Microelectromechanical Systems

1/2

ELEG-346/446: MEMS, Spring 2016 Final Sample Questions 1. Assume you are going to fabricate a MEMS silicon membrane with symmetrical structure using KOH etching of (100) Si wafer, as shown in Figure 1. The Si membrane is located in the middle of the wafer. The thickness of the (100) wafer is 600μm. You are going to use SiO2 as etching mask. After opening the etching window in SiO2 layer, you can etch both sides of Si in KOH solution simultaneously. The thickness of the membrane is t=40μm. The width of the Si membrane is W1=800μm. (1) What is the etching depth you need to etch from each side of the wafer to get 40μm thick Si membrane? (2) What is the SiO2 etching mask window you need to open at the top and bottom sides of Si wafer for etching (i.e. W2=?)? (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 minimum thickness of SiO2 layer in order to protect the Silicon wafer during etching?

Figure 1. Cross-sectional view of a Si membrane located in the middle of the wafer

2. (30’) A 2×2 binary reflective MEMS optical switch fabricated with SOI wafers and RIE technique is shown in Figure 2. Assume capacitance gap between movable and left/right fixed finger as d=2µm, device thickness t=200µm, number of comb finger groups N=100, overlap length between movable and fixed fingers: Lov=100µm, the width Wb, length Lb and thickness tb of each beam are 1µm, 400µm and 200µm respectively. The Young’s modulus of Si material is E=1.7×1011Pa. Dielectric constant of air is ε=8.85×10-12F/m. 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. What is the driving voltage DC voltage (Vd=?) to turn the optical switch in fully “ON” state?

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

2/2

3. What is GeneChip? Assume a GeneChip has 800000 different DNA probes, each DNA probe contains 20 nucleotides. Using photolithography to fabricate this GeneChip, how many photolithography masks should we have to make this GeneChip? 4. A bulk-micromachined MEMS variable capacitor using electrostatic comb-drive structure is shown in Figure 3. Assume there are N=80 movable fingers, initial overlap length between movable and fixed fingers is Lov=40µm, capacitance gap between movable and fixed fingers is d=2µm, device thickness is t=100µm, total spring constant of two folded beams is Ktot=12N/m, and dielectric constant of air is ε=8.85×-12F/m. 1). What is the initial capacitance (C0) when no driving voltage is applied? 2). If driving voltage Vd=60V is applied, what is the resulted displacement x of the movable fingers? What is the capacitance output (C’=?)? 3). This device can only increase the initial capacitance C0, but cannot decrease the output capacitance from C0. Can you think about a way to revise the structure design so that the capacitance output can be activated to be larger and smaller than the initial capacitance C0?

Figure 3. Bulk-micromachined MEMS variable capacitor