Microelectromechanical Systems

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EE 446 MEMS Spring 2015: Final Exam Name:______________________________________ Student ID: _________________ Please use very brief answer for each question. Please note that the grade is decided by the accuracy instead of the length of your answer. 1. (20’) 1). What is “stiction” problem in surface-micromachining? List 3 example surface forces which may lead to stiction in surface-micromachining. Why is stiction problem less threatening in bulk- micromachining? If we wish to reduce the stiction problem in surface-micromachining, would we prefer dry or wet etching of the sacrificial layer for releasing the movable microstructure? 2). What are the three categories of MEMS micromachining techniques? In LIGA process, why do we need X-ray lithography (i.e. why cannot we use regular photolithography)? 3). A MEMS thermopneumatic micropump is shown in Figure 1. It can be used for micro drug delivery application. Please briefly explain its working principle. What actuation technique is used for the device? How would we ensure that microfluid only flows from inlet to outlet, but not in the opposite direction? If we want to increase the pumping rate (how fast it can pump micrfluid from inlet to outlet) without changing the size of the device, would you suggest two possible choices?

Figure 1. A thermopneumatic micropump

2. (25’) A pixel of Digital Micromirror Device (DMD) device for DLP (Digital Light Processing) technology developed by Texas Instrument Inc. is shown in Figure 2. It has been widely used for light projection applications. 1). Please briefly explain its working principle. Why don’t we use it in analog mode (i.e. precisely control the rotation angle of the mirror)? What’s the material used for the mirror? Why is it selected as the mirror matieral? 2). How can we achieve different gray levels based on the digital operation of the micromirror? If you have 3 DMD chips, how would you achieve colorful projection on screen? If you have only 1 DMD chip, can you still achieve colorful projection on screen? If yes, how? 3). Why are the two torsional hinges designed to be along the diagonal axis of the mirror pixel? That is, why aren’t they aligned to the edges of the mirror pixel? 4). List the two major failure mechanisms of the DMD device. 5). Another novel MEMS device based on light diffraction is also used for light display application. It has even faster response time than DMD. Give the name of the device, no need for any explanation.

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Figure 2. Structure diagram of DMD device

3. (25’) A 2×2 binary reflective MEMS optical switch fabricated with SOI wafers and RIE technique is shown in Figure 3. Assume capacitance gap between movable and left/right fixed finger as d=2µm, device thickness t=80µm, number of comb finger groups N=80, overlap length between movable and fixed fingers: Lov=80µm, the width Wb, length Lb and thickness tb of each beam are 1µm, 200µm and 80µm respectively. The Young’s modulus of Si material is E=1.7×1011Pa. Dielectric constant of air is ε=8.85×10-12F/m. (Hint: Please refer to single-side comb driving in our MEMS structure slides). 1). Find the spring constant of each beam section Kb1=? 2). Are two beams connected in parallel or in series? Find the total spring constant of the whole device Ktot=? 3). In order to turn the optical switch from “ON” to “OFF”, the mirror needs to move away from cross- over point by 30µm. To achieve this, what is the required DC driving voltage applied between the movable and fixed comb fingers Vd=? 4). If we want to build a 128×128 (128 input fibers, 128 output fibers) switch network, how many such optical switches do we need? Large number of switches may reduce the yield and increase the cost for complex switch network. Can you suggest a better solution which can reduce the required number of optical switches? How many optical switches would you need then?

Figure 3. A 2×2 binary reflective MEMS optical switch element

4. (30’) An isolated RF tunable capacitor is shown in Figure 4. In the figure, the shaded and gray areas are anchored to substrate. The left driving portion and right capacitance output portion are physically connected by a connector, while they are electrically insulated. Two cantilever beams support the movable mass of the device. The device is fabricated with poly-silicon surface micromachining technology. 1). Why should the left and right portions of the device be physically connected but electrically insulated? 2). Assume there are totally Nc fixed fingers in the right portion (capacitance output portion), the capacitance output would be:

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d

tLN C ovc

2 

In it, ε is dielectric constant of air, ε=8.85×10-12F/m, t is device thickness, Lov is the overlap length between movable and fixed fingers, d is the capacitance gap. Assume we have Nc=160, t=2µm, d=2µm, Lov=32µm in static mode when there is no displacement of the movable mass, what is the static capacitance output C0? 3). Assume for each cantilever beam, the beam width Wb=1μm, length Lb=126μm, thickness tb=2μm. The Young’s modulus of poly-Si: E=1.70×1011Pa. Find out the spring constant Kb1 for each cantilever beam. 4). Are the two beams in parallel or in series? Find the total spring constant Kb of the whole device. 5). If we apply variable driving voltage V0 on movable driving fingers, but set the voltages on left and right fixed driving fingers as –VA and VA (constant voltages) separately. The electrostatic driving forces F1 (F2) along left (right) directions can be calculated as:

d

VVtN F Ad

2

)(2 1

2 0 

 ,

d

VVtN F Ad

2

)(2 2

2 0 

 .

In them, Nd is the number of left/right fixed driving fingers, t is device thickness, d is capacitance gap. Find out the equation for calculating the total driving force Ftot on the movable driving fingers. What is the relationship (linear or quadratic) between the total driving force Ftot and the driving voltage V0? 6). In this case, Nd=64, t=2µm, d=2µm. If VA=30V, but V0 changes from -30V to +30V, find out the total maximum displacement of the movable fingers toward the left (when V0=+30V) and right (when V0=-30V) separately. 7). Find out the maximum and minimum capacitance outputs of the device. What is the tunable ratio r=Cmax/Cmin of the output capacitance Cout for this variable capacitor device?

Figure 4. MEMS variable capacitor device

Due day: 05/04/2015 Monday before 12:00noon.