Dynamic Capacitance Extraction of A Triaxial Capacitive Accelerometer

Transcription

1 Dynamic Capacitance Extraction of A Triaxial Capacitive Accelerometer Zhenchuan Yang, Gang LI, Yilong Hao, Guoying Wu Institute of Microelectronics, Peking University, Beijing, China Abstract Capacitive sensing is widely used in micromachined sensors, such as accelerometers, pressure sensors, gyroscopes, etc. In order to achieve desired performance, the capacitance variation according to external excitation must be evaluated carefully. However, obtaining the analytical result is not easy, especially for complicated deformations. This problem can be solved in ANSYS by building the electrostatic model according to a structural analysis result, then extracting capacitance through CMATRIX. However, rebuilding the model manually is not efficient and is sometimes very difficult, given a complex model. In this paper, a dynamic capacitance extraction method is presented to solve this problem. This method is based on automatic mesh updating and physics environments. The analysis procedure is to first create the structural and electrostatic physics environment, then do the structural analysis in the structural environment, updating the mesh according to the result, and, lastly, extract capacitance through CMATRIX in an electrostatic environment. A triaxial capacitive accelerometer is used as an example to evaluate this method. The analysis results show that this method is efficient to achieve capacitance variation versus external excitation relation. Introduction Due to the advantages of high resolution, low temperature coefficient, simple fabrication processing, etc, capacitive sensing is widely used for micromachined high performance sensors, such as pressure sensors, accelerometers, gyroscopes, and so on. In order to obtain the desired performance, the relationship between capacitance change and external excitation must be studied carefully during device design. For simple design, this can be done with the analytical method. However, most devices are complicated and need numerical simulation to get the desired result. The standard simulation procedure is to do a structural analysis first, then build electrostatic model according to the structural analysis result, and then do an electrostatic simulation to extract capacitance. If the device structure or deformation is complicated, it will be very difficult to build the electrostatic model manually. Furthermore, even for simple devices, this method is not efficient. In order to overcome these problems, a new simulation method must be used. In this paper, based on the automatic mesh updating function provided by ANSYS, a sequential coupling simulation method for dynamic capacitance extracting is introduced. Using this method, a triaxial accelerometer is simulated. Principle The triaxial accelerometer structure consists of a proof mass and four beams suspending the proof mass (see Figure 1). When the proof mass is accelerated vertically (see Figure 2), it translates down along the z- axis and the suspending beams are bent symmetrically. When the proof mass is accelerated laterally (xaxis), it rotates along the y-axis (see Figure 3). Three pairs of capacitors (see Figure 4) are used to sense the three axis accelerations separately and simultaneously. Six capacitors have one common plate on the top surface of the proof mass. Capacitors C 1 ~C 5 are variable with respect to acceleration, while C 6 is a reference and has a constant value, which is half the values of C 1 ~C 4 but the same value as C 5. Capacitors C 1 and C 3, C 2 and C 4, and C 5 and C 6 are used to sense x-, y-, and z-axis acceleration, respectively. More detailed design and fabrication information about this accelerometer can be found in reference [1].

2 Figure 1. Schematic diagram and operating principle of the accelerometer: top view Figure 2. Schematic diagram and operating principle of the accelerometer: vertical acceleration applied

3 Figure 3. Schematic diagram and operating principle of the accelerometer: lateral acceleration applied Figure 4. The distribution of capacitors As mentioned above, when the accelerometer is accelerated vertically, the proof mass will translate down along the z-axis; therefore, capacitors C 1 ~C 4 produce common mode signals. Only C 56 ( C 56 =C 5 -C 6 ) has a differential mode signal. When the proof mass is subjected to a lateral acceleration in the x-direction, the mass rotates around the y-axis. Then C 13 ( C 13 =C 1 -C 3 ) produces a differential mode signal, while others do not change their values in the case of small deflection, because their geometric centers have a zero displacement. When the proof mass has z- and x- direction accelerations applied simultaneously, it translates in the z-direction and rotates along the y-axis. Then C 13 and C 56 produce differential mode signals separately and C 24 ( C 24 =C 2 -C 4 ) has a zero signal value. Because this structure is symmetric in the x and y directions, the results derived from the x direction are fit for the y direction and vice versa. According to analytical equations in reference [1], the scale factors for the lateral-axis and the z-axis are 4.69 ff and 4.71 ff respectively.

4 Analysis Procedure The sequential coupling method is used to extract the capacitance. The simulation procedure (see Figure 5) is as below. First the fully finite element model of the accelerometer including both structural and electrostatic elements (see Figure 6) is built. The element types for the structural and electrostatic models are Solid95 and Solid122, respectively. For simplicity, the fringe effect of the capacitors at the device edge is not fully considered (see Figure 7). Then physical environments are created for both the electrostatic and structural analyses. After that, the structural environment is read into database and acceleration loads are applied to the model, so the structural analysis is fulfilled. As the next step, the analysis result is read into database, and ANSYS command UPCOORD is used to update the meshing of the finite element model. After this step, the electrostatic model will change automatically according the structural analysis result. Finally, the electrostatic environment is read into the database, and the CMATRIX command is used to extract the capacitance. Therefore, the capacitances under certain applied excitation are obtained directly. If this procedure is put into a loop simulation, the relationship between capacitance change and a series of external accelerations can be obtained. Figure 5. Basic simulation procedure

5 Figure 6. Finite element model of accelerometer: whole structure Figure 7. Finite element model of accelerometer: close view

6 Analysis Results & Discussion Three different acceleration loads are simulated for the triaxial accelerometer. The applied acceleration is from -1.5 g to 1.5 g. The first analysis the accelerometer undergoes is x-axis-only acceleration (see Figure 8). The second analysis is z-axis-only acceleration (see Figure 9). The third analysis is simultaneous x- and z-axis acceleration, and the acceleration value is the same (see Figure 10). From the simulation results, we can derive that the scale factors for lateral-axis and z-axis are 4.58 ff and 4.76 ff, respectively. The cross sensitivity is also very low. The simulation results matched with the theoretical results very well. Figure 8. Capacitance change under x-axis acceleration Figure 9. Capacitance change under z-axis acceleration

7 Figure 10. Capacitance change under both x- and z-axis acceleration Conclusion A dynamic capacitance extraction method for micromachined capacitive sensor is introduced. This method is based on the sequential coupling and automatic mesh updating functions provided by ANSYS. A triaxial accelerometer is analyzed using this method. Through loop simulation, the scale factors of the accelerometer are obtained, which are consistent with theoretical results. The simulation results show that this method is efficient to achieve capacitance variation versus external excitation relation, and useful for capacitive sensors design. Reference 1. Gang Li, Zhihong Li, CongshunWang, Yilong Hao, Ting Li, Dacheng Zhang and GuoyingWu, Design and fabrication of a highly symmetrical capacitive triaxial accelerometer, J. Micromech. Microeng. 11 (2001)