Q-factor and frequency shift of resonating silicon diaphragms in air

Abstract

The dependence of the relative frequency shift and the Q-factor of the first two modes of vibration of square silicon diaphragms on the diaphragm geometry and the air pressure is investigated. The experimental results are compared with the theory, which is based on Lamb's theory for circular diaphragms. It assumes acoustic radiation to be the determining mechanism for the energy loss of the diaphragm. The experimental results for both the frequency shift and the Q-factor as a function of the pressure deviate from the theory. A possible explanation for this deviation is the assumption that viscous damping plays an important role. It is found that the vibrating diaphragm is able to put the whole wafer into vibration, which causes several interfering effects. This phenomenon limits the applicability of vibrating diaphragms in resonant sensors.

Exploring the resonant vibration of thin plates: Reconstruction of Chladni patterns and determination of resonant wave numbers

“…The K n spectrum is conspicuously different from the distribution of eigenvalues k n 1 ;n 2 . This result indicates that the effect of resonant frequency shifts [21][22][23] is extremely significant in the resonant vibration of thin plates for the Chladni experiment under the continuous excitation.…”

“…Substituting Eqs. (21) and (22) into Eqs. (9) and (10) and using c ¼ 0:02a À1 , the power transferred efficiency gðr 0 ;kÞ and the entropy distribution exp½Sðr 0 ;kÞ for the equilateral triangle plate can be calculated with the driving wave number as a variable.…”

“…It has been experimentally observed [18][19][20] that the strong coupling between the oscillation system and the driving source may cause the resonant frequencies to be significantly different from the eigenfrequencies, i.e., the so-called resonant frequency shifts. [21][22][23] Due to the shifts of resonant frequencies, the resonant mode is generally formed by a superposition of numerous degenerate eigenmodes or nearly degenerate eigenmodes, i.e., the so-called mode-mixing effect. [24][25][26][27] So far the principle for determining resonant frequencies has not been disclosed.…”

Dynamic Mechanical Simulation of Miniature Silicon Membrane during Air Blast for Pressure Measurement

“…Moreover, assuming that the acoustic damping is predominant [3], the quality factor Q of the membrane is inversely related to the equivalent pressure Pe applied on both sides of the membrane as shown in Equation (2).…”

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

“…Amabili [20] studied the free vibrations of circular plates resting on a sloshing liquid free surface; the liquid domain was limited by a rigid cylindrical surface and a rigid flat bottom. When the biosensors are used in liquid media, the effect of the fluid on the diaphragm must be investigated [21,22]. However, the residual stress was neglected in these studies.…”