Microelectromechanical Systems Project 1

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ELEG-446 MEMS (Microelectromechanical System), Spring 2018, Project #1: Vibrational Mode Simulation of a Silicon Bulk-micromachined MEMS Accelerometer 1. A MEMS beam-mass accelerometer structure is shown in the following figure. The accelerometer is fabricated with single-crystal silicon bulk-micromachining. Silicon mass is connected to two cantilever beams. Both beams are anchored to the frame at the fixed ends shown in the figure. Two cantilever beams have exactly the same width, length and thickness. The dimension parameters of the accelerometer are: Mass width Wm=6000μm, mass length Lm=4000μm, mass thickness tm=330μm. For each beam, beam width Wb=1abc μm (where “abc” are the last 3 digits of your student ID. For example, if the last three digits of your student ID are “456”, then the beam width is 1456μm), beam length Lb= 3000μm, beam thickness tb= 16μm. The gap between two beams is 1000μm. Two beams are in the same level and they are located in the central portion of the mass symmetrically. In other words, distance between top surface of the mass and the top surfaces of the beams = distance between bottom surface of the mass and the bottom surfaces of the beams distance between front surface of the mass and the front surface of beam1 = distance between back surface of the mass and the back surface of beam2 Given the density of silicon ρ=2.33×103kg/m3, the Young’s modulus of silicon material is E=170GPa (1Pa=1N/m2), Poisson ratio of silicon: ν=0.34. Use international unit systems in the following calculations.

Figure 1. Structure diagram of a silicon bulk-micromachined MEMS accelerometer

1). Cantilever beams can be treated as springs in MEMS devices. Use hand calculation to find the effective spring constant Kb for each individual cantilever beam (Kb1=Kb2=Kb). Are the two cantilever beams connected in parallel or series? Find the total effective spring constant Ktot for the whole device. 2). Use hand calculation to find out the mass of both beams Mb and the sensing mass Mm, and the ratio of Mb/Mm. Is the mass Mb of both beams much smaller than the sensing mass Mm? If there is an acceleration a (a=50g, where g is the gravity acceleration, 1g=9.8m/s2) toward the top, calculate the inertial force Fm experienced by the mass (Fm=-Mm·a). Which direction is the inertial force Fm in?

mass

Beam1

Wm

tm Lb

Wb tb

fixed areas

O(0,0,0)

Top view

Front view

Beam2 Side view

a

Lm

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3). Ignoring the mass of the cantilever beams, use hand calculation to find out the resulted deflection of the cantilever beams at their ends connected to the sensing mass Mm due to the inertial force Fm. Will the beams bend up or bend down? 4). Use hand calculation to find out the resonant frequency f0 of the accelerometer. 5). Briefly explain how we can use differential capacitance sensing technique to detect the displacement of the movable mass. 6). Assume the coordinates of the corner of the mass as O(0,0,0), using the dimensions given above, find out the coordinates (in units of µm) for all the key points in the diagram. (There are 8 key points for the mass and 8 key points for each of the two beams. Four key points are hidden in Figure 1, but you also need to mark their coordinates.). Mark them in the diagram. 7). With the above derived coordinates of key points, build the 3-D model of the accelerometer in ANSYS. After the 3-D model is built, rotate them to view from different angles. Capture a screen shot of your 3-D model, print it out and submit with your report. You can press “PrtScr” key in the keyboard to capture the screenshot. Since the background color in ANSYS is black, direct printing of the screenshot wastes ink of your printer. You can first paste your screen shot in Microsoft Paint (click Windows “Start—All Programs—Accessories—Paint”), and invert the color (In Microsoft Paint, click “Image—Invert Colors”). This will invert the background color to white. After that, you can cut the desired area of screen shot and paste it into a Microsoft Word file. This can save the ink of your printer. 8). Use ANSYS frequency simulation (modal analysis) to simulate the first five vibrational modes of the accelerometer and find the corresponding resonant frequencies. (Note: For 3D model, please use “Manual Size” for Meshing size control and set Tet element expansion TETEXPND=2.0 to reduce the number of nodes generated in meshing. Otherwise the number of nodes in meshing may exceed the limit and you may get an error in meshing.) Perform the animation of each vibrational mode in ANSYS, and observe how the beams are bending in each mode. Capture the screenshots of the five vibration modes and their corresponding resonant frequencies (make sure you invert the background color of the screenshot to white before printing). Adjust the views so that the bending shape of the beams are clearly visible in each mode. Attach those five screenshots in your report. In the working mode of the accelerometer, the beam should bend up and down due to inertial force. By observing the animations, identify which mode is the working mode for the accelerometer and its resonant frequency. Based on your results, fill in Table 1. Table 1. The first five vibrational modes of MEMS cantilever-mass accelerometer

Vibration Mode

Resonant frequency (kHz)

Description of beam vibration Working mode? (Yes/No)

Mode #1 f01= Hz

Mode #2 f02= Hz

Mode #3 f03= Hz

Mode #4 f04= Hz

Mode #5 f05= Hz

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Is the resonant frequency of higher vibrational modes far away from the working mode? Is the accelerometer stable in its working mode? The resonant frequency of the working mode from ANSYS simulation may be different from the hand calculation result (f0) you found in step (4). This is normal because the equation we used to find resonant frequency is based on simplified spring-mass model and it may introduce some error. The ANSYS simulation result is more accurate. Find out the relative error of frequency (REf=?) of hand calculation:

0 0

0

( _ ) ( ) 100%

( ) f

f hand calculation f ANSYS RE

f ANSYS

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Due date: 02/15/2018 (Thursday) in class.