Proceedings of the 2010 5th IEEE International Conference on Nano/Micro Engineered and Molecular Systems January 20-23, Xiamen, China
Application of Parallel Capacitor for Force Transferring in Resonant Micro Accelerometer Bai-Lin Li and Li-Li Chen School of Mechanical Engineering Southwest Jiaotong University Chengdu, People’s Republic of China e-mail:
[email protected]
Wu Zhou, Wei Su and Xiao-Ping He* Instute of Electronic Engineering China Academy of Engineering Physics Mianyang, People’s Republic of China e-mail:
[email protected]
Abstract —The characteristics of force transferring in parallel capacitor is presented, the external force applied on one plate can be transferred to another with a reverse direction and changed magnitude by coupling effect of mechanical domain and electric domain. The main principle of such behaviors is analyzed, and the relation of input and output is calculated by analytic method, it is indicated that the changed quantity is dependent on the ratio of electrostatic stiffness and mechanical stiffness. The application of this behavior in resonant micro accelerometer is then presented, the parallel capacitor is used as a leverage to transfer the external inertial force into the axial force of librating beam to change the natural frequency of resonator, so the acceleration applied can be measured by measuring the shift of frequency, finally, the structure of sensor is fabricated by Deep Reaction Ion Etching(DRIE) and silicon bonding technologies, and the test indicates the sensitivity of accelerometer is related to different voltage applied on capacitor.
A resonant micro accelerometer is presented in this paper is based on results from analyzing the characteristics of parallel capacitors which have the capacity to change the magnitude and direction of a force under a certain condition. Parallel plate capacitive sensing and driving are used widely in micro electro mechanical systems dues to its simple structure and easy integration to circuit, such as capacitive accelerometers [7], pressure sensors[8], actuators [9], electrostatic elastic hinge[10], electrostatic motor [11], and MEMS switch [12]. The studies before in parallel capacitors mainly concentrated on its pull-in behavior, including design consideration [13], calculation of pull-in voltage [14], work range extending [15] and nonlinear behavior [16] et al., this is aiming to another behavior in capacitor induced by electromechanical coupling effect, which can realize a transportation of external force. The process of the transfer of external force is derived by analytical method, the force balance equation is used to analyze the relationship between input and output, and the changed quantity of magnitude is presented, which indicates the capacitor has the same function as mechanical leverage for force transferring.
Keywords —MEMS, Accelerometer, Capacitor, Sensor
I.
INTRODUCTION
Resonant micro accelerometer, as an important inertial sensor in Micro-Electro-Mechanical Systems (MEMS) field, has been studied in many institutes and colleges because of its quasi-digital output signal which has a good resistance to disturbance and can be dealt in a simpler circuit. The most resonant accelerometers, however, go with structural stress and influenced by residual stress deeply, such as the one presented by A. A. Seshia et al. using surface micromachining [1] and the one created by C. Burrer et al. in bulk micromachining technology [2], besides, the sensitivity of this device is limited under current micro fabrication and its temperature dependence has a significant influence on its performance [3].
II.
The capacitor structure can be simplified as Figure 1, if the external force applied on the upper plate, the gap of capacitor changes followed by the electrostatic force shift, which acts on the lower plate and conveyed to spring, and then, the forcetransferring occurs.
ks
Many studies, therefore, focus on cultivating a new sensing structure or principle to improving its sensitivity and stress dependence, Y. Omura et al. [4] developed a new resonant micro accelerometer base on the change of librating beam’s rigidity, S. X. P. Su et al. [5], in 2005, used a two-stage leverage to improve the sensitivity of accelerometer, which could reach to 160Hz/g, H. C. Kim et al. [6] combined resonance theory and electrostatic stiffness to cultivate a new accelerometer whose frequency output is related to change of electrostatic stiffness instead of mechanical stiffness, reducing deeply the dependence of residual stress and processing error.
m
O
S
x
d
d0
km
Figure 1. Diagram of force-transferring model
*Corresponding author: Xiao-Ping He, Tel: +86 816 248 4595, Fax: +86 816 248 7594, E-mail:
[email protected].
978-1-4244-6545-3/10/$26.00 ©2010 IEEE
ANALYSIS AND THEORY
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The starting material is the silicon and glass. Firstly, a 28 μm dense boron layer is formed by diffusion under dry air box, as shown in (a) in Fig. 2, secondly, a hinge in (b) is etched for bonding structure layer and substrate, and then the deep etching technology is selected to fabricate the whole structure layer, as in (c); and the same time, the electrode of accelerometer is fabricated by three main steps, as shown in (d) ~ (f) in Fig.2, and the electrode layer constructed by Au under sputtering process. After structure layer and electrode layer are fabricated, bonding technology used to connect both layers together as (g), and then self-stop etching adopted to delete the silicon without diffusing boron and release the whole structure as in (h).
The force balance equation under external force can be expressed as
ΔF Fa = f ( ΔFm ) = ks (1 − δ )d − m kr
(1)
where Fm is the change value of nether spring, kr is the resultant stiffness of two mechanical springs in series, d is the initial gap of capacitor, ks is the stiffness of the upper spring, is the coupling factor, which can be expressed as
δ ≈ 1−
km d 2 xm ΔF d 2 = 1− m 2 2 ε SU ε SU
(2)
This type of process has advantage of less photoresists, only three times of lithography are needed in whole procedure of fabrication, one is for forming the bonding platform, and one is for fabricating the structure, and last is for fabricating the Au electrodes on glass. .
where S is the total effective area of capacitor, U is the DC voltage applied, is the permittivity, km is the stiffness of the lower spring. The change value of mechanical force in spring related to, but no longer equal to, the change of external force, and its relation depends on the parameters set in systems. If the notation of coefficient between mechanical force change and external force is introduced as
α=
ks d 3 km + k s − km ε SU 2
(3)
The conclusion is the extent of amplification is determined by the coefficient , if >1, the external force added to mechanical spring is shrunken, if =1, no change in value, if
