Mirau Interferometric Computer Microvision
by
Sall P. Desai
Submitted to the Department of Electrical Engineering and Computer
Science
in partial fulfillment of the requirements for the degree of
Master of Science in Electrical Engineering and Computer Science
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
September 2002
© Massachusetts Institute of Technology 2002. All rights reserved.
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Author .. .......................
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Department of krdfrical Engineering and Computer Science
September 5, 2002
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..... ... ......
A. . . . . . . . . . .
Certified by................
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Dennis M. Freeman
Associate Professor
Thesis Supervisor
Accepted by .............
.7,..
Arthur C. Smith
Chairman, Department Committee on Graduate Students
MASSACHUSETTS ISTITUTE
OF TECHNOLOGY
BARKER
NOV 1 8 2002
LIBRARIES
2
Mirau Interferometric Computer Microvision
by
Safil P. Desai
Submitted to the Department of Electrical Engineering and Computer Science
on September 5, 2002, in partial fulfillment of the
requirements for the degree of
Master of Science in Electrical Engineering and Computer Science
Abstract
High performance metrology systems are essential for in situ measurement of microelectromechanical systems (MEMS). A Mirau interferometric video system for
measuring three-dimensional motions of MEMS with nanometer resolution is demonstrated. The Mirau interferometric system combines the superior out-of-plane resolution of interference methods with the superior in-plane resolution of brightfield
computer microvision techniques to achieve full 6 degree-of-freedom motion measurements. Motion measurements of a surface micromachined lateral resonator demonstrate sub-nanometer resolution for both in-plane and out-of-plane translational motion, and sub-millidegree resolution for both in-plane and out-of-plane rotational motion. The interferometric images provide the capability for generating surface profiles
and in combination with stroboscopic illumination provide dynamic profiling capability. Dynamic profilometry with nanometer resolution is demonstrated with surface
micromachined polysilicon diffraction gratings. The Mirau interferometric computer
microvision system can be used to assess complex modes of motion and reconstruct
surface profiles of entire arrays of microelectromechanical devices.
Thesis Supervisor: Dennis M. Freeman
Title: Associate Professor
3
4
Acknowledgments
The past two years at MIT have been a tremendous learning experience for me. I
have been extremely lucky to have Denny Freeman as an advisor. His work ethic and
integrity have been a source of inspiration. Denny has taught me many things but
most importantly he's taught me how to think. I look forward to continue working
with him and hopefully someday earning a PhD. I would not have made it to MIT
without the help of my mentor from Carnegie Mellon - Kaigham "Ken" Gabriel. He
urged me to apply to MIT for graduate school and strongly suggested that I work with
Denny once I was accepted. I am deeply indebted to him for all his help and guidance
over the years. Andrew Berlin and John Gilbert were wonderful mentors during my
internship at Xerox PARC and were extremely helpful during the application process
for graduate school. I hope to work with them again sometime soon.
Graduate school wouldn't have been much fun if I hadn't joined the Micromechanics Group and had a chance to work with some of the hippest cats at MIT.
Dr. A. J. Aranyosi helped tremendously when I first joined the lab. He's put up with
all my stupid questions over the past two years and has helped immeasurably with
the writing and editing of this thesis. I've learnt a lot from him and I hope he's going
to be around for some time. Amy Englehart has been a delightful office-mate and a
great, great friend. She has always encouraged me to reach for my goals and to try
and get out of lab every once in a while. Kinu Masaki has never failed to cheer me up
when things were looking bleak (don't worry I won't leave MIT before you graduate!).
She has always offered to help with any problem and has kept me company during
many late evenings in lab. Roozbeh Ghaffari has been my partner in crime and I'm
looking forward to seeing our work on the cover of Science someday! Stanley Hong's
vast knowledge of optics has made for many fascinating discussions, I hope to work
with him more in the future. His comments on this thesis have been invaluable. Jekwan Ryu has always provided sagely advice and a helping hand. Andy Copeland has
asked many insightful questions and has provided interesting suggestions regarding
my research. Previous members of the lab, especially Michael Mermelstein, Abra5
ham McAllister and Michael Gordon, have always been willing to help out and have
entertained even my most inane questions.
Life outside of lab wouldn't be much fun without other curious characters I've
met at MIT and in Cambridge. Mekhail Anwar has always encouraged me to stop
taking things too seriously and urged me to "get a life". I have drunk large quantities
of coffee (Starbucks coffee, no less) with Luke Theogarajan.
Although he makes
every effort to make my life miserable, he means well. He has taught me to question
everything. Without his help and guidance I would not have made it through MIT.
Jaydeep Bardhan has helped a great deal by painstakingly editing this thesis. Laila
Bartlett has been a very kind friend. Her willingness to listen to any of my problems
has helped me through rough times.
Lastly, I would like to thank my parents (Pradip and Gargi) and my brother (Ravi)
for motivating me to finish by politely inquiring when I would start making realmoney
(sorry, it might still be a while!). Although they are halfway across the world, we still
manage to stay close, and I miss them dearly. I would have never studied engineering
if it weren't for Ravi's guidance. He has been a tremendous source of inspiration and
I will always look up to him for advice.
6
Contents
1
2
Introduction
13
1.1
W hat are M EM S?. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13
1.2
MEMS metrology tools ..........................
15
1.2.1
Laser Doppler vibrometer
15
1.2.2
Atomic force microscope . . . . . . . . . . . . . . . . . . . . .
16
1.2.3
Scanning electron microscope
. . . . . . . . . . . . . . . . . .
16
1.2.4
Optical profilometer
. . . . . . . . . . . . . . . . . . . . . . .
17
1.2.5
Capacitive sensor . . . . . . . . . . . . . . . . . . . . . . . . .
18
1.2.6
Computer microvision
. . . . . . . . . . . . . . . . . . . . . .
18
....................
1.3
Comparison of MEMS metrology tools
. . . . . . . . . . . . . . . . .
20
1.4
Motivation for interferometric computer microvision . . . . . . . . . .
21
23
Interferometric Computer Microvision
2.1
. . . . . . . . . . . . . . .
. . .
24
Coherence . . . . . . . . . . . . . . . . . .
. . .
25
Optical interferometry
2.1.1
2.2
Analyzing interferometric images
. . . . . . . . .
. . .
26
2.3
Linnik Interferometer . . . . . . . . . . . . . . . .
. . .
27
2.4
Mirau Interferometer . . . . . . . . . . . . . . . .
. . .
30
2.4.1
Assembly of interference system . . . . . .
. . .
30
2.4.2
Integration with microscopy system . . . .
. . .
30
2.4.3
Adjusting interference fringes
. . . . . . .
. . .
30
2.4.4
Phase-shifting using Mirau interferometer
. . .
33
. . .
35
2.5
Comparison of Mirau and Linnik interferometers .
7
3
2.5.1
A ssem bly . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35
2.5.2
Optical alignment . . . . . . . . . . . . . . . . . . . . . . . . .
35
2.5.3
Working distance . . . . . . . . . . . . . . . . . . . . . . . . .
36
2.5.4
Numerical aperture . . . . . . . . . . . . . . . . . . . . . . . .
36
2.5.5
Field of view
36
. . . . . . . . . . . . . . . . . . . . . . . . . . .
Image Acquisition
37
3.1
MEMS test structure setup
. . . . . . . . . . . . . . . . . . . . . . .
37
3.2
Waveform generation . . . . . . . . . . . . . . . . . . . . . . . . . . .
38
3.3
Video microscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
40
3.3.1
Interferometric image acquisition
. . . . . . . . . . . . . . . .
40
3.3.2
Brightfield image acquisition . . . . . . . . . . . . . . . . . . .
42
3.3.3
Image acquisition for noise analysis . . . . . . . . . . . . . . .
42
Stroboscopic illumination . . . . . . . . . . . . . . . . . . . . . . . . .
42
3.4
4 Motion Analysis
45
4.1
In-plane motion analysis . . . . . . . . . . . . . . . . . . . . . . . . .
45
4.2
Out-of-plane motion analysis from brightfield images
. . . . . . . . .
46
4.3
Out-of-plane motion analysis from interferometric images . . . . . . .
48
4.4
R esults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
48
4.4.1
Six degree-of-freedom motion measurement . . . . . . . . . . .
48
4.4.2
Out-of-plane motion measurements using brightfield images. .
51
53
5 Static and Dynamic Profilometry
5.1
MEMS test structure setup
. . . . . . . . . . . . . . . . . . . . . . .
53
5.2
Image acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
54
5.3
Static profilometry . . . . . . . . . . . . . . . . . . . . . . . . . . . .
55
5.4
Dynamic profilometry . . . . . . . . . . . . . . . . . . . . . . . . . . .
57
59
6 Summary and Discussion
6.1
Comparison of Mirau interferometric computer microvision to brightfield computer microvision . . . . . . . . . . . . . . . . . . . . . . . .
8
59
6.2
Disadvantages of Mirau interferometry
. . . . . . . . . . . . . . . . .
60
6.3
Implications for MEMS design . . . . . . . . . . . . . . . . . . . . . .
60
9
10
List of Figures
1-1
Microelectromechanical systems . . . . . . . . . . . .
14
1-2
Computer microvision system . . . . . . . . . . . . .
19
1-3
Brightness variations due to subpixel motion . . . . .
20
2-1
Schematic of Michelson interferometer
2-2
Coherence length schematic
2-3
. . . . . . . .
. . . . .
25
. . . . . . . . . . . . . .
. . . . .
26
Linnik interferometric computer microvision system
. . . . .
27
2-4
Images obtained with Linnik interferometric system
. . . . .
29
2-5
Mirau interferometer . . . . . . . . . . . . . . . . . .
. . . . .
29
2-6
Mirau interferometric computer microvision
. . . . .
. . . . .
31
2-7
Images obtained with Mirau interferometer . . . . . .
. . . . .
32
2-8
Phase-shifting using the Mirau interferometer
. . . .
. . . . .
34
2-9
Coherence length measurement of illumination source
. . . . .
35
3-1
Surface micromachined lateral resonator
. . . . . . .
. . . . .
38
3-2
XPOZ arbitrary waveform generation system . . . . .
. . . . .
39
3-3
Image acquisition for brightfield and interferometric imaging. . . . . .
41
3-4
Nichia LED illumination source . . . . . . . . . . . . . . . . . . . . .
43
3-5
Cree LED illumination source . . . . . . . . . . . . . . . . . . . . . .
44
4-1
In-plane motion analysis . . . . . . . . . . . . . . . . . . . . . . . . .
46
4-2
Out-of-plane motion analysis from brightfield images
. . . . . . . . .
47
4-3
Out-of-plane motion analysis from interferometric images . . . . . . .
49
4-4
Six degree-of-freedom motion measurements
. . . . . . . . . . . . . .
50
11
4-5
Frequency response for three degrees-of-freedom . . . . . . . . . . . .
51
4-6
Frequency response for out-of-plane motion using brightfield images .
52
5-1
Electrical setup for surface micromachined diffraction gratings
. . . .
54
5-2
Phase-shifting Mirau interferometry for profilometry . . . . . . . . . .
55
5-3
Static profiles of surface micromachined diffraction gratings . . . . . .
56
5-4
Dynamic profiles for surface micromachined diffraction gratings
. . .
57
12
Chapter 1
Introduction
1.1
What are MEMS?
Microelectromechanical systems or simply MEMS (Figure 1-1) integrate micrometerscale mechanical elements, sensors, actuators and electronics on a common substrate
through the use of microfabrication technology. The electronic components are fabricated using integrated circuit fabrication processes, whereas the micromechanical
components are fabricated using compatible micromachining processes that selectively etch away parts of a silicon wafer or add new structural layers to form mechanical/electromechanical devices.
While microelectronic integrated circuits can be thought of as the "brains" of
systems, MEMS enhance this information processing capability with "eyes", "ears")
and "arms" to allow microsystems to sense and control the surrounding environment.
MEMS technology has enabled the design of microsystems for DNA amplification
and identification, micromachined tips for Scanning Tunneling Microscopes (STMs),
biochips for detection of hazardous biological agents and micromechanical resonators
for high frequency signal processing applications.
13
Figure 1-1: Microelecromechanical systems encompassing a wide variety of applications and a broad spectrum of fabrication processes: (A) SEM image of CMOS
MEMS (Fedder et al., 1996) multiple degree-of-freedom microresonator fabricated at
Carnegie Mellon University, (B) Optical micrograph of surface micromachined polysilicon diffraction gratings fabricated at the State University of New York at Albany,
(C) Optical micrograph of surface micromachined lateral resonator fabricated using
Cronos MUMPs, (D) Optical micrograph of platinum diffraction gratings fabricated
at the Massashusetts Institute of Technology, (E) Optical micrograph of indexing
motor fabricated using Sandia SUMMiT4 fabrication process, and (F) SEM image
of Draper Laboratory tuning fork gyroscope (SEM picture courtesy Charles Stark
Draper Laboratory, Cambridge MA).
14
1.2
MEMS metrology tools
MEMS contain both electrical and mechanical subsystems, therefore to effectively
characterize MEMS we require at the very least both electrical and mechanical measurements. While an array of powerful tools such as sampling oscilloscopes and spectrum analyzers exist for testing the electrical behavior of fabricated microsystems,
there are comparatively few tools available for testing micromechanical behaviors of
such systems.
The need to improve the reliability of MEMS has prompted research in micromechanical motion characterization tools. Ideally, these metrology tools should be capable of measuring sub-micrometer displacements of features that range in size from a
few micrometers to a few millimeters. To allow for observing system dynamics, they
should be capable of time-resolved measurement. To allow for the study of motions
more complex than simple rigid-body translations and rotations, these characterization tools need to permit independent measurements of displacement or velocity at
multiple points on a structure. A number of commonly used MEMS metrology tools
are discussed in the following sub-sections.
1.2.1
Laser Doppler vibrometer
The laser Doppler vibrometer (LDV) is based on the principle of the detection of
Doppler shift of coherent laser light that is scattered from a small area of the device
under test. The device scatters or reflects light from the laser beam and the Doppler
frequency shift is used to measure the component of velocity which lies along the axis
of the laser beam. As the laser light has very high frequency, a direct demodulation
of the light is not possible. An optical interferometer is therefore used to mix the
scattered light coherently with a reference beam.
A photodetector measures the
intensity of the mixed light whose frequency is equal to the difference in the reference
and measurement beam frequencies. The LDV allows for real-time measurement of
motions of a single point on the device. A number of commercial laser vibrometer
systems are available for the measurement of both out-of-plane and in-plane motions.
15
1.2.2
Atomic force microscope
An Atomic Force Microscope (AFM) reconstructs surface profiles by scanning an
atomically sharp tip over a sample surface. Feedback mechanisms enable the piezoelectric scanners to maintain the AFM tip at a constant force (to obtain height information) or at a constant height (to obtain force information) above the sample
surface. The AFM tips are typically micromachined on silicon cantilevers. The primary purpose of an AFM is to quantitatively measure surface roughness and generate
three-dimensional topographical maps. They provide nominal 5 nanometer lateral
resolution and sub-nanometer vertical resolution. Quantifying surface roughness is
key to understanding the structure and integrity of thin films used in MEMS fabrication. Compared with optical interference techniques, the AFM provides unambiguous
measurement of step heights, independent of the reflectivity differences between materials. Compared with the LDV, the AFM is used solely for the profiling of static
surfaces.
1.2.3
Scanning electron microscope
The Scanning Electron Microscope (SEM) is one of the most versatile and widely used
tools for MEMS characterization. By scanning an electron probe across a device, high
resolution images of the morphology or topography of a device, with large depth of
field, at very low or very high magnifications can be obtained. The SEM allows for
three-dimensional imaging and characterization of topology of all visible surfaces. It
is widely used in the characterization of MEMS process sequences to quantify etch
depths, microstructure aspect ratios and film thicknesses. The images obtained in
the SEM provide qualititative judgements as to whether micromachined structures
have been adequately "released" 1 and the degree of curl and residual stress in the
"released" microstructures.
A conventional SEM provides adequate spatial resolution, but is inadequate for
resolving motions at frequencies greater than several tens of hertz because the illu1"Release" refers to the removal of sacrificial layers in a surface micromachining process to create
freely moving micromechanical structures.
16
minating electron beam is continuous. Several groups have designed custom fixtures
for operating and imaging moving micromachined structures in an SEM chamber
(notably Sandia National Laboratory's Failure Analysis group). This allows for true
three-dimensional imaging. However, since the frequencies of operation are in the
kilohertz and megahertz range, and the illuminating electron beam is not strobed,
quantitative estimates regarding motion can be difficult to make.
1.2.4
Optical profilometer
Surface profile measurement is an important tool for MEMS device characterization.
Surface flatness is of critical importance to optical MEMS devices in particular (such
as micromirrors and diffraction gratings, as shown in Figures 1-lB and 1-iD). Commercial profile measurement systems allow for either, (1) static profile measurement
of all structures within the field of view (e.g. Wyko Scanning White Light Interferometers), or (2) line-scanned dynamic profile measurements (e.g. Polytec PI Laser
Doppler). Profilometry allows for quantifying curl and residual stress in thin film
microstructures.
The benefits of optical surface profilometry include the ability to perform noncontact measurements of delicate surfaces and high measurement speed.
Various
methods of optical surface profiling have evolved, including phase-shifting interferometry, the measurement of local slopes using laser-based techniques, and the dynamic
detection of focus. Phase-shifting interferometry can be used to obtain fast, threedimensional profiles of smooth surfaces, with sub-A resolution where A is the wavelength of light used (Creath, 1988). Techniques for determining surface height using
phase-shifting interferometry typically involve the sequential shifting of the phase of
one beam of the interferometer relative to the other beam by known amount, and
measuring the resulting interference pattern intensity. The phase data are then processed by an unwrapping algorithm that removes phase ambiguities between adjacent
pixels.
17
Capacitive sensor
1.2.5
Capacitive measurements of motions of MEMS are commonly measured using two
electrodes: one attached to a moving part and one attached to a stationary reference
point. Relative motions of the electrodes change the capacitance between them, and
this change is detected electrically. Although the reference electrode can be external,
both the sense and reference electrode used in this capacitive "probe" method are
more commonly integrated into the MEMS design. Interpreting changes in capacitance as motion is complicated by the fact that three-dimensional motion can generate
ambiguous changes in capacitance. The electrostatic comb drive (Figure 1-1A and
1-1C) is a canonical MEMS sensor/actuator pair. The capacitance of the comb drive
changes if the fingers move in-plane or out-of-plane, so many modes of motion can
give rise to the same capacitance change. Using capacitive sensing techniques poses
several problems :
1. Multiple electrodes are required to measure three-dimensional motions.
2. Since the changes in capacitance are small (on the order of femtofarads), largearea electrodes are typically required.
3. The capacitive sensors require on-chip signal conditioning circuitry to minimize
parasitic capacitance, thereby requiring a more involved fabrication procedure.
4. Since the sense electrodes are fabricated along with the device they are susceptible to fabrication non-uniformities.
Thus, integrating electrodes for capacitive sensing of every possible mode of motion of a MEMS of even moderate complexity may not be practical.
1.2.6
Computer microvision
Our group has developed the computer microvision system (CMV), illustrated in
Figure 1-2, to enable in situ motion measurement of microelectromechanical devices
18
CCD
mere
digtzr
Ime
LED1LEeI.e
light
source
die
Ilmgoai
waveformtor
Illumination
waveform
00
450
focal plane #1
3150
00
focal plane #2
Figure 1-2: Computer microvision system. The test device is placed on the stage
of the microscope (left). A computer controls a signal generator that provides two
synchronized waveforms - one to the MEMS driver to drive the motions of the
device under test and one to the LED driver to strobe the LED light source. Typical
waveforms for the stimulus and illumination are shown in the bottom of the figure.
The first image is acquired with the CCD camera when light from the LED samples
the image at times corresponding to peaks in the stimulus waveform. Successive
images are acquired at different phases. Figure adapted from (Freeman et al., 1998).
(Freeman et al., 1998). Computer microvision performs in situ micromechanical motion measurement based on the combination of light microscopy, stroboscopic illumination, video imaging, and machine vision. The system was first used to measure the
motions of biological micromechanical structures in the inner ear (Davis, 1997). It has
since been used to measure a variety of man-made micromachines such as accelerometers and gyroscopes (and has been used to characterize the micromechanical motions
of all the MEMS shown in Figure 1-1). The brightfield computer microvision system
provides nanometer resolution for three-dimensional motions. The CMV system can
track the motion of a target with peak sinusoidal displacements as small as 2 nanometers under ideal conditions. Displacement estimates are accurate to within 10% as
compared to measurements made with a laser Doppler velocimeter (Aranyosi, 2002).
19
L
L
LLI
LD
LI
LI
DL
LI
LI
LI
LD
EI
LIL
LI
Dl
LL
D I
LIo
I
L
L
Dl
Figure 1-3: Variations in brightness caused by subpixel motions. The array of squares
in each panel represents the pixels of a video camera; the gray circle represents the
image of a simple scene; and the bar plots represent the brightness of a the row of
pixels indicated by the arrow. The three panels illustrate the rightward motion of the
gray circle. Although the displacements are less than a pixel, information about the
motion is available from changes in brightness of the pixels near the edges. Figure
adapted from (Gordon, 1999).
1.3
Comparison of MEMS metrology tools
Computer microvision techniques require the acquisition of images and then postprocessing to extract quantitative motion information. Hence CMV is not a real-time
motion measurement technique as compared to LDV and capacitive sensing techniquues. However, CMV is an image based method and simultaneously acquires the
information necessary for measuring motion for every structure in the image. Additionally, the CMV system provides inherently three-dimensional measurements of
motion. Other metrology methods are one-dimensional, such as LDV or capacitive
sensing. Measuring three-dimensional motions with LDV-based techniques requires
repositioning the experimental setup for each measurement direction.
Measuring
three-dimensional motions with capacitive sensing techniques requires multiple electrodes and additional design complexity. Hence, measuring motions with these techniques can be prohibitively time consuming. CMV uses stroboscopic illumination to
"freeze" the MEMS motion and hence provides a series of stop-action images from
which qualitative judgements of motion can be made. Such qualitative information is
invaluable in verifying quantitative motion estimates obtained from post-processing
20
the stop-action images. Such internal consistency checks are not available with other
metrology techniques.
CMV has a disadvantage in that it is limited to measuring periodic motions at
multiples of the fundamental frequency of an applied stimulus. Other techniques,
particularly LDV can be used for measuring arbitrary motions.
1.4
Motivation for interferometric computer microvision
The brightfield computer microvision system provides nanometer resolution for threedimensional motions. The noise floor of the CMV system for in-plane motions is
determined by low-frequency vibrations which are not damped by the vibration isolation table. These vibrations couple into the measurements due to the fact that the
acquisition of a single image often requires a large fraction of a second. This results in
low-frequency vibrations being aliased to the stimulus frequency and its harmonics.
The noise floor of measurements in the out-of-plane direction is an order of magnitude higher than for in-plane measurements. Out of plane resolution from brightfield
images depends critically on the out-of-plane resolution of the microscope objective.
Thus, high out-of-plane resolution requires optics with high numerical aperture. Generally, high numerical aperture can only be achieved for objectives with high magnifications. The higher the magnification, the smaller the field of view, given the
same camera. Hence, in brightfield imaging, there is a trade-off between high outof-plane resolution and field of view. Additionally, out-of-plane motion estimates are
made from image sequences taken over larger time periods, resulting in greater noise
contribution.
Interferometric systems (Guiterrez et al., 1998; Hart et al., 2000), on the other
hand, provide extremely high out-of-plane resolution (sub-nanometer) without the
need for high resolution microscopy objectives. This thesis demonstrates a Mirau interferometric computer microvision system which combines the superior out-of-plane
21
resolution of interference methods with the superior in-plane resolution of brightfield
computer microvision techniques to achieve full 6 degree-of-freedom motion measurements. Motion measurements of a surface micromachined lateral resonator (Figure
1-1C) demonstrate sub-nanometer resolution for both in-plane and out-of-plane translational motion, and sub-millidegree resolution for both in-plane and out-of-plane
rotational motion (Desai and Freeman, 2001). The data acquisition and motion measurement results are described in Chapters 3 and 4, respectively. The interferometric
images provide the capability for generating surface profiles and in combination with
stroboscopic illumination provides dynamic profiling capability. The application of
the system to dynamic profilometry is demonstrated with nanometer resolution dynamic profile measurements of surface micromachined polysilicon diffraction gratings
(Figure 1-1E). The image acquistion and analysis for static and dynamic profilometry
is described in Chapter 5.
22
Chapter 2
Interferometric Computer
Microvision
The primary goal of this thesis is to combine the superior out-of-plane motion resolution of interference techniques with the multi-dimensional, multiple-structure measurement capability of brightfield computer microvision techniques.
This chapter
describes interferometry techniques and their integration with computer microvision
based techniques.
Our group has previously investigated a custom built Linnik interferometer for
measuring out-of-plane motions of micromechanical devices. The results obtained
with this interferometric system demonstrated the sub-nanometer out-of-plane resolution of interferometric techniques (Hemmert et al., 1999). However, the Linnik
system required precise optical alignment, which was difficult to maintain. Even simple operations such as changing the test device required re-adjustment of the optical
components to micrometer precision. The commercial Mirau interferometer allows
for interferometric imaging without the need for precision alignment of the optical
components, since all the optical components have been aligned by the manufacturer.
The Mirau interferometer has been integrated with the computer microvision system
to allow for interferometric video microscopy.
23
2.1
Optical interferometry
Optical interference converts the difference in optical phase between two beams (due
to differences in optical path length) into optical intensity which can be sensed with a
photo-detector. Optical interference can be used to measure motion in one dimension.
The phase of the reflected light which depends on the path length changes when the
reflecting target moves towards or away from the detector, i.e. 2x path length change
for an x change in displacement. By measuring the phase of light reflected from the
target we can measure motion.
The phase of coherent light can be measured through interference. When two light
waves (of the same wavelength and polarization) are in phase, they constructively
interfere to form a bright region. Alternately, when the two light waves are out of
phase they destructively interfere to form a dark region. Two waves that interfere at
an angle form an alternating set of bright and dark regions called interference fringes.
Many different optical configurations can be used to obtain interference patterns.
One of the most basic interferometers is a Michelson interfometer which is illustrated
in Figure 2-1. The Michelson interferometer has two arms, a target arm and a reference arm. A beam emitted by the light source is split into two beams of nearly equal
intensity by a beam-splitter. One of these beams travels down the reference arm and
relects off a flat reference mirror. The other beam travels down the target arm and
reflects off the target to be imaged. The light produced by these two beams then
recombines and interferes at the beam-splitter. Since the lightwaves reflected by the
target and the reference mirror originate by splitting a beam emitted by the same light
source, these waves are mutually coherent, and consequently a two-beam interference
pattern is obtained. Motion of the target in the direction of light propogation results
in a change in the optical path length to the target, and a corresponding change
in the phase of the reflected beam. This phase change results in the modulation of
the interference fringe intensity. The modulation of the interference fringe intensity
encodes the motion of the reflecting target with sub-A resolution.
24
Detector -
Beam-splitter
Incident beam
Reference mirror
Target
Figure 2-1: Schematic of Michelson interferometer. The incident light from the light
source (black arrow) is split into two beams by a beam-splitter, one beam reflects off
the target (dark grey arrow) and the other reflects off the reference mirror (light grey
arrow). These reflected beams then combine and interfere at the beam-splitter (dark
and light grey dashed arrow) and the resulting interference pattern is collected at the
detector. The reflected beams have been offset slightly for clarity.
2.1.1
Coherence
Coherence is a measure of the spectral purity of a light source. An ideal monochromatic light source has an electric field that is a sinusoidal function of space and time.
Hence, by knowing the phase at one point in the monochromatic beam, we can determine the phase at any other point in the beam. No physical source has zero spectral
bandwidth. For a physical source, by knowing the phase at one point in the beam,
we can determine the phase at any other point in the beam only over a finite spatial
extent. This spatial extent is known as the coherence length of the light source (ideal
monochromatic sources have an infinite coherence length).
In the case of a Michelson interferometer, if the incident light beam were from an
ideal monochromatic source, an interference pattern would be generated irrespective
of the optical path lengths to the target and reference mirror. For incident light from
a physical source, interference would only be observed if the optical path lengths to
the target and reference mirror were matched to within the coherence length. Lasers
have extremely narrow spectral bandwidths and can have coherence lengths in the
25
coherent superposition
envelope
CI)
C
-
--
U)
incoherent
superposition
rn
C
I~
X/2
lengt
coeec
Reference mirror position (z)
Figure 2-2: Coherence length schematic. The intensity is plotted versus reference
mirror position (z). The region of coherent superposition defines the coherence length
of the illumination source.
range of kilometers. Although lasers are ideal for interferometry (and stroboscopic
interferometry due to their fast switching times), quantitative motion estimates from
images is complicated due to speckle 1. Light emitting diodes are characterized by a
short coherence length (typically about 10-15
[tim)
and do not create speckle patterns
when imaging MEMS. Consequently, we have used LEDs as illumination sources for
interferometric and brightfield imaging of MEMS devices.
2.2
Analyzing interferometric images
Interference fringes encode out-of-plane position. Several techniques are used to extract quantitative information regarding out-of-plane position from interferometric
images. This section describes a commonly used technique called phase-shifting interferometry. Techniques for determining surface height using phase-shifting interferometry typically involve the sequential shifting of the phase of the reference beam
of the interferometer (by moving the reference mirror) relative to the target beam
'Speckle is the grainy pattern observed when coherent light is used to illuminate a rough surface.
26
Optical
bench
Beam splitter
LED mount
Objectives
Target
CCD camera
Beam
splitter\
Shutter
Piezoelectric
actuator
Reference
mirror
LED
Objectives
CCD camera
Target
Reference
Piezoelectric
mirror
actuator
Figure 2-3: Linnik interferometric system. The left panel shows a schematic of the
Linnik interferometer. The right panel shows a photograph of a Linnik interferometric
system assembled on an optical bench. Adapted from (Hemmert et al., 1999).
by a known amount. This results in the "rolling" of the interference pattern across
the image so that each pixel in the image sequence collects an intensity that varies
sinusoidally with the position of the reference mirror. The amplitude of this sinusoidal variation is proportional to the reflectivity of the target. The phase of the
sinusoidal intensity variation encodes the relative out-of-plane position of the target.
The advantage of phase-shifting interferometry is that it provides out-of-plane position information for each pixel in the interferometric image independent of all other
pixels.
2.3
Linnik Interferometer
The Linnik interferometer is a variation of the Michelson interferometer, where objective lenses are placed at the ends of the target and reference arms of the interferometer.
This allows for interferometric imaging of microscopic targets such as MEMS. Light
from an LED is split into two beams by a 50-50 beam-splitter - one beam is focused
27
on the target, and the other beam is focused on the reference mirror. These two light
beams reflect off the target and the reference mirror respectively and recombine at
the beam-splitter. The resulting interference pattern is recorded by a CCD camera.
A Linnik interferometer was developed by Hemmert et al. (1999). It consists of
a custom-built microscope with two objective lenses (Zeiss LD-Epiplan 20x, 0.4 NA,
working distance: 9.8 mm, fitted with 160 mm tube-length correctors) positioned
to receive illumination from the split beam of a high-brightness LED (Nichia NSPG
500S LED, wavelength at maximum power A = 525 nm).
One objective lens is
focused on the target and the other is focused on a reference mirror. The same
beam-splitter used for illumination combines the reflected light from the target and
reference mirror (Figure 2-3), to generate interferograms.
Interferometric images
(as pictured in Figure 2-4) are generated in the coincident back-focal-planes of the
objectives. A piezo-electric actuator (NEC AE0505D08) supports the reference mirror
to change the phase in the interferogram by sub-wavelength adjustment of the optical
path-length difference. Brightfield images are also easily generated by closing the
shutter, thereby blocking the optical path to the reference mirror (Figure 2-4). Both
interferograms and bright field images were collected using a CCD array (Kodak
Megaplus 1.6i, 1534 x 1024 pixels with 9 pm spacing). The field of view was 690 Am
x 461 pm. An optical bench supported the apparatus. The Linnik interferometric
system was used to measure motions of a microfabricated lateral resonator (as shown
in Figure 1-iC). The results demonstrated nanometer resolution for in-plane motions
and subnanometer resolution for out-of-plane motions.
The short coherence length of the LED light source (approximately 15
[m)
re-
quired that the optical path lengths to the target and the reference mirror be matched
to within 15 pm. Focusing the target while matching the optical path lengths to this
precision is difficult and tedious. Consequently, this is an extremely difficult system
to setup and maintain.
28
100 pLm
100 Ltm
Figure 2-4: Images of surface micromachined lateral resonator obtained with Linnik
interferometer, brightfield image (left) with shutter blocked, interferometric image
(right) with shutter left open. Adapted from (Hemmert et al., 1999).
Spacer rings
Zeiss 20x
0.4 NA objective
Interferometer "focus"
adjustment
-
Tip/tilt adjustment-'%
screws
-
Double beam head
-
Reference plate
Reference mirror
positioner
Figure 2-5: Close-up view of Mirau interferometer.
29
Mirau Interferometer
2.4
The Zeiss Mirau interferometer consists of a double-beam head and a reference plate
(Figure 2-5). The reference plate has 3 circular mirrors with reflectivities of approximately 85%, 50% and 20%. A 50-50 beamsplitter is situated below the reference
plate. The Mirau interferometer is used with a Zeiss 20x 0.4 NA objective and can
be used to generate interference fringes with white or monochromatic light.
2.4.1
Assembly of interference system
The cover glass cap and holding ring of the Zeiss Epiplan LD 20x 0.4 NA objective
are removed, and the objective is screwed into the double-beam head of the interferometer. The width of the Mirau interferometer prevents it from being directly
mounted on the objective nanopositioner. To accomodate the interferometer two 1"
thick brass spacer rings are screwed into the end of the 20x objective.
2.4.2
Integration with microscopy system
The Mirau interferometric system is attached to the Zeiss Axioplan II microscope via
an objective nanopositioner (P720, PIFOC, Polytec PI), as shown in Figure 2-6. Light
projected from the objective is broken into two beams by the beamsplitter (Figure
2-3). One beam reflects off the target and the other beam reflects off the reference
mirror. These beams then combine and interfere at the beamsplitter. The resulting
interferometric image contains interference fringes with an inter-fringe distance of A/2,
where the wavelength of light A is 525 nm. Brightfield images are easily obtained by
rotating the reference mirror out of the optical path (Figure 2-6).
2.4.3
Adjusting interference fringes
High-contrast interference fringes are obtained by performing the following procedure:
1. The specularly reflecting object (in our case the MEMS under test) is brought
into the beam path and held in place on the microscope stage.
30
Objective
nanopositioner
20x Epiplan
LD objective
Zeiss Mirau
interferometer
Reference mirror
Reference
plate
Beam splitter
MEMS chip
Figure 2-6: Mirau interferometer. The left panel shows a schematic of the Mirau
interferometer. The Mirau interferometer consists of a reference mirror, reference
plate and a beamsplitter packaged into a single unit which mounts directly on a
Zeiss 20x Epiplan LD 0.4 NA microscope objective. Light from projected from the
objective is split into two beams by the beamsplitter. One beam reflects off the target
and the other beam reflects off the reference mirror. These reflected beams then
recombine and interfere at the beam-splitter. The right panel shows a photograph of
the Mirau interferometer mounted to the turret of a Zeiss Axioplan II microscope via
an objective nanopositioner.
31
-*-~-
I
-
--
----
-
~--
Zeiss 20x objective
Mirau interferometer
Glass window
100 m
Zeiss 20x objective
Mirau interferometer
Reference mirror
Reference plate
Beam splitter
100 pim
Figure 2-7: Interferometric and brightfield imaging using the Mirau interferometer.
The upper panel shows the Mirau interferometer configured for brightfield imaging,
with the reference mirror rotated out of the beam path. A sample brightfield image
recorded with a CCD camera is shown on the right. The lower panel shows the Mirau
interferometer configured for interferometric imaging, with the referece mirror placed
in the beam path. A sample interferometic image recorded with a CCD camera is
shown on the right.
32
2. The lower part of the double beam head is horizontally aligned using the tip/tilt
adjustment screws.
3. The reference plate is moved upwards by turning the "focus" ring on the interferometer counterclockwise.
4. The device under test is brought into focus using the fine focus control of the
microscope.
5. The edge of one of the reference mirrors is brought into the object field by
rotating the reference mirror positioner.
6. The interference system is lowered by turning the "focus" ring clockwise until
the edge of the reference mirror and the object are in focus at the same time.
The reference mirror is now rotated completely into the object field (using the
reference mirror positioner). Interference fringes are obtained, while keeping
the device in focus.
7. To optimize the contrast a suitable mirror is selected by rotating the reference
mirror positioner. Optimum contrast has been set when the object and the
reference mirror have the same reflecting power. To achieve this, each mirror
is brought partly into the object field to compare the brightness of the object
and the reference mirror, and the mirror that provides the highest contrast
interference fringes is selected.
2.4.4
Phase-shifting using Mirau interferometer
Phase-shifting techniques using the Mirau interferometer involve changing the target
path relative to the reference path. The reference mirror is fixed in the light path
and hence cannot be moved. Instead the entire interferometer is moved using the
objective nanopositioner. Motions of the nanopositioner alter the optical path length
to the target relative to the optical path length to the reference mirror (Figure 2-8).
This also changes the focus slightly but this change is small compared to the depth
of field of the objective (greater than 3 pm).
33
Zeiss 20x objective
Mirau interferometer
Reference mirror
Reference plate
Beam splitter
CO,
'
7
200
100
0
-200 -150 -100 -50
100 gm
0
50
100 150 200
Relative nanopositioner position z (nm)
Figure 2-8: Phase-shifting using the Mirau interferometer. The left panel shows an
interferometic image of a surface micromachined lateral resonator. The center of the
black rectangle indicates the pixel of interest. The right panel shows plots of the
brightness of the pixel at different positions of the objective nanopositioner (z). A z
value of "0" represents the plane of best focus. Positive values of z represent planes
below the best plane of focus and negative values of z represent the planes above
the best plane of focus. The circles represent the pixel brightness at a particular z
position. The plot shows the sinusoidal brightness variation of a pixel for different
positions of the objective nanopositioner.
34
200
C
.
100 -
I
'
'
I
'
-1.5 -1.2 -0.9 -0.6 -0.3
0
'
0.3
0.6
0.9
Relative nanopositioner position z (gm)
Figure 2-9: Coherence length measurement of Cree LED illumination source. Circles
indicate the brightness of the pixel of interest (indicated in Figure 2-8). This plot
experimentally verifies the theory presented in Figure 2-2. The interference fringe
modulation depth is within a factor of 2 over a range of 2 pum in z.
2.5
Comparison of Mirau and Linnik interferometers
2.5.1
Assembly
The Linnik interferometer was built on an optical table using custom-fabricated optical components. This is a time consuming process requiring considerable knowledge
of optical components.
Assembly of the Mirau interferometer is trivial in that it
simply requires screwing a Zeiss 20x objective into the double-beam head of the intereference system. This allows for even novices to generate interferometric images
within a matter of minutes.
2.5.2
Optical alignment
In comparison to the custom-built Linnik interferometer, the Mirau interferometer is
extremely easy to use, and can be readily integrated with a brightfield microscopy
system. The Mirau interferometer does not require precision alignment since all the
optical components are aligned by the manufacturer. In the Linnik interferometer
the short coherence length of the LED light source requires that the optical path
lengths be matched within 10-15 pm, which requires precision alignment of the optical
35
components for each target.
2.5.3
Working distance
Both the Linnik and Mirau interferometric systems used Zeiss LD-Epiplan 20x objective which has a working distance of 9.8 mm. This long working distance allows for
the integration of other pieces of experimental apparatus such as electrical probes or
vacuum fixtures. The beam splitter and reference mirror in the Mirau interferometer
reduce the working distance to 1.75 mm. This smaller working distance restricts the
experimental setup in that the MEMS devices must typically be wire bonded and the
structures to be measured should be near the surface of the package. By contrast, a
Linnik interferometric system provides the full 9.8 mm of working distance.
2.5.4
Numerical aperture
The Mirau interferometer is designed for use with a Zeiss LD-Epiplan 20x objective.
This limits the numerical aperture (NA) of the system since the 20x objective has an
NA of 0.4. In comparison the Linnik interferometer can be designed with higher NA
objectives.
2.5.5
Field of view
Generally, high numerical aperture can only be achieved for objectives with high
magnifications. A higher magnification objective provides a smaller field of view, given
the same camera. The Mirau interferometer can only be used with a 20x objective
and hence provides a 461 pm x 461 um field of view (using the Pulnix TMI010 CCD
camera). A larger field of view can be obtained by post-demagnification at the camera.
The Linnik interferometer can be designed with lower magnification objectives that
provide a larger field of view.
36
Chapter 3
Image Acquisition
Measuring the motions of MEMS using computer microvision based techniques requires two steps - image acquisition and motion analysis. During image acquisition
the device is electrically stimulated and a series of images is collected by stroboscopically "freezing" the MEMS motion. Motion analysis uses machine vision algorithms
to extract quantitative motion information from the images. This chapter discusses
the image acquisition techniques used for both brightfield and interferometric microscopy techniques. Motion analysis algorithms are discussed in Chapter 4. A light
microscope and camera image the MEMS test structures, while an electrical signal
drives the test structure. An array of light emitting diodes (LEDs) are strobed once
per stimulus period at a chosen phase to stroboscopically "freeze" the motion of the
device. This process is repeated over several stimulus phases and stimulus frequencies. Machine vision algorithms are used to estimate the change in position of the
device between successive images.
3.1
MEMS test structure setup
To demonstrate the 6 degree-of-freedom motion measurement capability of the Mirau
interferometric system, a surface micromachined lateral resonator fabricated using
MUMPs (Cronos Integrated Microsystems, USA) was electrically stimulated with a
sinusoidal voltage (10V peak-to-peak AC plus 50V DC bias) applied to one of the
37
Flexure
Structural anchor
Shuttle mass
'7-
Sinusoidal
Insulating silicon Structural anchor Interdigitated comb-finger
actuator
nitride layer
source
GND
Figure 3-1: Surface micromachined lateral resonator. The left panel shows an SEM
image of the left half of the lateral resonator showing a movable shuttle tethered by
folded flexures and interdigitated electrostatic comb finger actuators. The right panel
shows a brightfield image of the lateral resonator showing the electrical setup. The
shuttle mass was grounded and the sinusoidal drive was applied to the lower set of
comb fingers. The upper set of comb fingers were left electrically floating.
comb drives with the shuttle mass connected to ground (Figure 3-1).
The lateral
resonator was one of many micromechanical devices on a 1 cm 2 silicon die packaged
in a 84-pin PGA package. The package was mounted in a ZIF socket on a custom
designed printed circuit board (PCB), and the PCB was fixed to the stage using
magnets.
3.2
Waveform generation
The XPOZ system (Figure 3-2) generates a periodic stimulus waveform and an illumination waveform.
The stimulus waveform used for driving MEMS is typically
sinusoidal, but any periodic waveform that can be described by 65,536 12-bit samples
can be generated using the XPOZ system. The illumination waveform consists of
rectangular pulses synchronized with a particular phase of the stimulus, and drives
an LED connected to the microscope.
38
sramn
control
addr
data
waveform
eform
sthac
latch
power
relay
brightness
LED strobe
1LED
strobe
TTL signal
Figure 3-2: XPOZ arbitrary waveform generation system. The boxes denote integrated circuits and the lines denote interconnects. The numbers next to the lines
indicate the width of the interconnect bus (in bits). System timing is performed using a 10 MHz crystal oscillator. The FPGA executes digital logic configured by a PC
via the parallel port. SRAM stores digital samples of the waveform to be written to
the wavefrom D/A converter. The brightness DAC controls the voltage of the LED
driving signal. A TTL signal toggles the LED output, allowing the LED to be pulsed
at frequencies up to 5 MHz. Figure adapted from (Aranyosi, 2002).
The XPOZ system was designed by Prof. Dennis M. Freeman, Stan Hong, and
Tim Dunn. A field programmable gate array (FPGA, XC4O1OE, Xilinx, San Jose,
CA) provides user-programmable control of the stimulus and illumination waveforms.
The waveform to be generated is stored as 65,536 12-bit samples in SRAM. The
current stimulus phase is stored as a 32-bit value. The resulting system can generate
arbitrary periodic waveforms at frequencies ranging from approximately 2 mHz to 1
MHz with mHz resolution, using a 10 MHz crystal oscillator. The LED is strobed
with a TTL signal, which allows for stroboscopic illumination with 100 nanosecond
time resolution. The LED is controlled by a DAC which allows for precise control
over brightness.
39
3.3
Video microscopy
A CCD camera attached to the microscope is continuously exposed while the stimulus and illumination waveforms are generated. The resulting image on the CCD
camera shows all visible structures at a specific phase of the stimulus waveform. This
image is then read out and stored on a computer. This process is repeated with the
illumination pulses centered on a different phase of the stimulus. Once the images
at a number of evenly spaced phases (typically 8) of the stimulus are collected, the
objective is moved using a piezoelectric nanopositioner (PIFOC, Polytec PI). For
brightfield imaging, images are collected at 10 positions of the nanopositioner (z)
spaced by 2 pm. For interferometric imaging, interferograms are collected at 9 z
positions spaced by 30 nm (Figure 3-3). The process of collecting images at evenly
spaced phases of the stimulus is then repeated.
At each z position, images are collected at 8 evenly-spaced phases of the stimulus
waveform. The LED is driven with a 1/8 duty cycle centered on the phase of the
stimulus waveform.
The images are degraded by shot noise and so the exposure
time for the camera is set so as to maximize pixel brightness, thereby maximizing
the signal to noise ratio in the images. The ultimate resolution of the computer
microvision system is dependent on low frequency vibrations coupling into the system.
To damp out low frequency vibrations, the entire microscopy system was placed on a
vibration isolation table and in a clean air enclosure to minimize the effects of external
vibrations and air currents.
3.3.1
Interferometric image acquisition
For each of the 33 stimulus frequencies (from 1kHz to 50kHz) and 8 stroboscopic
phases, a sequence of interferograms is acquired for 9 different positions (z) of the
objective nanopositioner. Motions of the nanopositioner alter the optical path length
to the target relative to the optical path length to the reference mirror. This also
changes the focus slightly but this change is small compared to the depth of field of
the microscope objective (greater than 3 ,um; see Figure 3-3).
40
30 nm
-w
-
1002m
9 Rm
100
0gpm
Figure 3-3: Image acquisition for brightfield and interferometric imaging. The left
panel shows a brightfield image of the surface micromachined lateral resonator. The
black rectangle indicates a 20 x 20 pixel region of interest consisting of an antistiction dimple. Images of this region of interest are shown for 7 z positions spaced
by 2 pm. The arrow-head indicates the image at the best plane of focus. Images
above and below the best plane of focus are blurred. The right panel shows an
interferometric image of the lateral resonator. The same 20 x 20 pixel region of
interest is selected. Images of this region of interest are shown for 11 z positions
spaced by 30 nm. These images indicate that the dimple is still in focus for all z
positions. However, the interference pattern across the dimple changes for each z
position. The arrows extending from the brightfield to the interferometric image
indicate the change in scale of z from brightfield image acquisition to interferometric
image acquisition.
41
3.3.2
Brightfield image acquisition
Image acquisition for in-plane motion analysis
For each of 33 stimulus frequencies (from 1kHz to 50kHz), brightfield images at the
best plane of focus were obtained at 8 equally spaced phases of the sinusoidal stimulus
waveform.
Image acquisition for out-of-plane motion analysis
For each of 33 stimulus frequencies (from 1kHz to 50kHz), brightfield images were
obtained at 8 equally spaced phases of the sinusoidal stimulus waveform and at 9 z
positions (spaced by 2 pm) above and below the best plane of focus.
3.3.3
Image acquisition for noise analysis
After data were collected for both the interferometric motion measurement and brightfield motion measurement, the stimulus was turned off, and the exact same image
acquisition procedure was repeated five times.
3.4
Stroboscopic illumination
The brightfield computer microvision system utilized a high performance green LED
(Nichia NSPG500S), as pictured in Figure 3-4. The beam-splitter in the Mirau interferometer reduces the amount of light that reaches the camera. Interferometric
images taken with the Nichia LED had poor fringe contrast and due to the longer
exposure times were noisier.
To provide high-contrast interferometric images an array of 7 ultra-bright LEDS
(C505-CB290-E1000, Cree Research Inc., USA). To allow for high-speed switching
the XPOZ system was hard-wired so that the LED array was strobed with the TTL
signal and was driven with an external power supply (as opposed to the output of
the brightness DAC in the XPOZ system). The LED array and drive electronics are
42
Custom printed
circuit board
Nichia NSPG500S
surface mount LED
Electrical connections
for Zeiss Axioplan lamp
housing
Figure 3-4: Nichia NSPG500S surface mount LED, soldered onto a printed circuit
board.
pictured in Figure 3-5. The LED array was driven with a one-eighth duty cycle pulsetrain synchronized with one of 8 equally spaced phases of the stimulus waveform to
stroboscopically "freeze" the MEMS motion. The fast optical rise time of the LEDs
(approximately 30 ns) allows for stop-action motion analysis at frequencies of up to
tens of megahertz.
43
Cree C505-UB290
Resistors Switching transistors
Subcircuit x4 for
16 LED array
driving 16 LED array
1K
-----------------------------ZVP3409
TTL drive
from XPOZ
-
ZVN3306A
200
1
200
200
200
C505-UB290
I- -
-
--
-
-
GND
Figure 3-5: Illumination source for video microscopy, The left panel shows a photograph of the Cree LED array and drive electronics. The right panel shows the
schematic of drive electronics.
44
Chapter 4
Motion Analysis
Computer microvision is an image based technique. Images collected from the computer microvision system can be animated in sequence to allow a qualitative assessment of motion. This allows MEMS designers to actually "watch" motions of the
device under test and understand its failure modes. In addition to viewing the images, we can quantitatively measure the motion in three-dimensions of any structure
in the images.
Image resolution is limited by the optics used in the microscopy system, primarily
the microscope objective. The images acquired by the microscopy system are limited
in resolution to distances on the order of the wavelength of light (A) used (in our
case a green LED where A is approximately 505 nanometers).
The limitations on
motion resolution are different from those on image resolution. Motion resolution is
limited by the quantum nature of light and the detection/imaging system used (in
our case a CCD camera). This chapter describes analysis techniques for quantitative
motion estimation of six degree-of-freedom motions of a surface micromachined lateral
resonator (as shown in Figure 3-1).
4.1
In-plane motion analysis
We measure translational motion from video images using a gradient method (Davis
and Freeman, 1998a). The technique uses changes in brightness between images to
45
i*~j
-
Image 1
I!
--
Image 2
Stimulus
waveform
Image 8
-
Iumination
Time "O"
Time 7"
Time "1
----
Time "0"
Time 1"
,n 200
a,
C
S100
V '
Zio
'a''
0
0
A
22.5
45
X(gm)
100 .tm
Figure 4-1: In-plane motion analysis. Left panel shows a brightfield image of a
surface micromachined lateral resonator. The black rectangle indicates the region
of interest selected. The plot shows the pixel brightness in the region of interest at
2 consecutive times, time "0" and time "1". The shift between the two brightness
curves is estimated using a gradient method (Davis and Freeman, 1998a).
estimate motion. Motions as small as two nanometers can reliably be measured.
With 9pam x 9pum pixels on the CCD imager, the minimum resolvable motion is
subpixel. This technique for measuring translational motion is robust and precise;
but statistically biased. A linear bias compensation method is used to correct for the
linear component of the bias.
4.2
Out-of-plane motion analysis from brightfield
images
The brightfield CMV system can be used to measure out-of-plane motion.
Al-
though we cannot use optical sectioning to actually see "through" opaque structures,
three-dimensional images of opaque structures still provide information about threedimensional structure and motion. Image brightness is greatest when the structure
46
Zeiss 20x objective
Mirau interferometer
Glass window
-:
1
I
,
.
A77
7
I .
z
27
7
I
.
,
.
.
---- Time "0"
Time "1"
--
'
'
'
'
2
4
6
8
10
W200
7100
01
z
I
'
'
-8
-6
-4
I
'*
-2
0
Relative nanopositioner position z (pm)
x
Figure 4-2: Out-of-plane motion analysis from brightfield images. The left panel
shows a brightfield image of surface micromachined lateral resonator. The center of
the black rectangle indicates the pixel of interest. The right panel shows plots of the
brightness of this pixel across versus objective nanopositioner position at 2 times,
time "0" and time "1". A z value of "0" represents the plane of best focus. Positive
values of z represent planes below the best plane of focus and negative values of z
represent the planes above the best plane of focus. Notice that the brightness gradient
is much smaller than for in-plane motions as shown in Figure 4-1.
is in focus and decreases as the plane of focus is moved higher or lower. Images from
above the best plane of focus of a structure are blurred. As the structure moves
out-of-plane, the out-of-plane blurring pattern moves with the structure. Our motion
detection algorithm takes advantage of these changes in brightness to align threedimensional images of the moving microstructure taken at different phases of the
sinusoidal stimulus (Figure 4-2). Hence the algorithms used for tracking in-plane motions by computing in-plane gradients can be applied to track out-of-plane motions
by computing out-of-plane gradients (Davis and Freeman, 1998b).
47
4.3
Out-of-plane motion analysis from interfero-
metric images
For each stimulus frequency and stroboscopic phase, a sequence of interferograms is
acquired for different positions (z) of the objective nanopositioner. Each pixel in the
sequence collects an intensity that varies sinusoidally with z. The amplitude of this
sinusoidal variation is proportional to the reflectivity of the device. The phase of the
sinusoidal intensity variation encodes the relative out-of-plane position of the device.
For each stimulus condition, a set of images were acquired at uniform spacing along
z (Figure 4-3). For each pixel, the amplitude, phase, and period of brightness as a
function of z were fit with a sinusoid using a least-squares technique. Out-of-plane
motions were determined from the phase of the best fitting sinusoid.
4.4
4.4.1
Results
Six degree-of-freedom motion measurement
Stroboscopic interferograms at 9 z positions (separated by 30 nm) and one brightfield
image (at the best plane of focus) were analyzed for 8 stimulus phases for a 21 kHz
stimulus frequency. Results are illustrated in Figure 4-4. Brightfield images were analyzed to determine displacements in the x-direction, displacements in the y-direction
and in-plane rotations (about the z-direction).
These results are plotted as time
waveforms for two cycles of the stimulus (Figure 4-4, upper panel). Displacements
in the x-direction are approximately sinusoidal. The estimated amplitude and angle
are 128.9 nm and 14.2 degrees, respectively. The other in-plane measurements are
on the order of the noise floor of the measurement. Interferometric images were analyzed to determine displacements in the z-direction, rotations about the x-direction
and rotations about the y-direction. These results are plotted as time waveforms for
two cycles of the stimulus (Figure 4-4, lower panel). Displacements in the z-direction
and rotations about the y-direction are approximately sinusoidal. The estimated am48
Zeiss 20x objective
Mirau interferometer
Reference mirror
Reference plate
Beam splitter
-.:7z
I
---(n
100
1
II
-120
zytx
100 gm
Time "1
200
CD
-C
0)
Time "0"
'
1
-90
'
U
-60
'
I
-30
I
'
0
II
30
*
I
60
90
I
I
I
I
120
Relative nanopositioner position z (nm)
Figure 4-3: Out-of-plane motion analysis from interferometric images. The left panel
shows an interferometic image of a surface micromachined lateral resonator. The
center of the black rectangle indicates the pixel of interest. The right panel shows
plots of the brightness of the pixel versus objective nanopositioner position (z) at 2
times, time "0" and time "1". A z value of "0" represents the plane of best focus.
Positive values of z represent planes below the best plane of focus and negative values
of z represent the planes above the best plane of focus. The plots have much greater
contrast versus z as compared to those shown in Figure 4-2.
49
x-Translation (nm)
y-Translation (nm)
500 -
i
200 1
200]
Rotation about z (mDeg)
-200
-200
0
1
Stimulus period
-500
1
0
2
Stimulus period
1
0
2
Rotation about y (mDeg)
z-Translation (nm)
2
Stimulus period
Rotation about x (mDeg)
-500]
500_-_-
200J
0
[
0
-
0-
- 0
-
-200
-
-500
0
1
2
0-
1-500
0
Stimulus period
1
2
Stimulus period
0
1
2
Stimulus period
Figure 4-4: Six degree-of-freedom motion measurements, in-plane degrees of freedom
(upper panel), out-of-plane degrees of freedom (lower panel).
plitude and angle for displacement in the z-direction are 37.8 nm and 39.7 degrees,
respectively. The estimated amplitude and angle for rotation about the y-direction
are 62.3 millidegrees and 31.1 degrees, respectively. Rotation about the x-direction is
on the order of the noise floor.
Similar results were obtained for 33 frequencies from 1 kHz to 50 kHz. Amplitudes
and angles for displacements in the x-direction are illustrated by the circles in Figure
4-5 (left panel). These measurements were fit with a second-order resonance curve
(indicated by the solid line) which exhibited a sharp resonant peak (Q = 32.95) at
23.2 kHz. The phase response exhibited a sharp roll-off at resonance. The noise floor
was measured as 0.48 nm (indicated by the dashed line).
Amplitudes and angles for displacements in the z-direction are shown in Figure 4-5
(center panel). These measurements were fit with a second-order resonance curve with
resonance frequency of 29.85 kHz and
Q=
2.06. The noise floor of the measurement
was 0.44 nm.
Amplitudes and angles for rotations about the y-direction are shown in Figure
4-5 (right panel). These measurements were fit with a second-order resonance with
50
z-Translation
x-Translation
1000
fo=23.2 kHz
C
100
Q=32.9
_0
10
0)
Ca
1000
y-Rotation
)
fo=29.85 kHz
1000
0=2.06
100
I
fo=30.5 kHz
0=2.53
100
10
1
0.48 nm
1
CO
0.44nm
0.1
0.1
10
I.............I
180
""
0.3 m~e
0.1
1
1..I
180
------------
)1
1
60
.
10
50
I..........I
.
180-
--
CUn
I""BO
00)
-180
WU)1
-C
0-
1
10
Frequency (kHz)
1
10
Frequency (kHz)
50
1
1]..
0
Frequency (kHz)
SO
Figure 4-5: Magnitude and phase of frequency response for translation along x (left
panel), translation along z (center panel), and rotation about y (right panel)
resonance frequency of 30.55 kHz and Q = 2.53. The noise floor of the measurement
was 0.35 millidegree.
As expected from the design of the device, motions in the other three degrees
of freedom (namely, displacement in y-direction, rotation about the z-direction and
rotation about the x-direction) are small and comparable to the noise floor of the
measurement. Hence, frequency response data for these degrees of freedom are not
shown.
4.4.2
Out-of-plane motion measurements using brightfield images
Stop-action brightfield images at 10 z positions (separated by 2 pm) were analyzed for
8 stimulus phases at each of 33 frequencies (from 1 kHz to 50 kHz). Amplitudes and
angles of displacement in the z-direction are shown in Figure 4-6. These measurements
are compared to the fit derived from the interferometric z-displacement measurements,
which is shown by the solid line. The noise floor for the measurement was 4.1 nm
(indicated by the dashed line), roughly ten times the noise floor of the interferometric
measurement.
51
I
1000-1
E 100 -
.
I
I
fo=29.85 kHz
0=2.06
r
a))
-
0
(
.1 -1-
4.1 nm
r
0.110
0
-1
-
1
K
a)
C)
-
C
.
. I
180-
50
-180 1
Frequency (kHz)
10
50
Frequency (kHz)
Figure 4-6: Magnitude and phase of frequency response for out-of-plane motion (ztranslation) using brightfield images.
52
Chapter 5
Static and Dynamic Profilometry
Surface profile measurement is an important tool for MEMS device characterization.
Surface flatness is of critical importance to optical MEMS devices in particular (such
as micromirrors and diffraction gratings). Commercial profile measurement systems
allow for either (1) static profile measurement of all structures within the field of
view (e.g. Wyko Scanning White Light Interferometers), or (2) line-scanned dynamic
profile measurements (e.g. Polytec PI Laser Doppler).
The Mirau interferometric system allows for measurement of both static and dynamic profiles of all structures within the field of view. Using phase-shifting interferometry, the out-of-plane position of each individual pixel in an interferometric image
can be determined, independent of all other pixels. This provides high resolution
static profiling capability. Using this technique in combination with stroboscopic illumination, profiles can be reconstructed at different temporal phases of the stimulus
waveform, thereby enabling dynamic profilometry.
5.1
MEMS test structure setup
Electrostatically deformable surface micromachined diffraction gratings (designed at
the University at Albany, State University of New York) were used to demonstrate the
dynamic profiling capability of the system. Deformations were stimulated by applying
a 1 kHz sinusoidal waveform (20V peak-to-peak AC plus 30V DC bias) to the movable
53
-Polysilco
.....-.
.
-
beamys
..
.
f
Out-of-plane motion
Sinusoidal
source
n
Polysilicon
gnd electrode
Nitride insulating
layer
GND
Si substrate
GND
100 AiM
Figure 5-1: Electrical setup for diffraction gratings. The left panel shows a brightfield
image of the diffraction gratings. The line indicates the region of the cross-section.
The right panel shows a cross-sectional view of a single grating detailing a clampedclamped polysilicon beam actuated using an underlying polysilicon electrode.
grating with the underlying electrode grounded (Figure 5-1). The diffraction gratings
were wire-bonded and packaged in a 22-pin dual inline package (DIP). The DIP was
placed in a zero insertion force (ZIF) socket on a custom designed PCB. The PCB
was affixed to the microscope stage using magnets.
5.2
Image acquisition
Stimulus and illumination waveforms were generated using the XPOZ system (described in section 3-2). Interferometric images were recorded using a CCD camera
(Pulnix TM- 1010), and illumination was generated using the Cree LED array (Figure
3-5). For static profilometry, the device was not electrically stimulated, and stroboscopic interferograms were collected at 20 z positions separated by 50 nm. To
determine electrostatic deformations of the gratings, the device was driven with a
sinusoidal waveform and stroboscopic interferograms were collected at the same 20 z
positions at each of 8 stimulus phases.
54
Zeiss 20x objective
Mirau interferometer
Reference mirror
Reference plate
Beam splitter
100 pLm
Figure 5-2: Phase-shifting Mirau interferometery for profilometry. The left panel
shows an interferometric image of the diffraction gratings taken at the best plane
of focus. The right panel shows a schematic of the Mirau interferometer which is
positioned in 20 different z positions to collect phase-shifted interferograms.
5.3
Static profilometry
Static profiles were generated by analyzing the phase-shifted interferograms. Motions
of the objective nanopositioner alter the optical path length to the target relative to
the optical path length to the reference mirror. This path length difference causes the
interference pattern to "roll" across the image and each pixel in the sequence collects
an intensity that varies sinusoidally with z. The amplitude of this sinusoidal variation
is proportional to the reflectivity of the device. The phase of the sinusoidal intensity
variation encodes the relative out-of-plane position of the device. By extracting the
phase of a row of pixels along the length of the device (as shown in Figure 5-2) the
surface profile of the grating can be reconstructed. The profiles shown in Figure 52 indicate that the gratings are bowed and that the center point of the grating is
approximately 100 nanometers closer to the substrate than the anchored portions.
This curvature in the gratings is most likely due to residual stress 1 which is relieved
during microstructural "release".
'Any stress that is present in a thin film after deposition is termed as residual stress (Senturia,
2001). Residual stress can be decomposed into thermal mismatch stress and intrinsic stress. Thermal
mismatch stress arises from chemical reactions that take place at high temperatures, such as the
oxidation of silicon and the low pressure chemical vapor deposition (LPCVD) of silicon nitride.
55
Grating #1 profile
El
CI
r
I
175 pam
Grating #4 profile
-El
L
100 gm
I
175 pLm
Figure 5-3: Static profiles of surface micromachined diffraction gratings. The left
panel shows a brightfield image of 7 diffraction gratings. The dotted lines indicate the
row of pixels that were used to reconstruct the profile of the diffraction gratings. The
right panel shows plots of static profiles obtained from phase-shifted interferograms.
The upper plot was generated from the first grating in the image (called Grating #1)
and the lower plot was generated from the the fourth grating in the image (called
Grating #4).
56
Grating #1 profile
Grating #4 profile
E
E
C
0)
C:
0
Gra-ipse.Trigh
a1
profilesGatn
hosrcsrce
175urn
175urn
stmcsphsso.te1kz
f#r rting#4o
aeom
whch
lal
ilsrt
dfraiosoh
Figure 5-4: Dynamic profiles of surface micromachined diffraction gratings. The left
panel shows reconstructed profiles for Grating #1 for 8 stimulus phases of the 1 kHz
waveform. The device was not electrically stimulated and hence all the profiles are
super-imposed. The right panel shows reconstructed profiles for Grating #4 for 8
stimulus phases of the kHz
I
waveform, which clearly illustrate deformations of the
grating.
5.4
Dynamic profilometry
Dynamic profiles are determined from stroboscopic interferograms obtained at evenly
spaced phases of the stimulus. Since phase-shifted interferograms are collected at each
of the 8 evenly spaced stimulus phases, the out-of-plane position for each pixel in the
image can be determined, allowing for reconstruction of profiles for each stimulus
phase. By plotting the profiles for each stimulus phase, we can determine how the
device under test deforms during electrostatic actuation.
Out-of-plane positions along one grating are shown for 8 phases in Figure 5-4
(right panel).
For all phases, the profiles are bowed and the displacements of the
center point of the grating are approximately 100 nm closer to the substrate than
are the anchored portions of the grating. The bowing changes periodically with the
stimulus. The amplitude and angle of the displacements of the center of the grating
are 26.6 nm and 4.2 degrees, respectively. Not all gratings bowed identically. Figure
5-4 (left panel) shows results for a different grating that was not electrically stimulated
and all 8 phases show the same curvature.
57
58
Chapter 6
Summary and Discussion
We have obtained motion measurements of MEMS devices with an interferometric
imaging system utilizing a commercial Mirau interferometer. With this system we
demonstrated rigid body motion measurements with 6 degrees-of-freedom.
Noise
floors for translation measurements were sub-nanometer in all three directions. Noise
floors for rotational angle measurements were sub-millidegree for all three directions.
We have also demonstrated static and dynamic profilometry with nanometer resolution.
6.1
Comparison of Mirau interferometric computer
microvision to brightfield computer microvision
The Mirau interferometric system provides nanometer in-plane resolution and subnanometer out-of-plane resolution. Out-of-plane resolution is more than an order
of magnitude better than resolution of comparable brightfield measurements. Data
collection for the two systems is virtually identical and analysis is similar except for
the sinusoidal fits described in section 4.3.
59
6.2
Disadvantages of Mirau interferometry
The principal disadvantage of the Mirau interferometric system is that it greatly
reduces the working distance of the optical system compared to the Linnik interferometric system. The objective that we used (Zeiss LD-Epiplan 20x) has a working
distance of 9.8 mm which allows for the integration of other pieces of experimental
apparatus such as electrical probes or vacuum fixtures. The beam splitter and reference mirror in the Mirau interferometer reduce the working distance to 1.75 mm.
This smaller working distance restricts the experimental setup in that the MEMS
devices must typically be wire bonded and the structures to be measured should be
near the surface of the package. By contrast, a Linnik interferometric system using
the same objective would provide the full 9.8 mm of working distance.
6.3
Implications for MEMS design
Measuring complex modes of motion
Mirau interferometric computer micro-
vision allows for the measurement of six degree-of-freedom motion measurement of
all structures within the field of view. Using phase-shifting interferometry techniques
along with stroboscopic imaging allows for studying deformations of microstructures.
This allows MEMS designers and testers to effectively characterize MEMS and gain
valuable insight into internal failure modes of microfabricated devices.
"Watching" motion
Since computer microvision based techniques are image based
they provide powerful qualitative information to MEMS designers and testers who
can actually "see" the motions of the device. Interferometric techniques enhance this
qualitative aspect of computer microvision as they allow visualization of out-of-plane
translations and rotations.
Measuring arrays of devices
Computer microvision techniques acquire stop-
action images of moving structures for six degree-of-freedom motion measurement.
This allows for quantitative motion measurement for all structures within the field of
60
view. Hence, multiple devices and even arrays of devices can be characterized using a
computer microvision data set. This is of increasing importance as MEMS complexity
increases and large numbers of devices are fabricated on a single substrate.
Tools for MEMS metrology are just beginning to reach maturity. Each metrology
system has its share of advantages and disadvantages. The system presented here
combines the high-resolution out-of-plane measurement capabilities of interferometry
with the three-dimensional imaging of multiple structures and qualitative assessment
tools of computer microvision. The Mirau interferometric computer microvision system should prove to be a powerful new tool for MEMS designers.
61
62
Bibliography
Aranyosi, A. J. (2002).
Measuring sound-induced motions of the alligator lizard
cochlea, PhD thesis, Massachusetts Institute of Technology, Cambridge, MA.
Creath, K. (1988). Phase-shifting interferometry techniques, Progress in Optics XXIV
pp. 357-373.
Davis, C.
Q.
(1997).
Measuring nanometer, three-dimensional motions with light
microscopy, PhD thesis, Massachusetts Institute of Technology, Cambridge, MA.
Davis, C.
Q. and
Freeman, D. M. (1998a). Statistics of subpixel registration algo-
rithms based on spatio-temporal gradients or block matching, Optical Engineering pp. 1290-1298.
Davis, C.
Q.
and Freeman, D. M. (1998b).
Using a light microscope to measure
motions with nanometer accuracy, Optical Engineeringpp. 1299-1304.
Desai, S. P. and Freeman, D. M. (2001). Nanometer resolution of three-dimensional
motions using mirau interferometry, Proceedings, InternationalMEMS Conference, (IMEMS) 2001, Singapore.
Fedder, G. K., Santhanam, S., Reed, M. L., Eagle, S. C., Guillou, D. F., Lu, M. S. C.
and Carley, L. R. (1996).
Laminated high-aspect-ratio microstructures in a
conventional cmos process, Proceedings of the 9th IEEE International Workshop
on Micro Electro MechanicalSystems (MEMS '96), IEEE, San Diego, California.
63
Freeman, D. M., Aranyosi, A. J., Gordon, M. J. and Hong, S. S. (1998). Multidimensional motion analysis of MEMS using computer microvision, 1998 Solid-State
Sensor and Actuator Workshop, Hilton Head, South Carolina, pp. 150-155.
Gordon, M. J. (1999). Rotation analysis of a microfabricatedfatigue test structure,
Master's thesis, Massachusetts Institute of Technology, Cambridge, MA.
Guiterrez, R. C., Shcheglov, K. V. and Tang, T. K. (1998). Pulsed source interferometry for characterization of resonant micromachined structures, Digest, Solid
State Sensor and Actuator Workshop, Hilton Head, South Carolina.
Hart, M. R., Conant, R. A., Lau, K. Y. and Muller, R. S. (2000).
Stroboscopic
interferometer system for dynamic mems characterization, IEEE Journal of MicroelectromechanicalSystems pp. 409-418.
Hemmert, W., Mermelstein, M. S. and Freeman, D. M. (1999). Nanometer resolution
of three-dimensional motions using video interference microscopy, Proceedings,
Twelfth IEEE International Conference on Micro Electro Mechanical Systems,
(MEMS '99), IEEE, Orlando, Florida.
Senturia, S. D. (2001). Microsystem Design, 3rd edn, Kluwer Academic Publishers,
Norwell, MA.
64