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

2. CHAPTER 1, 2 & 3

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

4. 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

5. 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.

6. 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

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

8. 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 %?

9. Q2 solution

10. 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.

11. Q3 solution

12. 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.

13. Q4 solution

14. 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.

15. Q5 solution

16. 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.

17. Q6 solution