Abstract-In this paper, the design, modelling and simulation of a capacitive 3-axes MEMS accelerometer is presented. The design is based on the gyroscope developed by Said Emre Alper et al. and 3-axis accelerometer developed by H. Q. Deyou Fang, et al. The designed accelerometer consists of a lateral proof-mass for in-plane (x-y) acceleration sensing, and an unbalanced torsional proof-mass for out-of-plane (z) acceleration sensing. The torsoioal proof-mass is positioned in the cut-out portion of the lateral proof-mass. The structural thickness of the accelerometer is 30μm and is proposed to be fabricated using bulk micromachining. The base capacitance obtained from comb fingers in lateral direction is 0.3.19fF, and that in z direction is 0.1062fF. The change in capacitance is 38.2 zF/G for x and y-axis, and 13.310 zF /G for z-axis. The mechanical and electrical signal sensitivity of the accelerometer obtained in lateral axis is 36.7nm/G and for z-axis with 25% fraction hole size 27.6nm/G. the electrical sensitivity obtained for x and y-axis is 3.5 µV/G and for z-axis, it is 2.50 µV/G. The base capacitance, mechanical and electrical signal sensitivity is of the accelerometer are quite good as compared to those presented in the published literature. The transient analysis response obtained for the in-plane motion (x-y) is comparable with the published results. The out of plane transient response under partial vacuum and in the presence of etch holes is encouraging.
Keywords- Accelerometer; MEMS; ANSYS; Matlab
Introduction
A MEMS accelerometer consists of a proof-mass suspended using a compliant flexure anchored to the substrate. A number of microaccelerometers have been successfully fabricated using surface and bulk micromachining processes [1]. The sensitivity and natural frequency of the accelerometer mainly depend on the type of flexure used. Most MEMS accelerometers are single axis or dual-axes. There is a growing demand for three axes accelerometers especially in some applications such as inertial navigation systems. One way of realizing a 3- axis accelerometer is by assembling two or three accelerometers together. However, these accelerometers have issues such as axes alignment errors and increased size. Alternatively, monolithic 3-axis accelerometers are being developed. Although these accelerometers have either fabrication constraints of thin-film structures (i.e., thickness much smaller than the lateral dimensions), or high cost due to fabrication complexities [2-3] their performance is encouraging. Some monolithic 3-axis accelerometers are actually comprised of individual single-axis sensors with separate proof masses [4], resulting in relatively large sizes. One of the challenges in realizing a 3-axis accelerometer is z-axis sensing. The difficulty of z-axis sensing lies in the making of horizontal electrodes to sense out-of-plane displacement in the presence of large parasitic capacitance on the substrate, especially when differential sensing is needed. The z-axis capacitive sensing with torsion spring has been demonstrated [5], but it suffers from either non-differential sensing or complicated fabrication process. Another challenge in designing a 3-axis accelerometer is to decouple the motions of the structure in three mutually perpendicular directions to avoid or reduce the cross-axis sensitivity. Therefore, the main challenges for making three axes accelerometer are - the size factor, realizing z-axis sensing, and decoupling the motions of the structure in three mutually perpendicular directions. In this paper, design of 3-axis capacitive MEMS accelerometer is demonstrated with a view to overcome the above discussed issues. In the first section structure of 3-axes accelerometer is discussed. Next analysis and then performance of the accelerometer is discussed.
STRUCTURE OF A 3-AXES ACCELEROMETER
The design is based on the gyroscope developed by Said Emre Alper et, al. [6], and a 3-axes accelerometer developed by H. Q. Deyou Fang, et al [7]. The fabrication method can be used for the designed accelerometer is a bulk micromachining. The bulk micromachining has advantage over the surface micromachined accelerometer is that; more thickness can be achieved by the bulk micromachined structure as compared to that of surface micromachined structure thereby increasing the inertial mass. The structural dimensions of the accelerometer are given in table 1. The structural thickness of the designed accelerometer is taken 30µm, so it can be manufactured using bulk micromachined.
The structure of accelerometer is based on the gyroscope developed by Said Emre Alper et, al. [5], and a 3-axes
TABLE . STRUCTURAL DIMENSIONS OF THE 3-AXES ACCELEROMETER
Items
Dimensions
Lateral proof mass (µm-µm)
500-500
Torsional proof mass (µm-µm)
250-250
Movable drives (µm-µm)
50-500
Structure thickness (µm)
30
Lateral comb finger length (µm)
75
Z sensing comb finger length (µm)
50
All finger gaps (µm)
2.5
Lateral beams (l-w) (µm-µm)
75-1.5
Z torsional beams (l-w) (µm-µm)
50-1.5
The accelerometer consists of a lateral proof-mass for sensing the acceleration in lateral axis (i.e. x and y-axis). The unbalanced torsional proof mass is embedded in the lateral proof-mass for the sensing of z-axis acceleration sensing. The lateral proof-mass, along which the rotor comb-fingers attached, is anchored to the substrate through two pairs of symmetric straight beams. Similarly, the torsional proof-mass is suspended on the substrate by two straight beams. The symmetric beams are flexible in both x- and y-axis, allowing the dual-axis in-plane sensing by two separate groups of orthogonally-oriented comb-fingers. The schematic diagram of the accelerometer is shown in figure 1.
Figure 1 Structure of the 3-axes accelerometer designed
The effective mass of the accelerometer is the mass of the proof-mass and the (13/35)th times mass of the beams which are under acceleration [8]. The effective masses of the accelerometer are 1.46-10-8 Kg, 1.46-10-8 Kg, and 3.97-10-9 Kg respectively. The beam stiffness along x, y and z-axis are 40.56 N/m, 40.56 N/m, and 9.01-10-8 Nm/rad respectively. The damping ratios along x, y and z-axis are observed 0.033, 0.033, and 10.78 respectively.
It is observed that the damping ratio of torsional proof-mass is too high. It can affect the dynamic and noise floor of the accelerometer. It can be reduced by providing the damping holes (Etch holes).
We have taken three different sizes of the etch holes on the torsional proof-mass to analyze the performance of the torsional proof-mass. The three different sizes are 15µm-15µm (i.e. 36% fraction), 13.75µm-13.75µm (i.e. 25% fraction), and 12.5µm-12.5µm (i.e. 16% fraction). The total number of holes are 76. The schematic diagram of torsional proof-mass with etch hole is as shown in figure 2.
Figure 2 Torsional proof-mass with etch holes
The resulting mass, damping coefficient and damping ratio, due to the different sizes of hole sizes are given in table II.
TABLE Mass, Damping coefficient and damping ratio of torsional proof-mass at different etch hole sizes
Hole size
Mass of the torsional proof-mass (kg)
Damping coefficient
(Nm/s)
Damping ratio
36% fraction of etch hole
2.8 -10-9
2.07-10-5
0.06
25% fraction of etch hole
2.99-10-9
2.41-10-5
0.067
16% fraction of etch hole
3.16-10-9
2.78-10-5
0.074
In the next section, the numerical simulation is done using ANSYS® and MATLAB® to analyze the performance of the accelerometer.
NUMERICAL SIMULATION
The numerical simulation consists of static analysis, Modal analysis, and Harmonic analysis.
Static Analysis
The static analysis is done using software ANSYSY®. For static analysis, the excitation force applied on the accelerometer is 0.1N. The displacement of the accelerometer along the x, y, and z-axis for their respective force of 0.1N is shown in figure 3.
Figure3 Displacement accelerometer along x, y and z axis without and with considering etching holes
Table III shows the stiffness of the beam analytically and numerically.
TABLE Stiffness of beam along x, y and z-axis
Axis of displacement
Beam stiffness
% Error
Analytically
Numerically
x-axis (N/m)
40.56
39.51
2.59
y-axis (N/m)
40.56
39.18
3.40
z-axis (Nm/rad)
9.01-10-8
8.57-10-8
5.13
Modal Analysis
The modal analysis is done using the software ANSYS® to calculate the natural frequency numerically. The numerical results were validated by analytical calculations. The natural frequencies are also calculated manually using reference [9]. The modal analysis is done for all the above discussed cases of the accelerometer design. Table IV shows the natural frequencies of the accelerometer of the three orthogonal axes.
TABLE IV NATURAL FREQUENCIES OF THE ACCELEROMETER
Design condition
Natural frequency (Hz)
% Error
Numerically
Analytically
Without etch holes
fx
8298
8388
1.08
fy
8298
8388
1.08
fz
8708
10026
15.14
36% fraction etch holes on torsional proof-mass
fx
8298
8388
1.08
fy
8298
8388
1.08
fz
9765
10642
8.98
25% fraction etch holes on torsional proof-mass
fx
8298
8388
1.08
fy
8298
8388
1.08
fz
9565
11012
15.13
16% fraction etch holes on torsional proof-mass
fx
8298
8388
1.08
fy
8298
8388
1.08
fz
9399
10722
14.10
Dynamic Response of the Accelerometer
The dynamic response of the accelerometer can also be analyzed using software MATLAB®. The dynamic behavior of the accelerometer for x and y-axis is shown in figure 5.
Figure 5 Dynamic behavior of the Accelerometer for x and y-axis using Bode plot
RESULTS AND DISCUSSION
For x and y-axis capacitance sensing, we have provided 40 number of comb fingers, the length, width and thickness of each comb finger is taken as 75µm, 10 µm, and 30 µm, respectively. The base capacitance of accelerometer in lateral axes and z-axis obtained are 0.319fF and 0.1062fF respectively. The change in capacitance for x and y-axis is 38.2 zF/G and for z-axis, it is 13.310 zF /G.
Mechanical sensitivity of the accelerometer obtained for the lateral axes and z-axis is shown in table V
TABLE V MECHANICAL SENSITIVITY OF THE ACCELEROMETER
Axis of displacement of proof-mass
Mechanical sensitivity (m/G)
x-axis
3.67-10-10
y-axis
3.67-10-10
z-axis
3.34-10-10
z-axis (with 36% fraction hole size of torsional proof-mass)
2.65-10-10
z-axis (with 25% fraction hole size of torsional proof-mass)
2.76-10-10
z-axis (with 16% fraction hole size of torsional proof-mass)
2.86-10-10
The electrical signal sensitivity for x and y-axis is 3.5 µV/G and for z-axis, it is 2.50 µV/G
CONCLUSIONS
This paper presents the design and analysis of a 3-axes, capacitive MEMS accelerometer. The accelerometer consists of a lateral proof-mass for the acceleration sensing in lateral direction (i.e., x, y axes) and an unbalanced torsional proof-mass for z-axis acceleration sensing. The planar accelerometer has a uniform thickness of 30μm and can be manufactured by using bulk micromachining. The motions in the 3 orthogonal axes are decoupled, i.e., they do not interfere with one another, thereby eliminating the cross axis sensitivity. The base capacitance obtained using comb fingers in lateral direction is 0.3.19fF, and that in z direction is 0.1062fF. the change in capacitance is 38.2 zF/G for x and y-axis, and 13.310 zF /G for z-axis. The mechanical and electrical signal sensitivity of the accelerometer obtained in lateral axis is 36.7nm/G and for z-axis with 25% fraction hole size 27.6nm/G. the electrical sensitivity obtained for x and y-axis is 3.5 µV/G and for z-axis, it is 2.50 µV/G.
The combination of a lateral proof-mass and an unbalanced torsional proof-mass holds promises of providing a perfectly decoupled 3-axes accelerometer.
In order to reduce the z-axis damping coefficient four conditions are analyzed, (i.e., by vacuum packaging, with 36% fraction etch holes, with 25% fraction etch holes, and 16% fraction etch holes). The squeeze film damping and performance parameters of the 25% fraction etch holes gives better results. The harmonic and transient analyses indicate a satisfactory dynamic behavior of the accelerometer at x, y and z-axis.
