Micro-Electro-Mechanical-Systems EMT 452/3 Micro-Electro-Mechanical-Systems (MEMS)

CHAPTER 1, 2 & 3

Q1 Create a cantilever structure by using all the three micromachining techniques; bulk & surface micromachining and LIGA.

Material removed by etching Bulk Micromachining Material removed by etching Standard silicon wafer thickness Waste of material in bulk micromanufacturing Constraint base Die attach Silicon cantilever beam By bulk manufacturing

Surface Micromachining Step 1: Deposition of sacrificial layer Step 2: Patterning of the sacrificial layer Step 3: Deposition of structural layer (conformal deposition) Step 4: Liquid phase removal of sacrificial layer Step 5: removal of liquid - drying.

LIGA Ti (sacrificial layer) Silicon Substrate Deposit Ti as sacrificial layer 1 Ti Etch Ti Silicon Substrate 2 PMMA Silicon Substrate Ti X-Ray Lithography 3

LIGA Silicon Substrate PMMA Ti Patterning of PPMA 4 Ni Deposit Ni 5 Ni Silicon Substrate Ti PMMA Deposit Ni 5

Q2 A slender silicon beam is under a longitudinal tensile stress. The force is 1 mN, and the crossectional area is 20 μm by 1 μm. The Young’s modulus in the longitudinal direction is 120 GPa. 1. Find the relative elongation of the beam (percentage). 2. What is the force necessary to fracture the beam if the fracture strain of silicon is 0.3 %?

Q2 solution

Q3 Find the moment of inertia of the cantilever beams shown below. The material is made of single crystal silicon. The Young’s modulus in the longitudinal direction of the cantilever is 140 GPa.

Q3 solution

Q4 Find the force constant of the beam in Q3 if a force is applied in the longitudinal direction of the cantilever. The beam is 800 μm long in this case.

Q4 solution

Q5 A torsional bar is anchored on two ends, with a lever attached in the middle of the bar. A force, F=0.01 μN, is applied to the end of the lever. Determine the degree of angular bending due to the rotation of the torsional bars. Do not consider the bending of the flexural lever segment. The values of L, w, and t are 1000, 10, and 10 μm, respectively. The beam is made of polycrystalline silicon. Poisson’s ratio = 0.22 and E = 158 GPa.

Q5 solution

Q6 To build a 20-μm wide fixed-free cantilever beam with a force constant of 10 N/m and a resonant frequency of 10 kHz out of single crystal silicon, find the desired length and thickness of the cantilever beam. The Young’s modulus of silicon is 120 GPa. The density of the silicon material is 2330 Kg/m3. Select the correct answer from choice below and explain the reasoning behind your choice. (1) Length = 6.4 mm and thickness = 351 μm. (2) Length = 2.9 mm and thickness = 75.7 μm. (3) Length = 143 mm and thickness = 3.65 mm. (4) None of the above.

Q6 solution