and their optimized design. micro-diaphragm, membrane and plate, TD plate and TDK plate, dynamic behaviour, characterized description Diaphragm structures of micron scale play a significant role in microtransducers and micro-nano devices, as they can be used as elastic sensing elements of capacitive-type pressure, acceleration, sound and ultrasound, chemical and biological microtransducers. Micro-diaphragm structures of these devices are fabricated by using either surface micromachining sacrificial layer process or bulk micromachining plus bounding technology. Circular diaphragms (with radius of about 10-100 microns and thickness of about 0.3-10 microns, and sometimes coated also by a layer of nano-film) are commonly used, and their circumference is fixed on silicon backplate through side wall, such that there is a thin layer of airgap (with thickness of about 0.2-1 microns) between the diaphragm and backplate. The airgap is filled by air, or vacuum-sealed. Therefore, this kind of structures is also commonly called the micro-airgap structure, which can be viewed as a "sandwich" structure consisting of the diaphragm, airgap and backplate. The diaphragm and backplate are coated by metal electrode respectively, so that such a structure becomes a capacitive-type microtransducer. Since there is a micro-scale separation a normal voltage applied across these two electrodes then can ...

Effects of Residual Stress on the Hydro-Elastic Vibration of Circular Diaphragm

“…Moreover, the residual stress is an important influencing factor for the resonant frequency and sensitivity of the biosensors. Several researchers investigated the effects of residual stress on the diaphragm's resonant frequency, either theoretically or by finite element analysis [10][11][12]. They concluded that residual stress stiffens the diaphragm and increases its resonant frequency.…”