Student: Stanley

# MEMS Homework

EE-446 MEMS (Microelectromechanical Systems), Spring 2020, Homework #3. 1.(12’) Thermal oxide growth of Si in high temperature (>1000°C) is shown in Figure 1. The chemical reaction is: 2 2 Si  O  SiO The atomic weights of Si and O are 28 and 16 separately. That is, every 28 grams Si reacts with 32 grams of O2 to generate 60 grams of SiO2. The density of Si and SiO2 are given as: Density of silicon: 3 3 Si  2.3310 kg / m , Density of SiO2: 3 3 2.2 10 / 2  SiO   kg m . The surface area of silicon wafer is 1XY cm2 , where “XY” are the last two digits of your student ID. For example, if your student ID is 1234567, then the silicon wafer surface area is 167 cm2 . Assume tSi µm thickness of silicon is consumed during the oxidation process. 1). What is the total mass of Si consumed during oxidation? Using above chemical reaction and atomic weights data, find out the mass of the generated SiO2. 2). Using the density of SiO2, find out the thickness tox of the generated SiO2 layer. 3). Find out the ratio of tSi/tox. (Note: Your results in 1) and 2) may contain constants A and tSi.) Figure 1. Thermal oxidation of silicon wafer 2. (25’) The anisotropic etching profile of (100) silicon wafer in KOH solution is shown in Figure 2. Figure 2. Anisotropic etching profile of (100) silicon wafer in KOH solution Assume you are going to fabrication a MEMS silicon membrane for pressure sensor using KOH etching, as shown in Figure 3. The thickness of the (100) wafer is 4XYμm, where “XY” are the last two digits of your student ID. For example, if your student ID is 1234567, then the silicon wafer thickness is 467μm. You are going to use SiO2 as etching mask. The width of the membrane is W1=80μm. The thickness of the membrane is t=10μm. (1) What is the etching depth you need to etch down the bare Si wafer to get the Si membrane (t=10μm)? (2) What is the width (W2) of the window in SiO2 you need to open in the bottom side? (3) Assume you are going to use 40% KOH solution in temperature of 60°C. For this condition, the KOH etching rate for (100) silicon is 19.9μm/hr, the KOH etching rate for SiO2 is 76nm/hr. What is the etching time you need to etch the wafer to get the membrane? What is the minimum thickness of SiO2 you need as etching mask to protect the wafer during the whole etching process? 2 (4). Assume (100) silicon wafer has initial native oxide layer of 0.06µm (thickness). For (100) Si wafer at T=1100 oC, wet oxidation: A=0.1827µm, B=0.5289µm2 /hr. If we use this Si wafer to perform wet oxidation at T=1100 oC to get the minimum SiO2 thickness we need in step (3), how long should we perform the wet oxidation for the silicon wafer? (a). SEM photo of Si membrane (b). cross-sectional view (upside-down) Figure 3. Silicon membrane by KOH wet etching 3. (14’) 1). What are the ten basic steps of photolithography? (Names only, no need for explanation). 2). What is PVD and what is CVD for thin film deposition? List the names of four methods used to evaporate the source material in evaporation process for thin film deposition. (Names only, no need for explanation.) List ONE example chemical reaction you can use for CVD of polysilicon thin film deposition and its temperature needed. List TWO example chemical reactions you can use for CVD of SiO2 thin film deposition and its temperature needed. 3). What are the requirements for a successful silicon-glass anodic bonding? What is the difference between bulk-micromachining and surface-micromachining? 4. (12’) 1). Both surface-micromachining and Silicon-on-Glass (SoG) bulk-micromachining can make free-standing movable microstructures on substrate, but they use different ways to ensure the movable microstructure to be free-standing. How would they achieve this differently? 2). The term “mask” is used with different context in microfabrication literature. Explain briefly the following concepts (2~3 sentences for each concept): i). photolithography mask. ii). etching mask. iii). oxidation mask. iv). implantation mask. 3). What are lag effect and loading effect of DRIE process? Please explain the reasons for them. 5. (16’) A bulk-micromachined silicon-on-glass MEMS accelerometer is shown in Figure 4. The device can sense the acceleration perpendicular to the device plane. The central silicon mass is supported by four beams connected to the frame. If there is acceleration (a) along perpendicular direction, the central mass experiences an inertial force and the beams bend. Hence the gap between the central movable mass and bottom Al electrode on glass substrate will change, which in turn leads to the capacitance change. By measuring the capacitance change, the acceleration can be derived. The cross sectional view of the accelerometer is shown in Figure 4(b). 1). Use the cross sectional view, draw the fabrication flow chart of the device to show how the device is fabricated step by step using individual microfabrication processes. You can use the example in our slides for reference. 3 2). For the fabrication of this device, totally four times of photolithography steps are required: 3 times for silicon structure, and one time for aluminum bottom electrode. Assume positive photoresist is used, can you roughly sketch the patterns of four photolithography masks to be used? (a). Top view of the accelerometer (b). cross sectional view of the accelerometer Figure 4. A silicon-on-glass bulk-micromachined MEMS accelerometer 6.(16’) A surface-micromachined poly-Si MEMS bridge structure is shown in Figure 5. The accelerometer is fabricated with poly-silicon surface-micromachining technology. Poly-Si microbridge is connected to both poly-Si anchors which are anchored to the Si wafer substrate covered with a thin layer of 0.25µm Si3N4 film. The thickness of Si wafer is 400µm. The thickness of poly-Si layer is 2µm. The gap between free standing microbridge and the substrate is 3µm. The cross-sectional view of the structure is shown in Figure 6. (1). Draw the cross sectional view of the surface-micromachining fabrication flow chart for the MEME microbridge step by step, as shown in the class. Also show the thickness of each thin film layer in the flow chart clearly. (2). The top view of the microbridge is shown in Figure 5(b). You need two photolithography steps in the fabrication of the microbridge: one for patterning the anchors and one for patterning the poly-Si microbridge structure. Each photolithography process needs a photolithography mask to define the pattern you want. Assume positive photoresist is used, try to design the photolithography masks for each photolithography step. (Note: You need to sketch the shapes of your mask design, shade the dark region and leave the transparent region as blank). (a). 3D view (b). Top view Figure 5. Structure diagram of a poly-Si anchor bridge anchor Si Si3N4 4 Figure 6. Cross section view of Si MEMS microbridge 7.(15’) A surface-micromachined MEMS comb gyroscope developed by UC Berkeley in 1996 is shown in Figure 7. Figure 7. A surface-micromachined MEMS comb vibratory gyroscope 1). Sketch the simplified spring-mass model of the gyroscope, and briefly explain its working principle. Please clearly mark the direction of driving vibration and sensing vibration of the gyroscope. What are the actuation technique and sensing technique used (names only, no need for explanation)? What force (name only, no need for explanation) is used to sense the angular velocity? Why do we need to match the resonant frequencies of the driving vibration and sensing vibration modes of the gyroscope? 2). Assume the mass of the sensing mass as M. The system experience an angular velocity Ω (in unit of rad/sec) along Z direction. In the driving vibration mode, the sensing mass is activated into vibration along X direction with displacement x(t) A sin( t)  d  , where amplitude Ad=40μm, ω=2π×600 rad/sec, t is time. i). Find out the velocity of the mass dt dx t v t ( ) ( )  =? ii). Assume sensing mass M=0.2μg, input angular velocity Ω=1X°/sec=1X∙ (π/180) rad/sec, where X is the last digit of your student ID. For example, if your student ID is 1234567, then Ω=17°/sec=17∙ (π/180) rad/sec. What is the Coriolis force Fc(t) experienced by the sensing mass? Which direction is the Coriolis force along? Will the sensing mass be activated to vibrate along the direction of the Coriolis force? iii). If the total spring constant of the sensing beams is Ksens=0.2N/m, find out the resulted displacement ys(t) of the sensing vibration along Y direction. (Hint: ys(t)=Fc(t)/Ksens) 8. (15’) A 2×2 binary reflective MEMS optical switch fabricated with SOI (Silicon-on-Insulator) wafers and RIE (Reactive Ion Etching) technique is shown in Figure 8. Assume capacitance gap between movable and left/right fixed finger as d=2µm, device thickness t=80µm, number of 5 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, 2XYµm and 80µm respectively, where “XY” are the last two digits of your student ID. For example, if your student ID is 1234567, then your beam length is Lb=267µm. 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 “OFF” to “ON”, 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 8. A 2×2 binary reflective MEMS optical switch element Due on 04/20/2020, Monday in class.