Contents: - Introduction - MOEMS Applications - Actuation in MEMS - Characterization of MEMS - MOEMS challenges - References

1. O v e r v i e w o n
M O E M S
Hana Medhat Abdelhadi
B.Sc., German University in Cairo
Faculty of Information Engineering and Technology
Electronics Department

2. M O E M S
On-Chip Micro-Scaled Systems:
• Miniaturization  Portability
• Monolithic Micro-fabrication  Commerciality
• Arrayability  Multi-Purpose
• Re-Configurability  Functionality Tuning

3. M O E M S
Reversible Mechanical Perturbation by, e.g.:
• Electro-thermal Force
• Electro-static Force
• Piezo-electricity

4. M O E M S
Optical MEMS: Displays, e.g. Micro-Mirror Arrays

5. M O E M S
Optical MEMS: Diffractive Spectrometers, e.g. Tunable
Gratings

6. M O E M S
Optical MEMS: Interferometric Spectrometers, e.g.
Michelson Interferometer

7. M O E M S
Optical MEMS: Tunable Optical Resonators, e.g. VCSEL
swept laser source

8. M i c r o - O p t i c a l B e n c h e s
Component fabrication Requirements:
• High Verticality
• High Aspect Ratio
• Low Surface Roughness
• Control of Surface Curvature

9. L i t h o g r a p h y
Minimum Line width:
𝑊 𝑚𝑖𝑛 =
𝐾 ⋋
𝑁𝐴
Depth of focus:
𝜎 =
⋋
𝑁𝐴2
K is a measure of photo-resistivity; ⋋ is the source wavelength; 𝑁𝐴 is the numerical
aperture of the optical component

10. D R I E ( B o s c h P r o c e s s )
𝑆𝐹6 Plasma  Isotropic Etch
𝑆𝐹6 Plasma cycle +𝐶4 𝐹8 cycle  Anisotropic Etch + Scallops

11. M o n o l i t h i c
M i c r o - F a b r i c a t i o n

12. E l e c t r o - t h e r m a l
A c t u a t i o n
Electric Current Flow  Thermal Energy rises
Transient Deformation  Translational Actuation

13. U - S h a p e d B e a m
Resistivity of thin arm >> Resistivity of wide arm
Thin arm expands in length  Side deflection of the structure

14. U - S h a p e d B e a m
M a t h e m a t i c a l M o d e l
Temperature Profile in thin arm:
𝑇 𝑥 =
𝑉2
2𝐿2 𝜌𝐾 𝑝
𝐿𝑥 − 𝑥2 + 𝑇𝑠  𝑇 𝑚𝑎𝑥 𝑎𝑡 𝑥 =
𝐿
2
Beam Deflection:
d 𝑥 =
−𝛼
2ℎ
𝑇ℎ − 𝑇𝑐 𝑥2
Change in the beam’s length:
∆𝐿 = 𝐿(
𝑉2
12𝜌𝐾 𝑝
+ 𝑇𝑠)
V: Applied voltage; L: Length of thin arm; 𝐾 𝑝: thermal conductivity; 𝜌: 𝑟𝑒𝑠𝑖𝑠𝑡𝑖𝑣𝑖𝑡𝑦;
𝑇𝑠: 𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑎𝑟𝑚 𝑡𝑒𝑚𝑝; α: 𝑡ℎ𝑒𝑟𝑚𝑎𝑙 𝑒𝑥𝑝𝑎𝑛𝑠𝑖𝑜𝑛 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡

15. U - S h a p e d B e a m
M o d e l i n g

16. U - S h a p e d B e a m
P e r f o r m a n c e
Short Range Actuation
High Power Consumption

17. V - S h a p e d B e a m

18. V - S h a p e d B e a m
M a t h e m a t i c a l M o d e l
Maximum deflection (with no loading
force) :
𝑑 𝑚𝑎𝑥 = 2
tan 𝜃1
𝑘
tan
𝑘𝐿1
4
−
𝐿1
2
tan 𝜃1
For a desired deflection at a certain angle, we obtain
the force F and the required change in temp.:
∆𝑇 =
1
𝛼𝐿1
(∆𝐿1
′
+
𝐹𝐿1
𝑌𝑊𝐻
)
F is the applied force; Y is Young’s modulus; I is the moment of inertia of the beam; H is beam thickness; W is the
beam width; 𝐿1
′
is the corrected beam length for compression at the fixed side; k= 𝐹
𝑌𝐼

19. V - S h a p e d B e a m
P e r f o r m a n c e
Short range actuation.
High power consumption.

20. E l e c t r o - S t a t i c
A c t u a t i o n
Potential diff. between 2 conductors  Charge accumulation
Attraction Forces  Translational Actuation

21. P a r a l l e l P l a t e
M a t h e m a t i c a l M o d e l
Electrostatic Force:
𝐹𝑒 =
1
2
𝐶𝑉2
=
1
2
𝐴𝜀0 𝜀 𝑟
(𝑑)2
Restoring Spring Force:
𝐹𝑠 = 𝑘 𝑒 𝑥
Equilibrium  𝐹𝑒 = 𝐹𝑠 translational distance:
𝑥 =
1
2
𝐴𝜀0 𝜀 𝑟
𝑘 𝑒(𝑑)2
𝑉2
C is the capacitance; V is the applied voltage; A is the surface area, d is the initial gap, 𝑘 𝑒 is the
spring stiffness, x is the displacement.

22. P a r a l l e l P l a t e
P e r f o r m a n c e
Extremely Short
range actuation.
No power
consumption.
Low upper limit
Voltages.

23. C o m b - D r i v e
A c t u a t o r

24. C o m b - D r i v e
M a t h e m a t i c a l M o d e l
Electro-static force for N fingers:
𝐹 =
𝑁𝜀𝑡𝑉2
2(𝑑)2
Deflection at equilibrium:
𝑥 =
𝑁𝜀𝑡𝑉2
2𝑘 𝑒(𝑑)2
V is the applied voltage; t is the finger thickness, d is the initial gap, 𝑘 𝑒 is the spring stiffness, x
is the displacement.

25. C o m b - D r i v e
P e r f o r m a n c e
Long Range Actuation (400𝜇𝑚 at 35𝑉)
No power consumption
Resilient to non-linearity at large displacements

26. M E M S
C h a r a c t e r i z a t i o n
Electrical Model in Frequency Domain:
Resonance Frequency
Quality Factor
Optical Model in Time Domain:
Relative position/ Velocity
Microscopic Imaging

27. E l e c t r i c a l M o d e l
At resonance:
G 𝜔0 =
1
𝑅 𝑚
→ 𝜔0 & 𝑅 𝑚
𝐵 𝜔0 = 𝜔0 𝐶𝑠 + 𝐶 𝑝 → 𝐶𝑠 + 𝐶 𝑝
Generally:
𝐶𝑒𝑞 =
𝐵(𝜔)
𝜔
= 𝐶𝑠 + 𝐶 𝑝+
𝐿 𝑚(
𝜔0
2
𝜔2 −1)
𝑅 𝑚
2+ (𝜔𝐿 𝑚−
1
𝜔𝐶 𝑚
)2
→ 𝐶𝑒𝑞 𝑚𝑎𝑥
at
𝜕𝐶 𝑒𝑞
𝜕𝜔
= 0
𝐿 𝑚 =
𝜔0 𝑅 𝑚
𝜔 𝑒𝑞|1 −
𝜔0
2
𝜔 𝑒𝑞
2 |
→ 𝐶 𝑚

28. E l e c t r i c a l M o d e l

29. O p t i c a l M o d e l
L a s e r D o p p l e r T e c h n i q u e
BS1 + M1  Reference Beam
P+L+BS3  Modulated Beam
Reference Beam + BC  High Carrier Frequency
BS : Beam Splitter; L : thin lens; P: quarter wave plate; M: Mirror; BC: Bragg Cell; D: Detector

30. O p t i c a l M o d e l
L a s e r D o p p l e r T e c h n i q u e
A: AC Amplitude; 𝑓𝐵: carrier frequency; 𝜃 𝑚: modulation phase; 𝜃0: initial phase; 𝑓𝑚: doppler
frequency; 𝑣: velocity; 𝑠: displacement.
BS : Beam Splitter; L : thin lens; P: quarter wave plate; M: Mirror; BC: Bragg Cell; D: Detector
𝑖 𝑑𝑒𝑡 𝑡 = 𝐼 𝐷𝐶 + 𝐴𝑐𝑜𝑠 2𝜋𝑓𝐵 𝑡 + 𝜃 𝑚 + 𝜃0
𝜃 𝑚 𝑡 =
4𝜋𝑠(𝑡)
⋋
 𝑓𝑚 𝑡 =
2𝑣(𝑡)
⋋

31. O p t i c a l M o d e l
M i c r o - S c a n n i n g V i b r o m e t e r
Doppler technique + Array of points  Microscopic Imaging of MEMS motion

32. C h a l l e n g e s i n M E M S
Gaussian Beam Envelope:
𝐴 𝑟 =
𝐴
𝑞(𝑧)
exp −𝑗𝑘
𝜌2
2𝑞 𝑧
, 𝑞 𝑧 = 𝑧 + 𝑗𝑧0
Gaussian Beam Amplitude:
𝑈 𝑟 = 𝐴
𝑊0
𝑊(𝑧)
exp −
𝜌2
𝑊2 𝑧
exp(−𝑗𝑘𝑧 − 𝑗𝑘
𝜌2
2𝑅 𝑧
+ 𝑗𝛾 𝑧 )
𝜌2
= 𝑥2
+ 𝑦2
;
1
𝑞(𝑧)
=
1
𝑅(𝑧)
− 𝑗
⋋
𝜋𝑊2(𝑧)
; 𝑊 𝑧 = 𝑊0 1 + (
𝑧0
𝑧
)2; 𝑅 𝑧 = 𝑧(1 +
𝑧0
𝑧
2
) ;𝑊0 =
⋋𝑧0
𝜋
; 𝛾 𝑧 = 𝑡𝑎𝑛−1
(
𝑧
𝑧0
)

33. C h a l l e n g e s i n M E M S
D i f f r a c t i o n
Phase Difference:
∆𝜃 = 𝑘∆𝑧 +
𝑧 𝑚
𝑧 𝑚
2 + 𝑧0
2
−
𝑧 𝑟𝑒𝑓
𝑧 𝑟𝑒𝑓
2 + 𝑧0
2
+ (𝛾 𝑧 𝑚 − 𝛾 𝑧 𝑟𝑒𝑓 )
At
𝑧 𝑚
𝑧 𝑚
2+𝑧0
2 =
𝑧 𝑟𝑒𝑓
𝑧 𝑟𝑒𝑓
2+𝑧0
2  Single interference
fringe
Initial spot size is 30𝜇𝑚 with OPD of 500𝜇𝑚

34. C h a l l e n g e s i n M E M S
D i f f r a c t i o n
Single Fringe  Better Visibility iff Detector size is reduced
Detector Size Reduction  Throughput Reduction

35. C h a l l e n g e s i n M E M S
B e a m C o l l i m a t i o n
Gaussian Inherent Divergence Angle :
Limited propagation
Weak Coupling Efficiency

36. C h a l l e n g e s i n M E M S
B e a m C o l l i m a t i o n
Increase beam waist  Decrease Divergence Angle
𝐺𝑐 =
𝑊𝑜𝑢𝑡
𝑊𝑖𝑛
=
1
(1 −
𝑑𝑖𝑛
𝑓
)2+(
𝑧0
𝑓
)2
𝐺𝑐 :Beam Collimation Gain; 𝑑𝑖𝑛: distance bet. Incident beam waist and focal length of mirror; 𝑓: focal length of mirror

37. R e f e r e n c e s
(1) S.Kim; G. Barbastathis; and H. Tuller, “MEMS For Optical Functionality”, Journal of Electroceramics, 12, 133-144, 2004.
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38. R e f e r e n c e s
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SPIE, Vol. 7930, No. 73900J-9, 2016.
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Curved MEMS Mirror”, Micromachines, Vol. 8, No. 134, 2017.

39. T H A N K Y O U