UNIVERSITY OF CALIFORNIA
SANTA CRUZ
DESIGN, CHARACTERIZATION AND TESTING OF A
MICRO-ELECTRO-MECHANICAL SYSTEM (MEMS)
LAMELLAR GRATING INTERFEROMETER IN POLYMUMPSTM
A thesis submitted in partial satisfaction of the
requirements for the degree of
MASTER OF SCIENCE
in
ELECTRICAL ENGINEERING
by
Janelle A. Yong
June 2011
The Thesis of Janelle A. Yong
is approved:
Professor Joel A. Kubby, Chair
Professor Claire Gu
Professor Roberto Bogomolni
Tyrus Miller
Vice Provost and Dean of Graduate Studies
Table of Contents
List of Figures
iv
Dedication
v
Acknowledgments
vi
Abstract
vii
1 Introduction
1
2 Current Applications
2.1 “A Large-Travel Vertical Planar Actuator with Improved Stability” . . . . . . .
2.2 “Extending the Travel Range of Analog-Tuned Electrostatic Actuator” . . . . .
2.3 Novel Applications Utilizing LGIs . . . . . . . . . . . . . . . . . . . . . . . . . .
3
3
6
6
3 Lamellar Grating Interferometer Design
3.1 Design Goals . . . . . . . . . . . . . . .
3.2 MUMPs Processes . . . . . . . . . . . .
3.2.1 SOIMUMPsTM . . . . . . . . . .
3.2.2 PolyMUMPsTM . . . . . . . . . .
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8
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9
9
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4 Basic Mathematical Analysis
4.1 Lamellar Grating Interferometer Theory . . . . . . . . . . . . . . . . . . . . . .
4.2 Electrostatic Actuation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3 Expected Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13
13
14
15
5 Design Challenges
16
6 LGI Final Design
6.1 Overview of the LGI Final Design . . . . . . . . . . . . . . . . . . . . . . . . .
6.2 A Closer Look at LGI Cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
21
21
23
7 Testing of the LGI
7.1 Methods . . . . . . . .
7.2 Experimental Results 7.2.1 Cell A1 . . . .
7.2.2 Cell B2 . . . .
7.2.3 Cell C3 . . . .
29
29
31
31
36
38
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Static State
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iii
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Guidelines
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7.3
7.2.4 Cell D4 . . . . . . . . . . . . .
7.2.5 Cell D6 . . . . . . . . . . . . .
7.2.6 Cell C7 . . . . . . . . . . . . .
7.2.7 Cell F6 . . . . . . . . . . . . .
7.2.8 Cell F7 . . . . . . . . . . . . .
Experimental Results - Actuated State
7.3.1 Actuation Methods . . . . . . .
7.3.2 Actuation of Cell C7 . . . . . .
7.3.3 Actuation of Cell D7 . . . . . .
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40
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52
8 Future Work
55
9 Conclusion
59
10 Appendix: LGI Layout Images
10.1 Cross Sections: Column A . .
10.2 Cross Sections: Column B . .
10.3 Cross Sections: Column C . .
10.4 Cross Sections: Column D . .
10.5 Cross Sections: Column E . .
10.6 Cross Sections: Column F . .
10.7 Full Layouts . . . . . . . . . .
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Bibliography
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60
60
62
64
66
68
70
72
77
iv
List of Figures
1.1
Schematics of a combdrive rectangular diffraction grating illuminated by monochromatic light, and modulation of the zeroth order intensity as the grating depth d
is continually varied over a distance of multiple wavelengths [4] . . . . . . . . .
1.2
1
Fourier Transform Spectrometer (Michelson Interferometer) illustrating position
of the beam splitter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
2.1
Polychromator beam structure in cross-section for the unactuated state [2] . . .
3
2.2
Beam structure in the actuated state. The lower beam undergoes bending, while
the mirror beam (Poly-3 and Metal-1) remains flat and deflects vertically [2] . .
2.3
MEMCAD model showing a deformed upper beam due to a 20 MPa tensile stress
in both beam layers [2] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4
4
4
(a) Simulated displacement versus voltage for the multi-layer nonlinear spring
design. In this simulation: L = 600 µm, w = 20 µm, t1 = 1 µm, t2 = 2.5 µm,
g1 = 8 µm, g2 = 4 µm, E = 160 GPa, and s0 = 20 MPa. (b) Measured voltagedisplacement characteristics for devices with different beam segment lengths [2]
5
2.5
Leveraged bending (a) without being actuated and (b) under actuation [10] . .
6
3.1
Project specifications of finger size and period . . . . . . . . . . . . . . . . . . .
8
3.2
Cross sectional view showing all layers of the SOIMUMPs process (not to scale)
[9] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3
Cross sectional view showing all seven layers of the PolyMUMPs process (not to
scale) [5] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4
9
10
The structure is released with an HF solution and creates Poly1 rotor that rotates
around a fixed Poly2 hub. The stacks of Poly1, Poly2, and Metal on the sides
5.1
represent the stators used to drive the motor electrostatically [5] . . . . . . . .
12
PolyMUMPs layer thicknesses [5] . . . . . . . . . . . . . . . . . . . . . . . . . .
17
v
5.2
Enclose Layer 2 by Layer 1 where A = minimum boundary condition [5] . . . .
5.3
The wiring diagram showing the connections to the ground and voltage bond pads 19
5.4
Example of a cell whose reflective mirror layer is subject to topographical effects
from the Poly0 layer below . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5
18
19
The upper beam makes contact with posts of lower beam at which point the
upper beam bends upon further actuation, stiffening the lower beam [2] . . . .
20
6.1
Layout of one finger in Cell A1 . . . . . . . . . . . . . . . . . . . . . . . . . . .
23
6.2
Cross Section through a finger illustrating dimples in Cell A1 . . . . . . . . . .
23
6.3
3D rendering of CellA1 from L-Edit . . . . . . . . . . . . . . . . . . . . . . . .
23
6.4
Layout of one finger in Cell A2 . . . . . . . . . . . . . . . . . . . . . . . . . . .
24
6.5
Cross Section through a finger in Cell A2 . . . . . . . . . . . . . . . . . . . . .
24
6.6
Cross Section through a finger in Cell A3 . . . . . . . . . . . . . . . . . . . . .
24
6.7
Cross Section through a finger in Cell A4 . . . . . . . . . . . . . . . . . . . . .
25
6.8
Cross Section through a finger in Cell A5 . . . . . . . . . . . . . . . . . . . . .
25
6.9
Cross Section through a finger in Cell A6 . . . . . . . . . . . . . . . . . . . . .
25
6.10 Cross Section through a finger in Cell A7 . . . . . . . . . . . . . . . . . . . . .
26
6.11 Cross Section through a finger in Cell B1 . . . . . . . . . . . . . . . . . . . . .
26
6.12 Cross Section through a finger in Cell C2 . . . . . . . . . . . . . . . . . . . . .
26
6.13 Cross Section through a finger in Cell D3 . . . . . . . . . . . . . . . . . . . . .
27
6.14 Cross Section through a finger in Cell E4 . . . . . . . . . . . . . . . . . . . . .
27
6.15 Cross Section through a finger in Cell F5
. . . . . . . . . . . . . . . . . . . . .
27
6.16 Cross Section through a finger in Cell F6
. . . . . . . . . . . . . . . . . . . . .
28
6.17 Cross Section through a finger in Cell F7
. . . . . . . . . . . . . . . . . . . . .
28
7.1
Raw image of Cell A1 taken from the Veeco WYKO Interferometer . . . . . . .
30
7.2
Surface image of Cell A1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
31
7.3
2D profile image of the bondpads in Cell A1 . . . . . . . . . . . . . . . . . . . .
32
7.4
2D profile image of the Finger 3 in Cell A1 . . . . . . . . . . . . . . . . . . . .
33
7.5
2D profile image of the Finger 20 in Cell A1 . . . . . . . . . . . . . . . . . . . .
34
TM
7.6
Mechanical parameters of PolyMUMPs
process layers [5] . . . . . . . . . . .
35
7.7
3D image of Cell A1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35
7.8
Cross Section through a finger in Cell B2 . . . . . . . . . . . . . . . . . . . . .
36
7.9
Raw image of Cell B2 taken from the Veeco WYKO Interferometer . . . . . . .
36
7.10 2D profile images of (a) Finger 4, (b) Finger 6, and (c) Finger 29 in Cell B2 . .
37
7.11 Cross Section through a finger in Cell C3 . . . . . . . . . . . . . . . . . . . . .
38
vi
7.12 Raw image of Cell C3 taken from the Veeco WYKO Interferometer . . . . . . .
38
7.13 3D image of Cell C3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
39
7.14 2D profile images of (a) Finger 20, (b) Finger 25 and (c) Finger 35 in Cell C3 .
40
7.15 Cross Section through a finger in Cell D4 . . . . . . . . . . . . . . . . . . . . .
41
7.16 2D profile image of Cell D4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
41
7.17 Cross Section through a finger in Cell D6 . . . . . . . . . . . . . . . . . . . . .
42
7.18 3D image of Cell D6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
42
7.19 2D X-Profile image through a finger in Cell D6 . . . . . . . . . . . . . . . . . .
43
7.20 Cross Section through a finger in Cell C7 . . . . . . . . . . . . . . . . . . . . .
43
7.21 Raw image of Cell F6 taken from the Veeco WYKO Interferometer . . . . . . .
44
7.22 Surface image of Cell F6. Information is lost where there are black voids . . . .
44
7.23 Raw image of Cell F7 taken from the Veeco WYKO Interferometer . . . . . . .
45
7.24 Surface image of Cell F7. Information is lost where there are black voids . . . .
45
7.25 Block Diagram of the Actuation Setup . . . . . . . . . . . . . . . . . . . . . . .
46
7.26 Raw image of Cell C7 taken from the Veeco WYKO Interferometer . . . . . . .
47
7.27 Surface image of Cell C7 at 0V actuation . . . . . . . . . . . . . . . . . . . . .
48
7.28 3D image of Cell C7 at 0V actuation . . . . . . . . . . . . . . . . . . . . . . . .
48
7.29 2D profile image of Cell C7 at 0V actuation . . . . . . . . . . . . . . . . . . . .
49
7.30 Displacement in the Z-direction (µm) vs. Voltage (V) comparing the heights of
Finger 2 and Finger 3 in Cell C7. Voltage was applied to the “even” set of fingers 50
7.31 2D Y-Profile comparing the heights of Finger 2 and Finger 3 in Cell C7. 19.5 V
was applied . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
50
7.32 2D profiles of Cell C7 after 19.5V was applied. Pull-in occurs on Finger 38. Also
note the deflection of the overall surface, especially in the middle of the device.
51
7.33 2D Y-Profile image of Cell D7 at 0V actuation . . . . . . . . . . . . . . . . . .
52
7.34 2D Y-Profile comparing the heights of Finger 2 and 3 in Cell D7 at 25V actuation 52
7.35 2D Y-Profile comparing the heights of two fingers in Cell D7 at 50V actuation
53
7.36 2D Y-Profile comparing the heights of the pulled-in fingers in Cell D7 at 75V
actuation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
53
8.1
Descriptions of each cell in the revised LGI layout . . . . . . . . . . . . . . . .
55
8.2
Revised layout of the Lamellar Grating Interferometer . . . . . . . . . . . . . .
56
8.3
Updated design of the Test Structures. The fixed-fixed beam structure is on the
left and the cantilever beam structure is on the right . . . . . . . . . . . . . . .
8.4
58
Layout of the alignment test structures. Each dot on the grid represents a length
of 10 µm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
vii
58
10.1 Cross Section through a finger in Cell A1 . . . . . . . . . . . . . . . . . . . . .
60
10.2 Cross Section through a finger in Cell A2 . . . . . . . . . . . . . . . . . . . . .
60
10.3 Cross Section through a finger in Cell A3 . . . . . . . . . . . . . . . . . . . . .
60
10.4 Cross Section through a finger in Cell A4 . . . . . . . . . . . . . . . . . . . . .
61
10.5 Cross Section through a finger in Cell A5 . . . . . . . . . . . . . . . . . . . . .
61
10.6 Cross Section through a finger in Cell A6 . . . . . . . . . . . . . . . . . . . . .
61
10.7 Cross Section through a finger in Cell A7 . . . . . . . . . . . . . . . . . . . . .
61
10.8 Cross Section through a finger in Cell B1 . . . . . . . . . . . . . . . . . . . . .
62
10.9 Cross Section through a finger in Cell B2 . . . . . . . . . . . . . . . . . . . . .
62
10.10Cross Section through a finger in Cell B3 . . . . . . . . . . . . . . . . . . . . .
62
10.11Cross Section through a finger in Cell B4 . . . . . . . . . . . . . . . . . . . . .
63
10.12Cross Section through a finger in Cell B5 . . . . . . . . . . . . . . . . . . . . .
63
10.13Cross Section through a finger in Cell B6 . . . . . . . . . . . . . . . . . . . . .
63
10.14Cross Section through a finger in Cell B7 . . . . . . . . . . . . . . . . . . . . .
63
10.15Cross Section through a finger in Cell C1 . . . . . . . . . . . . . . . . . . . . .
64
10.16Cross Section through a finger in Cell C2 . . . . . . . . . . . . . . . . . . . . .
64
10.17Cross Section through a finger in Cell C3 . . . . . . . . . . . . . . . . . . . . .
64
10.18Cross Section through a finger in Cell C4 . . . . . . . . . . . . . . . . . . . . .
65
10.19Cross Section through a finger in Cell C5 . . . . . . . . . . . . . . . . . . . . .
65
10.20Cross Section through a finger in Cell C6 . . . . . . . . . . . . . . . . . . . . .
65
10.21Cross Section through a finger in Cell C7 . . . . . . . . . . . . . . . . . . . . .
65
10.22Cross Section through a finger in Cell D1 . . . . . . . . . . . . . . . . . . . . .
66
10.23Cross Section through a finger in Cell D2 . . . . . . . . . . . . . . . . . . . . .
66
10.24Cross Section through a finger in Cell D3 . . . . . . . . . . . . . . . . . . . . .
66
10.25Cross Section through a finger in Cell D4 . . . . . . . . . . . . . . . . . . . . .
67
10.26Cross Section through a finger in Cell D5 . . . . . . . . . . . . . . . . . . . . .
67
10.27Cross Section through a finger in Cell D6 . . . . . . . . . . . . . . . . . . . . .
67
10.28Cross Section through a finger in Cell D7 . . . . . . . . . . . . . . . . . . . . .
67
10.29Cross Section through a finger in Cell E1 . . . . . . . . . . . . . . . . . . . . .
68
10.30Cross Section through a finger in Cell E2 . . . . . . . . . . . . . . . . . . . . .
68
10.31Cross Section through a finger in Cell E3 . . . . . . . . . . . . . . . . . . . . .
68
10.32Cross Section through a finger in Cell E4 . . . . . . . . . . . . . . . . . . . . .
69
10.33Cross Section through a finger in Cell E5 . . . . . . . . . . . . . . . . . . . . .
69
10.34Cross Section through a finger in Cell E6 . . . . . . . . . . . . . . . . . . . . .
69
10.35Cross Section through a finger in Cell E7 . . . . . . . . . . . . . . . . . . . . .
69
viii
10.36Cross Section through a finger in Cell F1
. . . . . . . . . . . . . . . . . . . . .
70
10.37Cross Section through a finger in Cell F2
. . . . . . . . . . . . . . . . . . . . .
70
10.38Cross Section through a finger in Cell F3
. . . . . . . . . . . . . . . . . . . . .
70
10.39Cross Section through a finger in Cell F4
. . . . . . . . . . . . . . . . . . . . .
71
10.40Cross Section through a finger in Cell F5
. . . . . . . . . . . . . . . . . . . . .
71
10.41Cross Section through a finger in Cell F6
. . . . . . . . . . . . . . . . . . . . .
71
10.42Cross Section through a finger in Cell F7
. . . . . . . . . . . . . . . . . . . . .
71
10.43Entire layout of the Lamellar Grating Interferometer (Version 1) . . . . . . . .
73
10.44Description of each cell of the Lamellar Grating Interferometer (Version 1) . . .
74
10.45Revised layout of the Lamellar Grating Interferometer (Version 2) . . . . . . .
75
10.46Descriptions of each cell in the revised LGI layout (Version 2) . . . . . . . . . .
76
ix
For my boyfriend, Nick Lachica.
“ Something always brings me back to you. It never takes too long . . . ”
x
Acknowledgments
First of all, I would like to thank my advisor, Joel A. Kubby, and the other members
of my reading committee, Professors Claire Gu and Roberto Bogomolni, for taking the time to
review my thesis. I would also like to thank Silbiu Belicu and EPIR for funding the fabrication
of the Lamellar Grating Interferometer.
I would also like to thank the MEMS Research Laboratory at UC Santa Cruz for
taking the time to help me understand how to implement my design and how to use the various
apparatus in the labs for my testing. I would not have obtained all my valuable results if it
were not for Dmitry Medved, Bautista Fernandez, Oscar Azucena, Ziah Dean, Zachary Graham,
Andrew Norton, Dan O’Leary, Marco Reinig, and Xiaodong Tao.
Thank you to Team MUMPStars in the EE115 Introduction to MEMS Design Course
for working tirelessly with me to develop a revised Lamellar Grating Interferometer utilizing
the PolyMUMPSTM Fabrication Process for the second iteration of fabrication.
Thank you to Catherine Tien and Jillian Yong for reading through all of my revisions
of this thesis before it was sent to my reading committee. Also, thank you to all of my friends
and family for being supportive of me throughout this process and my entire academic career.
xi
Abstract
Design, Characterization and Testing of a Micro-Electro-Mechanical System
(MEMS) Lamellar Grating Interferometer in PolyMUMPsTM
by
Janelle A. Yong
The detection of airborne chemicals can be achieved through infrared spectroscopy.
Current infrared spectrometers are based on a Michelson interferometer design in which a
beam splitter is used to divide the radiation and is eventually reconstructed at a detector.
Here, information is gained from the interference pattern. However, Michelson interferometers
suffer from several disadvantages, namely its efficiency of 25%. But in order to create a more
sensitive and specific chemical detector, we must consider a design other than the Michelson
interferometer. Lamellar Grating Interferometers can be created in Micro-Electro-Mechanical
System (MEMS) technology. Lamellar Grating Interferometers use the principle of wavefront
division in which a monochromatic light hits a mirror grating consisting of alternating back
facets and front facets. Half of the light hits the back facets and the other half hits the front
facets. If we move one set of facets, the path difference between the two types of facets will
vary and we can create an interferogram with an efficiency close to 100%.
In this paper, a design for a MEMS Lamellar Grating Interferometer that operates in
the MWIR to LWIR spectral range is presented. In order to achieve this goal, I must consider
R process that is compatible with geometries greater than or equal to 5 µm. Also,
a MUMPs
a period Λ of 50 µm is expected to provide a good tradeoff between fill factor and divergence
angle requirements. The last consideration for the Lamellar Grating Interferometer is to achieve
maximum deflection for maximum resolution. Within my design, I propose 42 different designs
which are used to identify the optimal performance of the Lamellar Grating Interferometer.
R NT1100 White
Finally, testing and characterization are performed using the Veeco WYKO
R Software to analyze these results. Results on
Light Interferometer and the Wyko Vision32
the actuation of the Lamellar Grating Interferometer are also presented in this paper.
Chapter 1
Introduction
Lamellar Grating Interferometers are a special type of Fourier Transform Spectrometer. A plane wave propagates towards the grating where the wave is split into two; one half of
the plane wave reflects off of the front facets and the other half reflects off of the back facets.
Combining the interference patterns, we can detect the amplitude change depending on the
respective optical path differences from the front and the back facets. Then, we can directly
gather information from the 0th order diffraction pattern. This is important because we can
ignore larger orders of diffraction and only concern ourselves with the interference patterns of
the 0th order diffraction reflecting off of the front and back facets of the LGI [4].
Figure 1.1: Schematics of a combdrive rectangular diffraction grating illuminated by monochromatic light, and modulation of the zeroth order intensity as the grating depth d is continually
varied over a distance of multiple wavelengths [4]
1
Lamellar Grating Interferometers (LGIs) are advantageous in that they are much
simpler devices as compared to the Michelson Interferometer which is heavily dependent on
using a beam splitter in its optical system. A Michelson Interferometer works in a very similar
fashion by creating interference fringes by splitting a beam of monochromatic light. However,
the difference between the two is that this device uses the beam splitter to send one beam to
a translating mirror and another beam to a fixed mirror. The two beams reflect off of these
mirrors and are reconstructed at the detector. An interference pattern is created here when
the two beams travel different lengths.
Figure 1.2: Fourier Transform Spectrometer (Michelson Interferometer) illustrating position of
the beam splitter
Michelson Interferometers have low efficiencies (near 25%) and limited spectral range
because of the beam splitter. No such beam splitter is required in an LGI system. A miniaturized LGI is able to achieve higher resolution, high speed, and higher efficiency (close to
100%) for large wavenumbers [4]. These interferometers require a mechanical actuator to move
the back facet back and forth (i.e. tunable) to record the interferogram. The components
used to make the Micro-Electro-Mechanical Systems (MEMS) resonant structures have a very
small mass and therefore low inertia and make MEMS technology ideal for this application.
Especially with the MEMS resonating structure and overall miniaturization of the LGI, the
operation and fabrication is simpler, cheaper, and smaller than devices of the past. This design
can support a fully functional system. All you would need for an operational spectrometer [are]
integrations with a simple photodetector and readout circuit [1].
2
Chapter 2
Current Applications
2.1
“A Large-Travel Vertical Planar Actuator with Improved Stability”
In a recent paper published in 2003, Deutsch et al. investigated a polychromator,
which is a programmable electrostatically actuated diffraction grating. They reported achieving
3.9 microns of planar analog vertical travel with a polysilicon structure that operates in the
mid-wave infrared spectrum. The device they built had “512 grating elements, each 20 microns
wide and one centimeter in length” [2]. The process used to build the grating implements three
layers of polysilicon and two oxide layers; Oxide-2 is between Poly-1 and Poly-2 and Oxide-3
is between Poly-2 and Poly-3. A dielectric insulator is made out of Nitride-1 and Oxide-1 and
sits between the silicon wafer and Poly-1 (Figure 2.1).
Figure 2.1: Polychromator beam structure in cross-section for the unactuated state [2]
After etching away the oxide layers, they were left with a two-layer polysilicon beam
3
structure. When voltage is applied to the electrode created with Poly-1 layer and to the lower
beam in the Poly-2 layer, a difference in potential will attract these polysilicon layers to each
other. Poly-2 will be pulled down towards the Poly-1 layer, which in turn, also pulls down the
Poly-3 layer, the upper beam, a distance D, as seen in Figure 2.2.
Figure 2.2: Beam structure in the actuated state. The lower beam undergoes bending, while
the mirror beam (Poly-3 and Metal-1) remains flat and deflects vertically [2]
Deutsch et al. came across several design challenges for their polychromator, mainly
those surrounding tensile stress and the support structure. First, they found that the tensile
stress that was present in their design caused a contraction of the reflective mirror beam
towards the center. This contraction caused an asymmetry that made the pull-in occur at a
lower voltage and displacement. Their solution was to extend the mirror beam to connect at
a fixed support at the edge of the grating and observed that after actuation, the mirror beam
became flat after two or three segments. In Figure 2.3, they concluded that as the tensile stress
is increased, the actuation voltage required increased and the displacement at pull-in decreased.
Figure 2.3: MEMCAD model showing a deformed upper beam due to a 20 MPa tensile stress
in both beam layers [2]
Their second design challenge was based on the support structure due to the fabrication process and polychromator designs. They concluded that from the conformal layers
that form in surface micromachining, the supports are weaker since you do not achieve a solid
support. Instead you have one with an indentation from anchoring above layers to the ones
4
below. They also said that the thin structural layers in combination with the large sacrificial
layers make the supports worse as well. One solution they suggested was to introduce support
posts along the middle of each beam to balance out the beam and make it more rigid. A higher
pull-in voltage is required for a more rigid structure but a positive trade-off is that there is an
increase in the stability of vertical travel.
Most importantly, for their design, they were able to conduct Finite Element Analysis
and simulations. The following data in Figure 2.4 show (a) a simulated displacement versus a
range of voltages and (b) the measured voltage-displacement characteristics with varying beam
segment lengths. Both figures display a non-linear behavior within the 4 µm displacement and
at what voltage mirrors come into contact (i.e. touchdown). From their measured results, they
can also deduct that the two-beam structure becomes stiffer when the beam segment lengths
are decreased, therefore, requiring a larger pull-in voltage.
Figure 2.4: (a) Simulated displacement versus voltage for the multi-layer nonlinear spring
design. In this simulation: L = 600 µm, w = 20 µm, t1 = 1 µm, t2 = 2.5 µm, g1 = 8 µm,
g2 = 4 µm, E = 160 GPa, and s0 = 20 MPa. (b) Measured voltage-displacement characteristics
for devices with different beam segment lengths [2]
5
2.2
“Extending the Travel Range of Analog-Tuned Electrostatic Actuator”
The pull-in instability limits the travel distance of elastically suspended parallel-plate
electrostatic microactuators to about one-third of the undeflected gap distance. In another
paper, Elmer S. Hung and Stephen D. Senturia talked about the “leveraged bending” and
“strain-stiffening” methods for extending the travel range of electrostatic actuators. The leveraged bending effect can be used to achieve full gap travel at the cost of increased actuation
voltage while the strain-stiffening effect can be used to minimize actuation voltage. However,
the latter is due to the property of the material and is not an option for our design consideration
and will be explained in Chapter 5. This paper used grating-element actuators with 1 cm long
mirrors and achieved a stable vertical travel distances of 1.75 µm out of a 2 µm gap [10].
The leveraged bending methodology is used to work around the pull-in instability by
applying electrostatic force to only a portion of a structure, then using the rest of the structure
as a “lever” to position specific parts of the structure through a large range of motion. The
key to this method is that the electrostatically actuated portions of the structure deflect less
than the pull-in limit, while other portions of the structure can move through the entire gap.
Figure 2.5: Leveraged bending (a) without being actuated and (b) under actuation [10]
2.3
Novel Applications Utilizing LGIs
There is a need for LGIs to operate under sensitive conditions with very specific sen-
sors for various applications like the detection toxic materials, color measurement, quality and
process control, gas detection and chemical analysis [8]. More applications include environmental monitoring, food and beverage industry, imagery, telecommunication, life science, and
medical diagnostics. The realization of an affordable, compact, easy to handle LGI with high
6
resolution, high efficiency at high speeds makes this instrument ideal for all these different types
of applications.
7
Chapter 3
Lamellar Grating Interferometer Design
Guidelines
3.1
Design Goals
For this project, there were several guidelines and specifications to take into consid-
eration. To operate as a Lamellar Grating Interferometer, we must be able to build a variable
grating distance that forms an interferogram. To obtain this interferogram, we must be able to
obtain the 0th order diffraction from the grating and a Fourier transform that resolves in the
IR region. Ideally, we want a design similar to the following figure:
Figure 3.1: Project specifications of finger size and period
R that is comWe must design the LGI with a Multi-User MEMS Process, or MUMPs,
R process
patible with geometries greater or equal to 5 µm. We then have to consider a MUMPs
with design rules and fabrication geometries that agree with being able to operate in the MidWave Infrared (MWIR) to the Long-Wave Infrared (LWIR) spectral range and one that will be
8
able to give a maximum deflection for maximum resolution. Another consideration is to achieve
a period, Λ, of 50 µm which will provide a good tradeoff between fill factor and divergence angle
requirements.
3.2
MUMPs Processes
3.2.1
SOIMUMPsTM
SOIMUMPsTM is a silicon-on-insulator micromachining process. This is one of the
R program along with PolyMUMPsTM (disthree standardized processes as part of the MUMPs
cussed in Section 3.2.2) and MetalMUMPs, which is an electroplated nickel process.
SOIMUMPsTM implements four general features, outlined here [9]:
• The substrate used is a silicon-on-insulator (SOI) wafer with the following thicknesses:
– Silicon thickness: 10 ± 1 µm
– Oxide thickenss: 1 ± 0.05 µm
– Handle wafer (Substrate) thickness: 400 ± 5 µm
Figure 3.2: Cross sectional view showing all layers of the SOIMUMPs process (not to scale) [9]
• The Silicon layer can be used as the mechanical structure. Because it is doped and
patterned to the Oxide layer, it can be used as resistor structures and electrical routing.
• The Substrate layer can be patterned and etch from the “bottom” side through to the
Oxide layer. This is beneficial for the example of a Lamellar Grating Interferometer
9
because we can achieve a larger deflection than possible in PolyMUMPsTM . This design
was explored in another project exploiting the “through-hole structure” by Zhenxiao Liu
[7].
• A shadow-masked metal process is used to provide Metal features to the design. Such
features include bond pads, electrical routing, and optical mirror surfaces. The design for
the Lamellar Grating Interferometer by Z. Liu utilizes this Metal layer as the reflective
surface.
3.2.2
PolyMUMPsTM
PolyMUMPsTM is a general-purpose surface micromachining fabrication process of-
fered by the company MEMSCAP that offers a seamless transition between prototyping and
manufacturing. This fabrication process uses three layers of polysilicon as the structural material, oxide as the sacrifical layer, and a silicon nitride layer that serves as insulation between
the polysilicon and the substrate.
Figure 3.3: Cross sectional view showing all seven layers of the PolyMUMPs process (not to
scale) [5]
Poly0 is the first layer that is deposited upon the nitride layer. It is a Low Pressure
Chemical Vapor Deposition (LPCVD) polysilicon film with a thickness of 0.5 µm. Poly0 can
be patterned by a photolithography step in which a mask of photoresist is chosen and is
then plasma-etched away, leaving behind what polysilicon has been exposed. The process of
patterning the wafers with photoresists, etching and stripping the remaining photoresists is
repeated for every layer deposited in the PolyMUMPsTM process. Once all layers have been
deposited, the Oxide layers can be removed with a sacrificial etch of 49% buffered hydrofluoric
10
acid (HF), leaving the structural polysilicon layers behind. The layer thicknesses can be seen
in Figure 5.1.
PolyMUMPsTM has a few nuances unique to designing in surface micromachining and
in MEMS technology as a whole. These are all outlined the Design Handbook [5] and define the
mandatory rules (e.g. minimum line widths and spaces) and the advisory rules (e.g. nominal
spaces). These rules are in place to ensure that the tolerances of the lithographic process is
conserved. Otherwise, violations of these mandatory rules can result in “missing, undersized,
oversized or fused features.” Some of these rules describe the correct designs for holes, dimples,
anchors, and vias.
Holes are created in a special hole layer to provide for a shorter pathway for etchants
to etch through larger polysilicon features. Holes also have to be designed to agree with the
corresponding light field level, i.e. HOLE0 has to use the design rules in POLY0. Enclosure
rules must be obeyed when stacking layers such that the holes of the upper layer has to enclose
the next lower level by 2.0 µm (Rules T and U in the Design Handbook). For our design of the
LGI, we do not need to include holes. Lateral etch hole separations for both Poly1 and Poly2
are a maximum of 30 µm to ensure release of both Poly1 and Poly2 structures. Since the width
of each finger in the LGI design is 20 µm, we can exclude the holes.
Another type of “hole” is created for dimples. A hole is etched with a depth of 0.75
µm into the Oxide1 layer, which has a thickness of 2.0 µm. Poly1 is then deposited and fills
the hole to create the dimples which hang down from the Poly1 structural layer once Oxide1
is etched away. The purpose of dimples are to limit the amount of surface area that would
come into contact. With structures on the micro-scale, surface forces such as van der Waals
and capillarity play a major part in designing MEMS devices. Once the polysilicon layers come
into contact with each other across a “large” area, they get stuck to each other in a special
case called stiction [6].
Another design aspect to take into consideration with PolyMUMPsTM is the difference
between using anchors and Poly1-Poly2-Vias. Anchors are used to connect polysilicon layers to
the subtrate level. Anchors are treated as holes that are cut all the way through Oxide and Poly
layers so that when layers above are deposited, they fill in these holes and affix to the substrate.
Poly1-Poly2-Vias are similar in that they can affix the structural layers to each other, literally
for Poly2 to connect to Poly1, and can also create an electrical connection between the two
layers. But, these vias do not connect all the way down to the substrate. Anchors must be
used instead if a connection to the substrate is desired. Improper use of these two structures
can lead to fabrication errors. An example of an error due to leaving out anchors are released
bond pads. Since PolyMUMPsTM is a multi-user process, these bond pads will become released
11
after the sacrificial etch step and could land on other areas of the chip and even on other user’s
designs.
After all of the Design Rules are properly addressed, a released structure like in Figure
3.4 will be fabricated.
Figure 3.4: The structure is released with an HF solution and creates Poly1 rotor that rotates
around a fixed Poly2 hub. The stacks of Poly1, Poly2, and Metal on the sides represent the
stators used to drive the motor electrostatically [5]
12
Chapter 4
Basic Mathematical Analysis
4.1
Lamellar Grating Interferometer Theory
For this application, we are interested in operating the LGI within the Mid-Wave
Infrared (MWIR) spectrum for small wavelengths between 3 − 5 µm and a spectral resolution
∆k of 10 cm−1 where ∆k is calculated as
∆k = 1/OP D = 1/(2d)
(4.1)
where, OPD is the optical path difference and d is the maximum deflection of the optical
grating. This will be defined by the range of the MWIR spectrum as [λmin − λmax ], or [3 µm
- 5 µm] and in terms of wavenumber k = 1/λ, as [kmin − kmax ].
To observe how well the source is collimated, we must calculate the half divergence
angle θd with the following equation:
θd = tan (Ds /2f1 )
(4.2)
where, Ds is the size of the aperture source, and f1 is the focal length of the first collimating
mirror.
However, after the beam hits the collimated mirror, destructive interference occurs
since the rays that reflect off of the collimated mirror are unparallel due to the divergence effect.
So that we do not get destructive interference, we must set criteria for the half divergence angle
θd ≤
p
p
λmin /(2d) = ∆k/∆kmax
(4.3)
Also, the diffraction orders are observed at integer multiples of the angle λ/Λ. To
ensure we separate the 0th order from the 1st order diffraction, we must set another condition
13
that involves the grating period Λ with the following equation:
sin 2θd ≤ (λmin /Λ)
(4.4)
From the preceding equations, we can calculate the dimensions of our LGI. With
∆k = 10 cm−1 , d = 500 µm, a very large deflection.
4.2
Electrostatic Actuation
The design of each finger of the lamellar grating can be based on classic mechanical
structures such as fixed-fixed cantilever beams. The calculations will be based on a linear
model. Note, however, that once the deflection of the finger goes beyond the thickness of the
beam (the thickness of Poly1 is 2.0 µm), we can no longer use linear equations and must use
non-linear equations in the form of ax + bx3 . The two most dominant forces when actuating the mirror are the electrostatic force (created by capacitance between the actuator and
underlying electrode) and the mechanical spring force that will act to restore the actuator to
its undeformed dimensions. These forces have been modeled for fixed-fixed cantilever beams
and approximations to calculate critical voltage, maximum stroke, and displacement are well
understood. The equations for equating the electrical and mechanical forces are as follows:
0 AV
2z 2
Fe = Fm
(4.5)
= k(g0 − z)
(4.6)
2
where, A = the area of the capacitive plates, 0 = the permittivity of free space, g0 = initial
gap, and z = the distance between the fixed-fixed plate and the counter electrode.
We can calculate the pull-in voltage to be
s
VP I =
8km g03
270 A
(4.7)
For a fixed-fixed beam, the spring constant can be calculated as:
384EI
1
where I = ( hw3 )
L3
12
32Ehw3
Kf ixed−f ixedbeam =
L3
Kf ixed−f ixedbeam =
Also, the resonant frequency of a fixed-fixed beam can be approximated by:
s
r
1
Kf ixed−f ixedbeam
1
32Ehw3 /L3
fresonant =
=
2π
Mbeam
2π
Mbeam
14
(4.8)
(4.9)
(4.10)
4.3
Expected Values
Using these formulas, we can calculate the dimensions needed to achieve the frequency
for operating the device in order to account for noise.
With equation 4.8, the spring constant is
Kf ixed−f ixedbeam = .8192
(4.11)
Using equation 4.10, the estimated resonant frequency for our device with length L = 1000
µm, width W = 20 µm, and the thickness of the beam h = 2 µm is calculated as
fresonant
1
=
2π
s
32 × (160 × 109 P a) × (2 × 10−6 m) × (20 × 10−6 m)3 /(1000 × 10−6 m)3
(2330(kg/m3 )) × (2 × 10−6 m) × (1000 × 10−6 m) × (20 × 10−6 m)
(4.12)
fresonant = 14921Hz ≈ 15kHz
(4.13)
where Mbeam is the product of the length, width, thickness, and the density of Polysilicon.
Lastly, the pull-in voltage for a fixed-fixed beam with these dimensions is
Vpull−in = 10.85V
15
(4.14)
Chapter 5
Design Challenges
After doing our initial considerations and understanding our limitations with this
design, we do not believe that a deflection d = 500 µm will fulfill the spectral range required
for MWIR. We know that this will be a feat near-impossible to accomplish in MEMS technology
with specific fabrication processes. Put into perspective, the beam would have to deflect by 0.5
mm, which is approximately half of the size (length) alloted for the layout of one cell design.
Before we started our design, we had to choose between two different fabrication
processes: SOIMUMPsTM and PolyMUMPsTM , both described in Sections 3.2.1 and 3.2.2.
PolyMUMPsTM is a three-layer polysilicon surface micromachining process. SOIMUMPsTM is
used for micromachining Silicon-on-Insulator (SOI) structures with a 4-mask level patterning and etching process. SOIMUMPsTM technology’s main disadvantage is having only one
structural layer, which excludes the use of conventional hinges and joints, making the design
more difficult and more restricted versus the PolyMUMPs with three structural layers. However, SOIMUMPsTM provides highly planar surfaces which translate to a flat mirror when a
metal layer gets deposited on top. PolyMUMPsTM , on the other hand, is not as planar as
SOIMUMPsTM due to impurities in the Polysilicon. In our design, we are using a gold layer
on top of Polysilicon in many of our structures to overcome this drawback of the Polysilicon
surfaces [5] [9].
For the PolyMUMPsTM fabrication process, the fixed material layer thickness limits
the heights of the mechanical systems. A table presenting the material layer thicknesses is seen
in Figure 5.1. Consequently and more importantly, the limited thickness affects the maximum
stroke that can be achieved. We are limited to 2 microns from the Oxide 1 layer and therefore
the maximum stroke that can be achieved is one-third of the initial gap (i.e. ∼0.667 maximum
microns). On the same token, the thickness of the dimples needed on the Poly1 Layer to prevent
16
stiction to the Poly0 Actuator Layer measures 0.75 microns. Therefore, the maximum stroke
is physically limited to a maximum of 1.25 microns.
Figure 5.1: PolyMUMPs layer thicknesses [5]
Also, with the PolyMUMPsTM fabrication process, we have to work around a gap
between each fixed-fixed cantilever, or finger, of 5 µm. These wires have to travel from the
bond pads to the fingers directly to supply voltage. The bond pad for ground has to be
connected from the top of the design at the top of the fixed-fixed beam array to the counter
electrodes underneath each fixed-fixed beam, or finger. The left bond pad activates the “odd”
counter electrodes and the right bond pad activates the “even” counter electrodes producing a
binary grating. In one of our previous design considerations, we used 10 µm of spacing between
each fingers. The design rules state that in the Poly0 layer, you must have a minimum spacing
of 2 µm and a nominal spacing of 3 µm. Therefore, in between each finger, we must allot at
least 9 µm for the nominal spacings and the wires. This was our reason for choosing a spacing
of 10 µm. Ideally, we want each finger to be as close as possible to achieve higher efficiencies. In
other words, light will be lost when bounced off of the non-reflective Nitride surface in between
each finger. Our solution to this was to bring the fingers closer together from 10 µm to 5 µm.
However, there are several design rules that we must consider before bringing the
fingers closer together. First off, we would have to violate several enclosure rules in order to
keep a 5 µm gap between each finger and more importantly, a 20 µm reflective surface that
agrees with the period. Say we want to keep the 20 µm wide Metal layer. Each layer below
must enclose the layer directly above it by a minimum value as seen in Figure 5.2.
The distances that each layer must enclose another layer are:
• Poly2 enclose Metal 3.0 µm (Rule M)
• Poly1 enclose Poly2 4.0 µm (Rule O)
• Poly0 enclose Poly1 4.0 µm (Rule C)
17
Figure 5.2: Enclose Layer 2 by Layer 1 where A = minimum boundary condition [5]
Rule M in the Design Handbook [5] states that the Poly2 layer must enclose the Metal
layer by a minimum of 3.0 µm with the intention of not allowing the Metal to overlap the Poly2
layer. So, if we start with a width of 20 µm of Metal, the width of Poly0 after obeying these
particular design rules must be 42 µm. In addition to these enclosure rules, the minimum and
nominal spacing between Poly0, as mentioned previously, are 2.0 µm and 3.0 µm, respectively.
Therefore, the period taken across two fingers and two gaps is 90 µm, 40 µm larger than the
required period. We decided to intentionally violate these design rules to satisfy the period
specified for this project. Suggestions for future designs that agree with the enclosure rules are
made in Chapter 8. Also, discussion on violating the design rules is included in Section 7.3.3.
Instead of designing wires to connect to each electrode from between each side post,
we added wires that ran directly to the posts in the Poly1 layer from the left and right sides,
depending on if we are connecting to the “odd” or the “even” fingers. The ground electrodes
underneath each finger are connected to the bond pad at the top and wires do not have to be
redirected in between the posts. The following in Figure 5.3 shows this wiring scheme, which
is the essentially the same for all cells. This particular figure shows the wiring scheme for Cell
A1. The bond pad at the top serves as the ground and the bond pad to supply voltage is seen
at the bottom left. The ground bond pad connects the Poly0 layer of the bond pad to the
ground electrodes under each finger with a Poly0 wire with a width of 3 µm. The Poly1 layer
of the voltage bond pad is connected to a Poly1 wire, also a width of 3 µm, to every “odd”
finger. Not shown is the voltage bond pad on the right connecting to the “even” fingers.
In terms of optical optimization, the topography of the reflective mirror surface is
dependent on the layers below the top Metal Layer because in the PolyMUMPsTM fabrication
process, each layer is deposited conformally. The mirror surface can mimic the topographies
of the layers below, especially if the bottom electrodes in Poly0 are sectioned for leveraged
18
Figure 5.3: The wiring diagram showing the connections to the ground and voltage bond pads
bending, like in Figure 5.4. This will scatter the incident light on the LGI in an undesired way
and the efficiency will decrease.
Figure 5.4: Example of a cell whose reflective mirror layer is subject to topographical effects
from the Poly0 layer below
Another challenge we will face is that the Poly2 and Metal suspended beam above
Poly1 will curl up from the stresses of applying the metal. Adding metal will be more tensile on
top of the Poly2 layer, curling the beam up. The opposite would be if the metal was compressive
and curl the beam down. Our solution to this is to create a Poly1-Poly2-Via as a post at the
end of the Poly2/Metal beam that will prevent this beam from curling up. Also, if the Poly2
layer was not anchored down at the ends and we also assume that the Metal layer is not present,
the Poly2 layer will hit the posts from Poly1 when actuated, as seen in Figure 5.5. When the
Poly1 layer is pulled in towards the Poly0 electrodes, the Poly2 layer will make contact with
the posts and will bend upon further actuation. This will result in a stiffer structure [2].
19
Figure 5.5: The upper beam makes contact with posts of lower beam at which point the upper
beam bends upon further actuation, stiffening the lower beam [2]
20
Chapter 6
LGI Final Design
6.1
Overview of the LGI Final Design
The final design for the Lamellar Grating Interferometer is a 6 × 7 array of 42 similar
and independent cells, but each cell varies by one characteristic at a time. The design is
essentially a chip consisting of test structures to help aid in the optimization of the design of
the LGI and by changing one characteristic at a time, we are able to see distinct changes as
we observe neighboring cells. The LGI was designed in SoftMEMS 6.0 using the L-Edit layout
software in agreeance with the PolyMUMPsTM Design Rules. The chip area is 10000 µm ×
10000 µm. The overall layout of the LGI can be seen in Figure 10.43 in the Appendix.
Each cell (individual LGI) consists of 40 fixed-fixed beams in parallel, each beam is
called a “finger” and is labeled as “Finger 1” to “Finger 40” from the top-most finger to the
bottom-most. It also consists of three bond pads: one for ground and two for applying voltage.
One bond pad for voltage is connected to every other fixed-fixed beam (the “odd” fingers) while
the other bond pad is connected to all the other beams (the “even” fingers) so that we can
create a binary grating. Every other beam will be static and the other beams will move.
The chart in Figure 10.44 in the Appendix displays the different variables we plan
on testing. The first column, Column A, allows us to see the direct interactions between the
electrodes in Poly0 and the structural fixed-fixed beam in Poly1. Here, we will check the
differences between having one row of dimples (Cell A1, Column A, Row 1) as opposed to two
rows (Cell A2) and having dimples only in the middle of the beam for a length of 100 µm (Cell
A3).
The second and third column, Columns B and C, add Poly2 and Metal, respectively.
However, as we go down the rows, we change the length of the beam of Poly2 and Metal from
21
the entire length 1000 µm in Row 1, to 800 µm in Row 2, to 600 µm in Row 3, to 400 µm
in Row 4, and finally to 200 µm in Row 5. Each Poly2/Metal beam is anchored down with a
Poly1-Poly2-Via at each end to prevent curling. Note that the Poly2/Metal beam won’t always
be the same length as the Poly1 beam at 1000 µm. This is why we utilize the Poly1-Poly2-Via
instead of Anchor2 because Anchor2 will anchor all the way down to the Nitride layer and will
not conserve the fixed-fixed beam structures made of Poly1. There is also a Poly1-Poly2-Via
area located at the middle of each Poly2/Metal beam to prevent Poly2/Metal from coming
down under stresses and touching the top surface of Poly1. This could cause an unwanted
electrical short and would also benefit the structure by making it stiffer.
The next three columns, Columns D, E, and F, have all layers (Poly0, Poly1, Poly2,
and Metal) and implement leveraged bending as described previously in Section 2.2. Again,
we change the length of the beam of Poly2 and Metal as we go down the rows as described
previously. Our design idea here in these columns is to find an optimal Electrode Length (LE )
for our actuator. The challenge, however, is that if we decrease the size of the counter electrode,
we will see that the critical pull-in voltage increases dramatically. Therefore, we know that we
need to find a balance between maximizing the stroke while operating at lower voltage. For
these tests, we created electrode lengths of sizes LE = 100 µm in Column F, 200 µm in Column
D, and 300 µm in Column E to see which structure gives us a reasonable operating voltage
while achieving the relatively higher stroke.
The bottom two rows, Rows 6 and 7, follow the same pattern from having only
Poly0 and Poly1 in Column A, to adding Poly2 in Column B, and adding Metal for Columns C
through F. They also implement utilizing a full electrode for Cells A6, B6, and C6 and leveraged
bending for Cells D6 and E6, all in the similar pattern for Rows 1 through 5. The key idea we
are testing is the idea from Deutsch et al. by having Poly0 pull in Poly1, which in turn, moves
a flat Poly2 and metal layer. Row 6 contains one additional post in Poly1 in the center and
cuts the fixed-fixed beam in half at 500 µm. Row 7 contains two posts in Poly1, equally spaced
at around 320 µm, so that we have three fixed-fixed beams in series. The ground electrodes
are appropriately sized to fit under the fixed-fixed beams for each case.
Two more cells were added at the bottom right corner (Cells F6 and F7) to observe the
curling effect of adding Metal to Poly2. Cell F6 has a Poly2/Metal layer that is not anchored
down at the ends and is of length 1000 µm. Cell F7 is similar but has a Poly2/Metal length of
200 µm.
22
6.2
A Closer Look at LGI Cells
All of the following figures of cross-sections and 3D renderings in from the L-Edit
Software are exaggerated by 1000% in the z-direction larger than usual to be able to see the
layer thicknesses. Certain layouts of cells are highlighted in this section, including all of Column
A, Cell B1, Cell C2, Cell D3, Cell E4, Cell F5, Cell F6 and Cell F7. Cross sections of the cells
that are not included in this section can be found in the Appendix.
Cell A1 only contains layers Poly0 and Poly1. Poly0 (gold/orange color) has a full
electrode length beneath the fixed-fixed Poly1 (red color) beam. Dimples are spaced evenly
along the length of the beam in one row, as seen in the layout in Figure 6.1. The layout image is
a top view of one of the fingers. At the ends are gray squares depicting the anchors and smaller
squares outlined in black showing the dimples created in Poly1. The following cross-section
is taken through the dimples and a 3D rendering is taken with the 3D modeling toolbox in
L-Edit.
Figure 6.1: Layout of one finger in Cell A1
Figure 6.2: Cross Section through a finger illustrating dimples in Cell A1
Figure 6.3: 3D rendering of CellA1 from L-Edit
A few things to note: As mentioned previously in Section 2.1, there is an indentation
23
in the posts. This is from the conformal layers that form in surface micromachining and can
cause these posts to be weaker than more solid posts. Also, there is a small artifact from surface
micromachining in the small gap between the Poly0 under the posts and the electrode.
Cell A2 contains Poly0 and Poly1 layers. Similar to Cell A1, this cell has an electrode
length spanning the entire length beneath the fixed-fixed beam. All aspects of the design is
similar to Cell A1 but this layout differs from Cell A1 because you can see in Figure 6.4, it has
two rows of dimples instead of one. The cross section should look similar to Cell A1 since it
was taken through a row of dimples.
Figure 6.4: Layout of one finger in Cell A2
Figure 6.5: Cross Section through a finger in Cell A2
Cell A3 also has only Poly0 and Poly1 layers. It has a full electrode length in Poly0
and no changes have been made to Poly1. The key differences in this cell are the dimple
placement. There are two rows of length 100 µm, an equivalent of eleven dimples, centered
under the fixed-fixed Poly1 beam.
Figure 6.6: Cross Section through a finger in Cell A3
Cell A4 has layers Poly0 and Poly1 and implements leveraged bending. There are two
ground electrodes in Poly0 and each electrode has a length of 200 µm with a gap in between
each electrode of 580 µm. No changes have been made to Poly1 from previous cells. Dimples
in Cell A4 are centrally placed along the fixed-fixed beam for 200 µm and are placed in two
rows of 21 dimples.
24
Figure 6.7: Cross Section through a finger in Cell A4
The design of Cell A5 has layers Poly0 and Poly1. This cell also implements leveraged
bending by designing the lengths of the Poly0 ground electrodes to be 300 µm each with a gap
in between the electrodes for a length of 380 µm. Dimples are the same as in Cell A4 by having
two rows of dimples for a length of 200 µm.
Figure 6.8: Cross Section through a finger in Cell A5
Cell A6 also has layers Poly0 and Poly1. Starting on this row, we shortened the finger
length by adding a post in the center of the finger at 500 µm. Essentially, as you can see in
Figure 6.2, there are two fixed-fixed beams of length 500 µm each where, previously, there was
only one fixed-fixed beam for a length of 1000 µm. The ground electrode under each beam
spans the entire length of the space beneath the beams for 470 µm. There is a space of 10
µm on either end of the ground electrode so the Poly0 ground electrode does not come into
electrical contact with the Poly1 structural fixed-fixed beam.
Figure 6.9: Cross Section through a finger in Cell A6
Cell A7 is similar to Cell A6 and also has layers Poly0 and Poly1. Here, we split the
1000 µm beam by adding two posts equally spaced at 340 µm to have three fixed-fixed beams
in series. Again, there is a full ground electrode under each beam for a length of 300 µm. Two
rows of dimples are designed for a length of 260 µm centered along each fixed-fixed beam.
25
Figure 6.10: Cross Section through a finger in Cell A7
Cell B1 has layers Poly0, Poly1, and Poly2. It has a ground electrode spanning the
full length of the space beneath the Poly1 beam. It has similar dimples as Cell A2 with two
rows of dimples that also cover the full length of the beam. The Poly2 layer is designed with
a length of 1000 µm which is the same as the Poly1 layer. It is anchored down at each end to
prevent curling and is also connected at the middle to Poly1 with a Poly1-Poly2-Via.
Figure 6.11: Cross Section through a finger in Cell B1
Cell C2 has layers Poly0, Poly1, Poly2, and Metal. It has a ground electrode as well
as two rows of dimples spanning the full length of the space beneath the Poly1 beam. For this
design, Poly2 is shorter than the 1000 µm-long Poly1 fixed-fixed beam. Poly2 is 800 µm long
and uses Poly1-Poly2-Via at the ends, again to prevent curling, and also at the center of the
Poly2. A layer of Metal is deposited on the Poly2 for the same length of 800 µm.
Figure 6.12: Cross Section through a finger in Cell C2
Cell D3 is designed with layers Poly0, Poly1, Poly2, and Metal. All of the cells in
Column D implement leveraged bending. The ground electrodes are 200 µm with a gap between
the electrodes of 580 µm. Two rows of dimples are placed in this gap for 200 µm. The Poly2
layer is 600 µm long with Poly1-Poly2-Vias at the ends and in the middle. A Metal layer is
deposited on top of the Poly2 layer for the same length of 600 µm.
26
Figure 6.13: Cross Section through a finger in Cell D3
Cell E4 is designed with all layers of Poly0, Poly1, Poly2, and Metal. Column E
also implements leveraged bending. This cell in particular uses leveraged bending with ground
electrodes in Poly0 of length 300 µm with a separation between the electrodes of 380 µm.
Between this gap, two rows of dimples are designed to span 200 µm centered in the fixed-fixed
beam. The Poly2 and Metal layers are of equal length of 400 µm with Poly1-Poly2-Vias at the
ends and the middle.
Figure 6.14: Cross Section through a finger in Cell E4
Cell F5 has all layers of Poly0, Poly1, Poly2, and Metal and again implements leveraged bending. There are two ground electrodes in Poly0 that are 100 µm each with a gap
between electrode of 780 µm. There are also two rows of dimples for a length of 620 µm. The
Poly2 and Metal layers are 200 µm long and again are attached to Poly1 with a Poly1-Poly2-Via
at the ends and in the center.
Figure 6.15: Cross Section through a finger in Cell F5
Cell F6 was intentionally designed to be “broken”. This cell is similar to Cell D1 such
that it contains all layers: Poly0, Poly1, Poly2, and Metal. It implements leveraged bending
with two ground electrodes of length 200 µm and has two rows of dimples centered along the
beam for 200 µm. The Poly2 and Metal layers cover the extent of the Poly1 beam layer and
27
has a Poly1-Poly2-Via at the center at 500 µm. However, the Poly2 and Metal layers are not
anchored down at the ends to match the posts at the ends of the beams. Here, we expect
curling to occur and will be further discussed in Section 7.2.7.
Figure 6.16: Cross Section through a finger in Cell F6
Cell F7 was also intentionally designed to be “broken”. Again, this cell is similar
to another cell (Cell D5). All aspects of the design were kept constant except the 200 µm
Poly2 and Metal layers are no longer anchored with Poly1-Poly2-Vias at their ends, only in the
middle. We should expect curling to occur and the extent of the curling compared to Cell F6
will also be discussed further in Section 7.2.8.
Figure 6.17: Cross Section through a finger in Cell F7
28
Chapter 7
Testing of the LGI
This chapter is divided into three different parts. The first part steps through the
methods used during this testing process. The second part addresses the LGI chip as it came
R Software, such
back from the foundry. Here, we will outline features in the Wyko Vision32
as 2D and 3D profiles and surface information, that allowed us to obtain valuable data about
the chip. I will use Cell A1 as the main example and feature information about other cells.
The third part addresses the same chip under actuation using the same features as described
in the second part of this section.
7.1
Methods
After receiving the parts back from the foundry, thorough testing was performed by
obtaining scans via a white light interferometer and by applying voltages to the chip’s bondpads
R NT1100 White Light
for each cell. We plan on observing the deflections on the Veeco WYKO
Interferometer and to collect hard data. The interferometer is able to take measurements via
optical Phase-Shifting (PSI) and white light Vertical Scanning (VSI) and then outputs the scans
R Software for analysis. PSI measures smooth surfaces and
and data to the Wyko Vision32
small steps. VSI is able to measure rough surfaces and steps up to several millimeters high [12].
The basic interferometric principles of VSI reflects light from a reference mirror that combines
with light reflected from a sample. These lights combine, similar to the LGI application, to
create interference fringes of which the best-contrast fringe occurs at the best focus.
R NT1100 White Light Interferometer to
We used the VSI mode on the Veeco WYKO
R Software, you can access the Measurement Options
collect our data. In the Wyko Vision32
menu to set options for the VSI scan. The VSI options you can set for the Primary Scan
29
are the backscan, length, and the modulation threshold. After bringing your sample into focus
(recall that the interference fringes with the best contrast will occur at best focus), the system
will choose that focus point as its initial scan point. The backscan will obtain scans through
the focus (starting above the focus) as the camera captures frames of interference data at
evenly spaced intervals in the z-direction (i.e., will move vertically away from the sample). The
length of the scan is the distance from after the backscan taken to the value specified. These
lengths should consider the sample heights of the structures. In our case, the heights will
not exceed approximately 8 µm. The last parameter you can set is the modulation threshold.
This value specifies the lowest acceptable modulation for valid data. Any data points with a
modulation below this set amount is disregarded as bad data. The following values were set
for our application:
• Backscan 10 µm
• Length 10 µm
• Modulation Threshold 3%
The last two parameters set for imaging the LGI was to make sure that the software
recognizeds the physical optics of the Veeco White Light Interferometer. The objective chosen
was 2X and the Field of View (FOV) was chosen at 2.0X. The following image in Figure 7.1
exhibits fringes on the bond pads on the left and right side of the LGI as well as fringes on the
LGI itself and shows the last step before initializing the scan.
Figure 7.1: Raw image of Cell A1 taken from the Veeco WYKO Interferometer
30
7.2
Experimental Results - Static State
7.2.1
Cell A1
The following methods were taken for all the LGI cells on this chip. This section
R Software and we will use Cell A1 as an
will outline the features used in the Wyko Vision32
example.
After obtaining the initial scan of the cell as described in Section 7.1. The first image
that is produced is the surface image.
Figure 7.2: Surface image of Cell A1
The first characteristic of Figure 7.2 to note is the color range on the right side of
the screen that ranges from blue to red that corresponds to height levels in the scan. Blue
is shown to start at -0.30 µm and ends at red at 8.09 µm. Note that some of the fingers in
Cell A1 appear to be raised higher than other fingers in this design. As we step through other
renderings of the data, we will be able to visualize this better. Also important to note is that
the range starts at -0.30 µm. This value can be much more negative and in this case, it was
taken after we removed the terms such as the tilt (see left panel under “Processed Options”).
When the initial scan is taken, the chip can have a slope that can skew the collection of data.
The software is able to remove this tilt by entering the Mask Editor Menu. Next, you can
edit the Histogram which is a collection of wavelengths that correspond to the colors on the
range described previously. You can manually choose to remove values outside of your chosen
31
cursors, keeping the wavelengths that will be the ground plane. This ground plane will serve
as your true zero or a value very close to that. For our application, we choose the deep blue
color to be our ground plane since it was the lowest part of our design.
The next rendering we were able to obtain were 2D analyses. On this page, it shows
the surface image initally taken on the left-hand side. The top plot shows the X Profile through
the horizontal red line of the surface image and the bottom plot shows the Y Profile through
the vertical blue line. As a figure of merit to double-check that our ground plane is indeed flat,
2D profiles were taken through the ground bondpad and the right voltage bondpad.
Figure 7.3: 2D profile image of the bondpads in Cell A1
We also collected data through the length of the fingers of interest, especially the ones
that do not appear raised and those that are raised, as seen in Figures 7.4 and 7.5, respectively.
The first figure is taken of Finger 3 which is the third finger from the top. In the X Profile,
there is an addition of two more vertical cursors beneath one black and one white triangle.
Note that these triangles also appear in the surface image on the left. The distance between
the cursors in the X direction is given as 0.5010 mm. The next important value to take note of
is the Z-distance of 1.0798 µm. This means that this device has an initial displacement at the
center of the finger and isn’t what we are expecting from the cross section of Cell A1 in Figure
6.2.
On the right side of the screenshot in Figure 7.4 is a table of values. These values are
valid between the triangle cursors in the main X and Y Profiles.
• Rq : 2D roughness RMS
32
• Ra : 2D roughness average; mean of absolute values of surface from the mean plane
• Rt : Maximum height of the surface; vertical distance between Rp and Rv
• Rp : Maximum profile peak height over the entire dataset
• Rv : Maximum profile valley depth over the entire dataset
Finger 3 in Cell A1 shows that the 2D roughness in Rq is 0.43 µm and the RMS 2D
roughness, Ra , is 0.38 µm. The peak height across this section is 4.50 µm which is close to the
anchors at the edges of the fingers. The valley depth is 3.07 µm and is at the middle of the
finger.
Figure 7.4: 2D profile image of the Finger 3 in Cell A1
This next figure is taken of a raised Finger 20. Measurement cursors have not moved
between the X and Y profiles of Finger 3 and were kept constant at a difference of 0.5010 mm.
Across this section, Rq is 1.18 µm and the RMS 2D roughness, Ra , is 1.06 µm. This time, the
peak height in the center of the finger is 7.86 µm and the valley depth at the anchors is 4.30
µm.
We also took Y-profiles of both Finger 3 and Finger 20 through the center of the
LGI. A good comparison between raised fingers and unraised fingers can be observed and have
a discrepancy of about 5 µm. Some of the possibilities that could have caused this height
discrepancy are that the polysilicon beams at this length were too pliable and were more
susceptible to the stresses that were acting on it.
33
Figure 7.5: 2D profile image of the Finger 20 in Cell A1
In previous tests and research by Sharpe et al., they showed that the polysilicon
demonstrated brittle fracture in an entire set of experiments [11]. Mechanical properties are
governed by the Young’s Modulus, Poisson’s Ratio and the Fracture Strength and for the
PolyMUMPsTM process, the values are listed as:
• Young’s Modulus: 158 ± 10 GPa
• Poisson’s Ratio: 0.22 ± 0.01
• Fracture Strength: 1.21 ± 0.8 to 1.65 ± 0.28 GPa (smaller specimens have higher strength)
The fracture strength depends on the size of the specimen because when the dimension
of the specimen is small in comparison with the grain size, the mechanical properties are
dominated by the grain orientations. If these grains are not randomly oriented, there may be
a chance that the measured values can be slightly above or below the theoretical bounds. We
would also expect that for larger specimens, statistically, there would be more defects across a
larger area. For polysilicon, we expect the data for the measured strength to be scattered since
these types of materials depend on planar defects such as microcracks. The doping process can
also affect the fracture strenght by creating residual stresses, even though the annealing step
of the PolyMUMPsTM is used to intentional decrease these stresses. The values in Figure 7.6
34
show how much residual stress (MPa) is present and can be the cause of the initial deformations
of the fingers in Cell A1.
Figure 7.6: Mechanical parameters of PolyMUMPsTM process layers [5]
The last rendering we utilized in this software was a 3D image of Cell A1 in which we
are able to fully understand the rough topography of the LGI with only Poly0 and Poly1 layers.
We understand that polysilicon is very rough and the data obtained from this software verifies
how rough it is exactly. Also, we can deduct that the area of usable space on each finger of the
LGI is small since the fingers are already have a deflection in the middle. If a monochromatic
light is propagated towards the anchors at the edge of the LGI, the light would reflect back in
undesirable directions. Therefore, the polysilicon is not an ideal optical surface for practical
use of the LGI.
Figure 7.7: 3D image of Cell A1
35
7.2.2
Cell B2
Another cell that we imaged on the Veeco WYKO Interferometer was Cell B2. Cell
B2 has layers Poly0, Poly1, and Poly2. Poly1 is 1000 µm long and Poly2 is of length 800 µm.
It has two rows of dimples along the entire length of the finger and has a full Poly0 electrode
beneath the Poly1 layer.
Figure 7.8: Cross Section through a finger in Cell B2
For this scan, we were interested in observing the surface characteristics of adding
another polysilicon layer and to see the effects of shortening the Poly2 layer by 200 µm from
the anchors of Poly1. From the raw image in Figure 7.9, we can already observe a few fingers
that are reflecting light differently than the rest of the fingers. This shows that the surface has
a different initial deflection than the others.
Figure 7.9: Raw image of Cell B2 taken from the Veeco WYKO Interferometer
The following figures are 2D profile images taken of (a) Finger 4, (b) Finger 6, and
36
(c) Finger 29. These particular scans were taken because each represents a different X-Profile.
The profile of Finger 4 is observed across the 800 µm Poly2 layer with an RMS 2D roughness of
0.91 µm and a 2D roughness average of 0.73 µm. There is also a distance of 4.47 µm between
the lowest and the highest points between the cursors. The profile for Finger 4 is, for the most
part, uniform between these cursors, and is the representation of the majority of the fingers.
The profile of Finger 6 is also taken across the same 800 µm Poly2 layer. Values of
interest are Rq = 0.74 µm, Ra = 0.54 µm, and Rt = 4.19 µm. For all of these values, they are
each about 0.2 µm less than in Finger 4. This profile differs from Finger 4 in that more of the
area is raised (red), especially at the middle of the finger. There are three fingers in Cell B2
that resemble this profile.
Figure 7.10: 2D profile images of (a) Finger 4, (b) Finger 6, and (c) Finger 29 in Cell B2
The last profile type is of Finger 29. Again, the scan is taken between the same Poly2
length of the finger. Rq = 0.61 µm, Ra = 0.49 µm, and Rt = 2.46 µm. This finger is much
37
flatter and not as rough as the other two types of finger profiles. As you can see from the
surface image on the left-hand side, Finger 29 and Finger 39 appear to be a constant green
color and suggests that, since the Poly1 surface is the same color, Poly2 must have been pulled
in during fabrication.
7.2.3
Cell C3
Another set of scans were taken of Cell C3. This cell is fabricated with all layers,
Poly0, Poly1, Poly2, and Metal. The Poly0 electrode as well as two rows of dimples cover the
entire length beneath the Poly1 beam. The Poly2 and Metal layers are 600 µm long, centered
along the Poly1 beam.
Figure 7.11: Cross Section through a finger in Cell C3
Figure 7.12: Raw image of Cell C3 taken from the Veeco WYKO Interferometer
In the cells featured in this entire section, this is the first design in which a Metal layer
is deposited. As you can see in Figure 7.12, the reflective Metal layer is a lighter shade of gray
and is the same color as the metallic gold on the top of the three bondpads surrounding the
38
Lamellar Grating Interferometer. Another very important observation that we noticed after
taking these initial scans of the static case on the Veeco WYKO Interferometer is that with the
addition of Gold, the surface becomes a lot smoother. This can be observed in the 3D image
in Figure 7.13. By observation alone, the Poly1 layer appears rough in comparison to where
the Metal layer was deposited.
Figure 7.13: 3D image of Cell C3
We can take a closer look at the 2D profiles in the x-direction of individual fingers of
interest. There were three different types of profiles in this design. In Figure 7.14a, cursors
are set to find the roughness values for Finger 20 along the 600 µm Poly2/Metal layer. The
RMS 2D roughness Rq is 0.16 µm, the 2D roughness average Ra is 0.12 µm, and the peakto-valley distance Rt is 0.67 µm. Compared to Cell B2, the RMS roughness value is already
three to five times smaller, i.e. this finger in Cell C3 is smoother than all of the fingers that
were scanned in Cell B2. This is more evidence that the addition of gold makes the surface
smoother. We should also be concerned with the Rt value as there is a height discrepancy
between the Poly1-Poly2-Vias at the edge of the Poly2/Metal layer and the middle of the this
layer.
Figures 7.14b and 7.14c are 2D profile images of Fingers 25 and 35. For each of these,
the surface drops either on the left or right side of the Metal surface and is no longer flat across
like in 7.14a. The measurement of this valley is at an approximate height of 5.25 µm. Rq and
39
Ra are similar for both at approximately 0.30 µm and 0.24 µm, respectively.
Figure 7.14: 2D profile images of (a) Finger 20, (b) Finger 25 and (c) Finger 35 in Cell C3
7.2.4
Cell D4
Cell D4 is fabricated with the Poly0, Poly1, Poly2, and Metal layers. The fixed-fixed
beam made of Poly1 is still 1000 µm long but the Poly2 and Metal layer is 400 µm long. The
ends of the Poly2 and Metal layers are anchored with a Poly1-Poly2-Via to Poly. This cell
implements leveraged bending by splitting the Poly0 electrodes beneath the Poly1 beam into
40
two separate electrodes, each of which are length 200 µm.
Figure 7.15: Cross Section through a finger in Cell D4
Within the cursors in Figure 7.16, Rq is 0.16 µm and Ra is 0.13 µm. Even though
these values are small for the surface roughness, this structure might not be a good enough
reflective surface because of the curvature present on the topography. The light reflecting of
off the Poly2/Metal beam can come to a focus since the surface resembles a concave mirror.
Figure 7.16: 2D profile image of Cell D4
What is important to note here are the effects of conformal layering from the bottom
layers all the way up to the top-most layer. The split Poly0 electrodes perfectly frame the
Poly2/Metal layer such that no subsequent topography is shown. The only effects that should
be observed are the dimples and the Poly1-Poly2-Via in the middle of each finger.
7.2.5
Cell D6
Cell D6 breaks up the single 1000 µm-long fixed-fixed beam into two 500 µm-long
fixed-fixed beams in series. All layers are used. Leveraged bending is implemented under each
beam by creating split electrodes that are each 100 µm long.
In Figure 7.18, we can observe the effects of conformal layering over the Poly0 ground
electrodes in the topography of the gold. The 100 µm long ground electrodes are easily seen as
four columns down the length of the Lamellar Grating Interferometer. We can also see a divot
in the middle of all of the beams where there is an anchor separating the two beams at 500 µm.
41
This middle section of the finger is not ideal for the operation of being a reflective surface.
Figure 7.17: Cross Section through a finger in Cell D6
Figure 7.18: 3D image of Cell D6
In Figure 7.19, one 2D profile in the X-direction was obtained. We analyzed the
surface roughness (RMS and average) between the left set of beams and the right set of beams
in between the Poly0 ground electrode indentations, to avoid this step in the reflective surface.
For the left set of beams in Figure 7.19a, Rq = 0.10 µm and Ra = 0.08 µm. The peak-to-valley
distance Rt = 0.39 µm. For the right set of beams in Figure 7.19b, Rq = 0.12 µm and Ra =
0.09 µm. The peak-to-valley distance Rt = 0.43 µm.
These surfaces can serve as viable in the operation of the Lamellar Grating Interferometer because of the smaller values of surface roughness, but the other surfaces do not seem
like they will be beneficial. We were not expecting the additional topographical effects at the
anchors in the middle of each finger based on the cross section from L-Edit in Figure 7.17.
Therefore, we can only use the areas in between each of the anchors and even between the split
ground electrodes.
42
Figure 7.19: 2D X-Profile image through a finger in Cell D6
7.2.6
Cell C7
Cell C7 is similar to Cell D6 in Section 7.2.5 in that the 1000 µm beam is split into
smaller beams. Instead of having two fixed-fixed beams in series, we now have three beams in
series with equally spaced anchors 300 µm apart. Also, this cell does not use leveraged bending
and instead has three full Poly0 electrodes under each of the three Poly1 beams.
Figure 7.20: Cross Section through a finger in Cell C7
Figure 7.29 shows exactly how flat each beam surface is. Within the cursors, the Rq
value is 0.02 µm and the Ra value is also 0.02 µm. This proves to be an optimal reflective
surface. However, the actual area that we can use is much smaller for this type of design.
This will be a trade-off that must be considered since the amount of signal that can be read is
reduced significantly. Cell C7 will be further discussed in Section 7.3.2 with supporting figures.
43
7.2.7
Cell F6
Figure 7.21: Raw image of Cell F6 taken from the Veeco WYKO Interferometer
Cell F6 was described previously in Section 6.2. Recall, that the Poly2 and Metal
layers were not “anchored” down to the Poly1 below it to prevent curling. Instead we are
expecting these fingers to curl. The extent of the curling is what we are interested in finding.
Figure 7.22: Surface image of Cell F6. Information is lost where there are black voids
For Cell F6, the Poly2/Metal layer was 1000 µm long and was not anchored down.
You can see that on the raw image taken from the Veeco WYKO Interferometer, the surface is
only shiny at the middle where the Poly1-Poly2-Via is anchoring down the Poly2/Metal layers.
There are also three fingers where the light is reflecting off of the surface. The Veeco WYKO
Interferometer is unable to efficiently shine light onto the sample and retrieve information about
the sample. Therefore, information is lost where there are black voids in the image. This is
44
further exhibited in the surface image taken of Cell F6.
7.2.8
Cell F7
Cell F7 exhibited similar results as Cell F6. Again, we can see that on the Gold
surface for 200 µm in the middle of each beam, that only parts of it is able to reflect the light.
We are able to obtain surface information about these areas.
Figure 7.23: Raw image of Cell F7 taken from the Veeco WYKO Interferometer
For the darker regions on the Metal layer, we can see that on the surface image in
Figure 7.24, information is lost. On the edges of the Metal layers, we can conclude that these
beams in both Cell F6 and F7 are curling beyond a point that is usable. Unfortunately, because
we were unable to reflect light off of each Metal layer, we were unable to obtain 2D profiles to
fully understand just how much curling each finger experienced.
Figure 7.24: Surface image of Cell F7. Information is lost where there are black voids
45
7.3
Experimental Results - Actuated State
7.3.1
Actuation Methods
The next step in the Testing and Characterization of the Lamellar Grating Interfer-
ometer stage is to apply voltage onto the bondpads on each cell. As a review, there are three
bondpads for each cell. The top bondpad connects to the Poly0 ground electrode, the left
bondpad connects to the Poly1 layer on the “odd” fingers and the right bondpad connects to
the Poly1 layer on the “even” fingers. In order to apply this potential difference from voltage
to ground, we have to manually land probes onto each bondpad. But, first we implemented a
few checks before connecting the probes.
Figure 7.25: Block Diagram of the Actuation Setup
1. First, before connecting the probes to the bondpads, we connected the multimeter through
the “T-switch”, then through the 1 Mega-Ohm current-limiting resistor, and finally into
the output of the power supply.
2. Next, we turned on the power supply and checked if the voltage equaled zero. If not, we
reduced the voltage to zero and turned off the output from the power supply.
3. Land the probes manually onto the bondpads of the device and ensure that the probes
land as close to the center of the bond pads as possible.
4. Disconnect the 1 Mega-Ohm current-limiting resistor to also disconnect the circuit from
the power source.
5. Connect the multimeters through the “T-switch” to the probes and check for resistance.
Ensure that there is no electrical short.
6. If all checks are okay, connect all three devices (power supply, multimeter and probes)
together.
46
The previous block diagram in Figure 7.25 shows the setup that we used to supply
voltage to the Lamellar Grating Interferometer, including a multimeter which was used to
observe the actual output voltage from the supply and the probes that are used to directly
supply the voltage to the Lamellar Grating Interferometer.
7.3.2
Actuation of Cell C7
After connecting the probes to the bondpads, I took an initial scan of the Lamellar
Grating Interferometer. In the raw image in Figure 7.26, the probes can be seen as dark masses
coming into the view window from the top and from the right. For this set of data, we planned
on actuating the “even” set of fingers. We should also note that there are large specks of dust
or other debris on the surface of the Lamellar Grating Interferometer that cover the middle
section of Fingers 38, 39, and 40. Since this debris covers both “even” and “odd” fingers, we are
initially concerned that the device will short out, rendering the device useless. We completed
the checks and did not find that there was a short.
Figure 7.26: Raw image of Cell C7 taken from the Veeco WYKO Interferometer
Next, we followed the methods as outlined in Section 7.2.1 that obtain the overall
surface scan, 3D image and most importantly, the 2D profiles through one of the fingers. Once
again, note that the uniform red color across the Lamellar Grating Interferometer surface
indicates that none of the fingers are initially pulled in. We believe that the shorter beams
make the structure stiffer and the Poly0 ground full electrode does not play a major part in the
topography of the device. Less voltage is expected since the ground electrode has a maximum
area under the Poly1 beam. Recall the equation for pull-in voltage in Section 4.2 in which
the pull-in voltage is inversely related to the square of the area A. This is an ideal case to try
47
actuation.
Figure 7.27: Surface image of Cell C7 at 0V actuation
The 3D rendering also shows how uniform the surface is of the Lamellar Grating
Interferometer. The probes on the bondpads and the debris on the surface appear as voids in
the device only because information was not able to be obtained from these areas. This does
not mean that there are physical voids in the device.
Figure 7.28: 3D image of Cell C7 at 0V actuation
The 2D profile across the X-direction of one of the fingers is observed. We selected
cursors across the middle section of the finger and the distance in the Z-direction between these
points was 0.0195 µm. Note that both the RMS 2D roughness and the average 2D roughness
is 0.02 µm. This time, the Y-Profile that we will obtain has proven to be very important. This
profile is taken down the center through the middle section of each finger. We can see the 40
48
bumps that represent the fingers. All but two are at around the same height and so we chose
Fingers 2 and 3 to consistantly compare. Their initial distance in the Z-direction is 0.0141 µm.
Voltage is applied first in increments of 5 Volts, then in 2.5 Volts, and then 0.5 Volts as we get
closer to the expected pull-in voltage. Each time these increments in voltage are made, scans
were taken and data was analyzed from the 2D Profile in the Y-direction.
Figure 7.29: 2D profile image of Cell C7 at 0V actuation
The maximum amount of voltage that we were able to apply was 19.5 V before the
device experienced pull-in and the Poly1 layer came in contact with the Poly0 ground electrode
below. We were successfully able to deflect Finger 2 a distance of 0.5674 µm compared to
Finger 3, which was static. Also, despite the debris on the surface of the Lamellar Grating
Interferometer surface, the device still works up to 19.5 V. The deflection also agrees with the
fact that we should be able to achieve only one-third of the initial gap of 2.0 µm. 0.5674 µm
is 28.37 % and is close to the 33 % (one-third) limitation.
49
Figure 7.30: Displacement in the Z-direction (µm) vs. Voltage (V) comparing the heights of
Finger 2 and Finger 3 in Cell C7. Voltage was applied to the “even” set of fingers
Figure 7.31: 2D Y-Profile comparing the heights of Finger 2 and Finger 3 in Cell C7. 19.5 V
was applied
50
Figure 7.32: 2D profiles of Cell C7 after 19.5V was applied. Pull-in occurs on Finger 38. Also
note the deflection of the overall surface, especially in the middle of the device.
51
7.3.3
Actuation of Cell D7
The same methods were followed for the actuation of Cell D7. Cell D7 implements
leveraged bending and we should expect a larger voltage to actuate the fixed-fixed beams.
We applied voltage in 5V increments to the “odd” fingers and took scans on the White Light
Interferometer at every increment. However, as we reached voltages of 25V and higher on this
cell, we got very unexpected results. Next, we will highlight the Y-profiles of Cell D7 at 0V,
25V, 50V, and 75V.
At 0V, all of the fingers are at a constant height of 5.99 µm. Fingers 2 and 3 are
chosen for comparison with an initial displacement between these two fingers of 0.0518 µm.
Figure 7.33: 2D Y-Profile image of Cell D7 at 0V actuation
At 25V, we start to notice that some of the fingers are displaced. Comparing Fingers
2 and 3, there is a displacement of 0.1091 µm, but Fingers 2, 3, and 4 all pull in together. This
is not what we are expecting to happen since we are only actuating the “odd” fingers, i.e. only
Finger 3 should be displaced.
Figure 7.34: 2D Y-Profile comparing the heights of Finger 2 and 3 in Cell D7 at 25V actuation
At 50V, about half of the fingers are displaced but do not form the grating where
52
every other finger is displaced. It is no longer adequate to compare the differential heights of
Finger 2 and 3 since both fingers are pulled in. The Z-distance is measured between a finger
that is pulled in and one that is not. This value is 0.5313 µm.
Figure 7.35: 2D Y-Profile comparing the heights of two fingers in Cell D7 at 50V actuation
At 75V, all of the fingers are displaced at a constant height of 5.3795 µm, a difference
of 0.6105 µm from the unactuated state. If this Lamellar Grating Interferometer cell had
performed as expected, this deflection would be within 0.05 µm of the expected maximum
allowable stroke of one-third of the initial gap, or ∼0.667 µm.
Figure 7.36: 2D Y-Profile comparing the heights of the pulled-in fingers in Cell D7 at 75V
actuation
A possible reason for unactuated fingers being pulled-in is because there might be an
overlap of the Metal layer between each finger from the violation in the enclosure design rules.
We should expect that Cell D7 to behave just as well as Cell C7 but there may have been
an inconsistancy in the fabrication process that caused all of the fingers to pull in; the only
difference between Cells C7 and D7 is the leveraged bending and the split Poly0 electrodes of
length 50 µm each. The design rules state that if Metal is extended beyond the Poly2 layer,
53
the step at the Poly2 edge is poor and may result in mechanical failure [5]. This is evident
in this cell since all of the fingers eventually get pulled in at 75V, instead of only the “odd”
fingers being pulled-in.
More tests need to be conducted to other cells on this chip to fully understand the
operation of this iteration of the LGI. A future iteration of this design includes cells that do
not violate the enclosure rule and is explained in Chapter 8.
54
Chapter 8
Future Work
A similar project such as this was proposed to EE115 Introduction to MEMS Design,
a course aimed towards undergraduate students. The students work in teams to design, lay out,
R micromachining processes
and fabricate MEMS devices and test structures using the MUMPs
of SOIMUMPSTM or PolyMUMPsTM . The most recent offering of this course reviewed my
design of the Lamellar Grating Interferometer. It was also the first time a previous design was
fabricated and was characterized for the improvement of future designs. Team MUMPStars
focused their design on the PolyMUMPsTM fabrication process and worked closely with me to
develop their revised design. Based on my results and an understanding of the cell designs that
worked, I was able to make suggestions to Team MUMPStars on how to improve the design
and functionality of the Lamellar Grating Interferometer for the next fabrication run.
The final design on this second iteration is outlined in the following table:
Figure 8.1: Descriptions of each cell in the revised LGI layout
55
The layout of the design is as follows:
Figure 8.2: Revised layout of the Lamellar Grating Interferometer
The first suggestion was to improve the design of the dimples. In the previous design,
the placement of dimples were creating undesired divots in the topography of the reflective
surface. To improve on this and to try to remove these divots, the next design will use fewer
dimples and placed every 10 µm. Another issue that was not addressed in the previous design
was the proximity of the dimples to the electrodes in a design implementing leveraged bending.
If the dimples were too close to the Poly0 electrode, it could cause an electrical short as Poly1
is pulled in towards Poly0.
Another suggestion addresses the Poly0 electrode length in the case of leveraged bend56
ing. In the previous design, I used 50 µm, 100 µm, and 150 µm lengths and obtained the best
displacement when using the 100 µm length. Team MUMPStars varied their values and chose
an electrode length of 80 µm to address displacement and 150 µm to address the increase in
pull-in voltage.
Also to confront the issue of minimizing the pull-in voltage, Team MUMPStars will
try to find the optimal beam length as I did when I had beam lengths of 1000 µm, 500 µm,
and 300 µm. In my findings, I showed that in the actuated state, Cell C7 was successfully able
to achieve pull-in. Their proposal will include beam lengths from 300 µm to 600 µm in 100 µm
increments to see if the change in the beam length or the electrode length was the reason why
it was successful.
There are two additional cells in the Fourth Row that modify Cells A1 and A2.
Currently the width of each finger is 20 µm with a 5 µm gap in between each finger. However,
this violates a design rule in which the Metal layer must be enclosed by the Poly2 layer by 3
µm. A suggestion to Team MUMPStars is to keep the Metal layer of width 20 µm and increase
the Poly2 and the layers below to 26 µm and so on to agree with the design rules. Another
design rule states that there must be at least 2 µm of space between the two beams.
The last suggestion is to add a second ground electrode at the bottom of each LGI
design to check for continuity along the ground connections.
For the three test structures on the bottom of the first chip that was fabricated, we
used a cantilever beam structure and a fixed-fixed beam structure whose goal is to calculate
mainly the stress of the material. However, these structures were too long and were already
pulled in. A new design for these structures is proposed in Figure 8.3.
An alignment mark was also designed to find out if the layers are well aligned. A
revision to the current alignment mark design has been made to have an anchor in the center
with dimensions 50 µm × 50 µm. Poly0 and Poly1 were also deposited such that every overlap
will also create a 50 µm × 50 µm area. Figure 8.4 is an image of the layout used in L-Edit.
For the test structures discussed above, I propose that the placement of these structures be systematically scattered about the chip. This placement will be able to give us valuable
information based on any irregularities in stresses and layer thicknesses from the fabrication
process across the entire chip and will help us understand if, and most importantly, why there
are any issues with a design not functioning as expected.
57
Figure 8.3: Updated design of the Test Structures. The fixed-fixed beam structure is on the
left and the cantilever beam structure is on the right
Figure 8.4: Layout of the alignment test structures. Each dot on the grid represents a length
of 10 µm
58
Chapter 9
Conclusion
A novel Micro-Electro-Mechanical System (MEMS) Lamellar Grating Interferometer
test structure chip is discussed in this paper. Our approach aimed to find the optimal design
structure characteristics with the 42 different designs described in this paper. In our overall
design, we used the PolyMUMPsTM fabrication process and utilized the advantage of having
three structural layers. However, this process limits the stroke to one-third of the 2 µm gap
from the Oxide-1 sacrificial layer. Therefore, we explored changing one characteristic at a
time as we step through each of our designs. We used leverage bending to be able to get a
higher stroke while maintaining the fill factor. We prevented stiction from occuring by adding
dimples in the middle of the fingers in various patterns. By making the finger long enough
(L=1000 µm), we made sure that our design operates at a low voltage (Vpull−in =10.85V). We
also explored shortening this beam to 500 µm and 300 µm. We chose the width W=20 µm and
a 5 µm gap between the fingers to meet the period requirement of 50 µm.
Characterization through thorough testing was also performed on the fabricated MEMS
R NT1100 White Light InterferLamellar Grating Interferometer. We used the Veeco WYKO
R Software for further analysis. We obtained
ometer to collect our data in the Wyko Vision 32
surface images, 2D profiles, and 3D images of each of the cells. Next we were able to apply
voltage onto the cells and actuate the device to create the variable grating. We were able to
achieve successful actuation for Cell C7, a cell with a shorter beam length and a full electrode
length beneath the beam. A deflection of 0.5674 µm was achieved at 19.5V.
Revisions have been made to the MEMS Lamellar Grating Interferometer by using
the PolyMUMPsTM fabrication process. We hope that we are able to find the optimal design
specifications based on these revisions to the lamellar grating test structures and that further
characterization and testing is performed in the future.
59
Chapter 10
Appendix: LGI Layout Images
10.1
Cross Sections: Column A
Figure 10.1: Cross Section through a finger in Cell A1
Figure 10.2: Cross Section through a finger in Cell A2
Figure 10.3: Cross Section through a finger in Cell A3
60
Figure 10.4: Cross Section through a finger in Cell A4
Figure 10.5: Cross Section through a finger in Cell A5
Figure 10.6: Cross Section through a finger in Cell A6
Figure 10.7: Cross Section through a finger in Cell A7
61
10.2
Cross Sections: Column B
Figure 10.8: Cross Section through a finger in Cell B1
Figure 10.9: Cross Section through a finger in Cell B2
Figure 10.10: Cross Section through a finger in Cell B3
62
Figure 10.11: Cross Section through a finger in Cell B4
Figure 10.12: Cross Section through a finger in Cell B5
Figure 10.13: Cross Section through a finger in Cell B6
Figure 10.14: Cross Section through a finger in Cell B7
63
10.3
Cross Sections: Column C
Figure 10.15: Cross Section through a finger in Cell C1
Figure 10.16: Cross Section through a finger in Cell C2
Figure 10.17: Cross Section through a finger in Cell C3
64
Figure 10.18: Cross Section through a finger in Cell C4
Figure 10.19: Cross Section through a finger in Cell C5
Figure 10.20: Cross Section through a finger in Cell C6
Figure 10.21: Cross Section through a finger in Cell C7
65
10.4
Cross Sections: Column D
Figure 10.22: Cross Section through a finger in Cell D1
Figure 10.23: Cross Section through a finger in Cell D2
Figure 10.24: Cross Section through a finger in Cell D3
66
Figure 10.25: Cross Section through a finger in Cell D4
Figure 10.26: Cross Section through a finger in Cell D5
Figure 10.27: Cross Section through a finger in Cell D6
Figure 10.28: Cross Section through a finger in Cell D7
67
10.5
Cross Sections: Column E
Figure 10.29: Cross Section through a finger in Cell E1
Figure 10.30: Cross Section through a finger in Cell E2
Figure 10.31: Cross Section through a finger in Cell E3
68
Figure 10.32: Cross Section through a finger in Cell E4
Figure 10.33: Cross Section through a finger in Cell E5
Figure 10.34: Cross Section through a finger in Cell E6
Figure 10.35: Cross Section through a finger in Cell E7
69
10.6
Cross Sections: Column F
Figure 10.36: Cross Section through a finger in Cell F1
Figure 10.37: Cross Section through a finger in Cell F2
Figure 10.38: Cross Section through a finger in Cell F3
70
Figure 10.39: Cross Section through a finger in Cell F4
Figure 10.40: Cross Section through a finger in Cell F5
Figure 10.41: Cross Section through a finger in Cell F6
Figure 10.42: Cross Section through a finger in Cell F7
71
10.7
Full Layouts
72
Figure 10.43: Entire layout of the Lamellar Grating Interferometer (Version 1)
73
Figure 10.44: Description of each cell of the Lamellar Grating Interferometer (Version 1)
74
Figure 10.45: Revised layout of the Lamellar Grating Interferometer (Version 2)
75
Figure 10.46: Descriptions of each cell in the revised LGI layout (Version 2)
76
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