Effect of thermal stresses on stability and frequency response of a capacitive microphone

Abstract

This article deals with effects of thermal stresses on stability and frequency response of a fully clamped circular microplate, which acts as the diaphragm of a capacitive MEMS microphone. Static and dynamic pull-in phenomena limit the stable regions of a capacitive MEMS microphone. The results show that the non-dimensional static pull-in voltage of the studied case is about 5.23 (38.6 V). On the other hand, according to the results, the non-dimensional dynamic pull-in of the diaphragm is about 4.74 (34.98 V), which is as low as 90.63% of the static pull-in threshold. Because of the thermal expansion coefficient, diaphragm temperature increment leads to compressive thermal stresses and conversely, decrement of the diaphragm temperature creates tensile thermal stresses. The effect of temperature on the pull-in parameters is given by a design-correcting factor. As results demonstrate, the deflection of the diaphragm subjected to a given electrostatic force can be controlled by means of the temperature changes. In the absence of electrostatic force, as the results show, although temperature changes do not create any deflection, but for a critical temperature increment the diaphragm stiffness vanishes and the buckling phenomenon takes place. Effects of the electrostatic force and the temperature variation on the frequency response of the microphone subjected to a sound pressure wave are investigated. As the results illustrate, increment of the electrostatic force or increment of the diaphragm temperature increases the output level and sensitivity of the microphone and decreases the fundamental frequency of the microphone, limiting the upper band of its bandwidth. It is obvious that decrement of the diaphragm temperature acts conversely. In addition, the results show that in the presence of the electrostatic force sensitivity of the output level of the diaphragm to the temperature change increases.