Optimization of MEMS capacitive accelerometer
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A micro machined accelerometer based on an area variation capacitive sensing for more applications was developed, in this case, we will describe and improve in this work the efficacity as well as the sensitivity of a capacitive accelerometer based on an area of variation capacitive sensing considered as a micro system electro mechanical (MEMS) available and realizable. However, the simulation was performed using MATLAB as software used in complicated situation with an optimization of the several parameters of accelerometer and a single direction, which is consisted with mobile fingers and fixed fingers, as two springs which ensures the damping of the system. The general concept, main design considerations and performance of the resulted accelerometer was optimized and elaborated in order to obtain a good improvement.
KeywordsPolysilicon Beam Width Proof Mass Micro Electro Mechanical System Movable Plate
The micro electro mechanical system (MEMS) technology device design optimization is becoming an interesting and important research issue. However, various efforts on MEMS device design optimization and automation have been made as modeling and simulation of a capacitive micro machined accelerometer.
Compatibility with conventional CMOS provides advantages high yield and fast prototyping that should be adjustable and transferable to any CMOS foundry.
In this work, we present the difference and the relationship between the design optimization of a capacitance folded beam MEMS comb accelerometer device and the device sensitivity such as beam width, beam length, mass width. Based on the analysis, an optimized design of the MEMS comb capacitive accelerometer device is suggested.
2 CMOS micromachining process
After the sidewall of the microstructure is precisely defined, an isotropic SF6/O2 (RIE) is performed to etch away the bulk silicon and release the composite structure as shown in Fig. 1c (Zhang et al. 1999). Layout in the metal layers is designed to form beams, plates, and electrostatic comb fingers. Material property values for the composite structures include a density of 2,300 kg/m3 and a Young’s modulus of 62 GPa.
Electrically isolated multi-layer conductors can be routed in the composite structures, enabling more design options (compared to homogeneous conductor structures). For example, electrically decoupled sensing and actuating comb fingers may be built on the same structure and full-bridge capacitive differential and common centroid comb-finger designs can be readily implemented (Luo et al. 2002).
C para is the parasitic capacitance and C 1, C 2, C 3, C 4 represent the differential capacities between the movable fingers and the sensing fingers.
The most commonly used capacitive sense interface is a single-ended half-bridge interface shown in Fig. 3a. Change in capacitance can be measured by driving the ends of the bridge and taking the central node as the output. Fully differential interfaces are always preferred to their single-ended counterparts because of better power supply rejection and first-order cancellation of substrate coupling. Usually, differential capacitive sense interfaces have been implemented with polysilicon surface micromachining processes. In some designs displacement is sensed with a capacitive half-bridge by modulating the central node (the proof mass) and connecting the two fixed ends to a differential position sense interface as shown in Fig. 3b. Since there is only one modulation node instead of two differential ones, a significant common-mode signal will appear at the input nodes of the differential interface.
The difference between two parasitic capacitors (C p1, C p2) results in output offset which can be a great source of drift over environmental variations, such temperature and aging.
3 Principle of operation
The displacements of the proof mass imply an acceleration which can be measured by several methods. For the capacitive sensing approach, the displacement is detected by measuring the capacitance change between the proof mass and adjacent fixed electrodes. Low parasitic capacitance achieved from monolithic integration is the key to maximizing the performance with this technique.
4 Device design
The movable parts of this MEMS comb accelerometer consist of four folded-beams, a proof mass and some movable fingers. The fixed parts include two anchors and some left/right fixed fingers. The central movable mass is connected to both anchors through four folded beams.
In the right and left side of the each movable finger, there are left and right fixed fingers. The movable fingers constitute the differential capacitance pair C 1 and C 2 with left and right comb fingers (Sharma et al. 2012).
If is no acceleration (a = 0), the movable fingers are resting in the middle of the left and right fixed fingers, the left and right capacitance pairs C 1 and C 2 are equal. When is any acceleration a along horizontal direction parallel to the device plan, the proof mass M s experiences an inertial force become −M s ·a along the opposite direction. However, the beams deflect and the movable mass and movable fingers move for a certain displacement x along the direction of the inertial force. That automatically changes the left and right capacitance gaps; hence the differential capacitances C 1 and C 2 will also be changed. One can know the value and direction of acceleration one measuring the difference of the capacities change.
When there is no acceleration, a driving voltage V d is applied to the left or right fixed driving fingers.
The electrostatic force will attract the movable fingers toward the left or right direction. By measuring this displacement and comparing with good device response, one knows whether the device is good or faulty.
5 Mechanical suspension
The topology of folded beam with turns can provide a lower spring constant, and thus higher sensitivity.
6 Damping and quality factor
There are two categories of damping mechanisms. First, structural damping is caused by friction within composite structural (Zhang 1994). The second is viscous air damping at atmospheric pressure. For the lateral accelerometer, squeeze film damping which occurs when the air gap between two closely placed parallel surfaces changes, is not critical either.
7 Basic knowledge for capacitive MEMS
8 Analysis of the device
When an acceleration a along the horizontal direction parallel to the device plan is applied to the accelerometer, the beam deflects under the effect of inertial force. The deflection of beam is in opposite direction of the applied acceleration. The displacement sensitivity of the device is defined as the displacement of the movable mass and movable fingers per unit gravity acceleration g along devices sensitive direction. The beam-mass structure of the accelerometer can be treated as a simplified spring-mass model. The four folded beam can be treated as four springs connected in parallel.
In order to find out the sensitivity of a comb accelerometer, dynamic analysis must be performed. A MEMS comb accelerometer actually can be simplified by a spring-mass model. For each folded-beam, both sections of the beam can be treated as two springs connected in series. Each beam section can be treated as double-clamped beam model.
Assume for each section of the folded-beam, the beam width and length is W b and L b separately. The width and length of central proof mass are W m and L m separately. The device thickness (thickness of the poly-silicon layer) is h. There is N f totally sensing finger groups. For each movable finger, the finger width and length are W f and L f separately. When there is no acceleration, the capacitance gap between each movable finger and its left/right fixed fingers is d 0. The density ρ, Young’s modulus E of poly-silicon material and unit gravity are given as below (Xiong 2005).
The static sensing capacitance of the MEMS comb accelerometer when there is no acceleration (a = 0) is:
9 Sensitivity analysis
10 Presentations and analyzes studied model
We use MATLAB software to calculate the displacement, capacitance and sensitivity.
Physical and geometrical parameters of the model
Capacitance gap d 0
Device thickness h
Mass width W m
Mass length L m
Beam width W b
Beam length L b
Finger width W f
Finger length L f
Number of sensing fingers N f
Young’s modulus of poly-Si
1.72 × 1011 Pa
The dielectric constant of air ε 0
8.854 × 10−12 F/m
The density of poly-Si ρ
2.33 × 103 kg/m3
Gravity acceleration g
Movable sensing mass M s
Spring constant K total
The structural thickness layer in this device is limited to be 6 μm.
10.1 Movable mass displacement as a function of acceleration x = f(g)
However, we can say that the increase in acceleration implies an increase in the displacement sensibility.
10.2 Capacitance sensitivity S c = f(x)
10.3 Capacitance sensitivity S c = f(g)
It is clear that the accelerations increase implies an increase in the capacitance sensitivity S c ; this proves that one can count on this model to obtain a high precision sensitivity.
10.4 A beam width effect on displacement
In this case, the displacement of the folded beam comb accelerometer is inversely proportional to the third power of the beam width W b .
After the results obtained by simulation of some parameters accelerometer capacitive, we note that the geometry of the component such as the width and the length of the mobile fingers as those of spring take a very important role on the acceleration sensitivity.
Theoretically, we can narrow down the beam width W b to achieve very high device sensitivity. However, there is always a bottom limit for the beam width set by the minimum line width in a fabrication process. If the beam width is too narrow <2 μm, it will become very challenging to fabricate the beam because the beam is extremely fragile and can be easily broken.
Therefore, to obtaining a good performance and a good sensitivity of a capacitive accelerometer, it is very important to choose better parameters such as the beam width and the beam length (W b and L b ) which represents the suspension of the acceleration system.
Other share, the mobile fingers width and length (W F and L f ) which constitute the capacities between the mobile fingers and the fixed fingers influence directly the value of these capacities then acceleration, which requires a choice very precise of these parameters.
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