Development of Micromachined and Meso-scale Multi

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Development of Micromachined and Meso-scale
Multi-axis Accelerometers with
Displacement-amplifying Compliant Mechanisms
A thesis
Submitted for the Degree of
DOCTOR OF PHILOSOPHY
In The Faculty of Engineering
By
Sambuddha Khan
Department of Electronic Systems Engineering
Indian Institute of Science
Bangalore-560012
July 2013
©Sambuddha Khan, 2013
All rights reserved
i
Dedicated to
My beloved parents
and
My dearest wife, Ranu
ii
Table of Contents
TABLE OF CONTENTS ........................................................................................................ III
ACKNOWLEDGEMENTS ...................................................................................................... IX
ABSTRACT .......................................................................................................................... XI
PUBLICATIONS BASED ON THIS THESIS ........................................................................... XIII
LIST OF FIGURES .............................................................................................................. XV
LIST OF TABLES ............................................................................................................. XXIV
CHAPTER 1 .......................................................................................................................... 1
INTRODUCTION .................................................................................................................... 1
1.1
Background and motivation ................................................................................. 1
1.1.1 Need for mechanical amplification .................................................................. 4
1.1.2 Introduction to DaCMs .................................................................................... 5
1.1.3 DaCM vs. a simple mechanical lever .............................................................. 6
1.1.4 Rationale for choosing capacitive transduction .............................................. 8
1.1.5 Why meso-scale devices? ................................................................................. 9
1.1.6 Spring steel as a meso-scale material ............................................................ 10
1.2
Objectives and the scope of the thesis ............................................................... 11
1.2.1 Development of a wide-band single-axis micromachined capacitive in-plane
accelerometer with a DaCM. ..................................................................................... 11
1.2.2 Development of a dual-axis micromachined capacitive in-plane
accelerometer using a de-coupling mechanism and two DaCMs. ............................. 12
1.2.3 Development of a dual-axis wide-band micromachined capacitive in-plane
accelerometer without mechanical amplification. ..................................................... 12
1.2.4 Development of meso-scale spring steel accelerometers............................... 13
1.3
Organization of the thesis .................................................................................. 13
1.4
Closure ............................................................................................................... 14
CHAPTER 2 ........................................................................................................................ 15
LITERATURE REVIEW ........................................................................................................ 15
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2.1
A brief overview of micromachined accelerometers ......................................... 15
2.1.1 Operating principle of accelerometers .......................................................... 16
2.1.2 Types of micromachined accelerometers ....................................................... 21
2.1.2.1
Piezoresistive accelerometers ......................................................................................... 21
2.1.2.2
Piezoelectric accelerometers .......................................................................................... 22
2.1.2.3
Capacitive accelerometers .............................................................................................. 23
2.1.2.4
Resonant accelerometers ................................................................................................ 23
2.1.2.5
Optical accelerometers ................................................................................................... 24
2.1.2.6
Tunneling accelerometers ............................................................................................... 25
2.1.2.7
Thermal accelerometers .................................................................................................. 26
2.1.2.8
Electromagnetic accelerometers ..................................................................................... 26
2.1.3 Key specifications of an accelerometer ......................................................... 27
2.1.3.1
Axial sensitivity .............................................................................................................. 27
2.1.3.2
Cross-axis sensitivity or Transverse sensitivity ............................................................. 28
2.1.3.3
Frequency response and bandwidth ............................................................................... 28
2.1.3.4
Nonlinearity .................................................................................................................... 29
2.1.3.5
Dynamic range ................................................................................................................ 29
2.1.3.6
Resolution ....................................................................................................................... 29
2.2
Noise in micromachined accelerometers ........................................................... 30
2.3
Compliant mechanisms ...................................................................................... 34
2.4
Displacement-amplifying Compliant Mechanisms (DaCMs) ........................... 35
2.4.1 Spring-Lever (SL) model of a DaCM ............................................................. 36
2.4.2 An Accelerometer with a DaCM .................................................................... 38
2.4.3 Spring-Mass-Lever (SML) model of an accelerometer with a DaCM ........... 40
2.4.3.1
Computing the lumped parameters of the DaCM .......................................................... 43
2.4.4 Re-designing a DaCM using a stiffness map-based method .......................... 44
2.5
Capacitive micromachined accelerometers from the literature ......................... 46
2.5.1 Out-of-plane capacitive microaccelerometers ............................................... 47
2.5.2 In-plane capacitive microaccelerometers ...................................................... 54
2.5.3 Tri-axial accelerometers ................................................................................ 62
2.5.4 Micromachined accelerometers with mechanical amplifiers ........................ 67
2.6
Closure ............................................................................................................... 70
CHAPTER 3 ........................................................................................................................ 72
DESIGN CASE STUDIES ....................................................................................................... 72
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3.1
Introduction ........................................................................................................ 72
3.2
Sub-micro-g micromachined capacitive in-plane accelerometers by Abvolvand
et al. [19] ....................................................................................................................... 73
3.2.1 Mechanical design ......................................................................................... 73
3.2.2 Design analysis .............................................................................................. 73
3.2.3 Figure of Merit (FoM) of capacitive micromachined accelerometers .......... 74
3.3
Modification of Abdolvand et al. 2007 [19] using a DaCM .............................. 75
3.3.1 Design of the DaCM using the stifness map-based method ........................... 76
3.3.2 Modified mechanical design .......................................................................... 76
3.3.3 Analysis of the modified design...................................................................... 77
3.4
A micro-g SOI capacitive in-plane accelerometer by B. V. Amini 2006 ........... 79
3.4.1 Mechanical design ......................................................................................... 79
3.4.2 Design of a DaCM for the modified design ................................................... 80
3.4.3 Modified mechanical design .......................................................................... 82
3.4.4 Analysis of the modified design...................................................................... 82
3.5
Conclusions ........................................................................................................ 83
CHAPTER 4 ........................................................................................................................ 85
DEVELOPMENT OF A SINGLE-AXIS CAPACITIVE IN-PLANE ACCELEROMETER WITH A
DACM ................................................................................................................................ 85
4.1
Design specifications ......................................................................................... 85
4.2
Design of the DaCM for the given specifications .............................................. 87
4.3
Mechanical design of the accelerometer with a DaCM ..................................... 91
4.3.1 Analytical modeling ....................................................................................... 92
4.3.2 Finite element analysis of the design ............................................................. 92
4.3.2.1
4.4
Comparison of designs with and without a DaCM ........................................................ 92
Fabrication and Prototyping ............................................................................... 95
4.4.1 Fabrication process ....................................................................................... 95
4.4.2 Fabricated device........................................................................................... 97
4.5
Die-level characterization .................................................................................. 97
4.5.1 Base capacitance measurement ..................................................................... 98
4.5.2 Measurement of geometric amplification of the DaCM ................................ 99
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4.5.3 Extraction of in-plane frequency response .................................................. 100
4.5.4 Study of the step-response of the device ...................................................... 102
4.6
Integration and Packaging................................................................................ 102
4.6.1 Device integration and wire-bonding .......................................................... 104
4.7
Testing and calibration ..................................................................................... 104
4.7.1 Axial sensitivity measurement ...................................................................... 105
4.8
Cross-axis sensitivity measurement ................................................................. 106
4.9
Closure ............................................................................................................. 107
CHAPTER 5 ...................................................................................................................... 109
DEVELOPMENT OF A DUAL-AXIS LOW-G CAPACITIVE IN-PLANE ACCELEROMETER WITH
TWO DACMS ..................................................................................................................... 109
5.1
A Dual-axis accelerometer ............................................................................... 109
5.2
De-coupling of the in-plane axes ..................................................................... 109
5.3
Mechanical design of the dual-axis accelerometer .......................................... 110
5.4
Modeling and analysis ..................................................................................... 113
5.4.1 Design of the DaCM .................................................................................... 113
5.4.2 Analysis of the mechanical design ............................................................... 114
5.4.2.1
Analytical modeling ..................................................................................................... 114
5.4.2.2
Finite element analysis ................................................................................................. 114
5.5
Fabrication and prototyping ............................................................................. 117
5.6
Die-level characterization ................................................................................ 118
5.6.1 Measurement of the geometric amplification of the DaCMs ....................... 118
5.6.2 Measurement of in-plane frequency response ............................................. 119
5.6.3 Study of the step-response of the device ...................................................... 121
5.7
Die-to-die hybrid packaging ............................................................................ 122
5.8
Testing and calibration ..................................................................................... 122
5.9
Conclusion and closure .................................................................................... 125
CHAPTER 6 ...................................................................................................................... 126
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DEVELOPMENT OF A DUAL-AXIS WIDE-BAND ACCELEROMETER WITHOUT MECHANICAL
AMPLIFICATION ............................................................................................................... 126
6.1
Acclerometer specifications ............................................................................. 126
6.2
Mechanical design of the wide-band dual-axis accelerometer ........................ 127
6.3
Design analysis ................................................................................................ 129
6.4
Extension to tri-axial design ............................................................................ 132
6.5
Fabrication and Prototyping ............................................................................. 132
6.5.1 Microfabrication process ............................................................................. 133
6.6
6.5.1.1
Phase-I........................................................................................................................... 133
6.5.1.2
Phase-II ......................................................................................................................... 136
Die-level characterization ................................................................................ 139
6.6.1 Extraction of the frequency response ........................................................... 142
6.6.2 Study of the step-response ............................................................................ 143
6.7
Integration and Packaging................................................................................ 145
6.8
Testing and Calibration .................................................................................... 145
6.9
Conclusion ....................................................................................................... 148
CHAPTER 7 ...................................................................................................................... 150
DEVELOPMENT OF MESO-SCALE SPRING-STEEL ACCELEROMETERS .......................... 150
7.1
Objective of the work....................................................................................... 150
7.2
Accelerometers in micro and meso scale ......................................................... 151
7.3
Single-axis meso-scale spring steel accelerometers with and without a DaCM
152
7.3.1 Mechanical designs ...................................................................................... 152
7.3.2 Analysis and performance comparison ........................................................ 153
7.3.3 Prototyping .................................................................................................. 157
7.3.4 Signal conditioning using a Hall-effect proximity sensor............................ 158
7.3.5 Integration and packaging ........................................................................... 160
7.3.6 Testing and calibration ................................................................................ 160
7.4
Development of a dual-axis meso-scale spring-steel accelerometer without
mechanical amplification ............................................................................................. 161
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7.4.1 First prototype of meso-scale dual-axis accelerometer ............................... 162
7.4.1.1
Design ........................................................................................................................... 162
7.4.1.2
Finite element analysis of the design ........................................................................... 163
7.4.1.3
Prototyping.................................................................................................................... 164
7.4.1.4
Packaging and integration to Hall-effect sensors......................................................... 165
7.4.1.5
Calibration and testing .................................................................................................. 166
7.4.2 Second prototype of a dual-axis meso-scale spring-steel accelerometer .... 169
7.5
7.4.2.1
Design ........................................................................................................................... 169
7.4.2.2
Prototyping and Integration .......................................................................................... 169
7.4.2.3
Testing and result .......................................................................................................... 172
Conclusion and Closure ................................................................................... 173
CHAPTER 8 ...................................................................................................................... 176
CONCLUSION AND FUTURE SCOPE ................................................................................... 176
BIBLIOGRAPHY ................................................................................................................ 179
viii
Acknowledgements
I would like to take the opportunity to express my deepest gratitude to my advisor
Professor G. K. Ananthasuresh for guiding and encouraging me throughout my PhD
work. I learnt a lot from him during the course of my PhD. The first thing that I learnt
was how to aim for the sky while keeping my feet on the ground. I also learnt sagacious
ways of adapting what is available to solve a problem. His insights into problems were
always invaluable. His enthusiasm for work was indeed very inspiring. I would also like
to convey my gratitude to my other advisor Professor H. S. Jamadagni. Even though my
interactions with him were limited, they were perspicacious nonetheless. I have always
benefited from those interactions because of his smart and intelligent way of looking into
problems from different angles. I will always be indebted to both my advisors.
I would like to thank Professor Rudra Pratap, Professor Navakant Bhat, Professor
Bharadwaj Amrutur, and Dr. M. M. Nayak for their insightful suggestions that helped me
in generating new ideas. I am immensely grateful to them for giving me much needed
advice and encouragement.
I acknowledge the Multi-Disciplinary Multi-scale Device and Design (M2D2)
Laboratory,
Mechanical
Engineering
Department,
and
the
Micro
and
Nano
Characterization Facility (MNCF), Centre for excellence in Nano Science and
Engineering (CeNSE), Indian Institute of Science, for providing me with computational
and experimental facilities.
Futhermore, I acknowledge the Naval Physical and Oceanographic Laboratory
(NPOL), Kochi and the Indian Space Research Organization (ISRO) for their financial
support for the studies carried out in this thesis. My sincere thanks go to Dr. Vinay
Natarajan, Sc. “F”, NPOL, and Dr. E. Varadarajan, Sc. “D”, NPOL, for their immense
support during the course of this work.
Here, I would also like to thank the Society for Integrated Circuit Technology and
Applied Research (SITAR) for aiding some of my experimental work. My sincere
acknowledgement goes to Mr. Nitin Ghodgaonkar, Si2 Microsystems, Bangalore for his
continuous support in carrying out the packaging work for the devices developed during
my PhD thesis work.
ix
The successful completion of work depends largely on the encouragement and
support of many others. Therefore, I am thankful to all my friends and colleagues for their
warm and generous support. The exchange of technical ideas with Thejas, Charanjeet
Malhi, Sudhanshu Shekar, Ranajit Sai, and Santosh D. have been illuminating and very
constructive. They have been tolerant and supportive of me throughout. I deeply
appreciate that. I thank all of my labmates Santosh Bhargav, Shanthanu Chakravarthy,
Nandhini Devi Nehru, Moumita Ghosh, Dr. Annem Narayana Reddy, Dr. Sourav Rakshit,
Dr. Sudarshan Hegde, Ramnath Babu T.J. and Dr. Sangamesh R. Deepak for their
invaluable support. I would also like to thank Ramu G, Ravi Kumar and B. M. Vinod
Kumar for their extensive support in developing the spring-steel accelerometers using
wire-cut EDM and CNC milling.
Last but not the least, I am immensely grateful to my parents Mr. Sibdas Khan and
Mrs. Sabita Khan, and my wife, Ranu, who stood by me when I was sailing through
troubled waters during my PhD. I am indebted to them for their love and support.
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Abstract
Simultaneously achieving high-sensitivity and a large resonance frequency of
micromachined accelerometers is difficult because of the inherent trade-off between the
two. In this thesis, we present a mechanical displacement-amplifying technique that is
amenable to micromachining to enhance sensitivity without compromising on the
resonance frequency and cross-axis sensitivity. Depending on the requirements of
sensitivity alone or sensitivity and resonance frequency, Displacement-amplifying
Compliant Mechanisms (DaCMs) are designed using the selection map-based technique,
which indicates the limits of what is possible for given specifications on size and
microfabrication.
In order to prove the benefits of a DaCM, we modified the designs of two very
sensitive capacitive micromachined accelerometers from the literature by incorporating
DaCMs and showed that, within the same footprint on the chip, the displacement
sensitivity could be enhanced by more than 60% while the resonance frequency was also
improved by more than 30%. As the focus of the thesis is to explore the integration of
DaCMs into accelerometers, the analytical, computational, and practical aspects are
discussed in detail. Both single and dual axis in-plane accelerometers are considered. The
fabrication processes used are Silicon-on-Insulator Multi-user MEMS Processes
(SOIMUMPs) and a customized Silicon-on-Insulator (SOI) based process. The fabricated
accelerometers are packaged and brought to the product form. They were tested at the die
level as well as in the packaged form.
Under dynamic conditions, the measured amplification factor of the fabricated
single-axis in-plane accelerometer was observed to be 11. The overall dimension of the
accelerometer was 4.25 mm × 1.25 mm. The first in-plane natural frequency of the
fabricated accelerometer was found to be 6.25 kHz. The voltage sensitivity of the
packaged accelerometer with the DaCM measured 26.7 mV/g at 40 Hz with differential
capacitance sensitivity of 3926 ppm/g around the base capacitance of 0.75 pF.
The fabricated dual-axis accelerometer has a special configuration of twelve
folded-beam suspension blocks that de-couple any displacements along the two in-plane
orthogonal axes. The decoupling feature is retained even after adding the DaCMs along
both the axes. The total device size was 8.6 mm × 8.6 mm. The device was also fabricated
xi
and packaged inside a ceramic flat-pin package using hybrid die-to-die wire-bonding.
Die-level dynamic characterization showed that the average geometric advantage
achieved using the DaCMs is 6.2 along both the in-plane axes. The measured axial
voltage sensitivity of about 580 mV/g for both the axes was achieved with a cross-axial
sensitivity of less than 2% and a natural frequency of 920 Hz. The static capacitance
sensitivity was found to be 0.296 × 106 ppm/g with a base capacitance of 0.977 pF. Also
presented in this work is a wide-band dual-axis accelerometer without an amplifying
mechanism. Its first two in-plane modal frequencies measured 14.2 kHz. The measured
sensitivity of the packaged accelerometer along both the axes of the device was found to
be 62 mV/g at 200 Hz.
Aiming at towards cost-effective accelerometers for small-volume markets, we
also developed a single-axis and two dual-axis meso-scale spring-steel in-plane
accelerometers equipped with Allegro A1395 linear Hall-effect sensors for sensing the
displacement of the proof-mass. The single-axis in-plane meso-scale accelerometer also
contains a DaCM. It is observed through simulation that the single-axis design with a
DaCM is 39% more sensitive and has 41% more bandwidth compared to a single-axis
design without a DaCM. The measured sensitivity of the fabricated single-axis springsteel accelerometer with a DaCM was found to be 71.4 mV/g with a minimum resolvable
acceleration of 14 milli-g. The unique features of the first generation of dual-axis
accelerometers are that a rechargeable Li-ion battery adds to the proof-mass. It also
contains a de-coupling mechanism that can decompose any planar acceleration into its
axial components. The second generation of dual-axis accelerometers is more compact in
size. All the mechanical elements of the accelerometers are made of EN J42/AISI 1080
spring steel foil machined using Wire-cut Electro-Discharge- Machining. The measured
sensitivity of the first generation of dual-axis meso-scale accelerometers is 78 and 108
mV/g along the X and Y axes whereas the second generation device exhibits a sensitivity
of 40 mV/g for both the axes. The thesis concludes that the sensitivity of a displacementbased sensor can be improved using a suitably designed DaCM without compromising the
resonance frequency and hence the bandwidth. Furthermore, the work describing the
development of meso-scale accelerometers also establishes spring steel as a viable
material for meso-scale applications.
xii
Publications based on this Thesis
Journal articles
1. The SmartDetect Project Team, “Wireless Sensor Networks for Human Intruder
Detection,” in Journal of the Indian Institute of Science; A Multi-disciplinary
Reviews Journal, Vol. 90, No. 3, 2010, pp. 347-380.
2. Khan, S. and Ananthasuresh, G. K., “Improving the Sensitivity and Bandwidth of
In-Plane
Capacitive
Micro-accelerometers
using
Compliant
Mechanical
Amplifiers,” in IEEE Journal of Microelectromechanical Systems. DOI:
10.1109/JMEMS.2014.2300231 (in press)
3. Khan, S. and Ananthasuresh, G. K., “A Wide-band Micromachined In-plane
Single-axis Capacitive Accelerometer with a Displacement-amplifying Compliant
Mechanism” in Mechanics-based Design of Structures and Machines. (in press)
Reviewed conference proceedings
1. Khan, S. and Ananthasuresh, G. K., “Performance Enhancement of a Dual-Axis
Micro-Accelerometer Using Compliant Displacement-amplifiers,” accepted in
IEEE Transducers 2013 and Eurosensors XXVII, Barcelona, Spain, June 2013.
2. Khan, S. and Ananthasuresh, G. K., “Sensitivity Enhancement of a Dual-axis Inplane Capacitive Micro-accelerometer using Compliant Displacement-amplifiers,”
in 5th ISSS National Conference on MEMS, Smart Materials, Structures and
Systems, Sep. 21-22, 2012, Coimbatore, India. (Recognized with the best Postgraduate Student paper award.)
3. Khan, S., Prasanna, D., and Ananthasuresh, G. K., “A Compact In-plane Dualaxis Spring-steel Accelerometer,” in 5th ISSS National Conference on MEMS,
Smart Materials, Structures and Systems, Sep. 21-22, 2012, Coimbatore, India.
xiii
4. Khan, S., Varadarajan, E., Natarajan, V., and Ananthasuresh, G. K., “Dynamic
Characterization of a Fabricated Dual-axis In-plane Capacitive Accelerometer for
High-frequency Applications”, Proc. of International Conference on Smart
Materials Structures and Systems (ISSS-2012), January 04-07, 2012, Bangalore,
India.
5. Khan, S. and Ananthasuresh, G. K., “Micromachined Accelerometers with
Mechanical Amplification”, in International Conference on Microactuators and
Micromechanisms (MAMM-2012), January 19-20, 2012, CSIR-CMERI, India.
6. Khan, S., Muddukrishna, P., and Ananthasuresh, G. K., “Development of a Mesoscale Dual-axis Steel Accelerometer with Hall-effect Sensors,” in 15th National
Conference on Machines and Mechanisms (NaCoMM-2011), Chennai, India,
December 1-2, 2011, Paper no. NaCoMM 2011-141.
7. Thejas, Hegde, S., Khan, S., Ananthasuresh, G. K., Bhat, N., Pratap, R., “High
Resolution Inertial Sensors”, ISSCC SRP, San Francisco, USA (Feb, 2010).
8. Khan, S., Thejas, Bhat, N., and Ananthasuresh, G. K., “Design and
Characterization of a Micromachined Accelerometer with a Mechanical Amplifier
for Intrusion Detection,” in 3rd National ISSS Conference on MEMS, Smart
Structures and Materials, Kolkata, Oct. 14-16, 2009.
xiv
List of Figures
Figure 1.1: A block diagram representation of two types of accelerometers: (a) with an
amplifying mechanism and (b) without it. ........................................................................... 5
Figure 1.2: A Displacement-amplifying Compliant Mechanism (DaCM) integrated to the
proof-mass of an accelerometer. A sense-comb is attached at the output end of the DaCM
whereas the input end is attached to the proof-mass............................................................ 6
Figure 1.3: A lumped model of an accelerometer with a compliant lever that uses a
small-length flexural pivot reported in [19]. ........................................................................ 7
Figure 2.1: Applications of accelerometers with respect to the operating bandwidth and
frequency of application. ................................................................................................... 16
Figure 2.2: A second order spring-mass-damper model representing an accelerometer. . 17
Figure 2.3: A typical frequency response of an accelerometer with different types of
damping.............................................................................................................................. 19
Figure 2.4: A step excitation function. ............................................................................. 20
Figure 2.5: A typical step response of a second order system showing damped
oscillations with logarithmic decay. .................................................................................. 21
Figure 2.6: A typical mounting arrangement of an accelerometer showing the axial and
transverse axes. .................................................................................................................. 28
Figure 2.7: A block diagram of a micromachined accelerometer device along with a PCB
for power supply and additional signal conditioning. ........................................................ 31
Figure 2.8: A typical calibration curve of an accelerometer showing the effect of total
noise on sensor characteristics. .......................................................................................... 31
Figure 2.9: (a) Spring-Lever (SL) model of a DaCM, (b) SL model of an accelerometer
with a DaCM. It can be noted that all the lumped masses are ignored in this model. ....... 37
Figure 2.10: Schematic of an accelerometer with a DaCM. The sense-combs are attached
at the output end of the DaCM where as the proof-mass is connected at the input end of
the DaCM. .......................................................................................................................... 39
Figure 2.11: (a) An accelerometer with a DaCM with sense combs attached at the output
side of the DaCM, (b) A conventional design of a capacitive micromachined
accelerometer without any amplifying mechanism. .......................................................... 40
xv
Figure 2.12: (a) A lumped Spring-Mass-Lever (SML) model of an accelerometer with an
inverting DaCM, (b) A lumped model of a conventional accelerometer with proof-mass
and suspension. .................................................................................................................. 41
Figure 2.13: The graphical user interface of the stiffness map-based re-design method
used to design the DaCMs in this thesis. ........................................................................... 46
Figure 2.14: Re-design of the DaCM using parameter curves. ........................................ 46
Figure 2.15: A cross-section view of the device reported by Seidel et al. 1990 [81]. ...... 47
Figure 2.16: An image of the reported surface micromachined Z-axis accelerometer by
Lu et al. [83]. ...................................................................................................................... 48
Figure 2.17: (a-c) An isometric, top and side view of the z-axis accelerometer design by
Yazdi and Najafi [86] and (d) an SEM image of the fabricated device Yazdi et al. [87] .. 50
Figure 2.18: The fabrication process flow of the z-axis accelerometer with vertical combs
by Tsuchiya and Funabashi 2004 [90]. .............................................................................. 51
Figure 2.19: A cross-sectional view of the design of the z-axis accelerometer using SOG
structure by Weiping et al. [91]. ........................................................................................ 52
Figure 2.20: (a) The fabrication process steps used to realize the z-axis accelerometer
with gap-closing differential sensing electrodes by Hsu et al. [92], (b) an image of the
fabricated device. ............................................................................................................... 54
Figure 2.21: (a) ADXL 50, surface micromachined lateral accelerometer architecture
[94], (b) An SEM image of the ADXL 50. (Courtesy: www.analog.com)........................ 56
Figure 2.22: An iMEMS in-plane accelerometer with a very low noise floor reported by
Jiang et al [99]. ................................................................................................................... 57
Figure 2.23: A schematic view of the SOG in-plane accelerometer reported by Chae et al.
2002 [104]. ......................................................................................................................... 59
Figure 2.24: A top view and a cross section view of the in-plane accelerometer reported
by Chae et al. 2004 [13]. .................................................................................................... 59
Figure 2.25: An SOI-based single axis in-plane accelerometer with CMOS IC placed on
thick SOI wafer (Amini and Ayazi 2004) [106]. ............................................................... 60
Figure 2.26: The process flow for the SOI-based micro-gravity accelerometer [15]. ...... 61
Figure 2.27: SEM images of a fabricated HARPSS accelerometer [17]. ......................... 62
Figure 2.28: A schematic of a sub-micro-gravity accelerometer with a very thick proofmass by Abdolvand et al. [19]. .......................................................................................... 63
Figure 2.29: (a) A top view and (b) an isometric view of the biaxial SOG accelerometer
reported by Liu et al. [108]. ............................................................................................... 64
xvi
Figure 2.30: A tri-axial accelerometer die containing three different sensing element for
the three axes reported by Lemkin and Boser 1999 [112]. ................................................ 65
Figure 2.31: (a) An SEM image of the tri-axial accelerometer developed by Chea et al
[116] using both surface and bulk-micromachining processes, (b) The packaged tri-axial
accelerometer by Chae et al. [116] along with a Σ-∆ switched capacitor circuit inside a
dual-in-line (DIP) package. ................................................................................................ 66
Figure 2.32: A schematic of the capacitive low-g tri-axis accelerometer reported by Hsu
et al. [118]. ......................................................................................................................... 67
Figure 2.33: A schematic of a resonant micromachined accelerometer with a two-stage
microleveage mechanism developed by Su et al. [44]. ...................................................... 68
Figure 2.34: An SEM image of a fabricated out-of-plane accelerometer with a
displacement amplifier that transforms and amplifies the out-of-plane linear motion to
angular motion [120].......................................................................................................... 69
Figure 2.35: A schematic of an in-plane capacitive accelerometer with a mechanical
lever for displacement amplification developed by Zeimpekis et al. 2012 [20]. ............... 70
Figure 3.1: A solid model of an accelerometer with a thick proof-mass developed by
[19]. .................................................................................................................................... 74
Figure 3.2: The first two simulated modes of vibration of the accelerometer developed by
Abdolvand et. al. 2007 [19]. .............................................................................................. 75
Figure 3.3: A graphical user interface (GUI) for the selection map based method
describing the re-design of an existing DaCM from [47] using parameter curves. The
initial position of the DaCM to be used with the current feature size is shown as a point
on the graph. The area enclosed by a green curve shows the feasible stiffness map for the
given specification. The parameter curves are drawn from the initial position of the
mechanism and show that the selected mechanism can be brought inside the feasible
stiffness map by varying the parameters e.g. in-plane beam width, thickness, size of the
mechanism along X and Y of the mechanism. .................................................................. 78
Figure 3.4: Re-design of the DaCM by varying the parameters along the parameter
curves to achieve feasible k ci , kco , and n values for the mechanism. ............................. 78
Figure 3.5: (a) The design of the DaCM used in the modified design of [19], and (b) a
Solid model of the modified design of [19] with a smaller proof-mass, a stiffness matched
DaCM occupying an area of 7 mm × 7 mm....................................................................... 79
xvii
Figure 3.6: The first five modes of vibration of a modified version of a similar
accelerometer with a DaCM and with an equal footprint. ................................................. 80
Figure 3.7: (a) The design of the SOI accelerometer reported in [16], (b) The first two
modes of the accelerometer reported in [16]. .................................................................... 81
Figure 3.8: (a) A modified design of [16] using a DaCM, and (b) The design of the
DaCM used in the modified design of [16]. ...................................................................... 82
Figure 3.9: The first five modes of vibration of the modified design of [16] using a
stiffness matched DaCM. ................................................................................................... 83
Figure 4.1: Specifications for a wide-band single-axis capacitive micromachined
accelerometer. .................................................................................................................... 86
Figure 4.2: An SML Model of a single-axis accelerometer with a non-inverting type
DaCM ................................................................................................................................. 89
Figure 4.3: (a) A feasible map for the user-specifications noted in Eq. (50), (b) the
mechanism selected for re-design with the parameter curves. .......................................... 90
Figure 4.4: The optimal design of the DaCM achieved after size-optimization............... 91
Figure 4.5: A continuum model of an accelerometer with an optimally designed DaCM
............................................................................................................................................ 93
Figure 4.6: (a-d) The first four mode shapes of an accelerometer with a DaCM. ............ 94
Figure 4.7: Two accelerometers in undeformed and deformed configurations. (a) with a
DaCM, and (b) without a DaCM. Although the footprint of both is the same, the
displacement of the sensing combs is greater in (a) than that in (b). ................................. 95
Figure 4.8: The first four modes of vibration of an accelerometer without a DaCM but
with a larger proof-mass occupying the same footprint..................................................... 96
Figure 4.9: A cross-section of a typical device fabricated using the SOIMUMPs [123]
process................................................................................................................................ 96
Figure 4.10: A mask layout of a fabricated single-axis accelerometer with a DaCM. ..... 97
Figure 4.11: SEM images of an accelerometer fabricated using the SOIMUMPs process.
............................................................................................................................................ 98
Figure 4.12: A fabricated device with its compliant acrylic holder under a Micro System
Analyzer for die level characterization. ............................................................................. 99
Figure 4.13: Measurement of Geometric amplification by the DaCM used in the
accelerometer (a) Displacement of the output side and the input side of the DaCM
measured when the device is actuated electrostatically, and (b) The DaCM used in the
accelerometer under the LDV showing the measurement points. ................................... 100
xviii
Figure 4.14: (a) In-plane frequency response of a single-axis accelerometer captured
using MSA 500, (b) the phase response of the device. .................................................... 101
Figure 4.15: An experimentally obtained step response of a single-axis accelerometer.
.......................................................................................................................................... 102
Figure 4.16: A functional block diagram of MS3110, a universal capacitive readout
[126]. ................................................................................................................................ 103
Figure 4.17: A fabricated accelerometer integrated and wire-bonded on a gold plated
PCB along with the capacitance extraction readout IC MS3110. .................................... 104
Figure 4.18: An integrated and packaged accelerometer mounted on an LDS vibration
shaker table. ..................................................................................................................... 105
Figure 4.19: The calibration curve of a packaged accelerometer at 40 Hz. ................. 106
Figure 4.20: The dynamic response of both the accelerometers where the standard
accelerometer experiences an axial load and a single-axis accelerometer experiences an
off-axial load. ................................................................................................................... 107
Figure 4.21: The off-axial sensitivity curve for a packaged single-axis accelerometer. 107
Figure 5.1: (a) A schematic showing two independent actuations of the Proof-mass using
an XY flexure mechanism, (b) A parallel arrangement of an XY Stage. ........................ 110
Figure 5.2: (a) The schematic and (b) the layout of a dual-axis capacitive lateral
accelerometer with a decoupling mechanism and two inverting DaCMs........................ 112
Figure 5.3: A simulated image of a dual-axis in-plane accelerometer with two DaCMs
under a 1 g body-load along both the axes. The decoupling mechanism decouples the
applied acceleration into its corresponding axial components and the two DaCMs amplify
the displacement of the proof-mass along both the axes. ................................................ 115
Figure 5.4: (a-c) The first three modes of vibration of a dual-axis accelerometer with
DaCMs. It can be seen that the first two modes are in-plane modes with identical
frequencies, whereas the third mode is an out-of-plane mode at a higher frequency. ..... 116
Figure 5.5: A simulated image of a dual-axis accelerometer without any mechanical
amplification under a 1 g body-load along both the axes. The accelerometer occupies the
same footprint area as does the design with two DaCMs. Thus, the accelerometer contains
a larger proof-mass compared to that of the design with DaCMs. .................................. 117
Figure 5.6: (a-c) Optical micrographs (top view) of a fabricated dual-axis accelerometer
die, (d-e) Tilted SEM images of the device showing parts of the DaCM and the sensecomb present in the accelerometer. .................................................................................. 118
xix
Figure 5.7: Time vs. Displacement plot, captured by the Laser Doppler Vibrometer, of
the input and output ports of the DaCMs present in the dual-axis accelerometer along both
the axes. The displacement amplification by the DaCMs can be measured by taking the
ratios of the displacement amplitudes at any time at the output to the input ports of the
DaCMs. ............................................................................................................................ 119
Figure 5.8: Experimentally obtained Bode plot (Displacement amplitude in (a) and Phase
in (b)) of the accelerometer showing the frequency response of the device at both the
input and output of the DaCMs. ....................................................................................... 120
Figure 5.9: Experimentally obtained step response of the accelerometer captured using a
Laser Doppler Vibrometer to study the dynamic behaviour of the device along both the
axes. ................................................................................................................................. 121
Figure 5.10: (a) LTCC substrate developed for packaging the dual-axis accelerometer
with DaCMs, (b) Hybrid die-to-die packaging of a dual-axis accelerometer die along with
two MS3110 dies inside a ceramic flat pin package. ....................................................... 123
Figure 5.11: (a) Experimental setup for static calibration of the packaged dual-axis
accelerometer using a turn table. The MS3110 evaluation board was required only at the
beginning of the test to program the MS3110 ASIC dies. Once programmed, the
evaluation board was disconnected while testing. (b) Both the static and dynamic
calibration curve for the dual-axis accelerometer along the X and Y axes where the
sensitivities of the packaged dual-axis accelerometer can be found from the slope of the
calibration curves. ............................................................................................................ 124
Figure 5.12: The off-axis sensitivity curve that is obtained by rotating the device while
keeping the sensitive axis horizontal. .............................................................................. 125
Figure 6.1: (a) A modified configuration for improved de-coupling of X-Y axes [130],
(b) Mechanical design of the dual-axis lateral capacitive accelerometer. ....................... 129
Figure 6.2: The FEA solution shows the response of the device on application of bodyforce along both the axes. ................................................................................................ 130
Figure 6.3: (a) First two in-plane modes of vibration, (b) the out-of-plane mode, and (c)
simulated frequency response of the device for both the axes......................................... 131
Figure 6.4: (a-l) Phase-I of the custom SOI-based process flow to fabricate a bulkmicromachined wide-band dual-axis accelerometer. ....................................................... 136
Figure 6.5: (a-f) Phase-II of the custom SOI-based process flow to be followed to extend
the dual-axis accelerometer to a tri-axial accelerometer.................................................. 138
xx
Figure 6.6: A 6 inch mask layout containing designs of wide-band dual-axis
accelerometers. The same mask layout can also be used for the fabrication of tri-axial
accelerometers.................................................................................................................. 139
Figure 6.7: (a-g) Scanning electron microscope (SEM) images of the fabricated dual-axis
accelerometer showing different parts of the accelerometer. .......................................... 142
Figure 6.8: The diced devices placed inside a Gel-pack container for shipment. .......... 142
Figure 6.9: (a-b). Experimentally obtained frequency response of the device along the X
and Y axes. ....................................................................................................................... 143
Figure 6.10: (a) Experimentally obtained response of the accelerometer due to a step
excitation (b) Exponential decay of the step response of the accelerometer along both the
axes. ................................................................................................................................. 144
Figure 6.11: (a) Schematic of the PCB that contains two MS3110 ICs for both the X and
Y axes, power supply including the voltage regulator and the output ports, (b) The wideband dual-axis accelerometer wire-bonded inside a 44-pin LCC package, and (c) The
custom-designed and developed evaluation board along with the packaged dual-axis
accelerometer. .................................................................................................................. 147
Figure 6.12: The experimental setup to test the integrated and packaged dual-axis
accelerometer on a vibration shaker table. ....................................................................... 147
Figure 6.13: The calibration curve of the packaged dual-axis accelerometer at different
frequencies. ...................................................................................................................... 148
Figure 7.1: Size comparison of a meso-scale spring-steel accelerometer with respect to a
commercially available micromachined accelerometer mounted on its evaluation board.
.......................................................................................................................................... 151
Figure 7.2: The top view of the designs of the two meso-scale accelerometers along with
their dimensions. The left one is a single-axis meso-scale accelerometer with a DaCM
whereas the right one is without a DaCM. ....................................................................... 153
Figure 7.3: The 3D model of (a) the single-axis meso-scale spring steel accelerometer
with a DaCM and (b) the one without a DaCM. .............................................................. 154
Figure 7.4: Static finite element analysis of (a) the single-axis meso-scale accelerometer
aided with a DaCM and (b) the one without a DaCM using COMSOL Multiphysics. ... 155
Figure 7.5: The simulated first four modes of vibration of the single-axis meso-scale
spring steel accelerometer model with a DaCM. ............................................................. 156
Figure 7.6: The simulated first four modes of vibration of the single-axis meso-scale
spring steel accelerometer model without a DaCM. ........................................................ 156
xxi
Figure 7.7: The deflection at the output of the DaCM due to the application of a crossaxial load of 1 g applied along the X-axis of the device. ................................................. 157
Figure 7.8: The Wire-cut Electro-Discharge-Machining facility at the Department of
Mechanical Engineering, Indian Institute of Science, Bangalore. ................................... 158
Figure 7.9: The machined parts of the spring-steel accelerometer with a DaCM before
manual assembly. ............................................................................................................. 158
Figure 7.10: (a) A linear Hall-effect sensor and the Neodymium disc magnet, (b) A
custom PCB with the Hall-effect sensor soldered on it, (c) The calibration curve of the
linear Hall-effect sensor used for this work. .................................................................... 159
Figure 7.11: The experimental setup for the static testing of the fabricated single axis
spring-steel accelerometer with a DaCM using a vertical turn-table. .............................. 160
Figure 7.12: Experimentally obtained calibration curve of the single-axis spring-steel
accelerometer with a DaCM. ........................................................................................... 161
Figure 7.13: (a) A modified XY flexure used as a dual-axis accelerometer, (b) An
isometric view of the first prototype of a meso-scale dual-axis accelerometer with two Liion batteries attached to the top and bottom of the metal proof-mass, (c) A side view of
the proposed device showing the arrangement to increase the proof-mass using Li-ion
batteries and steel blocks. ................................................................................................ 163
Figure 7.14: FE simulation showing the XY flexure mechanism de-coupling two
different input accelerations along its X and Y axes. ...................................................... 164
Figure 7.15: The XY stage used for the first prototype of a dual-axis spring-steel
accelerometer realized on 0.5 mm thick spring steel foil using Wire-cut EDM.............. 165
Figure 7.16: (a) The first prototype of a packaged meso-scale spring steel dual-axis
accelerometer with a yellow cover and (b) without a cover exposing the top Li-ion battery
acting as the extra proof-mass as well as the power source for the Hall-effect sensor at
Port Y. .............................................................................................................................. 166
Figure 7.17: An experimental setup showing the developed first prototype of a mesoscale dual-axis spring-steel accelerometer being calibrated with respect to a reference
accelerometer on a vibration shaker table. ....................................................................... 167
Figure 7.18: (a) A plot showing the simulated and experimentally obtained frequency
response of the first prototype of the meso-scale dual-axis spring-steel accelerometer for
both the X and Y axes, (b) A plot showing an experimentally obtained calibration curve
of the sensor for both X and Y axes. ................................................................................ 168
xxii
Figure 7.19: Design of the suspension of the second prototype of an in-plane dual-axis
spring-steel accelerometer. .............................................................................................. 170
Figure 7.20: Wire-cut patterned spring-steel sheet with its suspension and provisions for
mounting the proof-mass pieces, magnets, and Hall-effect sensors along with their PCBs.
.......................................................................................................................................... 170
Figure 7.21: The complete accelerometers in an acrylic casing with the IC on a PCB, two
extra plus-shaped masses attached on the spring-steel foil, the leads for taking the
readings. One set of PCB is seen at the top while the other is underneath and on the right
side, where the leads can be seen. There are two other plus-shaped masses underneath on
the other side of the spring-steel foil................................................................................ 171
Figure 7.22: An experimental setup for dynamic testing of the developed second
prototype of the meso-scale spring-steel accelerometer using an LDS shaker table. ...... 172
Figure 7.23: An experimentally observed frequency response of the second prototype of
the meso-scale spring-steel accelerometer along both the axes. ...................................... 173
Figure 7.24: Dynamic calibration curve of the second prototype of the meso-scale springsteel accelerometer along both the axes. .......................................................................... 173
xxiii
List of Tables
Table 3.1: Comparison between existing accelerometers with modified designs using
DaCMs. .............................................................................................................................. 77
Table 4.1: Comparison of the specifications of the DaCM in an accelerometer. ............. 93
Table 5.1: Lumped parameters of a dual-axis in-plane accelerometer. .......................... 113
Table 5.2: Performance specifications of the dual-axis accelerometer. .......................... 114
Table 6.1: Target specifications of a wide-band tri-axial accelerometer. ....................... 127
xxiv
Chapter 1
Introduction
Summary
The background and motivation of the thesis is discussed briefly. The need for mechanical
amplification is discussed in the context of performance enhancement of micromachined
capacitive in-plane accelerometers. A brief introduction to Displacement-amplifying
Compliant Mechanisms (DaCMs) is provided. The rationale for using DaCMs instead of
simple levers for enhancing the sensitivity of micromachined in-plane capacitive
accelerometers is explained. Also discussed is the justification behind utilizing spring
steel as a material for developing meso-scale accelerometers for low-volume
applications. The objectives and the scope of this thesis are discussed. The chapter ends
with a description of the organization of the thesis.
1.1 Background and motivation
This thesis deals with three different aspects related to accelerometers: (i) a method to
enhance both the sensitivity and bandwidth of in-plane micromachined accelerometers by
using compliant mechanical amplifiers and thus obviating the compromise between the
sensitivity and bandwidth of the sensors without adding much noise to the sensors; (ii) the
development of wide-band multi-axis micromachined accelerometers to show that it is
possible to develop silicon-based wide-band (bandwidth of 6-8 kHz with sensitivity of the
order of 100 mV/g) micro-accelerometers that are currently rare; and (iii) the
development of meso-scale in-plane accelerometers to establish spring steel as a viable
material for developing low-cost accelerometers for low-volume production.
Micromachined accelerometers are increasingly used in many applications because
of the emergence of silicon micromachining technology that enables successful
miniaturization and batch fabrication of small-footprint, cost-effective accelerometers.
But, the commercialization of high-resolution (e.g., µg, i.e., one millionth of the
acceleration due to gravity, i.e., 9.81 ×10-6 m/s2) accelerometers are not as successful as
accelerometers with low (> 0.1 g) to medium (> 1 milli-g) resolution. Some applications
that require high-resolution accelerometers are inertial navigation, tilt control in
1
Chapter 1
spacecraft, surveillance, oil exploration, and earthquake detection, etc. High-resolution
accelerometers require the noise-floor of the entire system to be very small. Several
techniques have been adopted to attain high resolution, highly sensitive accelerometers.
They include a tunneling current-based technique [1]-[7] and a laser interferometry-based
[8]-[10] technique, which are not suitable for light-weight and portable applications. On
the other hand, other relatively simple techniques such as capacitive [11]-[20],
piezoelectric [21], [22], piezoresistive [23]-[26] and resonant-mode [28]-[31] require
sophisticated interface electronics. Among these relatively simple transduction
techniques, the capacitive transduction principle is found to be the most popular and
widely used for developing high-resolution and highly sensitive micromachined
accelerometers. These accelerometers require structures with a very high aspect ratio,
slender suspension beams, very narrow sense-gaps, all of which demand complex
micromachining processes [11]-[17], [19]. Moreover, the fabricated devices are to be
packaged in a vacuum in order to maintain a low level of thermo-mechanical or Brownian
noise. All of these requirements make the sensors very expensive.
Some applications such as underwater sound navigation and ranging in
submarines, machined health monitoring, etc., also require large bandwidths. This
requires high resonance frequency and low damping. The commercial market for wideband accelerometers is still dominated by conventional piezoelectric macroaccelerometers with a relatively low sensitivity of 5-10 mV/g [32]-[35]. The typical
volume of a packaged macro-accelerometer is around 5 cm3. Multi-axis macroaccelerometers are almost twice the size of single-axis ones [35]. Furthermore, such bulky
accelerometers are designed to have a natural frequency of the order of 40 kHz or more in
order to achieve a 3 dB bandwidth of 8-10 kHz [32]-[35]. Most of these commercially
available wide-band micro-accelerometers are also single-axis accelerometers [36] with a
very low sensitivity of the order of tens of mV/g with a very high noise floor of the order
of thousands of g
Hz . Multi-axis micro-accelerometers are generally developed by
mounting multiple single-axis accelerometers orthogonally inside a single package which
thus increases the package size [37]. Simultaneously achieving high sensitivity and high
bandwidth is difficult because of the inherent tradeoff between the two. A mechanical
amplification of the displacement helps to some extent in reducing this compromise, as
shown in this thesis. In order to understand this, we need to discuss the basic operating
principle of accelerometers.
2
Chapter 1
An accelerometer has two parts: a mechanical structure and signal conditioning
electronics. For an accelerometer, the acceleration signal is detected first by the
mechanical components, i.e., the proof-mass and the suspension beams. The minimum
detectable acceleration depends upon the sensitivity of the mechanical components. This
means that with improved sensitivity, a small acceleration signal applied to the
accelerometer would be able to create a large mechanical movement that would produce a
signal greater in magnitude than the total noise floor of the accelerometer.
The major source of noise present in micromachined mechanical structures is
mechanical-thermal noise or Brownian noise [38] whereas the noise in the signal
conditioning electronics interface is known as the electronic noise. A detailed discussion
on Brownian noise in micromechanical structures, and the various types of electronic
noise sources is given in the next chapter. A noise analysis of a micromachined
accelerometer shows that the overall sensor performance becomes dominated by the noise
of the signal conditioning electronics as the sensitivity of the mechanical part improves
[18]. The best way to improve the mechanical sensitivity of an accelerometer is to
increase the inertia of the device and decrease the effective structural stiffness [19]. This
indicates that the sensitivity of the mechanical structure has to be enhanced in order to
achieve high mechanical resolution. Consequently, the operational bandwidth of the
sensor decreases.
In this thesis, we aim to enhance mechanical sensitivity by incorporating a
mechanical displacement amplifier in accelerometers without compromising on the
bandwidth of the sensor and increasing the noise significantly. The technical premise for
our work is mechanical amplification, which can improve the sensitivity of the sensor
beyond the best that could be done with the signal conditioning interface electronics. The
mechanical amplifiers used in this thesis are designed using elastically deforming
compliant structures that help to amplify the displacement of the proof-mass. They are
known as Displacement-amplifying Compliant Mechanisms (DaCMs).
In this thesis work, we design and develop both capacitive type micromachined inplane accelerometers and meso-scale spring steel in-plane accelerometers that use
DaCMs. Therefore, we begin by justifying the need for mechanical amplification in the
context of enhancing the performance of in-plane accelerometers. Then, we provide a
brief introduction to DaCMs, which is followed by the rationale behind the selection of
DaCMs over simple mechanical levers. We also justify our choice of capacitive
3
Chapter 1
transduction. We close the chapter by providing the motivation for using spring steel as a
material for developing meso-scale accelerometers before outlining the specific
objectives, scope and organization of the thesis.
1.1.1 Need for mechanical amplification
To appreciate the use of mechanical amplification in micromachined accelerometers, let
us consider two types of micromachined capacitive in-plane accelerometers: one with a
micromechanical structure, a mechanical amplifying mechanism and signal conditioning
circuitry and the other, a conventional one, without the amplifying mechanism but with
the same mechanical structure and capacitance sensing interface circuit. Suppose, xm is
the thermal-mechanical or Brownian noise in the micromechanical structure; xm , the
Brownian noise in the amplifying mechanism; xe , the total electronic noise in the
capacitance sensing interface circuit; xs , the acceleration signal at the input of both the
accelerometers; Am , the amplification factor or gain of the mechanical amplifier and Ae ,
the gain of the capacitance sensing interface circuit as shown in Figure 1.1.
As the existence of thermal-mechanical noise in any structure is due to the
damping mechanism in that structure [38], a micromachined mechanical amplification
mechanism consists of a few tiny slender beams of very small mass. They do not contain
any capacitive combs that can give rise to any squeeze film damping or slide film
damping [39]-[42]. Thus, xm is negligibly small compared to xm . The signal-to-noise
ratio of the output1 and output2 can be expressed as:
SNRoutput1 
SNRoutput2 
Ae Am xs
xs

Ae Am  xm  xm   xe Ae x  x  1 x
m
m
e
Am
(1)
Ae xs
xs

 xm  xe  Ae xm  xe
It can be seen from Eq. (1) that SNRoutput1  SNRoutput2 as xm is very small
compared to xm and Am is greater that unity. This means that the signal-to-noise ratio and
the resolution of any accelerometer can be improved by incorporating a mechanical
amplification mechanism. Using mechanical amplification, the sensitivity of the
mechanical structure can also be improved. Here, in this thesis, mechanical amplification
4
Chapter 1
is done by amplifying the displacement of the proof-mass. As can be seen from Eq.(1),
not only is the SNR better in the micromachined accelerometer with the mechanical
amplifier, but the magnitude of the output of the accelerometer is also greater than that of
the accelerometer without it.
xs
xm
xm
Micromachined
structure
Mechanical
Amplifier
( Am )
(a)
xm
(b)
Ae
output1
Capacitance sensing
electronic interface circuit
xe
Micromachined
structure
xs
xe
output2
Ae
Capacitance sensing
electronic interface circuit
Figure 1.1: The block diagram representation of two types of accelerometers: (a) with an
amplifying mechanism and (b) without it.
1.1.2 Introduction to DaCMs
A Displacement-amplifying Compliant Mechanism (DaCM) is a compliant equivalent of a
conventional mechanical lever. It is a single-input-single-output type mechanism where
an input force or displacement applied at the input point generates an amplified output
displacement at the output point using a single elastic continuum [43]. It uses elastic
deformation of its members to transform or transfer an input displacement, force or
energy to the output. The mechanism is designed such that there is a geometric advantage
(GA) due to which the output port of a DaCM displaces more than its input port. The
value of the GA is dependent on the geometry of the DaCM. The amplification of
displacement from the input to the output end of a DaCM is used in this thesis to enhance
the sensitivity of in-plane accelerometers. DaCMs are amenable for microfabrication
because they do not have joints and thus most of them are available in one piece. There is,
thus, no wear, backlash or friction associated with joints. Furthermore, they make use of
5
Chapter 1
2D geometry with uniform thickness and hence they can easily be lithographically
patterned and microfabricated.
1.1.3 DaCM vs. a simple mechanical lever
A mechanical amplifier can be as simple as a lever [19], [30], [31], [44] or as elaborate as
a Displacement-amplifying Compliant Mechanism (DaCM) [43] shown in Figure 1.2. The
input of the DaCM is attached to the proof-mass. As can be seen in Figure 1.2, a sensecomb is attached at the output of the DaCM where the displacement is significantly more
than that at the proof-mass. The ratio of the output and input displacements of a DaCM,
as defined earlier, is its geometric advantage (GA). The benefits of a DaCM over levers
can be understood from the following analysis.
Sense-comb
DaCM
Anchor
Proofmass
Figure 1.2: A Displacement-amplifying Compliant Mechanism (DaCM) integrated to the
proof-mass of an accelerometer. A sense-comb is attached at the output end of the DaCM
whereas the input end is attached to the proof-mass.
Shown in Figure 1.3 is the main component of a compliant lever used in [19] for
amplification of the displacement as well as to serve as the suspension for the proof-mass.
It uses a small-length flexure pivot [45], which can be modeled as a hinged lever with a
torsional spring of spring-constant  in series with a linear spring with spring-constant k a
. The deformation of the wide lever arm is ignored as it is shown in [19] to have little
influence. The two spring-constants are given by
ka 
6
EA
L
(2)
Chapter 1

EI
L
(3)
where L is the length of the pivot, A  tw is the area of the cross-section of the pivot, and
I  tw3 /12 is the moment of inertia with w denoting the in-plane width and t the
thickness of the beam; and E is Young’s modulus. As per Figure 1.3, the displacement
uout of the sense-comb (denoted with a lumped quantity msc ) due to the inertial force
experienced by the proof-mass (denoted with m pm ) and msc due to applied acceleration a
can be computed as
uout


l
li lo  m pm  o msc  a
li
 m pm  msc  a  



ka
(4)
Wide lever arm
Small-length flexural pivot

m pm
msc
a
uout
uin
ka
li
lo
Figure 1.3: The lumped model of an accelerometer with a compliant lever that uses a
small-length flexural pivot reported in [19].
It is clear from Eqs. (2) and (3) that k a and  are large when L is small, as is the
case with small-length flexural pivots. Then, the absolute displacement of the sense-comb
(i.e., uout ) will be small. Additionally, as per the second term on the right hand side of Eq.
(4), if the lever ratio ( lo / li in Figure 1.3) is larger than unity, uout will not be at its
maximum; indeed, uout will be the largest when li  lo . This means that the proof-mass
and the sense-comb should be combined and kept towards the other end of the lever, i.e.,
farthest from the flexural pivot, for getting the largest value of uout . It must be noted that
this argument is valid under static conditions only; displacement under dynamic
conditions can be analyzed in a similar manner.
7
Chapter 1
Further improvement in uout is possible if the lever arm is made sufficiently
narrow instead of using the flexural pivot, within the same footprint. Two possible
drawbacks of this are that the out-of-plane stiffness and the resonance frequency will be
reduced as compared to those with the lever based on the flexural pivot. One way to
alleviate this is to decrease the size of the proof-mass. But a reduced proof-mass
decreases the inertial force, and, in turn, decreases the displacement at the sense-comb,
and, hence, the sensitivity too. Instead of this, the space relieved by decreasing the size of
the proof-mass can be utilized to append a DaCM so that substantially amplified
displacement at the sense-comb is obtained. The design of the DaCM should be such that
the out-of-plane stiffness and the resonance frequency are not hampered. DaCMs are also
used in actuator applications for increasing the stroke [46], [47].
1.1.4 Rationale for choosing capacitive transduction
Micromachined accelerometers can be categorized into at least eight different types based
on the different sensing techniques they use. They are piezoresistive accelerometers,
piezoelectric accelerometers, capacitive accelerometers, resonant accelerometers, optical
accelerometers, tunneling accelerometers, thermal accelerometers and electromagnetic
accelerometers. The principles of operation of all these types of accelerometers are given
in the next chapter. All these types of accelerometers except the thermal accelerometers
make use of the displacement of the proof-mass to sense the applied acceleration. Among
these eight types of accelerometers, the most widely used one is the capacitive
accelerometer because of its advantages over the other types. Micromachined
accelerometers have relatively simple mechanical structures compared to other types, and
hence are easier to fabricate. In addition, they exhibit very high sensitivity, very good
linearity, and excellent noise performance. They also consume less power and they have a
very low temperature-induced drift. The use of capacitive comb-drives makes them
amenable to force feedback. Thus, capacitive accelerometers are widely preferred in
consumer applications due to their high performance, reliability, and low cost. Capacitive
interfaces have several attractive features such as that they are available in both analog
and digital form. The capacitance sensing signal conditioning circuit can also be
monolithically embedded on the same substrate along with the mechanical components.
Capacitive accelerometers are available in single-axis, dual-axis and tri-axial form.
Additionally, capacitive accelerometers are displacement-based transducers which open
8
Chapter 1
up the scope to incorporate mechanical amplifiers, specifically DaCMs, along with their
mechanical structures to enhance performance. The DaCMs are well suited for capacitive
in-plane micromachined accelerometers as they both have 2D, i.e., planar topology.
The sensitivity of a capacitive accelerometer with a differential capacitor
arrangement is linearly proportional to the displacement of the sense-comb, u :
 2uCbase 
 C 
V
K

K
g
 g 
 gd 0 
(5)
where V / g denotes the change in the output voltage per unit acceleration due to
gravity g , K the gain of the electronic circuit measured as V/pF, C the change in
capacitance, Cbase the base capacitance, and d0 the gap between the successive fingers of
the sensing comb. The capabilities of the microfabrication process decide Cbase and d0
(i.e., how many fingers can be packed, and how narrowly, into the available space). The
electronic interface decides K . This leaves u for improving the sensitivity by suitably
designing the mechanical sensing element of an accelerometer. A DaCM helps increase
the value of u .
1.1.5 Why meso-scale devices?
Lithography-based silicon micromachining technology is well developed today. Many
commercial silicon micro sensors are available. Despite many advantages, two problems
remain: first, silicon processing requires large investments in processing and packaging,
which are not economically viable when the lot size is not large; second, the packaged
size is not always small because of the supporting electronics and power supply that are
necessary when the device is integrated into a system. Even though the packaged
accelerometers themselves are very small, they often require evaluation boards, batteries
or an external power supply, and mountings that make them big. The rationale for opting
for a meso-scale sensor element is that packaged silicon-based micromachined devices
are anyway going to have a size compatible with the meso-scale. So, making the sensor
element up to 10 times bigger does not compromise the size of the packaged sensor. A
pertinent question that becomes the premise for the last part of this thesis is: why cannot
materials and manufacturing techniques from the macro domain be scaled down? Silicon
is a good mechanical material at the micro scale, but steel is an excellent material at the
macro scale. Manufacturing techniques can be derived from the much explored and well
9
Chapter 1
developed macro-scale manufacturing method i.e. the popular workshop technology. We
chose wire-cut electro-discharge-machining (EDM) for this work. Eventually, batch
fabrication can also be done using punching and we, thus, get an economic advantage. In
this thesis, we explore spring steel as a mechanical material at the meso-scale. Mesoscale, for the purpose of this thesis, refers to a size that is smaller than the traditional
macro scale but bigger than the size of the micro machined devices. Its range is roughly
100s of microns to tens of mm.
The aforementioned rationale led us to the investigation of spring-steel
accelerometers, grippers, and XY stages at the meso-scale using primarily Wire-cut
EDM. Another advantage at this scale is that a variety of off-the-shelf actuators and
sensors can be integrated and assembled. The work done on the development of mesoscale spring steel accelerometers is reported in this thesis.
1.1.6 Spring steel as a meso-scale material
In terms of machining and processing, meso-size has not been explored much. In such a
meso-scale range (100s of µm to a cm), the choice of materials changes; silicon is no
more the best material because it cannot be made bigger than a few mm in plane while its
thickness is severely restricted. It is difficult to get deformable silicon components in this
size. Achieving tall silicon features, the so-called high-aspect-ratio structures [48], is
expensive. Polymers such as SU-8 and polydimethylsiloxane (PDMS), too, have their
own inherent limitations because of their low strength and Young’s modulus,
respectively. On the other hand, some metals are eminently amenable. Wire-cut EDM,
laser machining, and even micro milling and drilling [49] are possible with metals. While
they may need serial processing and hence may be expensive for making many devices,
punching, forming, and sheet bending are suitable for economical batch-production.
Towards this, punching and blanking are already being explored as viable alternatives
[50]. Among the suitable materials available at the meso-scale for realizing deformable
mechanical elements, spring steel (AISI 1050, EN J42) is a good candidate because of its
high yield strength and low cost. Its yield strain is about 0.45%. The cost-related
advantages of spring steel remain relevant even when the volume of market is low. This is
because an expensive clean-room environment is not necessary and the material needed is
cheap. As a matter of reference, it costs only Rs. 200 per kg (approximately) in the form
of thin foils of thickness in the range of 0.25 mm to 2 mm.
10
Chapter 1
1.2 Objectives and the scope of the thesis
As stated earlier, the primary objective of the thesis is to establish mechanical
amplification as an effective method of improving the sensitivity of micromachined inplane capacitive accelerometers and meso-scale spring steel accelerometers without
compromising the bandwidth of the sensors. The other objective of the thesis is to study
the feasibility of using spring steel as a material for meso-scale devices.
To prove the effectiveness of DaCMs, we first compare one of the most sensitive
single-axis capacitive micromachined accelerometers and another with a large resonant
frequency reported in the literature with modified designs that include DaCMs occupying
the same footprint and under identical conditions. Later, the concept of using DaCMs in
accelerometers was validated by developing and demonstrating both single-axis and dualaxis micromachined capacitive in-plane accelerometers with DaCMs. We also report the
development of a wide-band dual-axis micro-accelerometer without using any compliant
mechanical amplifiers. In the last part of the thesis, we again make use of the method of
mechanical amplification in designing a single-axis meso-scale in-plane spring steel
accelerometer to prove that the application of compliant mechanical amplifiers is scale
independent, i.e., they can be used as well in meso-scale devices. In this part of the thesis,
we also develop a meso-scale dual-axis accelerometer without a mechanical amplifier. By
successfully developing multi-axis accelerometers using spring steel, we reaffirm the
viability of spring steel as a suitable material at the meso-scale. The work done in this
thesis is itemized and discussed next.
1.2.1 Development of a wide-band single-axis micromachined capacitive in-plane
accelerometer with a DaCM.
A single-axis capacitive micromachined accelerometer was designed using a DaCM and a
differential capacitance sense-comb. The designed device was fabricated using a multiuser foundry process called Silicon-on-insulator Multi-user MEMS processes
(SOIMUMPs). The fabricated device was tested at the die-level and then packaged on a
printed circuit board with an off-the-shelf integrated chip for measuring changes in
capacitance. The dynamic properties of the accelerometer, e.g., the frequency response of
the device, the amplification obtained using the DaCM, the step-response of the
accelerometer were obtained from the die-level dynamic characterization of the device
using a Laser Doppler Vibrometer(LDV). The packaged accelerometer was then placed
11
Chapter 1
on a vibration shaker platform for calibration. The packaged device was calibrated with
respect to a standard commercially available accelerometer mounted on the same
platform. A dynamic base excitation was applied in the form of acceleration through the
shaker platform and the device was subjected to that. The output of the packaged
accelerometer was monitored to obtain the calibration curve of the accelerometer.
1.2.2 Development of a dual-axis micromachined capacitive in-plane accelerometer
using a de-coupling mechanism and two DaCMs.
Also presented in this thesis is the design of an in-plane dual-axis capacitive
accelerometer with an XY decoupling mechanism made of 12 folded beam suspensions
and two DaCMs that de-couples and amplifies the displacements along the two in-plane
orthogonal axes. The lumped parameter modeling and the finite element simulation of the
mechanical components of the accelerometer including the DaCMs is also discussed. The
SOIMUMPs process was used to fabricate the designed device. The in-plane dynamic
characterization on the fabricated device was performed using LDV. Finally, the
fabricated device was packaged using a hybrid System-in-Package (SiP) technique. The
quasi-static testing and calibration of the packaged dual-axis accelerometer was
performed by mounting the packaged accelerometer on a vertical turn-table and then
applying acceleration on the device by rotating the turn-table precisely. The dynamic
calibration of the device was also performed by mounting the device on the platform of a
vibration shaker and then applying different values of acceleration at a constant
frequency.
1.2.3 Development of a dual-axis wide-band micromachined capacitive in-plane
accelerometer without mechanical amplification.
A dual-axis wide-band capacitive in-plane accelerometer was also designed without
DaCMs but with the help of the aforementioned de-coupling arrangement. The axial
components of the applied acceleration were captured by measuring the change in
capacitance in the sense-combs attached to the XY de-coupling stage. This device was
fabricated using a custom bulk-micromachining process that uses SOI wafers. This
process is separated into two phases: Phase I and Phase II. Phase I is used to fabricate
dual-axis accelerometers without DaCMs. These fabricated dies are characterized under a
Laser Doppler Vibrometer to study the die-level frequency response and the step
response. Later these dies are packaged and then calibrated on a vibration shaker table.
12
Chapter 1
1.2.4 Development of meso-scale spring steel accelerometers
We also present, here, the work done on the development of single-axis and dual-axis
meso-scale spring steel in-plane accelerometers equipped with Hall-effect sensors. First,
we designed two single-axis meso-scale accelerometers using spring steel with the same
footprint. Among the two, the first design contains a DaCM and the second does not. To
fit the DaCM in the same footprint area, the proof-mass size of the first design was
reduced. The two devices were fabricated by cutting a 0.5 mm thick spring steel foil using
a wire-cut EDM process. The extra mass was attached to the top and bottom of the proofmass of both the designs by machining 2 mm thick spring steel metal pieces using CNC
milling. It was experimentally shown that the prototype of the first design exhibits more
sensitivity and bandwidth than the prototype of the second design. Thus, the very first
claim was reaffirmed even for meso-scale devices.
Later, we also designed and developed a dual-axis meso-scale accelerometer using
spring steel which also contains a de-coupling mechanism that provides perfect decoupling of the motions in the two in-plane orthogonal directions. One more extra feature
is the use of rechargeable Li-ion batteries as a part of the proof-mass in addition to
serving as the power source. The device was assembled inside an acrylic casing manually.
The prototype was mounted on a shaker table and then tested and calibrated successfully
with respect to a reference accelerometer. Thus, the development of these meso-scale
accelerometers proves spring steel to be a suitable material for developing low-cost mesoscale devices even in the case of low volume production.
1.3 Organization of the thesis
The organization of the rest of the thesis is as follows:
In the second chapter, we present the literature review. The relevant topics that are
covered are: the different state-of-the art in-plane micromachined accelerometers,
different capacitive sensing techniques, different types of amplifying mechanisms used in
micromachined accelerometers, different mechanical amplification mechanisms used for
sensor application, different types of Displacement-amplifying Compliant Mechanisms
and their applications.
13
Chapter 1
In the third chapter, we discuss two design case studies to show that improved
performance can be achieved by incorporating DaCMs with existing accelerometers from
the literature.
In the fourth chapter, we present the development of a single-axis wide-band
capacitive in-plane micromachined accelerometer with a DaCM. In this chapter, we start
with the design of the single-axis accelerometer with a DaCM, then the fabrication, dielevel characterization, packaging, testing and calibration.
In the fifth chapter, we present the development of a dual-axis capacitive in-plane
micromachined accelerometer with a de-coupling mechanism and two DaCMs.
In the sixth chapter, we discuss the development of a dual-axis wide-band
capacitive in-plane micromachined accelerometer with a de-coupling mechanism but
without any mechanical amplification.
In the seventh Chapter, we perform a feasibility study of using spring steel as a
viable material for developing meso-scale multi-axis accelerometers with and without
DaCMs.
In the eighth Chapter, we conclude the work presented in the thesis along with
possible future extensions.
1.4 Closure
An overview of the work done in this thesis is presented in this chapter after providing the
necessary background and motivation for the work. The primary motivation of the work
is related to the performance enhancement of in-plane accelerometers. In this thesis, we
worked on the development of two types of in-plane accelerometers with mechanical
amplifiers. They are capacitive type micromachined accelerometers and meso-scale
spring steel accelerometers. An explanation is provided to justify the need for mechanical
amplification in accelerometers. Mechanical displacement amplification is possible by
using either a conventional mechanical lever or a DaCM. In this context, a DaCM is
introduced and the advantages of a DaCM over conventional mechanical levers are
discussed. Also presented is the rationale for developing meso-scale devices using spring
steel as the structural material followed by the specific objectives of the thesis. The
organization of the thesis is also indicated. The next chapter reviews all the relevant
literature in detail before the specifics of the work are presented in subsequent chapters.
14
Chapter 2
Literature review
Summary
This chapter contains a review of some literature in the field of micromachined
accelerometers, mechanical displacement amplifiers such as conventional mechanical
levers and Displacement-amplifying Compliant Mechanisms (DaCMs) applied to
different sensors and actuators, and, meso-scale sensors that are relevant to the work
done in this thesis. The chapter begins with a brief introduction to micromachined
accelerometers along with the principles of operation of accelerometers, different types of
micromachined accelerometers, and a few important specifications that define the
performance of accelerometers. Noise in micromachined accelerometers is an important
aspect that has a direct influence on the performance of micromachined accelerometers
and, thus, various sources of noise present in an accelerometer are discussed briefly.
Since this thesis deals with the capacitive type of micromachined accelerometer, a few
relevant capacitive surface and bulk micromachined in-plane, out-of-plane and tri-axial
accelerometers are reviewed here followed by the different fabrication techniques used
for developing these accelerometers. A few accelerometers containing mechanical
amplifiers reported to date are described.
2.1 A brief overview of micromachined accelerometers
An accelerometer is an electromechanical transducer that measures the constant or timevarying acceleration of a body on to which it is mounted. An example of constant
acceleration is the acceleration due to gravitational force, whereas an example of timevarying acceleration is the movement or vibration of a body. Accelerometers can also be
used to measure quasi-static acceleration such as the tilt or angle of a slowly rotating
object.
Before the advent of micromachining technology, all the sensors used to be large
in size. In the late 1960s and early 1970s, with the invention of Microelectromechanical
systems (MEMS) technology, the miniaturization of sensors started. Researchers and
scientists in this industry and academia started fabricating micron sized moving structures
15
Chapter 2
by modifying the fabrication process used in fabricating integrated chips (ICs), commonly
known as micromachining. Since then, the micromachining process has come a long way
and several sensors such as accelerometers, gyroscopes, pressure sensors, micromirrors
and
microphones have been miniaturized
and
marketed successfully. These
micromachined sensors dominate today’s market because of three major advantages over
conventional sensors and actuators, namely, high performance, low cost, and low power
consumption.
Among
the
microsensors,
micromachined
accelerometers
or
microaccelerometers are the most successful commercial sensors in recent days with a
wide range of applications. Typical applications of accelerometers include airbag
deployment in cars, active suspensions, adaptive brakes, alarm systems, home appliances,
mobile phones and tablets, machine control and vibration monitoring, machine health
monitoring, inertial navigation systems, tilt measurement and control in spacecraft and
aircraft, crash-test in automobiles, oil exploration, surveillance, earthquake detection, etc.
Different applications require different range of accelerations to be detected in a different
frequency ranges as shown in Figure 2.1.
107
106
Machine health
monitoring
Bandwidth in Hz
105
104
Shock
measurement
SONAR
3
10
Seismometry
102
101
Micro-gravity
and space
100
Airbag
10-1
Biomedical
-2
10
10-3
Inertial navigation
-6
10
10-5
10-4
10-3
10-2
10-1
101
100
Measurement of acceleration in g (1 g = 9.81 m/s2)
102
Figure 2.1: Applications of accelerometers with respect to the operating bandwidth and
frequency of application.
2.1.1 Operating principle of accelerometers
In most accelerometers, the acceleration is sensed by measuring the displacement of the
moving mass suspended by springs or suspensions. A single degree-of-freedom lumped
16
Chapter 2
spring-mass-damper ( k  m  c ) model of an accelerometer is shown in Figure 2.2. In the
schematic, the acceleration of the frame ( a ) exerts an inertial force ( ma ) (due to D’
Alembert’s force) on the proof-mass (m) via the spring ( k ) and the damper (c ) . The
displacement of the fame is denoted by x and that of the lumped mass is denoted by y .
The relative displacement experienced by the spring and damper is z  y  x . Thus, the
equation of motion of the lumped model can be expressed as:
my  c ( y  x )  k ( y  x )  0
(6)
By substituting z  y  x , Eq. (6) can be written as
m( 
z  
x)  cz  kz  0
 mz  cz  kz  mx  F (t )
(7)
where F (t ) is the applied force on the frame.
a
k
c
ma
y
x
Figure 2.2: A second order spring-mass-damper model representing an accelerometer.
We assume that the applied forces and the corresponding displacements are
harmonic functions. Thus, we substitute x  X sin t with amplitude, X and frequency,
 and z  Z sin(t   ) with amplitude, Z , frequency  and phase between the
displacement and the exerted force,  in Eq. (2) to obtain the solution which is given by
Z

2
n2  X
1   n 2    2  n  


 
2
and
17
(8)
2
Chapter 2
  tan 1
2 ( n )
(1  ( 2 n2 ))
(9)
where
n  k m is the natural frequency of undamped oscillation,
  c cc is the damping factor or the damping ratio and
cc  2 k
m
 2mn  4km is the critical damping.
It can be seen from Eq. (8) that when the device is operated at a frequency much
lower than the resonant frequency, i.e. when    n , the denominator becomes unity.
Thus, we get
Z
2 X
a
 2
2
n
n
Z
1
m
S  2 
a n k
(10)
where a   2 X is the applied acceleration. Z a is the relative displacement of the proofmass due to the applied acceleration. Thus, Z a can be termed as the sensitivity ( S ) of
the accelerometer. It can be seen that the response, i.e. a n2 stays constant for a certain
band of frequency. Generally, the band from zero to the frequency where the response
changes by 3 dB is known as the bandwidth of the device. The bandwidth of the
accelerometer is thus dependent on the natural frequency n of the device which is equal
to
k m . So, there is an inherent trade-off present between the sensitivity and bandwidth
of the accelerometer. Thus, high sensitivity accelerometers cannot be operated in wide
bandwidth and wide-band accelerometers cannot be highly sensitive.
When the operating frequency becomes equal to the natural frequency of the
device, then the non-dimensional amplitude of displacement Z X reaches its maximum
value of 1 2 and the phase between the applied force and the obtained displacement,  ,
becomes 900. The sharpness of the resonance is measured by the quality factor, Q , which
is related to the damping of the system, given by Eq. (11)
18
Chapter 2
Q
n
1
2 km


2
c
2  1
(11)
where  n is the resonant frequency and  2 and 1 are the two frequencies on either side
of the resonance where the displacement amplitude becomes 0.707 times the
displacement at resonance as shown in Figure 2.3. These frequency points are also known
as half-power points. The quality factor is the ratio of the stored mechanical energy to the
energy dissipated by damping.
Figure 2.3: A typical frequency response of an accelerometer with different types of
damping.
Let us consider a spring-mass-damper system perturbed by a step excitation with
magnitude F0 . The step excitation function, which is shown in Figure 2.4, can be
described by Eq. (12).
F (t )  0 for t  0
 F0 for t  0
(12)
The solution of Eq. (7) can be expressed by Eq.(13) [51].
z
F0 
ent
cos
1 
k 
1  2


1   2 n t   


(13)
where
  
2 
 1  
  tan 1 
(14)
The rate of the exponential decay of the damped oscillation is governed by the
factor  n where
19
Chapter 2
n  c 2m
(15)
F0
0
Time (t )
Figure 2.4: A step excitation function.
Eq.(16) indicates that the frequency of damped oscillation,  d , can be estimated
from the time constant of the damped oscillation,  d , as shown in Figure 2.5.
d 
2
d
 n 1   2 
(16)
The amount of damping present in the system can be determined by measuring the
rate of decay of the damped oscillation [51]. The logarithmic decrement,  , which is the
natural logarithm of any two successive amplitudes of the damped oscillations, shown in
Figure 2.5, can be expressed as
 t
Z
e n1
2
 
  ln 1  ln  t   ln e n d  n d 


n
1 d
Z2
1  2
e
(17)
The value of the damping factor  can be estimated by finding the natural
frequency of the accelerometer,  n , from the experimentally obtained frequency response
of the device and by measuring the rate of the exponential decay of the damped
oscillations and then equating it with  n as given in Eq.(15). The experimental value of
 can also be found by measuring the two successive amplitudes of the damped
oscillation and taking the natural logarithm of the two and equating it to
in Eq.(17).
20
2
1  2
as given
Chapter 2
Exponential decay
Z1
Z2
d
Figure 2.5: A typical step response of a second order system showing damped
oscillations with logarithmic decay.
2.1.2 Types of micromachined accelerometers
Almost all micromachined accelerometers have a basic structure that consists of a proofmass or an inertial mass that is suspended by a spring and a dampening mechanism and a
signal transduction element. The proof-mass experiences the acceleration force which is
mass times the applied acceleration. Due to the application of the acceleration force, the
proof-mass is displaced from its initial position. The amount of displacement is thus a
measure of the applied acceleration. The transduction element senses the displacement
signal and converts it into a voltage signal. Depending on the type of signal transduction
element used, micromachined accelerometers can be classified into eight groups. Each
type of accelerometer has certain merits and demerits. Therefore, different types of
accelerometers are used for different applications.
2.1.2.1 Piezoresistive accelerometers
Principle of operation
The piezoresistive transduction technique is one of the most widely used techniques in
micromachined accelerometers. In this type of accelerometer, piezo-resistors are
embedded into the suspension beams of the accelerometer in a Wheatstone bridge
configuration. The bending of these beams due to the displacement of the proof-mass on
the application of external acceleration causes strain in the piezo-resistors which, in turn,
21
Chapter 2
alters the resistance of the piezo-resistors. The change in resistance is detected by
measuring the output voltage of the Wheatstone bridge.
Typical applications
Airbag deployment, Crash testing, high shock measurement in automobiles etc.
Merits
a) Simple mechanical structures and easy fabrication process.
b) Simple electronic signal conditioning circuitry.
Demerits
a) High-temperature dependency.
b) Low voltage sensitivity.
2.1.2.2 Piezoelectric accelerometers
Principle of operation
Piezoelectric accelerometers utilize the piezoelectric effect of quartz crystal or certain
ceramic materials to measure dynamic changes in mechanical variables, e.g. acceleration,
vibration, and mechanical shock. The piezoelectric accelerometer consists of an active
piezoelectric material which is sandwiched between the proof-mass on one side and a
rigid sensor base on the other side. When the accelerometer is subjected to dynamic
acceleration, the piezoelectric material experiences a dynamic force which is equal to the
mass of the proof-mass times the applied acceleration. Due to the piezoelectric effect, the
charge output of the piezoelectric material is proportional to the applied force and thus the
applied acceleration. Some piezoelectric accelerometers also contain a preamplifier that
transforms the high-impedance charge output of the piezoelectric material into a low
impedance voltage signal.
Typical applications
Machined vibration monitoring and control, structural health monitoring, suitable for high
frequency applications e.g. SONAR, acoustic emission etc.
Merits
a) Wide bandwidth.
b) Excellent linearity over their dynamic range.
22
Chapter 2
c) No moving parts - no wear.
d) Self-generating - no external power required.
Demerits
a) Low sensitivity.
b) Low resolution.
2.1.2.3 Capacitive accelerometers
Principle of operation
In a capacitive accelerometer, the proof-mass moves in the opposite direction of the
applied acceleration resulting in a change in capacitance between two parallel plates, one
fixed and the other attached to the proof-mass. Therefore, the change in capacitance is a
measure of the applied acceleration. All capacitive accelerometers come with a signal
conditioning circuitry that converts the change in capacitance into a change in voltage.
Typical applications
Inertial navigation, micro-gravity and space applications, tilt measurement, surveillance
applications, oil explorations and earth quake detection etc.
Merits
a) High sensitivity.
b) Very low temperature drift.
c) Good linearity.
d) Amenability to force-feedback.
e) Low noise.
Demerits
a) Prone to parasitic capacitance.
b) Prone to Electro-magnetic interference.
2.1.2.4 Resonant accelerometers
Principle of operation
23
Chapter 2
In resonant accelerometers, input acceleration is detected in terms of a shift in the
resonant characteristics of a sensing device coupled to the proof mass. The inertial force
felt by the proof-mass due to the applied acceleration is transferred to a micro bridge or a
tuning fork that is coupled to the proof-mass. The change in force in the tuning fork,
which is proportional to the applied acceleration, changes its resonance characteristics.
Typical applications
Monitoring
of
structural
and
machine
vibration,
navigation
grade
precision
accelerometers etc.
Merits
a) Wide dynamic range.
b) Wide bandwidth.
c) Quite sensitive
d) Quasi-digital nature of the output.
e) Excellent repeatability.
Demerits
a) Need for vacuum packaging increases the complexity.
b) Signal feed-through.
c) Relatively high noise.
2.1.2.5 Optical accelerometers
Principle of operation
In optical accelerometers, the applied acceleration displaces the proof-mass leading to
modulations of intensity, polarization, or phase of the optical signal. This change in the
optical signal is a measure of the acceleration to be measured.
Typical applications
Inertial navigation, spacecraft etc.
Merits
a) Extremely low noise.
24
Chapter 2
b) High resolution.
c) Highly sensitive.
d) Immune to electromagnetic interference and temperature.
Demerits
a) Limited dynamic range.
b) Requires extensive control architecture.
c) Complex fabrication process.
2.1.2.6 Tunneling accelerometers
Principle of operation
Tunneling accelerometers use an electron tunneling phenomenon in which a current is
passed between two conductive layers separated by a very small gap of the order of a few
Å. One of the conductive layers is essentially the proof-mass of the accelerometer with a
sharp tip. This tunneling current varies exponentially with the distance between the two
conductive plates. The change in current due to the displacement of the accelerometer due
to the applied acceleration is measured to find the applied acceleration on the proof-mass.
Typical applications
Micro gravity measurement in space, inertial navigation, etc.
Merits
a) High precision, resolution and sensitivity.
b) Wide bandwidth.
Demerits
a) High drift.
b) Fabrication of the tunneling tip is relatively complicated.
c) Non-linear variation of tunneling current with distance
d) Bulky setup and limited portability.
e) Need for an extensive control mechanism for the tunneling tip.
25
Chapter 2
2.1.2.7 Thermal accelerometers
Principle of operation
In thermal accelerometers, a hot air bubble between a pair of electrodes is used as the
proof-mass. The temperature difference between the two plates is zero when there is no
applied acceleration. As acceleration is applied, the hot air bubble moves towards one
electrode opposing the inertial force. This makes the electrode nearer to the bubble hotter
than the other electrode, thus creating a temperature difference which is then picked up by
a thermocouple. The measured temperature difference is a function of the applied
acceleration.
Typical applications
Consumer electronics and gaming applications, automobiles etc.
Merits
a) No moving mechanical parts.
b) Simple signal conditioning circuitry.
c) Amenable to monolithic fabrication.
d) High survivability to shock.
Demerits
a) Low resolution.
b) Very high temperature-induced drift and high power dissipation.
2.1.2.8 Electromagnetic accelerometers
Principle of operation
An electromagnetic accelerometer consists of two planar coils, one on the moving proofmass and the other on the substrate. One of the coils (known as the primary coil) is used
to generate an alternating electromagnetic field. An induced voltage is generated in the
secondary coil with the amplitude proportional to the distance between the two coils.
Thus, the displacement of the proof-mass due to the applied acceleration is detected by
measuring the output voltage of the secondary coil.
Typical applications
26
Chapter 2
Aircraft, automobiles machine vibration monitoring etc.
Merits
a) Simple signal conditioning circuitry.
b) Simple structure.
c) Very low temperature drift.
Demerits
a) High electro-magnetic interference.
b) Low resolution.
c) High power consumption.
2.1.3 Key specifications of an accelerometer
One of the most important aspects of selecting an accelerometer for a specific application
is to understand the key specifications of the accelerometer. These specifications are the
set of performance parameters of the accelerometer that describes the accelerometer. A
few key specifications of an accelerometer are described next.
2.1.3.1 Axial sensitivity
Axial sensitivity, denoted by S , is the ratio of the change in acceleration (mechanical
signal) to the change in the output signal (electrical signal). It is also defined as the ‘scale
factor’ of the accelerometer. This defines the ideal, linear relationship between input
acceleration and electrical output. Sensitivity is generally specified in units of mV/g or
their equivalent, at a particular supply voltage for analog-output accelerometers, and the
lowest significant bit per g (i.e., LSB/g) for digital-output accelerometers. It is valid for a
specific range of frequency. Axial sensitivity is sometimes specified with % tolerance,
e.g. ±5% or ±10%. This ensures that the sensitivity of the accelerometer will remain
within the stated tolerance deviation around the specified nominal sensitivity. For a triaxial accelerometer, the axial sensitivities along the X, Y and Z axes are denoted by SX ,
SY and SZ . The sensitivity is also temperature dependent, i.e., the specified temperature
is valid over a range of temperatures. It is usually specified by a % change of sensitivity
per oC. The temperature drift of sensitivity is caused because of the change in thermal
stresses in the mechanical structure of the accelerometer, the change in the velocities of
27
Chapter 2
the surrounding air particles and the thermal coefficient of the signal conditioning circuit
components.
2.1.3.2 Cross-axis sensitivity or Transverse sensitivity
Cross-axis sensitivity or transverse sensitivity is the sensitivity of the accelerometer in the
axes that are orthogonal to the sensitive axis, as shown in Figure 2.6. This is measured by
the voltage obtained at the output of the accelerometer when an acceleration applied to
the device is normal to the sensitive axis. Cross-axis sensitivity is generally specified by
the % of the axial sensitivity. This basically indicates the coupling of the sensitive axis to
the other orthogonal axes. For a tri-axial accelerometer, each axis has two cross-axis
sensitivities. As an example, for an accelerometer that is sensitive to the X axis, the two
cross-axis sensitivities can be expressed as
SXYCross 
SXZCross
SXY
 100%
SX
S
 XZ  100%
SX
(18)
Mounted
accelerometer
Axial-direction
(Sensitive axis)
Transverse axis
Mounting platform
Figure 2.6: A typical mounting arrangement of an accelerometer showing the axial and
transverse axes.
2.1.3.3 Frequency response and bandwidth
The frequency response of an accelerometer is also an important specification that tells
the user how the sensitivity of the accelerometer varies as a function of frequency. It is
also termed the amplitude and phase response of the accelerometer. The frequency
response is also specified by a tolerance band, e.g., ±3dB. For a typical accelerometer, the
sensitivity remains constant within a range of frequencies before attaining resonance. The
range of frequencies in which the sensitivity of the accelerometer remains within the band
28
Chapter 2
of ±3dB is known as the 3dB bandwidth of the accelerometer. In general, accelerometers
are operated in the frequency range in which the response is flat.
2.1.3.4 Nonlinearity
Ideally, the output of an accelerometer should maintain a linear relation with the applied
acceleration. However, this is not true in many cases. The nonlinearity of an
accelerometer is the measure of the deviation of the output of the accelerometer as
compared to the ideal linear sensitivity curve. If is often expressed as the ± % of a fullscale range (%FSR). Nonlinearity can be expressed as
% Nonlinearity=
Maximum deviation (g)
×100%
Full-scale output (g)
(19)
2.1.3.5 Dynamic range
The dynamic range of an accelerometer is the maximum amount of dynamic acceleration
that the accelerometer can measure accurately. Typically, it is specified by ± g. The
dynamic range of an accelerometer may differ from the static range because of the
overshoot present in the response of the accelerometer when a dynamic excitation is
given. It generally differs for open-loop accelerometers in which the displacement of the
inertial mass is not controlled by any means.
2.1.3.6 Resolution
The resolution of an accelerometer is the smallest detectable increment in acceleration. It
is one of the most important specifications as it determines the smallest change in input
that can be detected. The resolution is generally measured by measuring the noise-floor of
the sensor as the noise determines the minimum resolution of the sensor. The bandwidth
of an accelerometer is also related to the measurement of resolution. The resolution can
be improved by decreasing the bandwidth of the output low-pass filter. The resolution is
calculated by the following equation
R  N  BWLPF 1.6
where N is the power spectral density of noise in
the low-pass filter at the output of the sensor.
29
g
Hz
(20)
, and BWLPF is the bandwidth of
Chapter 2
2.2 Noise in micromachined accelerometers
Figure 2.7 shows the components of a micromachined capacitive accelerometer device,
which includes a mechanical element; electronics to measure the change in capacitance in
response to applied acceleration; and a printed circuit board (PCB) that serves the dual
purpose of housing the power supply and additional signal conditioning circuitry as well
as providing mechanical anchoring of the packaged accelerometer and the capacitance
read-out integrated circuit (IC). Also shown in Figure 2.7 is noise that is inherent in
mechanical and electronic elements. While sensitivity depends on the design of the
mechanical element and the capacitance read-out IC, the resolution also depends on the
noise present in the device as a whole. The total noise present in an accelerometer not
only degrades the performance of the accelerometer, but also reduces the quality of output
of the sensor. Figure 2.8 shows how the calibration characteristic of an accelerometer is
affected by the total noise present in the system. The total noise defines the limit of
detection or the minimum detectable acceleration of an accelerometer.
Noise in micromachined accelerometers has two major sources, intrinsic (internal)
and extrinsic (external) [52]. Noise interference from the external world such as ambient
electromagnetic interference, power supply noise, and environmental sound and vibration
come under the extrinsic sources of noise. These types of noise interferences could be
ameliorated by choosing proper shielding mechanisms such as a Faraday cage, a vibration
isolation platform, and a regulated power supply.
There are two root causes for the presence of intrinsic or inherent noise in any
engineering system. One is the quantum or discrete nature of the electrons, photons,
atoms and molecules in and around the system. The other reason is the statistical variation
of the energies and motions of these quanta. In large systems, the magnitude of the
discrete and statistical variation of energies and motions is negligible compared to the
magnitude of the signal. As the size is reduced, the signal magnitude decreases and the
intrinsic noise becomes relatively large as compared to the signal strength, thus affecting
the signal-to-noise ratio of the entire system.
30
Chapter 2
Thermo-mechanical
noise
Electronic
noise
Mechanical
Element
Interface Electronic
ASICs
Mechanical
Mounting
Evaluation board
with power supply
Input
acceleration
Output
Voltage
Sources of
noise
Unwanted
extrinsic noise
Figure 2.7: Block diagram of a micromachined accelerometer device along with the PCB
for power supply and additional signal conditioning.
Limit of
detection
Output voltage
Dynamic range
ΔO
ΔI
Sensitivity =
ΔO
ΔI
Total noise output
Input acceleration
Figure 2.8: A typical calibration curve of an accelerometer showing the effect of total
noise on sensor characteristics.
In micromachined accelerometers, the two major sources of intrinsic noise are:
Brownian noise or thermal-mechanical noise and electronic noise. Brownian noise is due
to the unbalanced fluctuating forces caused by the random collision of surrounding air
particles with the proof-mass and other micro structures of the accelerometer. It is also
called ‘random walk noise’ [52]. According to the Fluctuation-Dissipation theorem [38],
31
Chapter 2
each system will have a dissipation mechanism if there exists a fluctuating force in that
system which decays through the dissipation mechanism. The dissipating mechanism is
the mechanical resistance which is analogous to Johnson’s noise in electrical resistance.
The fluctuating force acts as the noise and dissipates through the damper with damping
coefficient D . According to the Nyquist theory, the spectral density of the fluctuating
force in a system with a mechanical resistance (damping coefficient) of D can be
expressed by Eq.(21).
Ff  4kBTD
(21)
Hz , kB is the Boltzmann constant (1.38 × 10-23
where F f is the fluctuating force in N
J K-1) and T is the absolute temperature in Kelvin. Using Eq. (21), the Brownian Noise
Equivalent Acceleration (BNEA) measured in
BNEA 
m s2
, is given by
Hz
4k BTD
4k BT 0

m
Qm
(22)
where 0 is the natural frequency in Hz, Q the quality factor, and m the mass in kg. The
quality factor Q induced by the squeeze film damping between the dynamic and
stationary comb electrodes in a capacitive in-plane accelerometer can be expressed using
Eq. (23) [79].
Q
d03 mk
ne eff lo h3
(23)
where d0 is the gap between the moving and stationary comb, ne is the number of
dynamic combs, eff is the effective coefficient of air viscosity (18.5 × 10-6 N s m-2), lo is
the overlap length of the dynamic combs with the stationary combs and h is the thickness
of the accelerometer. It can be seen that increasing mass and decreasing air damping can
improve the mechanical noise floor.
The other type of intrinsic noise present in the micromachined accelerometer is the
electronic noise in the signal conditioning circuit that can be categorized into three basic
types. They are as follows.
32
Chapter 2

Thermal noise or Johnson noise: This is due to the temperature induced
fluctuations in the charge carriers in any conductor.

Generation and recombination noise: This is caused by the random production
and annihilation of the electron-hole pairs in semiconductors.

Flicker noise or Pink noise or 1 f noise: This is due to the variable trapping and
release of charge carriers in the conductors.

Shot noise: This noise is generated due to the random arrival time of the charge
carriers in the conductors.
The total effect of all the aforementioned noise sources determines the resolution
of the capacitance sensing circuit. Thus, the total electronic noise can be expressed in
terms of the resolution of the capacitance sensing interface circuit
 Cmin 
and the
capacitance sensitivity  S  C g  of the microaccelerometer. The electronic noise, also
termed as circuit noise equivalent acceleration (CNEA) can be expressed by Eq. (24)
CNEA 
Cmin  m s 2 


S  Hz 
(24)
The capacitance sensitivity of a micromachined capacitive in-plane accelerometer
with a differential capacitance arrangement can be expressed as:
S
C 2Cb m 2Cb 1 2 0 r nelo hm



g
d0 k
d 0 02
d02k
(25)
where Cb is the rest capacitance between one side of the stationary combs and the
dynamic combs, 0 is the first in-plane natural frequency of the accelerometer,  0 is the
absolute permittivity (8.854 × 10-12 F m-1) and  r is the relative permittivity of air which
is almost equal to unity.
It turns out that in integrated micromachined sensors, total electronic noise often
dominates its mechanical counterpart [18] as the mechanical sensitivity improves. This
implies that, in addition to making the best efforts to compensate for electronic noise, it
makes sense to amplify the signal by mechanical means because the corresponding noise
will not appreciably hamper the overall resolution; in fact, enhanced mechanical
sensitivity improves the signal-to-noise ratio and thus the resolution.
33
Chapter 2
2.3 Compliant mechanisms
Compliant mechanisms are mechanisms that make use of elastic deformation of their
flexural members to transform or transmit any displacement, force or energy from an
input port to an output port [53]. The input port is a point on the mechanism where an
input force or displacement is applied and a desired force or displacement is obtained at
the output port which is a separate point on the mechanism. There could be general input
or output ports on a mechanism. This thesis uses the single-input-single-output type of
compliant mechanisms. Compliant mechanisms have certain advantages over
conventional mechanisms with rigid links and joints: (i) no rigid links or joints, (ii) no
friction and backlash, (iii) no wear and tear associated with joints, (iv) fewer parts, (v) no
assembly required and (vi) a 2D planar topology which is suitable for microfabrication.
Unlike conventional rigid-link mechanisms, compliant mechanisms can store elastic
energy by deforming their structural members. Despite the many advantages of compliant
mechanisms, there are a number of difficulties associated with their design. Traditional
kinematics itself is quite insufficient, and it has to be combined with non-linear elastic
deformation theory as compliant mechanisms undergo large deformations. Thus, the
effects of geometric nonlinearity need to be included in the elastic analysis. The effect of
high stress values in the slender beams and the corner regions should also be taken into
account while designing compliant mechanisms.
Different methods have been proposed for the systematic design and synthesis of
compliant mechanisms in the last two decades. They can be broadly categorized as
kinematics-based
approaches,
continuum-based
approaches
and
building-block
approaches. In the kinematics-based approach, a known compliant topology is
represented and synthesized using rigid-body linkages with joint springs and is called a
pseudo-rigid-body model. A pseudo-rigid body model for designing compliant
mechanisms with small-length flexural pivots was presented by Howell and Midha (1994)
[45]. The continuum-based approach, on the other hand, focuses on the determination of
the topology, shape and size of the mechanisms. A topology optimization technique was
used by Anathasuresh (1994) [54], Frecker et al. 1997 [55], Sigmund 1997 [56] and
Saxena and Anathasuresh 1998 [56] to synthesize compliant mechanisms. A shape and
size optimization technique was used along with topology optimization by Bendsøe and
Sigmund 2003 [58], and Xu and Anathasuresh 2003 [59]. The effect of geometric
nonlinearity was considered in finite elements for topology optimization to synthesize
34
Chapter 2
large-deflection compliant mechanisms by Saxena and Ananthasuresh, 2001 [59] and
Pedersen and Sigmund, 2001 [60]. In the building-block based approach, compliant four-
bar building blocks or compliant dyad building blocks are added together to design a
compliant mechanism [61], [63].
A number of working prototypes of compliant mechanisms have been
systematically synthesized and demonstrated in the past decade. A compliant one-piece
stapler has been demonstrated by Ananthasuresh and Saggere (1995) [64] without the
hinge and the spring of a conventional stapler. Several compliant grippers, reported in the
literature [55], [60], have been designed using topology optimization. Various other
mechanisms such as Displacement-amplifying Compliant Mechanisms (DaCMs), bistable
mechanisms, micromachined AND gate [64], bicycle clutches [53], frequency multipliers,
and path generating devices [66] have been designed and demonstrated by various
research groups. Among all these compliant devices, DaCMs have gained a lot of interest
for many researchers for their inherent amplifying properties. DaCMs have been designed
by topology optimization as well as by conventional linkage designs [64], [67]-[69] for
piezoelectric and electrostatic actuation. As stated earlier, DaCMs are used in this thesis
for improving the performances of micro and meso-scale accelerometers.
2.4 Displacement-amplifying Compliant Mechanisms (DaCMs)
DaCMs constitute a class of compliant mechanisms that, as their name suggests, amplify
the applied displacement, thus acting like levers but with some stiffness due to their
inherent geometry. They have the unique advantage of having higher amplification
factors for a given area of a fixed aspect ratio than traditional levers, since they make use
of a 2D topology to achieve the amplification. Thus, DaCMs are becoming increasingly
popular for micro-machined devices because of their amenability to micro-fabrication as
they do not have joints. A variety of 2D DaCMs are available in the literature. Most of
them were invented keeping in view their application to micro and nano systems.
DaCMs were first used to amplify the output of piezoelectric stack actuators.
Piezo-electric material has become increasingly popular in positioning devices due to its
accuracy and ease of use [70]. These stacks generate high forces but small displacements
of around 10  m for a 1 cm stack. Piling on more stacks gives more deflection, but
affects the mechanical robustness of the stack at the same time. So, displacement
amplification is the only viable solution to get high output displacement. Later, many
35
Chapter 2
attempts were made to use DaCMs to amplify the displacement of many high-precision
actuators [67], [69], [71]. Canfield and Frecker (2000) [67] and Maddisetti and Frecker
(2004) [68] have also used amplifying mechanisms which were optimized for both static
and dynamic loads with piezoelectric actuation. Du and Lau (2000) [71] synthesized
elliptic amplifiers for ink-jet print head actuators using continuum element optimization
under dynamic conditions. A spring-mass-lever (SML) model that captures the static and
dynamic performance of a DaCM attached to an accelerometer was also proposed by
Krishnan 2006 [43]. The SML model applied to the design of an accelerometer with a
DaCM, as explained in [43], is given in Section 2.4.3.
2.4.1 Spring-Lever (SL) model of a DaCM
A Spring-Lever (SL) model of a DaCM is a two degrees-of-freedom lumped parameter
model that can be used for a simple and quick static analysis of the mechanism. In an SL
model, the DaCM is represented by a combination of a lever and springs. The effect of
the mass of its elastic members is ignored. It being a single-input-single-output type
mechanism, a DaCM has two ports: the input port and the output port. The stiffness of the
mechanism felt at the input port is termed the input stiffness, k ci ; and the stiffness at the
output port is called the output stiffness, kco . The amplification by the DaCM is called the
inherent geometric amplification, n , of any mechanism that can be modeled using a
mechanical lever with a fulcrum and with an arm ratio n:1. The two stiffness values k ci
and kco can be modeled by attaching two springs, one at the input port and the other at the
output port of the lever. The SL model of a DaCM is shown in Figure 2.9a. It can be seen
that the arrangement of the springs and the leverage mechanism is such that any
displacement at the input port causes an amplified displacement at the output port with
the direction of motion reversed. This type of DaCM is called an inverting DaCM.
Similarly, a non-inverting DaCM can also be modeled.
Figure 2.9b shows the SL model of an accelerometer with a single-input-singleoutput type DaCM. A suspension ks which is the suspension stiffness of the sensor is
added to the input port of the DaCM whereas another external suspension kext is added to
the output port of the DaCM. It is worth noticing that the model does not contain any
lumped mass to keep it simple. In order to derive the static equilibrium equation for the
model, we start with the potential energy PE of the entire SL model.
36
Chapter 2
PE  SE  WP
(26)
Where SE is the strain energy of the system and WP is the work potential which is the
negative of the work done by all the external forces. PE can be expressed as:
PE 
1
1
1
1
2
kci uin2  k s uin2  kco (uout  n  uin ) 2  kext uout
 Fin uin  Fout uout
2
2
2
2
(27)
Differentiating PE with respect to the two degrees of freedom uin and uout and
equating them to zero, the static equilibrium equations can be obtained.
PE
 kci uin  k s uin  kco (uout  n  uin )(  n)  Fin  0
uin
(28)
PE
 kco (uout  n  uin )  kext uout  Fout  0
uout
(29)
uout
kco
Fout
Output port
Input port
n :1
uin
Leverage mechanism
with a fulcrum
k ci
Fin
(a)
kext
Fout
uout Output side
uin
kco
n.uin
ks
Input side
n :1
DaCM
k ci
Fin
(b)
Figure 2.9: (a) Spring-Lever (SL) model of a DaCM, (b) SL model of an accelerometer
with a DaCM. It can be noted that all the lumped masses are ignored in this model.
37
Chapter 2
Eqs. (28) and (29) can be used to determine the expression for kci and kco in terms
of other known stiffness and force parameters and for a known value of n . The values of
kci and kco can be expressed as:
kci 
Fin  k s uin  n( Fout  kext uout )
uin
(30)
Fout  kext uout
uout  nuin
(31)
kco 
These two equations can be expressed in a matrix form in terms of the input-output
forces and displacements:
 kci  ks  n 2 kco

nkco

nkco   uin   Fin 
   

kext  kco  uout   Fout 
(32)
In the absence of the sensor stiffness, ks and the external stiffness, kext , Eq. (33)
can be simplified as:
 kci  n 2 kco

 nkco
nkco   uin   Fin 
   

kco  uout   Fout 
(33)
2.4.2 An Accelerometer with a DaCM
The schematic of a lateral capacitive accelerometer with a DaCM is shown in Figure 2.10.
It consists of a proof-mass along with its mechanical suspensions and feedback-combs
that can be called the actuation side; a DaCM; and sense-comb fingers along with
external suspensions that can be called the sensing side. Accelerometers have sensecombs at the points of maximum displacement, and feedback combs at points that
experience maximum inertial force. In conventional accelerometers, both sense-combs
and feedback combs are located on the proof-mass, which is the point of maximum
displacement as well as the point that experiences maximum inertial force.
However, by appending the accelerometer to a DaCM, the maximum deflection is
obtained at the output of the DaCM, whereas the inertial force is experienced by the
proof-mass. Thus, sense-combs need to be located at the output of the DaCM while the
feedback-combs are to be located on the proof-mass. The DaCM amplifies the
displacement from its input end to its output end thereby increasing the sensitivity and
resolution of the device compared to its conventional counterpart. An inverting DaCM is
38
Chapter 2
used in this design. An inverting DaCM reverses the sign of the displacement between its
input and outputs. The design of the DaCM was obtained through topology optimization
[43],[46], shape and size optimization, and intuitive modifications.
External suspension
Suspension stiffness  kext 
Sense-comb mass  mext 
kci , kco , mci , mco , n
DaCM
Anchor
Suspension Stiffness  k s 
Proofmass
Inertia
Feed-back combs
Figure 2.10: Schematic of an accelerometer with a DaCM. The sense-combs are attached
to the output end of the DaCM whereas the proof-mass is connected to the input end of
the DaCM.
The sense-comb fingers are used to sense and transduce the displacement of the
proof-mass and the DaCM into a change in capacitance. Since enough combs need to be
packed at the sensing port, a considerable mass is added there. This mass experiences
swaying moments when the acceleration is applied in the cross-axis direction. This causes
considerable cross-axial deflection owing to the relatively flexible regions at the output of
the DaCM. External suspensions connected at the end of the sense-comb reduce this
cross-axial deflection. The external suspension has been designed to offer high cross-axis
stiffness and very low axial stiffness. This external suspension stiffness should be small
enough to prevent a large reduction in the sensitivity of the accelerometer. The increased
stiffness due to the DaCM also enhances the natural frequency of the device, which helps
to increase the bandwidth of the sensor. The design of the DaCM and the external
suspension has also been optimized to achieve high axial and low cross-axis sensitivities.
The combs attached to the proof-mass experiencing the inertial force can be used for
force feedback when operated in a closed-loop mode.
An accelerometer with a mechanical amplifier (here, a DaCM) is shown in Figure
2.11a. It occupies an area of L1L2 . Let its displacement at the sensing comb fingers be m .
Now, imagine another accelerometer, shown in Figure 2.11b, that occupies the same area
39
Chapter 2
L1L2 but does not contain the DaCM and the additional suspension with its sensing
combs. In the later case, the proof-mass will be larger in size and hence it experiences
more force than the one with the DaCM. So, it may actually give more absolute
movement of the electrostatic comb. Let, this displacement be  p . Therefore, we want
the net amplification, which is equal to  m  p , to be substantially more than unity. This
calls for a careful comparison of the two cases. For this purpose, we use the lumped
spring-mass-lever (SML) model of the DaCM [43], [76], [77] that is useful to analyze the
overall assembly.
(a)
(b)
Figure 2.11: (a) An accelerometer with a DaCM with sense combs attached at the output
side of the DaCM, (b) A conventional design of a capacitive micromachined
accelerometer without any amplifying mechanism.
2.4.3 Spring-Mass-Lever (SML) model of an accelerometer with a DaCM
A two degrees-of-freedom (dofs) lumped spring-mass-lever (SML) [43] model of an
accelerometer with a DaCM is shown in Figure 2.12a. The five lumped parameters
pertaining to the DaCM, shown in the region enclosed with red dashes, capture its
essentially static and dynamic behavior. The parameters kci and kco denote the stiffness
of the DaCM on its input and output sides, respectively. Likewise, mci and mco denote
the inertia felt on the input and output sides. The inherent geometric advantage between
the input and output sides is denoted by n .
40
Chapter 2
Also shown in Figure 2.12a are the lumped parameters pertaining to the proofmass ( m pm ) and its suspension (ks ) as well as the mass of the sense-comb ( msc ) and its
suspension ( k ext ) . This should be contrasted with the lumped model of an accelerometer
without a DaCM, which is shown in Figure 2.12b. Here, k s denotes the stiffness of the
suspension and mpm the combined mass of the proof-mass and the sensing combs.
kext
uout Output side
msc
uin
mco
Fout
ks
kco
n.uin
n :1
m pm
mci
DaCM
Input side
k ci
Fin
(a)
k s

uout
mpm
(b)
Figure 2.12: (a) Lumped Spring-Mass-Lever (SML) model of an accelerometer with an
inverting DaCM, (b) Lumped model of a conventional accelerometer with proof-mass and
suspension.
Let us assume that the physical forms corresponding to the two lumped models in
Figure 2.11a-b occupy the same footprint on the chip and have the same minimum and
maximum feature sizes of a microfabrication process. A fair comparison of the two is to
be done by comparing the displacements of the sense-comb in the two cases and not just
the inherent amplification, n , which can be as large as 100 or more. In the case of the one
without a DaCM (see Figure 2.11b), the displacement of the sensing comb is the same as
that of the proof-mass. Its steady-state value under applied acceleration a is given by Eq.
(34).
41
Chapter 2
 
uout
mpm a
(34)
k s
The case in Figure 2.12a which leads to the following expression for the steadystate displacement of the sense-comb under the same acceleration, is given by Eq. (35).
uout 
 nk
k
co
m pm  msc kci  msc k s  n 2 msc kco  a
2
co kci  kco k s  k ext kci  kext k s  n kext kco 
(35)
The preceding equation is derived by writing the static equilibrium equations of
the two-degrees-of-freedom model in Figure 2.12a with Fin   m pm  mci  a
and
Fout   mco  msc  a . Now, the net amplification ( NA) between the two cases is given by
Eq. (36).
nkco m pm  msc kci  msc ka  n 2 msc kco  k s

uout
NA 


uout
 kco kci  kco ks  kext kci  kext ks  n2kext kco  mpm
(36)
It may be noted that NA is independent of the applied acceleration. It is this net
amplification that should be made as large as possible to show the effectiveness of a
DaCM in increasing sensitivity over a device that does not use a DaCM. As can be seen
in Eq. (36), it depends on all the five lumped parameters of the DaCM as well as on those
of the proof-mass, mass of the sense-comb, and their suspensions.
Another important consideration is the fundamental (i.e., the lowest) resonant
frequency of the model in Figure 2.12a. By writing the equation governing the free
vibration of the lumped system in Figure 2.12a, an analytical formula for the fundamental
resonance frequency can be expressed using Eq. (37) [76].
f0 
2
             
1
2 2
(37)
Where

k
ci
 ks  n 2 kco 
m
ci
 mpm 
;
k
m
co
co
 kext 
 msc 
; and  
4n2 kco2
 mci  mpm   mco  msc 
The frequency given by Eq. (37) using the lumped model is shown to be a good
estimate of that of the complete model computed using the modal analysis of the
complete finite element model [76] of the system.
42
Chapter 2
Before explaining how a DaCM is designed as per the specifications on the
sensitivity and resonance frequency, it is pertinent to explain how the lumped parameters
of the DaCM are computed using the complete model.
2.4.3.1 Computing the lumped parameters of the DaCM
In order to find the strain energy and the kinetic energy of the entire system, these lumped
parameters are to be extracted properly. The four lumped parameters ka , ma , kext and mext
can easily be found using the standard Finite Element (FE) analysis. The method to
determine the other five lumped parameters i.e. kci , kco , mci , mco and n of a DaCM [76],
[77], used in the accelerometer, is described next. Finding the values of these lumped
parameters of a DaCM is neither a standalone analytical technique nor a complete FE
analysis; it is a method where both of them are used simultaneously.
Let the two degrees-of-freedom shown in Figure 2.12a be uin and uout , which are
the displacements corresponding to the forces Fin and Fout acting at the input and output
sides of the DaCM. The values of kci and kco can be found by applying a static
equilibrium condition to this two degrees-of-freedom SML model using Eqs. (38) and
(39).
kci 
Fin  ks uin  n  kext uout  Fout 
uin
kco 
 kext uout  Fout 
nuin  uout
(38)
(39)
Equations (38) and (39) can be used to find the stiffness parameters of the DaCM
with the help of two simple FE analysis runs of the meshed model of only the DaCM with
two different load conditions. In the first load condition, uin is found by applying a
known value of Fin at the input side of the DaCM while keeping Fout  0 . Similarly, in
the second load condition, uout is found by applying a known value of Fout at the output
side of the DaCM while keeping Fin  0 . The values of ks and kext are zero in these two
load conditions as the analysis considers only the DaCM.
43
Chapter 2
The extraction of mci and mco also requires the same two static FE analyses with
two different load conditions as used to determine kci and kco . Here, we make use of all
the dofs of the meshed FE model. The lumped masses of the DaCM, mci and mco , can be
found by equating the kinetic energies of the SML model and those of the FE model
under two different load conditions.
1
1
 N
mci uin12  mco uout12   U12i vi
2
2
2 i 1
(40)
1
1
 N
mci uin 2 2  mco uout 2 2   U 22i vi
2
2
2 i 1
(41)
Where U1 and U 2 are the displacement vectors of all the dofs of the FE meshed model
for two different load conditions, vi is the volume of the i th finite element and  is the
density of the material used for the fabrication of the accelerometer with the DaCM. The
quantities uin1 and uout1 are the input and output side displacements of the DaCM in the
first load condition whereas uin2 and u out 2 are for the second load condition. The
parameters mci and mco can be found by solving Eqs. (40) and (41). The value of n can
be found by taking the ratio of the output side displacement to the input side displacement
in the first load condition, i.e., n  uout1 uin1 . In order to achieve NA  1 for a given
values of ka , ma , ma , kext and mext , a selection map-based method is used to design a
stiffness-matched DaCM with optimal values of kci , kco and n .
2.4.4 Re-designing a DaCM using a stiffness map-based method
Many working prototypes of DaCMs have been synthesized and are reported in the
literature [64]-[75]. A catalog has been created with quantitative details of these
mechanisms. In this thesis, DaCMs are used to enhance the mechanical sensitivity of a
displacement-based sensor such as an accelerometer. If incorporated into a sensor, these
DaCMs act like mechanical levers with some inherent mass and stiffness which alters the
performance of the sensor. Thus, a DaCM cannot directly be picked from the catalog and
incorporated with a sensor unless the inherent stiffness values of a DaCM properly match
the suspension stiffness of the sensor. Here, we do not design a new DaCM using an
optimization method. Instead, we select a DaCM from the database and re-design it using
44
Chapter 2
interactive size and shape optimization for stiffness-matching. The stiffness-matching is
done by selecting a DaCM from the database of the catalogue and then optimizing and redesigning a DaCM with optimal values of kci and kco using the user-inputs for ks , ms , kext
and mext as reported in [76].This method uses a pragmatic design approach based on
selection maps [76].
The selection map-based method allows the user to provide user-specifications,
within bounds, around their nominal values. This leads to a set of inequalities that bind
the values from above and below. This can be given by the Eq.(42).
FinL  Fin  FinH
uinL  uin  uinH
FoutL  Fout  FoutH
uoutL  uout  uoutH
(42)
ksL  ks  ksH
kextL  kext  kextH
These six inequalities are solved along with the equilibrium equations from the
SML model given in Eqs. (38) and (39) to get several continuous sets of feasible values
of kci , kco and n . Using these values, the kco vs. kci map or the stiffness map is drawn as
shown in Figure 2.13.
It should be noted that this map is a projection of a feasible volume in the 3D
space of kci - kco - n onto the 2D space of kci - kco . Therefore, for every point inside the
feasible map there is a corresponding valid range for n . On the same map, the kci , kco
and n values of existing DaCMs are computed and plotted as individual points. If any
point lies within the feasible map and the n value of the corresponding mechanism
matches, then that particular DaCM satisfies the user-specification.
Any mechanism that does not lie inside the feasible map can be interactively
optimized and re-designed to bring that mechanism inside the feasible map as illustrated
in Figure 2.14. To re-design the in-plane width of the beams of the mechanism, the outof-plane thickness of the mechanism and the size of the mechanism along the two inplane directions can be varied. The procedure for solving inequalities and equations is
implemented in an interactive program written in MATLAB. Two complete examples of
re-designing DaCMs using the selection map-based method are discussed in Chapter 3.
45
Chapter 2
Re-design
parameters
Stiffness map
Figure 2.13: The graphical user interface of the stiffness map-based re-design method
used to design the DaCMs in this thesis.
Point outside the
stiffness map
Parameter
curve
Figure 2.14: Re-design of the DaCM using the parameter curves.
2.5 Capacitive micromachined accelerometers from the literature
The development of MEMS accelerometers began in the early 1980s. Researchers from
academia and industry all over the world started exploring micromachined
accelerometers. Micromachined capacitive accelerometers can be categorized into three
types:
out-of-plane
micromachined
accelerometers,
in-plane
micromachined
accelerometers and tri-axial accelerometers. In-plane micromachined accelerometers can
46
Chapter 2
again be sub-divided into single-axis and dual-axis in-plane accelerometers. As stated
earlier, all micromachined capacitive accelerometers use the displacement of their proofmasses, which is later converted into voltages using capacitance extraction signal
conditioning circuitry. All micromachined capacitive accelerometers consist of a moving
electrode which is generally the proof-mass of the accelerometers, and a pair of static
electrodes. The in-plane accelerometers generally use capacitive comb-drives that are
attached to the proof-mass whereas the out-of-plane accelerometers use normal plate
electrodes placed on the top and bottom of the proof-mass at a certain distance.
2.5.1 Out-of-plane capacitive microaccelerometers
One of the first reported micromachined capacitive accelerometers is an out-of-plane
accelerometer also known as a z-axis accelerometer developed by Petersen et al. 1982
[79], where a cantilever beam accelerometer is presented integrated with Metal Oxide
Semiconductor (MOS) detection circuitry.
In 1983, Rudolf published a paper on a
capacitive vertical micro-accelerometer that uses a plate suspended by two springs and
behaves like both an electrode and a proof mass at the same time [80]. Further
improvement is reported by Seidel et al. 1990 [81] where the sensing element consists of
a differential capacitance which is formed by a full wafer thick bulk-micromachined
silicon proof-mass and two counter electrodes situated on anodically bonded glass wafers
at a distance of 5 µm from the moving mass as shown in Figure 2.15. The proof-mass is
suspended by at least eight cantilever beams placed on both sides of the proof-mass. The
device shows 1pF/g capacitance sensitivity over a rest capacitance of 10 pF with a
measurement range of ±5 g and a minimum resolvable acceleration of 1 milli-g.
Suspensions
Fixed Electrodes
Silicon Proof-mass
Figure 2.15: A cross-section view of the device reported by Seidel et al. 1990 [81].
In the same year, i.e., in 1990, Rudolf [82] published one more work on an out-ofplane accelerometer for micro-gravity measurement in spacecraft. This work is based on a
glass-silicon sandwich structure integrated with a capacitance-sensing CMOS integrated
47
Chapter 2
circuit. The voltage sensitivity of the device was reported as 5 V/g with a working range
of ±0.1 g. The measured resolution of the device was 1 µg at 1 Hz with a cross-axis
sensitivity of 0.4% and a bandwidth of 100 Hz.
Later in 1995, Lu et al. [83] reported a polysilicon-based surface micromachined
out-of-plane accelerometer that was monolithically integrated to the capacitance detection
circuitry realized using 3 μm BiCMOS technology. Being a surface micromachined
accelerometer, the mass of the proof-mass is only 0.5 micro-grams and the spring
constant is 1.1 N/m. An image of the reported device is shown in Figure 2.16. A forcefeedback control was used to achieve a resolution of 1.6 milli-g
Hz with a minimum
resolvable acceleration of 11.3 milli-g for a 50 Hz bandwidth. The problems associated
with this type surface of micromachined devices are: (i) high possibility of stiction
because of the 1 µm gap between the moving mass and the stationary electrode, (ii) low
stiffness leading to low pull-in voltage and sagging of the mass, (iii) a small gap leads to
large squeeze-film damping and an increased value of thermal noise affecting the
resolution of the device.
Figure 2.16: An image of the reported surface micromachined Z-axis accelerometer by
Lu et al. [83].
In 1995, to avoid the problems of surface micromachined out-of-plane
accelerometers the first SOI capacitive accelerometer which had a swastika-shaped spring
structure and a 10 μm thick structural layer, which was able to detect accelerations in the
z-direction, was reported by Y. Matsumoto et al. [84]. In 1997, Van DrieEnhuizen et al.
[85] fabricated an accelerometer with silicon fusion bonding and a Deep Reactive Ion
48
Chapter 2
Etching (DRIE) process. DRIE allows thick device layers (200 μm) to be defined with a
high aspect ratio of the order of 25:1, resulting in high sensitivity and low cross-axis
sensitivity. The bandwidth of the reported device is 1 kHz with the voltage sensitivity
being 700 mV/g. In the same year, Yazdi and Najafi presented a novel all-silicon singlewafer fabrication technology that uses both surface and bulk micromachining processes
for developing high precision capacitive accelerometers [86], [87]. This type of hybrid
approach was followed to achieve a large proof-mass, small damping and a small airgap
for a large change in capacitance. The bulk-microfabrication part of the process provides
a large proof-mass by using the whole wafer thickness, whereas the surface
micromaching part provides a large sense capacitance by utilizing a thin sacrificial layer.
The sense electrodes are formed by depositing a 2 μm thick polysilicon film with
embedded 25-35 μm thick vertical stiffeners over the thin sacrificial layer. Perforations
were provided on the polysilicon electrodes by pattering holes on the polysilicon
electrode. The sensitivity of the devices with 2 mm × 1 mm proofmass were reported to
be 2 pF/g, whereas the sensitivity of the devices with 4 mm × 1 mm proof-mass were 19.4
pF/g. The calculated noise floor of the two devices in the atmosphere was reported as
0.23 µg/√Hz and 0.16 µg/√Hz respectively. The mechanical design of the device is given
in Figure 2.17(a-c) and the fabricated prototype is shown in Figure 2.17d.
Yazdi et al. [88] reported that sub-μg resolution can be obtained without vacuum
packaging. For this purpose, they proposed a new z-axis accelerometer design with a
fixed electrode, a movable electrode and proof mass. A very high sensitivity of 100 pF/g
was achieved by using a thick silicon proof mass and a narrow uniform air gap of 1.4 µm
over a large area of 2.6 mm × 1 mm. The mechanical noise floor was reduced by
incorporating damping holes in the electrodes. The mechanical noise of the device was
reported as 0.18 μg/√Hz.
In Xie and Fedder [89], a z-axis accelerometer is reported. It utilizes the sidewall
capacitance change of the multi-conductor comb fingers type of capacitive sensing
architecture. The fabrication of the designed device has a fully differential capacitance
bridge interface and is CMOS-compatible. The measured resonant frequency of the
fabricated device was found to be 9.3 kHz. The device sensitivity was reported as 0.5
mV/g with a dynamic range of ±27 g and a noise floor of 6 mg/√Hz.
49
Chapter 2
(a)
(b)
(c)
(d)
Figure 2.17: (a-c) Isometric, top and side view of the z-axis accelerometer design by
Yazdi and Najafi [86] and (d) the SEM image of the fabricated device Yazdi et al. [87]
One more paper by Tsuchiya and Funabashi [90] also uses comb fingers to sense
Z-axis acceleration differentially. It is an SOI based capacitive accelerometer that is
fabricated using a newly proposed two layer masking process that realizes vertical comb
electrodes of different movable and fixed heights. Figure 2.18 shows the fabrication
technique to realize a z-axis SOI accelerometer with vertical comb electrodes. The proofmass size was 1.1 mm × 1.1 mm × 15 µm. Although the process is novel, the device
suffers from a relatively poor sensitivity of 1.1 fF/g compared to conventional z-axis
accelerometers that use top and bottom electrodes.
50
Chapter 2
Figure 2.18: The fabrication process flow of the z-axis accelerometer with vertical combs
by Tsuchiya and Funabashi 2004 [90].
Another z-axis capacitive Silicon-on-Glass (SOG) accelerometer has also been
reported by Weiping et al. [91] which is fabricated by anisotropic bulk micromachining of
silicon wafers. The top and bottom electrodes are realized by coating Cr/Au on glass
wafers bonded to the silicon proof mass. Figure 2.19 shows a cross-sectional view of the
design.
Hsu et al. [92] presented a novel z-axis accelerometer on an SOI wafer with gapclosing differential sensing electrodes. The reported Z-axis accelerometer has four
advantages: (1) the proof-mass is increased by combining both structural and substrate
silicon layers of the SOI wafer, (2) improved sensitivity is achieved by the gap-closing
differential electrodes design, (3) the electrical interconnection between the device and
handle silicon layers of the SOI wafer is done using metal vias, and (4) the sensing gap
51
Chapter 2
thickness is precisely defined by the buried-oxide layer of the SOI wafer which is 2 µm.
The accelerometer was fabricated using a process shown in Figure 2.20a. Figure 2.20b
shows the fabricated z-axis accelerometer. The fabricated device was integrated with a
universal capacitance extraction ASIC, namely, MS3110. The device was reported to
have a voltage sensitivity of 196.3 mV/g with a capacitance sensitivity of 42.5 fF/g. The
cross-axis sensitivity of the device was measured to be 1.96% and the noise floor was
0.76 milli-g/√Hz.
Glass
Suspension
Silicon
Proof-mass
Fixed
electrodes
Glass
Figure 2.19: The cross-sectional view of the design of the z-axis accelerometer using
SOG structure by Weiping et al. [91].
It is evident from the above literature review on out-of-plane accelerometers or zaxis accelerometers that two different approaches were followed to develop z-axis
accelerometers: (1) a suspended proof-mass electrode sandwiched between two static
electrodes placed at the top and bottom of the proof-mass at a very small distance of the
order of a few microns, (2) capacitive comb fingers that are attached to the proof-mass
move vertically along with the proof-mass. A change in the overlap area between
dynamic and static comb fingers gives rise to a change in capacitance which is the
measure of the applied acceleration. The first approach is more popular in both surface
and bulk-micromachined processes.
Surface micromachined z-axis accelerometers are not as sensitive as bulkmicromachined ones due to the obvious reason of the use of the entire wafer thick proofmass in bulk micromachined devices, whereas the proof-mass in surface micromachined
devices is very thin. The other reason for high sensitivity in case of bulk-micromachined
z-axis accelerometers is the availability of a wide electrode overlap area that is of the
same size as the proof-mass surface area. But, in the case of in-plane capacitive
52
Chapter 2
accelerometers,
designing
a highly
sensitive
micromachined accelerometer
is
comparatively more challenging than achieving a large overlap area with a very small
sense gap since this requires high-aspect ratio structures which, in turn, increase the
complexity of the fabrication process. In the next section, we will present a
comprehensive review on in-plane accelerometers and show how different researchers
have solved this problem.
(a)
Figure 2.20: (a) The fabrication process steps used to realize the z-axis accelerometer
with gap-closing differential sensing electrodes by Hsu et al. [92] (contd.).
53
Chapter 2
(b)
Figure 2.20: (a) The fabrication process steps used to realize the z-axis accelerometer
with gap-closing differential sensing electrodes by Hsu et al. [92], (b) the image of the
fabricated device.
2.5.2 In-plane capacitive microaccelerometers
As the name suggests, in-plane accelerometers are made to sense accelerations that are
parallel to a horizontal plane. Thus, this type of accelerometer contains proof-masses that
move parallel to that plane. Almost all in-plane capacitive type accelerometers use a set
of capacitive comb fingers to sense the displacement of their proof-masses. To date
research on capacitive in-plane accelerometers has mostly focused on: (i) design of the
proof-mass and the suspension, (ii) techniques to increase the thickness of the proof-mass,
(iii) methods to reduce the sense-gap between the static and moving combs, (iv) damping
issues related to the in-plane movement of the proof-mass and (v) improving the key
specifications of the accelerometers.
Research on in-plane micromachined accelerometers also started with the
invention of surface micromachining processes that were derived from popular CMOS
fabrication processes. CMOS integrated surface micromachined processes started gaining
importance over hybrid accelerometers because they were amenable to the monolithic
integration of micromachined devices and the sensing electronics on the same chip. The
advantages of monolithic integration are smaller die size, higher sensitivity, good
capacitance resolution, low parasitic capacitance and low power requirement. However,
inertial-grade accelerometers could not be fabricated using surface micromachining
technology because of their poor sensitivity due to the small size of the proof-mass.
Furthermore, these devices are prone to pull-in because of low stiffness suspensions and
54
Chapter 2
gaps, which reduce the sense voltage that can be applied for sensing. But these
accelerometers are best suited for batch-fabrication and, thus, still dominate the
commercial market for automobile and consumer electronics industries.
One of the earliest surface micromachined in-plane capacitive accelerometers
(ADXL 50) was developed by Analog Devices Inc. and reported in Sherman et al. [93]
and Kuehnel and Sherman [94]. This is a polysilicon-based lateral capacitive
accelerometer that is monolithically integrated to the capacitance detection circuitry on
the same chip. The polysilicon proof-mass contains differential interdigitated fingers that
changes capacitance when the proof-mass moves laterally in the plane of the
accelerometer surface as shown in Figure 2.21a. The sensor has an in-built force-balance
mode that controls the displacement of the proof-mass and thus reduces noise and
distortion. The overall sensitivity of the device was reported as 20 mV/g with a dynamic
range of ± 50 g that makes the sensor suitable for the automobile industry. An SEM
image of the fabricated ADXL 50 is shown in Figure 2.21b.
Later in 1995, Chau et al. [95] reported a more sensitive surface micromachined
in-plane accelerometer with a modified suspension structure using a folded beam
suspension. This was also a monolithic accelerometer integrated with bipolar MOS
interface circuitry. This accelerometer was made for low-g applications with a dynamic
range of ±5 g. The noise floor of the sensor was reported as 0.6 milli-g/√Hz with a
voltage sensitivity of 200 mV/g and a bandwidth from DC to 4 kHz. Another lateral
surface micromachined accelerometer with a fully differential capacitive interface was
presented by Lemkin et al. 1996 that has an on-chip A/D converter and electronics to
minimize the systematic offset and errors due to switch charge injection. The measured
noise floor of the device was 500 µg/√Hz, with a fullscale range of ±3.5 g.
Ha et al. [97] reported a surface micromachined accelerometer with variations in
the overlap area of its interdigitated combs along with separate force-rebalancing
electrodes. The grid-type proof-mass was made of a 7 μm thick polysilicon layer
supported by four thin beams and suspended above a silicon substrate at an air gap of 1.5
μm. In this structure, sense electrodes are placed beneath the moving mass and the
acceleration is detected by the change in overlap area of the electrodes. The noise floor of
this accelerometer is measured as 274 μg/√Hz with a voltage sensitivity of 95 mV/g and a
bandwidth of 1 kHz.
55
Chapter 2
Anchors
C+
Suspensions
Polysilicon
proof-mass
CStatic
combs
Moving
combs
(a)
(b)
Figure 2.21: (a) ADXL 50, a surface micromachined lateral accelerometer architecture
[94], (b) An SEM image of the ADXL 50. (Courtesy: www.analog.com)
Zhang et al. [98] reported a monolithic lateral capacitive accelerometer designed
and manufactured in a conventional CMOS process. The aim of this paper was to solve
the inherent out-of-plane curling problem of the released polysilicon layer post CMOS
processing. Here, the curling of the composite structural layers is compensated to first
order through a curl matching technique. The fabricated accelerometer has a measured
sensitivity of 1.2 mV/g and with a noise floor of 0.5 milli-g/√Hz.
In the year 2002, Jiang et al. [99] presented an integrated surface micromachined
lateral capacitive accelerometer where the noise floor was 2 µg/√Hz in vacuum, which is
comparable to the noise performance of bulk-micromachined accelerometers. The
accelerometer was fabricated using an integrated MEMS (iMEMS) technology with a 6
μm-thick structural polysilicon layer and 0.8 μm transistor feature size for CMOS
electronics. Figure 2.22 shows the die photo of the fabricated device. The complete size
56
Chapter 2
of the die is 3.5 mm × 3.5 mm in which 1.1 mm × 1.1 mm was used as the mechanical
structure area. The proof-mass is very small in size, 920 μm × 880 μm, and weighs 3.6
μgram. Differential sensing combs were used to sense the change in capacitance. In the
same year, Luo et al. [100] published another paper on lateral post-CMOS
micromachined accelerometers. The sensor showed a dynamic range of ±13g with a 1
milli-g/√Hz noise floor.
It can be concluded from the previous examples that surface micromachined inplane accelerometers cannot exhibit high sensitivity and high resolution even though low
gaps and sufficiently flexible suspensions are made using surface micromachining
processes. This is because the small proof-mass decreases the overall sensitivity and
increases noise. Although vacuum packaging substantially reduces the mechanical
thermal noise of surface micromachined accelerometers and lowers the output noise floor,
it is desirable to operate accelerometers in an atmosphere rather than operating them in a
vacuum as vacuum packaging increases the complexity and manufacturing cost by a
couple of folds.
Mechanical sensor element
Figure 2.22: An iMEMS in-plane accelerometer with very low noise floor reported by
Jiang et al [99].
Researchers, therefore, began looking into bulk micromachining technology that
could provide high aspect ratio structures, larger proof-masses, and large capacitance
areas. Thick suspensions, however, become very stiff. Furthermore, the fabrication of
57
Chapter 2
very small sense-gaps becomes very challenging. Then, the gradual evolution of
accelerometers towards high resolution and sensitivity lead to a combination of the
advantages of surface and bulk micromachining processes where huge proof-masses were
obtained by bulk micromachining while small gaps and suspensions were realized by
surface micromachining. Therefore, we present a brief review on bulk-micromachined inplane capacitive accelerometers that are most relevant to this thesis.
In order to increase the proof-mass size above what is typically achievable using
surface micromachining, Silicon-On-Insulator (SOI) or wafer-bonded accelerometers
utilizing Deep Reactive Ion Etching (DRIE) technology have been developed [101][104]. These accelerometers utilize a 25-120 μm thick single-crystal silicon proof-mass to
reduce overall system noise. The in-plane accelerometers reported by Ishihara et al. [101]
and Lemkin et al. [103] are based on the SOI-MEMS technique where the SOI wafers are
patterned using DRIE to achieve the thick proof-mass and associated capacitive combs.
The weight of the proof-mass in those accelerometers were in the range of 80 ~ 100 mg.
The measured capacitance sensitivity was around 50 ~ 100 fF/g with a noise floor of 25
µg/√Hz. Figure 2.23 shows a schematic view of the SOG in-plane accelerometer structure
reported by Chae et al. [104]. The accelerometer has a 120 μm thick proof-mass
suspended over a glass substrate. This structure is simple and utilizes the well known
lateral combs for sensing and force feedback, but has a very large proof-mass and sense
capacitance because of the substantial thickness of the device structure and the small
sensing gap realized by DRIE. The process requires 3 masks with 5 process steps. The
fabricated device exhibits a static capacitance sensitivity of 0.7 pF/g.
In 2004, Chae et al. [13] reported a high-sensitive, low-noise in-plane silicon
accelerometer with CMOS readout circuitry. This accelerometer uses both surface and
bulk-micromachining techniques for fabrication. It contains a 500 µm-thick, 2.4 mm × 1
mm proof-mass that is fabricated with an isotropic bulk-micromachining process while
the high aspect ratio vertical polysilicon sensing electrodes were formed using a trench
refill process. The thick proof-mass is suspended with polysilicon spring structures of 2.5
µm thick. The electrodes are separated from the proof-mass by a gap of 1.1 µm formed by
etching the sacrificial silicon dioxide layer. Figure 2.24 shows the top view and the crosssectional view of the proposed in-plane accelerometer. The measured noise floor of the
mechanical device was 0.7 µg/√Hz with a capacitance sensitivity of 5.6 pF/g. The
fabricated accelerometer was hybrid-assembled along with a CMOS Σ-Δ switched
58
Chapter 2
capacitor circuit. The voltage sensitivity of the packaged sensor is 0.49 V/g with a total
noise floor of 1.6 µg/√Hz.
Figure 2.23: A schematic view of the SOG in-plane accelerometer reported by Chae et al.
2002 [104].
Figure 2.24: The top view and the cross sectional view of the in-plane accelerometer
reported by Chae et al. 2004 [13].
On successful development of the DRIE technique, SOI wafers, with thick
structural layers have started gaining a lot of attention from various researchers for
developing accelerometers with thick proof-masses and sense-electrodes with vertical
sidewalls. Amini and Ayazi [106] presented the first SOI-based capacitive accelerometer
with 40 μm structural thickness that was fabricated with a simple backside dry release
process. A 2.5 V 14-bit fully differential ΣΔ interface circuit was fabricated at the National
Semiconductors Corporation with a 0.25 μm process and was able to operate at 1MHz clock
frequency. The capacitance sensitivity of the device was found to be 0.2 pF/g with a
59
Chapter 2
Brownian noise floor of 1 µg/√Hz. The fabricated accelerometer was wire-bonded to the
interface IC which shows a voltage sensitivity of 0.5 V/g with a resolution of 110 µg at 75
Hz.
Figure 2.25: The SOI-based single axis in-plane accelerometer with CMOS IC placed on
a thick SOI wafer (Amini and Ayazi 2004) [106].
The same group developed and reported a similar kind of SOI-based in-plane
accelerometer with a thicker structural layer of 50 µm, in 2005 [15]. The proof-mass size
was 4 mm × 3 mm with a total sensor size of 5 mm × 5mm. The silicon under the proofmass was removed from the backside of the wafer by etching the handle silicon layer all
the way to the buried silicon dioxide in an inductively coupled plasma (ICP) system using
the Bosch process. The buried oxide was removed using a dry reactive ion etching (RIE)
technique. Then the wafer was flipped and the accelerometer structure was patterned and
etched on the 50 µm thick structural layer using a DRIE process. The process is
stictionless, simple and needs only two masks. The process flow for developing this
accelerometer is shown in Figure 2.26. Due to the use of a thicker structural layer, the
capacitance sensitivity of the accelerometer was found to be 0.3 pF/g. This accelerometer
was also packaged with a capacitance detection interface circuit fabricated using a 0.25
µm N-well CMOS process. The reported resolution of the accelerometer system was 11
µg/√Hz at 2 Hz with a voltage sensitivity of 0.75 V/g.
Later in 2006, an in-plane high-sensitive microgravity capacitive high aspect ratio
polysilicon and single crystal silicon (HARPSS) accelerometer was reported by
Monajemi and Ayazi [17]. The HARPSS process was initially proposed by Ayazi and
Najafi 2000 [107] and is also a mixed mode (surface + bulk) micromachining process.
This process can create structures with very high aspect ratio of the order of 200:1
60
Chapter 2
compared to the DRIE process where the aspect ratio is limited to 30:1. Vertical
corrugation in silicon electrodes was proposed in this paper to reduce the mechanical
noise of the sensor. The accelerometer has a 60 µm thick perforated proof-mass
suspended by four single crystal silicon tethers. Figure 2.27 shows the fabricated
HARPSS single-axis lateral accelerometer. The static sensitivity of the fabricated sensor
was found to be 4.5 pF/g with a voltage sensitivity of 0.25 V/g. The total noise of the
sensor measured 0.95 µg/√Hz.
50 µm thick structural layer
Oxide
Substrate Layer
Backside DRIE
Dry etch of buried oxide
DRIE from the top
Figure 2.26: The process flow for the SOI-based micro-gravity accelerometer [15].
The most sensitive SOI-based accelerometer reported to date was developed by
Abdolvand et al. [19]. This ultrasensitive sub-micro-gravity accelerometer uses the entire
thickness of the structural layer and the substrate layer of a thick SOI wafer for its proofmass. High aspect ratio sense-gaps were realized by depositing an extra layer of
polysilicon on the sidewalls of the trenches fabricated by a normal DRIE process. It is
shown that, using this process an aspect ratio of 40:1 can be achieved without using
mixed mode micromachining technique. This accelerometer uses an SOI wafer with a 100
µm thick structural silicon layer with a 400 µm thick handle layer. The design of the
device was patterned first by etching the structural layer of the SOI wafer using front side
61
Chapter 2
DRIE. Thus, the sense-combs become 100 µm thick. Later, the handle layer is also
patterned to realize the 400 µm thick proof-mass. Thus, the proof-mass becomes 500 µm
(100 µm + 400 µm) thick. A schematic diagram of the accelerometer is shown in Figure
2.28a while two SEM images of the fabricated device are shown in Figure 2.28 (b-c). The
fabricated device was mounted on a custom printed circuit board (PCB) where the
capacitance extraction interface IC was also mounted. The interface IC was fabricated in
an AMI 06 process. The interface circuit is a switched capacitor charge amplifier coupled
with a correlated double sampling technique. The measured noise floor of the
accelerometer integrated with the interface circuit was reported as 213 ng/√Hz. The
capacitive sensitivity of the accelerometer is 35 pF/g with a voltage sensitivity of 105
mV/milli-g. The device is so sensitive that the interface IC saturates only at ±20 milli-g
which is equivalent to less than 2o of rotation.
Figure 2.27: The SEM images of the fabricated HARPSS accelerometer [17].
In the same year, 2007, Liu et al. [108] reported a high-sensitive capacitive biaxial
microaccelerometer using a highly symmetrical microstructure with a single proof-mass
and four folded beams suspensions as shown in Figure 2.29. The measured sensitivity
was about 458.15 fF/g for both the axes. A silicon-on-glass fabrication process was used
for realizing the device.
2.5.3 Tri-axial accelerometers
Tri-axial capacitive accelerometers are developed to sense accelerations along all the
three X, Y and Z axes at a time using a capacitive transduction technique. Two different
techniques are generally followed to design tri-axial accelerometers: (i) using a single
proof-mass, (ii) three single-axis accelerometers hybrid-mounted on the faces of a cube.
In the first technique, the suspension of the proof-mass is designed in such a way such
62
Chapter 2
that the proof-mass is able to move in all three directions with very low cross-axis
displacement. As this type of accelerometer has only one sensing element, the device
dimensions are smaller.
(a)
(b)
(c)
Figure 2.28: The schematic of the sub-micro-gravity accelerometer with a very thick proofmass by Abdolvand et al. [19].
63
Chapter 2
Here, in-plane acceleration is detected by a change in capacitance in the comb
drives attached to the proof-mass whereas out-of-plane acceleration is detected by placing
electrodes at the top and bottom of the proof-mass. On the other hand, the second
technique uses three single-axis accelerometers mounted orthogonally to each other along
the three axes inside a package. Thus, the dimension of this type of accelerometer
becomes larger compared to the first type. Tri-axial accelerometers reported to date use
either surface micromachining or bulk micromachining or mixed mode micromachining
processes.
(a)
(b)
Figure 2.29: (a) The top view and (b) the isometric view of the biaxial SOG
accelerometer reported by Liu et al. [108].
In the late 1990s, a few integrated single-chip three-axis capacitive
microaccelerometers were reported [109]-[111]. In Mineta et al. [110], a tri-axial
capacitive accelerometer which has uniform sensitivities in all the three axes was
developed. The sensor contains a glass-silicon-glass structure with a thick proof-mass
fabricated using wet etching and a bulk-micromachining technique. Due to their thick
suspension beams, and low-performance readout circuit, their sensitivity, at its best, was
reported as 40 mV/g with a very high cross-axis sensitivity of the order of 10%. One of
the earliest surface micromachined monolithic tri-axial accelerometers using a single
proof-mass and with an integrated CMOS interface circuit was reported by Lemkin and
Boser [111]. The design of the accelerometer is such that it has equal compliance along
all the three axes. In-plane acceleration is detected by the comb fingers attached to the 2.3
µm thick proof-mass, whereas out-of-plane acceleration is detected by the electrode
placed below the proof-masses. Due to the use of smaller and lighter proof-mass, the
sensitivities along the three directions are not that good and were reported as 0.24 fF/g for
64
Chapter 2
the X and Y axis and 0.82 fF/g along the Z axis with a measured noise floor of 0.7 millig/√Hz for all the axes. Later, another similar type of tri-axial accelerometer with an
improved CMOS interface circuit was reported by Lemkin and Boser [112]. The sensor
die consists of three different sensing elements for the X, Y and Z axes as shown in
Figure 2.30. Due to the use of a small proof-mass the best achieved noise floor was
reported as 110 µg/√Hz. Bütefisch et al. [113] proposed a new three-axes monolithic low-g
accelerometer fabricated using a single step anisotropic wet chemical etching in KOH
using (111) planes as a physical etch stop. Another paper by Li et al [114] uses
anisotropic KOH etching and anodic bonding to realize a highly symmetrical capacitive
tri-axial accelerometer. The measured sensitivities for the X, Y and Z axes are 30 mV/g,
30 mV/g and 37 mV/g, respectively. Takao et al. 2001 [115] integrated a sub-micron
CMOS interface circuit along with the anisotropic bulk-micromachined sensing element
to develop a tri-axial capacitive accelerometer.
Figure 2.30: The tri-axial accelerometer die containing three different sensing element
for the three axes reported by Lemkin and Boser 1999 [112].
In 2005, Chae et al. [116] published a monolithic three axes micro-g
micromachined silicon capacitive micro accelerometer. They combined the previously
fabricated lateral and z-axis accelerometers using a mixed mode (surface + bulk)
micromachining process [87], [105] in order to achieve a three axes micro-accelerometer
structure. Figure 2.31 shows the hybrid-integrated three axes monolithic accelerometer
65
Chapter 2
structure. The reported noise floors for lateral accelerometers were 1.6 μg/√Hz and for the
vertical accelerometer were 1.08 μg/√Hz with a dynamic ±1g measurement range.
(a)
(b)
Figure 2.31: (a) The SEM image of the tri-axial accelerometer developed by Chea et al
[116] using both surface and bulk-micromachining processes, (b) The packaged tri-axial
accelerometer by Chae et al. [116] along with the Σ-∆ switched capacitor circuit inside a
dual-in-line (DIP) package.
Sun et al. [117] reported a novel single proof mass tri-axis capacitive CMOS
MEMS accelerometer to reduce the die size of the three axes sensor. In this study, a
serpentine spring is designed to reduce the cross axis sensitivity of the z-axis
accelerometer. The sensitivities and nonlinearity (indicated in parentheses) of each
direction were reported as 0.53 mV/g (2.64%) of the X-axis, 0.28 mV/g (3.15%) of the Yaxis, and 0.2 mV/g (3.36%) of the Z-axis. The cross-axis sensitivities were reported
between 1% to 8.3% and the measured noise floor was 120 milli-g/√Hz for the X-axis,
271 milli-g/√Hz for the Y-axis and 357 milli-g/√Hz for the Z-axis. Hsu et al. [118]
66
Chapter 2
reported a compact accelerometer, which integrates three spring-proof mass systems into
a single structure to sense tri-axial motion shown in Figure 2.32. Silicon-on-glass (SOG)
micromachining and deep reactive-ion etching (DRIE)-based processes were adopted to
fabricate this accelerometer with a high-aspect-ratio sensing structure. The voltage
sensitivities of the accelerometer are 1.434 V/g for the Z-axis and a high resolution of 49
µg/√Hz. The sensitivity and cross-axis sensitivity along the X-axis are 1.442 V/g and
0.03% and those of the Y-axis are 1.241 V/g and 0.21%, respectively.
Figure 2.32: Schematic of the capacitive low-g tri-axis accelerometer reported by Hsu et al.
[118].
2.5.4 Micromachined accelerometers with mechanical amplifiers
The use of compliant mechanical levers in a micromachined accelerometer was reported
by Su and Yang [31] where a two stage microleverage mechanism was optimized and
used in a resonant micro-accelerometer for force amplification. The force amplifier
amplifies the inertial force felt by the proof-mass and transfers it to a micro-bridge or a
tuning fork, coupled to the proof-mass that senses the change in force by the change in its
resonant frequency. By stacking two stages of microleverage mechanisms, a higher force
amplification was obtained. It is found that the compliance of both the stages needs to be
distributed appropriately in order to achieve the desired amplification in both of them.
Later in 2004, Pedersen and Seshia [30] presented a paper on the optimization of a
compliant force amplifier mechanism in a surface micromachined resonant accelerometer.
As the noise floor and sensitivity of a device are dependent on the gain of the force
67
Chapter 2
amplifier mechanism, optimization of the force amplifier mechanism is necessary. The
manufacturing process and the device geometry were used as the constraints for the
topology optimization of the force amplifier mechanism. A single-stage force
amplification factor greater than 100 was reported from the results of the optimization
process.
In 2005, Su et al. [44] fabricated and tested a resonant accelerometer with a twostage microleverage mechanism using a SOI-MEMS process. The compliant
microleverage mechanism amplifies the force on the double-ended tuning fork that acts as
the inertial force sensor for the resonant accelerometers. The structural layer is 50 µm
thick and is fabricated using a DRIE process. The two-stage microleverage mechanisms
which have an amplification factor of 80 were designed for force amplification to
increase the overall sensitivity to 158 Hz/g. Trans-resistance amplifiers are designed and
integrated on the same chip for output signal processing. The schematic of the resonant
accelerometer with a two-stage microleverage mechanism is shown in Figure 2.33.
Figure 2.33: The schematic of a resonant micromachined accelerometer with a two-stage
microleverage mechanism developed by Su et al. [44].
68
Chapter 2
In 2008, Krishnan and Anathasuresh [43] proposed the use of Displacementamplifying compliant mechanisms (DaCMs) for sensor applications. The objective of the
paper was to design compliant amplifying mechanisms that could be incorporated to
enhance the sensitivity of micromachined capacitive in-plane accelerometers. A lumped
spring-mass-lever (SML) model that captures both the static and dynamic effects of
appending a DaCM to a sensor was introduced. A few new DaCM topologies were
developed in this paper using topology optimization, size, and shape optimization.
In 2010, Ya’akobovitz and Krylov [120] reported a new design of an out-of-plane
micromachined capacitive accelerometer that incorporates a mechanical amplifier that
transforms a linear out-of-plane motion of its proof-mass into an amplified angular
motion. The accelerometer with the mechanical amplifier was fabricated using an SOI
wafer with a 35 µm device layer thickness. The proof-mass is as big as 2025 µm × 2025
µm with the sensing element the size of 1000 µm × 1000 µm. The measured resonance
frequency of the sensing plate is 2.92 kHz whereas that of the proof-mass is 12.94 kHz.
The measured displacement amplification factor is 8.8. The SEM image of the fabricated
device is shown in Figure 2.34.
Figure 2.34: The SEM image of the fabricated out-of-plane accelerometer with a
displacement amplifier that transforms and amplifies the out-of-plane linear motion to
angular motion [120].
The latest publication on the application of displacement amplification in
capacitive micromachined accelerometers is by Zeimpekis et al. 2012 [20], where a
mechanical amplifier is used to improve the sensitivity of a lateral capacitive
micromachined accelerometer. This paper uses a conventional mechanical lever for the
amplification of displacement of the proof-mass. An in-plane single-axis accelerometer
69
Chapter 2
was designed with an amplification factor of 40 whereas the measured amplification of
the fabricated device was 38.8. The detailed analysis for this device is given in Section
1.1.3. It is clearly noticeable that even after an amplification of nearly 40 times, the
displacement sensitivity of the accelerometer is very small, and is only 0.16 µm/g. Due to
the use of a large circuit gain of 22 V/pF, the output voltage sensitivity of that device
becomes 2.39 V/g with an output noise floor of 50 µg/√Hz. The schematic of the
accelerometer design is shown in Figure 2.35.
Figure 2.35: The schematic of an in-plane capacitive accelerometer with a mechanical
lever for displacement amplification developed by Zeimpekis et al. 2012 [20].
2.6 Closure
In this chapter, a brief overview of micromachined accelerometers is provided. The
principle of operation of accelerometers along with different types of accelerometers is
discussed. Also discussed are the key specifications that define the performance of an
accelerometer. The noise present at the output signal of an accelerometer is because of
different types of noise that affect different parts of an accelerometer sensor. Brownian
noise affects the micromechanical structures of an accelerometer while electronic noises
affect the associated signal conditioning electronics. Furthermore, some unwanted
external interferences from the external world also corrupt the output of an accelerometer.
A brief introduction to compliant mechanisms, especially Displacementamplifying Compliant Mechanism (DaCM), is given. Different design methodologies for
the systematic design of compliant mechanisms are discussed briefly. A comprehensive
review on the DaCMs available in the literature is discussed along with their applications.
A lumped spring-lever (SL) model and a spring-mass-lever (SML) model of an
70
Chapter 2
accelerometer with a DaCM is described. It is found that the SML model is capable of
capturing the static and dynamic properties of an accelerometer with a DaCM. It is
mentioned that we do not design any new compliant mechanisms in this thesis to use
them in accelerometers. Instead, we make use of the database of compliant mechanisms
and redesign them using a stiffness map-based technique for this type of practical
application.
We also present here a brief review on capacitive micromachined accelerometers.
In-plane, out-of-plane and tri-axial accelerometers in the literature are discussed. All
these accelerometers use either a surface micromachining technique, a bulkmicromachining technique or a combination of both surface and bulk-micromachining
techniques for their fabrication. Surface micromachined accelerometers lack high
sensitivity as they use thin structural layers. They also have a high noise floor. But the
major advantage of surface micromachined accelerometers is that they are amenable to
on-chip CMOS integration. An integrated MEMS (iMEMS) process is a surface
micromachined process that is being successfully used for the fabrication of
accelerometers for automobile and consumer electronic industries. However, very highsensitive inertial grade accelerometers cannot be fabricated using surface micromachining
technique.
Later,
different
researchers
reported
accelerometers
using
bulk-
micromachining techniques and combined surface and bulk-micromachined techniques to
realize micro-gravity accelerometers. It is found that all these microfabrication techniques
for inertial grade accelerometers either require a complicated fabrication process along
with a low noise signal conditioning interface circuit. Thus, the aim of this thesis is to use
compliant mechanical amplifiers which can improve the sensitivity of the accelerometers
without complicating the process flow further. The use of mechanical levers is proposed
for resonant accelerometers as force amplifiers. Recently, mechanical levers were also
used for in-plane capacitive accelerometers. We showed that it is advantageous to use a
DaCM instead of a mechanical lever to improve the performance of in-plane
micromachined capacitive accelerometers.
In the next chapter, we perform two design case studies where we consider two
highly-sensitive accelerometers to show that their performance can be improved by
incorporating DaCMs along with the reported designs within the same footprint.
71
Chapter 3
Design case studies
Summary
This chapter presents two design case studies where it is shown that simultaneous
enhancement of sensitivity and bandwidth is possible if DaCMs are incorporated in the
designs of in-plane capacitive accelerometers. To do this, two in-plane accelerometers,
one with very high sensitivity and the other with moderately high sensitivity and a large
bandwidth, are chosen. These designs are modified by incorporating DaCMs while
keeping the footprint, out-of-plane thickness, and minimum feature size, the same. The
modified designs are simulated, and the performance parameters, such as displacement
sensitivity, natural frequency, and the figure of merit (FoM) are compared with those of
the original designs. It is proved that the incorporation of DaCMs is helpful in improving
the sensitivity without compromising on the bandwidth.
3.1 Introduction
The development of highly-sensitive and high-resolution capacitive micromachined
accelerometers with microfabrication constraints is a challenge faced by the researchers
in this field. As discussed in the previous chapter, high performance out-of-plane (z-axis)
accelerometers are comparatively easier to fabricate than in-plane (x-y axes)
accelerometers because the entire thickness of the wafer can be used to make larger
proof-masses and larger electrodes [13] for out-of-plane accelerometers. The
development of highly-sensitive and high-resolution in-plane accelerometers requires
high-aspect-ratio vertical electrodes with a very small sense-gap. This can be achieved by
depositing polysilicon in the sidewall of the etched sense-comb as reported in [19] or a
combined surface and a bulk micromachining process as reported in [13]. They both
require sophisticated and, hence, expensive microfabrication processes.
Here, two case studies are presented to show that improved performance can be
achieved by incorporating DaCMs with existing accelerometers. By performance, we
mean a static displacement sensitivity (i.e., the displacement of the sense-comb per unit
applied acceleration due to gravity) and the resonance frequency of the device. Static
72
Chapter 3
displacement sensitivity is directly proportional to static capacitance sensitivity, i.e., the
change in capacitance per unit acceleration due to gravity. The two case studies are
related to the accelerometers reported in [19] and [16]. The incorporation of a DaCM
does not require any extra microfabrication process steps. It can be fabricated along with
the other parts of the accelerometer. But, it consumes extra space in the silicon wafer
which is also an expensive factor in microfabrication processes. Hence, for a fair
comparison, the footprints of the modified designs were kept the same as those of the
reported ones. This means that the modified designs have smaller proof-masses than the
original ones.
3.2 Sub-micro-g micromachined capacitive in-plane accelerometers by
Abvolvand et al. [19]
3.2.1 Mechanical design
In the reported design of the single-axis in-plane capacitive accelerometer by Abdolvand
et al. [19], the overall size of the accelerometer is 7 mm × 7 mm with a top-side proofmass as big as 5 mm × 7 mm shown in Figure 3.1. The accelerometer was fabricated
using a silicon-on-insulator (SOI) wafer with a 100 µm thick structural silicon layer. By
backside Deep Reactive Ion Etching (DRIE) and Inductively Coupled Plasma (ICP) oxide
etch, a part of the 400 µm thick substrate layer that is beneath the top-side proof-mass
was used as an extra proof-mass. The size of this added proof-mass is 4.7 mm × 6.7 mm ×
400 µm. A pitch of 60 µm was used to accommodate 110 sense-combs on each side of the
accelerometer’s proof-mass. An initial sense-gap of 9 µm, between the dynamic comb
and the static comb, was narrowed down to 4 - 5 µm by adding an extra process step of
sidewall deposition of polysilicon. The detailed design specifications of the accelerometer
are given in the second column of Table 3.1.
3.2.2 Design analysis
A static finite element (FE) analysis using COMSOL Multiphysics [78] shows that the
static displacement sensitivity of the accelerometer is approximately 6.5 µm/g which
corresponds to a static capacitance sensitivity of more than 30 pF/g. The effect of
geometric nonlinearity was considered in all the FE simulations performed in this paper.
The first mode of vibration was found to be an in-plane motion with a frequency of 195
73
Chapter 3
Hz whereas the second mode is an out-of-plane mode at 1900 Hz, which is much higher
than the operational bandwidth of the device.
Suspension beam
Sense-comb
Proof-mass
Figure 3.1: The solid model of an accelerometer with a thick proof-mass developed by
[19].
The effective in-plane stiffness
 k s  of the accelerometer is reported as
approximately 58 N/m whereas the effective inertia  m s  of the accelerometer is given as
approximately 38 × 10-6 kg. The simulated first two modes of vibration of the
accelerometer are shown in Figure 3.2.
3.2.3 Figure of Merit (FoM) of capacitive micromachined accelerometers
In this section we introduce a Figure of Merit (FOM) for capacitive micromachined
accelerometers. The voltage sensitivity of capacitive micromachined accelerometers
solely depend on the displacement sensitivity which is the displacement
u 
of the
sensing combs per unit applied acceleration due to gravity i.e.  u g  . The FoM combines
static deflection of the sense-comb per unit g acceleration (u / g ) and the resonance
frequency ( f0 in Hz and 0 in rad/s). It is a non-dimensional number that is suitable for
comparing sensors of different sizes. The FoM can be expressed as
u
u
FoM    0 2  4 2   f 0 2
g
g
74
(43)
Chapter 3
Table 3.1 includes the FoM of the micromachined accelerometers from the
literature and the modified designs of these accelerometers. The calculated value of FoM
for the accelerometers in [19] is 10.3.
1st eigen frequency ~ 195 Hz
2nd eigen frequency ~ 1901 Hz
Figure 3.2: First two simulated modes of vibration of the accelerometer developed by
Abdolvand et al. 2007 [19].
3.3 Modification of Abdolvand et al. 2007 [19] using a DaCM
In comparison to the accelerometer reported in [19], we propose a modified design of an
accelerometer containing a DaCM and with an equal footprint area of 7 mm × 7 mm. The
modified design contains a smaller proof-mass of 3.9 mm × 5 mm, a properly selected
and re-designed DaCM, and a set of capacitive combs attached at the output port of the
DaCM. The thickness of the DaCM, combs and suspensions are considered to be 100 µm
as used in the design in [19]. The proof-mass in the modified design is smaller but the
thickness is considered to be 500 µm (i.e. 100 µm of structural layer + 400 µm thick
substrate layer of the SOI wafer) as it is in the original design.
75
Chapter 3
3.3.1 Design of the DaCM using the stifness map-based method
The selection and re-design of the DaCM used for this modified model is performed using
the stiffness map-based method discussed in section 2.4.4. For this, the lumped mass
 m s  and stiffness  k s  values of the input side of the modified accelerometer model are
simulated using FE analysis as 20.8 × 10-6 kg and 58 N/m respectively. The lumped mass
 mext  and stiffness  kext  values of the output side of the same model are also simulated
as 0.4 × 10-6 kg and 0.3261 N/m respectively. We used these values as input userspecifications to the method to arrive at the inequalities:
190μN  Fin  210 μN; 2 μm  uin  3μm
3 μN  Fout  4μN; 7 μm  uout  11μm
(44)
50 N/m  ks  70 N/m; 0.3 N/m  kext  0.4 N/m
These values are used to draw the feasible kco vs. kci map shown in Figure 3.3. It
can be observed that none of the mechanisms from the literature lie inside this feasible
map. Therefore, the first closest mechanism taken from [47] is chosen for re-designing.
The initial position of the DaCM with its current feature size is shown as a point on the
graph. By varying the dimensional parameters, such as in-plane beam width, thickness,
and size of the mechanism along the X and Y axes, a few parameter curves are drawn. It
is observed that a feasible design of the mechanism is possible by moving along the
parameter curves. The optimal design of the DaCM is attained as shown in Figure 3.4
with an in-plane beam width of 6.5 µm, thickness 100 µm and the size of the DaCM
along X and Y as 6.9 mm and 0.758 mm respectively. It can also be noted that the value
of n of the modified mechanism lies within its maximum and minimum values as shown
in Figure 3.4. The optimal design of the DaCM has the values of kci and kco as 31.06
N/m and 18.23 N/m respectively. The values of mci and mco for the mechanism are found
to be 0.124 ×10-6 kg and 0.1 × 10-8 kg, respectively using Eqs. (10) and (11) respectively.
3.3.2 Modified mechanical design
The isometric view of the modified accelerometer along with the re-designed DaCM is
shown in Figure 3.5a-b. The first in-plane modal frequency of the modified design can be
analytically estimated using Eq. (37) as 265 Hz whereas the static displacement
sensitivity of the model is calculated as 10.39 µm/g using Eq. (35). By using Eqs. (36)
76
Chapter 3
and (43), the value of NA and FoM are found to be approximately 1.62 and 30.3
respectively.
Table 3.1
Comparison between the existing accelerometers with the modified designs using DaCMs
Specifications
Proof-mass weight
In-plane effective
Accelerometer
Modified
Accelerometer
Modified
by Abdolvand et.
Design of [19]
by B. V. Amini
Design of [16]
al. 2007 [19]
using a DaCM
2005 [16]
using a DaCM
~ 38 mg
~ 20.8 mg
~ 1.6 mg
~ 1.07 mg
57.3 N m
59.1 N m
154.6 N m
320.6 N m
195 Hz
270 Hz
1556 Hz
1947 Hz
6.5 m g
10.51 m g
0.102 m g
0.127 m g
10.3
30.3
9.6
19.0
structural stiffness
First In-plane
modal frequency
Static displacement
sensitivity
Figure of Merit
(FoM)
3.3.3 Analysis of the modified design
A static FE analysis is also performed on the solid 3D model of the modified design of
the accelerometer. It shows that the static displacement sensitivity of the accelerometer is
10.51 µm/g with the first in-plane modal frequency at 267 Hz. The simulated value of NA
is found to be 1.6. This validates the effectiveness of the lumped SML model. The modal
responses of the modified design are shown in Figure 3.6.The analysis confirms that, by
design, we have achieved a sensitivity enhancement of 60% as compared to the reported
design in [19]. By design, an improvement of the resonance by approximately 34% is also
achieved. The detailed simulated performance specifications for the modified single-axis
accelerometer with a DaCM are given in the third column of Table 3.1.
77
Chapter 3
Initial position of the mechanism
with current features
In-plane width curve
Thickness curve
DaCM
used
Size-in-Y curve
Size-in-X curve
Feasible kco vs. k ci map
Figure 3.3: The graphical user interface (GUI) for the selection map based method
describing the re-design of an existing DaCM from [47] using parameter curves. The
initial position of the DaCM to be used with the current feature size is shown as a point
on the graph. The area enclosed by a green curve shows the feasible stiffness map for the
given specification. The parameter curves are drawn from the initial position of the
mechanism and show that the selected mechanism can be brought inside the feasible
stiffness map by varying the parameters e.g. in-plane beam width, thickness, size of the
mechanism along X and Y of the mechanism.
nmax = 6.05
nmin = 5.76
n = 6.04
Figure 3.4: Re-design of the DaCM by varying the parameters along the parameter
curves to achieve feasible kci , kco , and n values for the mechanism.
78
Chapter 3
(a)
Anchored
Sense-comb
Proof-mass
(b)
Figure 3.5: (a) The design of the DaCM used in the modified design of [19], and (b)
Solid model of the modified design of [19] with a smaller proof-mass, a stiffness matched
DaCM occupying an area of 7 mm × 7 mm.
3.4 A micro-g SOI capacitive in-plane accelerometer by B. V. Amini 2005
3.4.1 Mechanical design
The accelerometer reported in the PhD thesis of B. V. Amini [16] is a micro-gravity
single-axis capacitive accelerometer with an overall device size of 5 mm × 6 mm. The
device contains a proof-mass as large as 2 mm × 6 mm with 90 sensing electrodes along
each side of the accelerometer. A solid proof-mass without any perforation resulted in
more than a 25% increase in mass and improved mechanical noise performance. The
weight of the proof-mass was 1.7 mg as the device was fabricated using SOI wafers with
a structural layer thickness of 50 µm. The pitch between two sense-combs was kept as 60
µm with a sense-gap of 2.3 µm. The base capacitance of the sense-comb was 7.5 pF with
a static capacitance sensitivity of 0.8 pF/g and a voltage sensitivity of 0.8 V/g. The
corresponding static displacement sensitivity was simulated to be 0.102 µm/g. The first
natural frequency of the device was found to be around 1.6 kHz whereas the FoM is
79
Chapter 3
found to be 9.6. Figure 3.7a shows the detailed dimensions of the device. The first two
modes of vibration of the reported device are shown in Figure 3.7b.
1st eigen frequency ~ 267 Hz (in-plane)
1580 Hz
1980 Hz
2514 Hz
(out-of-plane)
2655 Hz
(out-of-plane)
Figure 3.6: First five modes of vibration of the modified version of a similar
accelerometer with a DaCM and with an equal footprint.
3.4.2 Design of a DaCM for the modified design
The same stiffness map-based method that is used to design the DaCM for the improved
version of [16] is used here. The specifications for the selection-based method are as
follows.
8μN  Fin  12μN; 30 nm  uin  40 nm
0.1μN  Fout  0.2μN; 0.125μm  uout  0.225μm
240 N/m  k s  260 N/m; 0.1N/m  kext  0.2 N/m
80
(45)
Chapter 3
The bounds were chosen as per the design of [16] and the anticipated enhancement
in the modified design. The feasible stiffness map was drawn and a suitable mechanism
was selected and interactively designed. The details are not presented for the sake of
brevity. The values of the re-designed DaCM are: k ci = 151.8 N/m, kco = 106.5 N/m, n =
-6.08, mci = 1.88311 × 10-8 kg, and mco = 1.61055 × 10-9 kg. Its static displacement
sensitivity is 0.127 µm/g, NA is 1.27, effective in-plane stiffness is 320.6 N/m and
effective mass is 1.07 mg, resonance frequency is 1947 Hz and FoM is 19.
(a)
1947 Hz
1556 Hz
(b)
Figure 3.7: (a) The design of the SOI accelerometer reported in [16], (b) The first two
modes of the accelerometer reported in [16].
81
Chapter 3
3.4.3 Modified mechanical design
The detailed design of the modified accelerometer and the re-designed DaCM are shown
in Figure 3.8a-b.
Sense-comb
DaCM
Proofmass
(a)
Anchored
(b)
Figure 3.8: (a) The modified design of [16] using a DaCM, and (b) The design of the
DaCM used in modified design of [16].
3.4.4 Analysis of the modified design
The first five simulated modes of the modified design are shown in Figure 3.9. As can be
seen in the fourth and fifth columns of Table 3.1, the sensitivity of [16] is enhanced from
82
Chapter 3
0.102 µm/g to 0.127 µm/g, by 25%. At the same time, the first resonance frequency, too,
went up from 1556 Hz to 1947 Hz, by 25%.
1947 Hz
2849 Hz
3527 Hz
3559 Hz
4430 Hz
Figure 3.9: The first five modes of vibration of the modified design of [16] using a
stiffness matched DaCM.
3.5 Conclusions
Based on the two case-studies and our general understanding of DaCMs, we claim that
the perfomance of any displacement-based sensors such as accelerometers could be
improved in terms of sensitivity and resonance frequency (and hence the bandwidth).by
designing and incorporating a properly designed DaCM within the same footprint area.
This also indicates that for a given microfabrication process, the sensitivity of any
capacitive accelerometers can be enhanced by using a DaCM instead of increasing the
size of the proof-mass. If either of these two performance characteristics is considered to
be more dominant than the other, one can expect to achieve significant enhancement of
83
Chapter 3
one without overly compromising on the other by using a DaCM as compared to without
it.
In addition to these two case studies that show the advantage of using DaCMs in
accelerometers, we also design a wide-band single-axis accelerometer and a low-g dualaxis in-plane capacitive accelerometer with two DaCMs. These designed devices,
presented in the forthcoming chapters, were fabricated, characterized, packaged and
tested to prove the functionality of DaCMs in micromachined accelerometers.
84
Chapter 4
Development of a single-axis capacitive inplane accelerometer with a DaCM
Summary
With the premise that a Displacement-amplifying Compliant Mechanism (DaCM) can be
used to enhance the sensitivity and natural frequency of the micromechanical component
of accelerometers, we present here the development of a single-axis wide-bandwidth
capacitive in-plane micromachined accelerometer with a DaCM. A (DaCM) is appended
to the usual sensing element comprising a proof-mass and a suspension. A differential
comb-drive arrangement is used for capacitive-sensing. The DaCM is designed to match
the stiffness of the suspension so that there is substantial net amplification. A springmass-lever model is used to estimate the lumped parameters of the system. The DaCMaided accelerometer and another without a DaCM—both occupying the same footprint—
are compared to show that the former gives enhanced sensitivity: 8.7 nm/g vs. 1.4 nm/g
displacement at the sensing-combs under static conditions. A prototype of the DaCMaided microacclerometer was fabricated using bulk-micromachining. It was tested at the
die-level and then packaged on a printed circuit board with an off-the-shelf integrated
chip for measuring changes in capacitance. Under dynamic conditions, the measured
amplification factor at the output of the DaCM was observed to be about 11 times larger
than the displacement of the proof-mass, thus validating the concept of enhancing the
sensitivity of microaccelerometers using mechanical amplifiers. The first in-plane natural
frequency of the fabricated accelerometer was found to be 6.25 kHz. The packaged
accelerometer with the DaCM was found to have 26.7 mV/g sensitivity at 40 Hz.
4.1 Design specifications
In this section, we discuss the target specifications of a wide-band single-axis capacitive
accelerometer with a DaCM that will be designed and developed. Being a capacitive type
accelerometer, it contains interdigitated sensing-combs. The design plan for the singleaxis accelerometer with a DaCM is as follows. A proof-mass with appropriate mass will
be chosen. A set of capacitive combs will be attached to the proof-mass so that they can
85
Chapter 4
be used to actuate the device electrostatically for self-testing, testing at the die-level, and
for feedback operations. That is, the combs attached to the proof-mass can also be used to
provide electrostatic force feedback if the device is operated in a closed-loop
configuration. A suitably designed DaCM will be incorporated in the design. The input
port or the input side of the DaCM will be attached to the proof-mass whereas the output
side will be used for sensing. Another set of sense-combs will be attached to the output
end of the DaCM. An external suspension also needs to be present to control the off-axial
swaying of the sense-comb. Figure 4.1 shows the nominal sizes of the different
components of the sensing element of the accelerometer along with the approximate
target values for the specifications. As shown in the figure, the proof-mass is assumed to
be 2.1 mm × 1.2 mm × 25 µm in size. This is partly dictated by the target size of the
overall sensing element which is taken to be less than 4.25 mm × 1.5 mm where an area
of 2.15 mm × 1.25 mm is kept for the proof-mass and its suspensions. The resulting mass
(0.0461mm3 × 2300 kg/m3 = 106.1 × 10-9 kg ) multiplied by the acceleration due to
gravity (i.e., 1 g acceleration) gives the force experienced by the proof-mass as 1.06 µN.
With the combs attached to the proof-mass, the total force due to 1 g acceleration comes
to 1.2 µN, as indicated in Figure 4.1.
1.25 mm
4.25 mm
Sense combs with
suspensions  mext , kext 
uout
DaCM
( k ci , kco , n , mci , and mco )
0.7 mm
0.7 mm
uin
Proof-mass with
suspensions
 ma , ka 
2.15 mm
Proof-mass combs
0.7 mm
k ext = 6.8 N/m
mext = 9.9×10-9 kg
uout = 10×10-9 m
uin = 1×10-9 m
Fin = 1.2×10-6 N
ma = 0.12×10-6 kg
ka = 1201 N/m
f0 = 6 kHz
kci = ?
kco = ?
n= ?
mci = ?
mco = ?
Figure 4.1: Specifications for the wide-band single-axis capacitive micromachined
accelerometer.
86
Chapter 4
The fabrication process to be used here is a multi-user MEMS process, namely
SOIMUMPs (www.memscap.com), that uses Silicon-on-Insulator (SOI) wafers with a
structural layer thickness of 25 µm. This thickness is assumed for all the components. The
suspension of the proof-mass comprises four units of folded-beam arrangements with
each beam being 300 µm long and 12 µm wide. Each unit of folded-beam suspension
occupies 0.27 mm × 0.3 mm space. The net in-plane stiffness of all these suspensions was
found to be 1201 N/m. Thus, the net usable area by the proof-mass becomes 1.845 mm2
(1.2 mm × 1.2 mm + 2 × (0.45 mm × 0.45 mm)). A space of 1.25 mm × 0.7 mm is
allocated for the electrostatic combs attached to the proof-mass. This set of combs is also
needed to measure the displacement of the proof-mass so that it can be compared with the
amplified displacement measured at the output of the DaCM. A space of 1.25 mm × 0.7
mm is allocated to the sensing combs and their suspension which is called as an external
suspension. The stiffness of this external suspension is 6.8 N/m while its mass is 9.9 × 109
kg. The remaining area, i.e., 1.25 mm × 0.7 mm is available for the DaCM.
Additionally, we also require that the first two natural frequencies be around 6 kHz, as
indicated by f0 in Figure 4.1.
4.2 Design of the DaCM for the given specifications
The stiffness-based selection method uses the user-specifications and allows for userspecified variations around the nominal specifications to arrive at a set of inequalities that
bind the values from above and below. This yields
FinL  Fin  FinH
uinL  uin  uinH
FoutL  Fout  FoutH
uoutL  uout  uoutH
(46)
ksL  ks  ksH
kextL  kext  kextH
f0 L  f0  f0 H
The inequalities in Eq. (46) are solved in conjunction with the equilibrium
equations pertaining to the SML model of an accelerometer with a non-inverting DaCM
shown in Figure 4.2 along with the stiffness and inertia of the input and output sides. In
Section 2.4.3, we discussed the SML model of an accelerometer with an inverting DaCM.
But, in this design, we propose to use a non-inverting DaCM. Therefore, the equilibrium
87
Chapter 4
equations pertaining to that are given again for the sake of clarity. Here, ks is the stiffness
of the suspension attached to the proof-mass along with the proof-mass combs, m pm its
mass; kext the stiffness of the suspension attached to the sense-comb and mext the mass of
the sense-comb attached to the output of the DaCM. There are five parameters in the
SML model of the non-inverting DaCM as depicted in Figure 4.2: k ci , kco , n , mci , and
mco which denote the input stiffness, output stiffness, inherent amplification that is equal
to the ratio of the output to input displacements, uout uin , input inertia, and output inertia,
respectively. The equations relating the user-specifications and SML parameters are given
by [77]
kci 
Fin  ks uin  n  Fout  kext uout 
uin
kco 

2
k

ci
 ks  n 2 kco 
m
ci
 m pm 

 Fout  kext uout 
uout  nuin
(47)
(48)
 kco  kext 
 mco  mext 
  kci  ks  n 2 kco   k  k  
4n 2 kco2
co
ext





  mci  m pm 
 mco  mext    mci  m pm   mco  mext 

2
(49)
By solving Eqs. (46), (47)-(49), we can find the feasible values of k ci , kco , n , mci ,
and mco . Using these, two feasible maps are drawn, one kco vs. k ci and the other mco vs.
mci [77]. On the same maps, the values of kco , k ci , mco , and mci computed for different
DaCMs are plotted as individual points. For a point lying inside both the feasible maps, if
the value of n corresponding to the point on the feasible maps matches [77], then the
corresponding DaCM satisfies the specifications. If none of them lie inside the map, the
pre-defined parameters of a selected DaCM closest to the feasible map can be
interactively varied to enter the feasible map. The parameters include the size of the
DaCM, its cross-sectional dimensions, thickness, and material properties. At this point,
the method also allows the user to choose a manufacturing process and enter its limits
such as the minimum feature size, overall size, etc. These are taken into account in
drawing the curves emanating from the point corresponding to the DaCM selected for re88
Chapter 4
design. The details of this procedure are in [77]. A simple example with the specifications
pertaining to the accelerometer of this work will now be used to illustrate the procedure
using the kco vs. k ci map.
Fout
kext
uout
mext
mco
uin
kco
n :1
ks
m pm
nuin
DaCM
Fin
mci
kci
Figure 4.2: An SML Model of a single-axis accelerometer with a non-inverting type
DaCM
From Figure 4.1, we take the following specifications excluding the inertia effects
to arrive at the inequalities:
1.0μN  Fin  5μN; 1nm  uin  1.5 nm
10 nm  uout  15 nm; 1200 N/m  ka  1250 N/m
(50)
6 N/m  kext  8 N/m
and use the equations from Eqs. (47) and (48) modified for steady-state conditions under
the applied acceleration of 1 g:
kci 
kco
ma g  ka uin  n  mext g  kext uout 
uin
 m g  kext uout 
 ext
(51)
uout  nuin
By using Eqs. (50) and (51), we get the feasible map shown in Figure 4.3a. It should be
noted that this map is a projection of a feasible volume in the 3D space of kci -kco -n on to
the 2D space of kci -kco . Therefore, for every point inside the feasible map of Figure 4.3a,
there is a corresponding range for n . The procedure for solving the inequalities and
equations is implemented in an interactive program written in Java [121], which is
available at www.mecheng.iisc.ernet.in/~m2d2/CMdesign. It can be seen in Figure 4.3a
89
Chapter 4
that though three compliant mechanisms lie inside the feasible map, none of them fall in
the valid range of n . Therefore, the next closest mechanism is chosen for re-design (see
Figure 4.3b). The minimum feature size of 4 µm was used in the interactive program as
per the chosen microfabrication process based on lithography. The maximum stress
computed by the program is also monitored so that it lies well below the permissible
strength of single-crystal silicon. By following the procedure for re-design, which was
noted earlier, a design that satisfies the static requirements is obtained.
Initial position of the
mechanism
(a)
Size-in-Y curve
Feasible mechanism
Size-in-X curve
In-plane width curve
(b)
Figure 4.3: (a) Feasible map for the user-specifications noted in Eq. (50), (b) the
mechanism selected for re-design with the parameter curves.
By following a similar procedure for the dynamic specifications and working with
kco vs. k ci as well as mco vs. mci maps, a suitable DaCM that satisfies the specifications
shown in Figure 4.1 is obtained. It is shown in Figure 4.4. Since the procedure of varying
the parameters of the DaCM keeps the relative proportions of the cross-sections of all the
90
Chapter 4
beams constant, a further step of size-optimization is performed. In this, the in-plane
widths of the beam segments of the DaCM shown in Figure 4.4 are varied independently
to obtain a larger value of n than is possible with the interactive procedure.
Figure 4.4: Optimal design of the DaCM achieved after size-optimization.
The finalized dimensions of the non-inverting DaCM are shown in Figure 4.4. As
noted earlier, the out-of-plane thickness of this mechanism is 25 µm. The final design of
the DaCM obtained after size-optimization has the following values: k ci = 1658.4 N/m,
kco = 33.23 N/m, n = 13.9, mci = 1.57 × 10-8 kg and mco = 7.2 × 10-10 kg. It is worth
noticing that the output stiffness of the DaCM is very small compared to the input
stiffness. When this DaCM is integrated to an accelerometer with a suspension stiffness
of the order of 1200 N/m, the first mode of vibration with the lowest natural frequency
will be dictated by the two softer springs of spring constants kco and kext and the effective
mext . It will be seen later that the first in-plane natural frequency is lowered due to the
presence of a comparatively softer part in the design.
4.3 Mechanical design of the accelerometer with a DaCM
The device is designed as planned. The optimally designed DaCM is incorporated into the
accelerometer. It can also be seen that the designed DaCM fits into the area specified for
the DaCM. The proof-mass is suspended by four units of folded-beam suspensions. One
end of the proof-mass is connected to the input of the optimized DaCM and the other end
is connected to a set of capacitive combs called as actuating combs. The output of the
DaCM is attached to another set of capacitive combs known as sensing combs where the
91
Chapter 4
capacitance change due to proof-mass displacement will be sensed. The sense-comb set
contains 150 sets of finger-pairs with 125 µm overlap length and 3 µm sense-gap. Thus,
150 finger-pairs form a differential capacitor with 75 finger-pairs on each side.
4.3.1 Analytical modeling
The performance parameters of the accelerometer with a DaCM can be extracted using
the SML model discussed in Section 2.4.3. Using the formula in Eq. (35), the static
displacement sensitivity of the accelerometer can be calculated as 9.12 nm/g. Again, the
analytically calculated first in-plane natural frequency of the accelerometer with the
optimally designed DaCM is found to be 6.27 kHz. The Net Amplification (NA) achieved
by using the DaCM can be analytically estimated to be 6.85 as per Eq. (36).
4.3.2 Finite element analysis of the design
Table 4.1 shows the specifications of the optimized DaCM for the accelerometer. The
second column of Table 4.1 shows the values as calculated by the interactive program,
which uses a beam-based finite element analysis. The continuum design (see Figure 4.5)
that can be transferred to mask layout software is analyzed using COMSOL Multiphysics
software [78]. The values obtained with this are shown in the third column of Table 4.1.
The minor discrepancies between the analytically extracted performance parameters of
the model and the simulated values are attributed to the effects of fillets and etch-holes,
and the differences in beam and continuum finite elements. The first four simulated mode
shapes are shown in Figure 4.6a-d. As can be noticed, the first mode shape is an in-plane
mode as desired at a frequency of 6.7 kHz. This decides the bandwidth of the sensor.
As noted in the introductory section, it is important to compare the performance of
the accelerometer with the DaCM with that of the one without a DaCM with equal area
occupying the chip. This is discussed next.
4.3.2.1 Comparison of designs with and without a DaCM
Figure 4.7a-b show two accelerometers that occupy the same area on the chip. The one in
Figure 4.7a contains a DaCM while the other in Figure 4.7b does not. The deformed
configurations shown in the figures were obtained by performing a nonlinear finite
element analysis under 1 g body force in both cases. The deformations are exaggerated
for the purpose of visual illustration. However, the scale factor of exaggeration is not
equal in the two figures. As per the simulations, the displacement of the sensing combs in
92
Chapter 4
Figure 4.7(a) is 8.70 nm and that in Figure 4.7 (b) is 1.37 nm. Thus, there is an
enhancement by a factor of 6.35.
Sense-comb
DaCM
Proof-mass
Actuating-comb
Figure 4.5: Continuum model of the accelerometer with an optimally designed DaCM
Table 4.1
Comparison of the specifications of the DaCM in an accelerometer
Specifications
Analytical SML model
FE Simulation using
COMSOL
kci (N/m)
1541
1658.4
kco (N/m)
25.3
33.23
n
13.9
15.26
mci (kg)
1.49 × 10-8
1.57 × 10-8
mco (kg)
6.8 × 10-10
7.2 × 10-10
f0 (kHz)
6.27
6.7
uout per g (m/g)
9.12 × 10-9
8.7 × 10-9
NA
6.85
6.35
93
Chapter 4
Both the designs, i.e., the one with and without a DaCM have a simulated base
capacitance equal to 0.745 pF (considering the fringe field correction factor [122]), and
the changes in capacitance per 1g applied acceleration are 4.3 fF and 0.68 fF respectively.
The in-plane cross-axis sensitivities are calculated to be 1.12% and 5.84%. It is
interesting to notice that the design with the DaCM is better than the one without it from
the viewpoint of cross-axis acceleration, too. Actually, this is not surprising because
amplification is present only in the intended direction and not in the one perpendicular to
it. Therefore, the effect of cross-axis acceleration is considerably lower on the change in
capacitance as compared to the effect of acceleration along the intended axis.
(a) 6.7 kHz
(b) 15.75 kHz
(c) 18.31 kHz
(d) 19.63 kHz
Figure 4.6: (a-d) First four mode shapes of the accelerometer with a DaCM.
While it is advantageous to include a DaCM, as explained in the preceding
discussion, there are also two shortcomings. First, the maximum stress in the design with
the DaCM is 0.11 MPa as compared to 0.04 MPa for 1 g acceleration. This is because the
DaCM has a number of slender beam segments that undergo large deformation and hence
have higher levels of stress. However, this is not a serious shortcoming because the stress
levels can be kept low while designing the device as is the case with the design in Figure
4.7a. Second, the first fundamental natural frequencies of the designs with and without
the DaCM are 6.7 kHz and 12.7 kHz. This implies that the bandwidth is lower for the
design with the DaCM. It should be noted, however, that this is not always the case. The
94
Chapter 4
addition of a DaCM not only increases the mass but also increases the stiffness in the
intended direction. So, by suitably designing the DaCM, the bandwidth need not be
compromised. Additionally, as per the results of the mode shape analysis performed for
the two devices, the first mode shape of the design without the DaCM (i.e., Figure 4.7b)
is an out-of-plane mode which is clearly shown in Figure 4.8. In view of this, it is indeed
an advantage to include a DaCM because it helps the designer make the first natural
frequency correspond to a desired in-plane mode.
(a)
(b)
Figure 4.7: Two accelerometers in undeformed and deformed configurations. (a) with the
DaCM, and (b) without the DaCM. Although the footprint of both is the same, the
displacement of the sensing combs is greater in (a) than in (b).
4.4 Fabrication and Prototyping
4.4.1 Fabrication process
The designed accelerometer with a DaCM was fabricated using the Silicon-on-Insulator
Multi-User MEMS Processes (SOIMUMPs) [123]. The SOIMUMPs process is a simple
four-mask level patterning and etching process that makes use of SOI wafers. It starts
with a highly doped 150 mm n-type double-side polished SOI wafer with a 25 µm device
95
Chapter 4
layer thickness. The process begins with the deposition of pad-metal which is a metal
stack of 20 nm of chrome and 500 nm of gold. In the next step, the 25 µm-thick silicon on
the device layer is lithographically patterned from the top with the mask that contains the
designed devices, and, subsequently, etched using the DRIE technique. The 2 µm-thick
buried-oxide layer and 400 µm-thick substrate silicon layer of the SOI wafer are etched
from the backside using another DRIE process to release the devices as shown in Figure
4.9. These two layers are etched completely wherever required to form a trench from the
backside while keeping the front structural layer covered.The mask layout that was used
to fabricate the single-axis accelerometer with a DaCM is shown in Figure 4.10.
Mode1: 13.66 kHz
Mode1: 12.7 kHz
Mode1: 21.67 kHz
Mode1: 21.45 kHz
Figure 4.8: First four modes of vibration of the accelerometer without a DaCM but with a
larger proof-mass occupying the same footprint.
Gold contact pad; 0.65 µm
Structural silicon layer; 25µm
Buried oxide layer; 2µm
Substrate
400 µm
Backside
Trench
silicon
layer;
Figure 4.9: Cross-section of a typical device fabricated using the SOIMUMPs [123]
process.
96
Chapter 4
Figure 4.10: The mask layout of the fabricated single-axis accelerometer with a DaCM.
4.4.2 Fabricated device
The scanning electron microscope (SEM) images of the fabricated device are shown in
Figure 4.11a-b. Figure 4.11a shows the DaCM in a close-up view. It can be seen that the
most slender beam, i.e., the narrowest beam, is thicker than its in-plane width. Indeed, its
aspect ratio is 6:1. Figure 4.11b shows a close-up view of the comb-fingers. The in-plane
width of each finger is 4 µm while the out-of-plane thickness is 25 µm. The gap between
the adjacent moving and fixed fingers is 3 µm.
4.5 Die-level characterization
A die-level characterization is performed on the fabricated device before it is packaged
and integrated to the signal conditioning electronic interface. A few tests that are
performed during the die-level characterization of the fabricated capacitive accelerometer
are (i) measurement of the base capacitance of the sense-comb when the device is at rest,
(ii) measurement of the geometric amplification of the DaCM, (iii) extraction of the inplane frequency response of the fabricated accelerometer; and (iv) extraction of the
damping co-efficient from the step response of the device. Except for the first test, i.e.,
97
Chapter 4
the measurement of the rest capacitance of the sense-comb, all the other measurements
were performed using Polytec MSA 500, a Laser Doppler Vibrometer (LDV). The
measurement of static rest capacitance was performed under a probe-station.
(a)
(b)
Figure 4.11: SEM images of the accelerometer fabricated using the SOIMUMPs process.
4.5.1 Base capacitance measurement
The base capacitance was measured using Agilent 4294A, a precision impedance
analyzer. The device was placed on a probe-station and the metal contact pads on the
device were probed using needles connected to the manipulators. Two manipulators were
used for this purpose. The two manipulators along with the needles were initially
connected to 4294A and the static capacitance between the long wires connected to those
manipulators was compensated for. Then the needles were placed precisely on the device
contact pads. A small AC signal with a 10 mV peak-to-peak amplitude over a DC bias of
100 mV was used for the measurement of capacitance. The measurements were
performed by sweeping the frequency of the ac signal from 1 MHz to 10 MHz. The
capacitance of the sense-comb at the left of the device was found to be 3.47 pF, whereas
the same in the right sense-comb was found to be 3.39 pF. It can be noted that there is a
large mismatch between the designed value of the sense-comb capacitance and the
measured value of the sense-comb capacitance. This mismatch could be due to the
presence of parasitic capacitance as all the unused structures were floating electrically
during the measurement.
98
Chapter 4
4.5.2 Measurement of geometric amplification of the DaCM
The measurement of the geometric amplification of the DaCM entails a time-domain
dynamic characterization, which was performed by actuating the fabricated single-axis
accelerometer laterally by applying alternating voltage at its contact pads and then
measuring the lateral displacement at the input and output points of the DaCM. The
lateral displacements were found using a method called stroboscopic video microscopy
[124]. This technique uses Light-emitting Diodes (LEDs) for imaging and measurement
of the lateral displacements. Apart from the time domain measurement, the frequency
response and the step response of the device were also captured optically using the
equipment and analyzed to study the dynamic behavior of the device.
Micro System
Analyzer
42.5 Volt AC Supply
Probe tips
SOIMUMPs die on
a compliant acrylic
holder
Figure 4.12: Fabricated device with its compliant acrylic holder under a Micro System
Analyzer for die level characterization.
During the die-level characterization, the accelerometer die was placed under the
LDV, as shown in Figure 4.12, using a compliant acrylic holder [125] made to hold small
micromachined devices that are too delicate to handle manually. An alternating voltage of
42.5 V was applied at the proof-mass comb to actuate the device using the probes. The
LDV can perform a non-contact type real-time LED-based imaging and displacement
measurement using the stroboscopic principle under a video microscope. The measured
99
Chapter 4
displacements of the input and the output sides of the DaCM in the accelerometer are
plotted in Figure 4.13a. The input and output sides of the DaCM are marked in Figure
4.13b. It can be seen from Figure 4.13a that the output of the DaCM moves by 461 µm
whereas the input moves by only 41 µm for the actuation force generated due to the
application of the 42.5 V AC supply. Thus, the geometric amplification measured for the
DaCM is 461/41  11.24.
(a)
(b)
Figure 4.13: Measurement of Geometric amplification by the DaCM used in the
accelerometer (a) Displacement of the output side and the input side of the DaCM
measured when the device is actuated electrostatically, and (b) The DaCM used in the
accelerometer under the LDV showing the measurement points.
4.5.3 Extraction of in-plane frequency response
The die-level frequency response was also measured using the LDV by applying an
alternating voltage of 5 V over a DC bias of 5 V with varying frequency. The frequency
of the alternating voltage was varied from 100 Hz to 20 kHz. The LDV measures the
100
Chapter 4
displacement of the point of interest (here the output side as marked in the Figure 4.13b)
at each frequency and then gives the frequency response of the device. It can be observed
from the Figure 4.14a that the first in-plane natural frequency
kHz with a half-power bandwidth
 f 
 f0 
of the device is 6.254
of 2.156 kHz. The measured quality factor
 Q  f 0  of the device is approximately 2.9. This is quite low but can be improved

f 

significantly when the accelerometer is packaged in a vacuum. The phase response is also
shown in Figure 4.14b. It is worth noticing that the phase changes by 90o during
resonance.
f =
2156
(a)
(b)
Figure 4.14: (a) In-plane frequency response of the single-axis accelerometer captured
using MSA 500, (b) the phase response of the device.
101
Chapter 4
4.5.4 Study of the step-response of the device
The method of extraction of the damping factor from the step response of an
accelerometer is given in Section 2.1.1. During the step response measurement, a step DC
voltage of 50 V was applied and the displacement at the output side of the DaCM was
optically recorded using the LDV. The step response of the device is shown in Figure
4.15. The two successive peaks of the damped oscillations are found to be Z1 = 5.078 ×
10-7 m and Z 2 = 1.727 × 10-7 m. Using Eq. (17), the value of the damping factor  was
found to be 0.1694. From Eq. (11), the value of the measured quality factor  Q  was
found to be 2.95 which closely matches the measured quality factor
Q 
from the
frequency response of the device.
Z1
Z2
Figure 4.15: Experimentally obtained step response of the single-axis accelerometer.
4.6 Integration and Packaging
The next step to die-level characterization of the fabricated single-axis accelerometer was
the integration and packaging of the accelerometer along with a signal conditioning
electronic interface. It being a capacitive accelerometer with differential capacitance, a
capacitance extraction electronic circuitry, capable of measuring a differential
capacitance, was required for this purpose. Thus, a commercially available off-the-shelf
universal capacitance readout application specific integrated circuit (ASIC) namely
MS3110 [126] was integrated to the fabricated accelerometer.
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Chapter 4
MS3110 is available in both Integrated Circuit (IC) form as well as in die form. In
this case, MS3110 ICs were used for interfacing. MS3110 required a supply voltage of
+5V DC for its operation along with a few de-coupling capacitors. According to the
datasheet, it has a capacitance resolution of 4 aF/√Hz. It also has several interesting
features such as provisions for programmable gain and DC offset trim, and programmable
bandwidth adjustment from DC to 8 kHz. It also has an on-chip EEPROM for the
programming and storage of settings. The functional block diagram of MS3110 is given
in Figure 4.16.
MS3110
MEMS
V2P25 / V_Neg
Bandwidth
CF
CS1_in
Gain (G)
CS1
Low pass filter
A
CS2_in
Buffer
Vo/p
CS2
V2P25
Offset
V2P25 / V_Neg
Figure 4.16: The functional block diagram of MS3110, a universal capacitive readout
[126].
The two capacitances CS1_in and CS2_in are the two parts of the differential
capacitance from the micromachined accelerometer. All the other capacitances, i.e.,
CS1, CS2 and CF are basically capacitances of capacitor banks in-built to the MS3110
ASIC and they are digitally programmable. V2P25 is a reference DC voltage of 2.25 V.
V_Neg is generally kept at ground potential. The bandwidth of the low pass filter, the
offset and the gain (G) can also be programmed using the graphical user interface (GUI)
provided as an interface to the ASIC. The output voltage from the MS3110 ASIC can be
expressed as
Vo/p = (G × 2.25 × 1.14 × (CS2 T -CS1T )/C F ) + VRef
103
(52)
Chapter 4
where CS2T  CS2_in + CS2 , CS1T  CS1_in + CS1 and VRef can also be set to
2.25 V. By choosing CF = 5.13 pF, G = 4, and CS1 = CS2 = 0, then the circuit gain of the
MS3110 ASIC becomes 2 mV/fF.
4.6.1 Device integration and wire-bonding
The fabricated single-axis accelerometer die was packaged along with a MS3110 IC on a
custom-designed gold-plated printed circuit board (PCB), shown in Figure 4.17a. The
PCB was fabricated to house the MS3110 IC, passive capacitors for additional signal
conditioning, the power supply port, and the micromachined accelerometer die. The
accelerometer die was attached to the gold-plated pads on the PCB using conductive
silver epoxy and then wire-bonded using 1 mil gold wire to establish the connection
between the die and the MS3310 IC, as shown in Figure 4.17b. A ball-to-wedge
thermosonic wire-bonding was performed between the gold pads on the accelerometer die
and the gold plated pads on the PCB. A transparent acrylic cap was used to seal the wirebonded die to protect it from possible contamination.
MS3110
(a)
(b)
Figure 4.17: Fabricated accelerometer integrated and wire-bonded on a gold plated PCB
along with the capacitance extraction readout IC MS3110.
4.7 Testing and calibration
Electrical testing and calibration were performed on the integrated and packaged device
using a vibration shaker table [127]. The calibration of the packaged and integrated
accelerometer was performed by mounting it on the LDS vibration shaker table shown in
Figure 4.18. The shaker table along with the device under examination was shaken at
104
Chapter 4
different acceleration values and at different frequencies. A Digital Storage Oscilloscope
was used to record the data from the output of the sensor integrated to the MS3110 IC and
the output of the reference tri-axial micromachined accelerometer (Model: EK3L02AS)
made by ST Microelectronics [128]. Thus, the SOIMUMPs single-axis accelerometer
integrated with MS3110 IC was tested and calibrated with respect to the reference
accelerometer.
Oscilloscope
DC Power
Accelerometer under test
Supply
LDS Shaker
Figure 4.18: Integrated and packaged accelerometer mounted on the LDS vibration
shaker table.
4.7.1 Axial sensitivity measurement
The response from the standard accelerometer under applied 1 g sinusoidal acceleration
can be seen on the oscilloscope shown in Figure 4.18. The output voltages of the
accelerometer at different acceleration values were measured and the calibration curve of
the device at 40 Hz is shown in Figure 4.19. The sensitivity of the accelerometer is
determined from the slope of the calibration curve. The achieved sensitivity of the device
is 26.7 mV/g at 40 Hz. By a simple calculation, it can be said that the change in
capacitance that is detected by MS3110 due to the application of 1 g of dynamic
acceleration is 13.35 fF whereas the simulated value of a change in capacitance was 4.3
fF which was performed under a static load. The large mismatch between the simulated
and experimental value could be because of the difference in the design value of the
sense-comb capacitance and its measured value. The other reason could be because of the
open-loop operation of the accelerometer where there is no control over the transient
105
Chapter 4
movement of the accelerometer’s proof-mass and the sense-comb. Thus, the presence of
overshoot in the open-loop dynamic response could give rise to more proof-mass
displacement than the value obtained from the static analysis. It can be seen that the
sensitivity improvement by a factor of 11 on using the DaCM brought the change in
capacitance to a measurable range. Thus, this work demonstrated the feasibility of
enhancing sensitivity through mechanical amplification for wide-band operation.
Output voltage in mV
40
Output voltage vs. Applied acceleration
Linear fit
35
30
25
20
15
Sensitivity = 26.71 mV/g
10
5
0.2
0.4
0.6
0.8
1
1.2
1.4
Applied acceleration in g (1g = 9.81 m/s2)
Figure 4.19: Calibration curve of the packaged accelerometer at 40 Hz.
4.8 Cross-axis sensitivity measurement
The packaged accelerometer along with the evaluation board with the MS3110 IC was
mounted on the shaker table such that the applied acceleration became perpendicular to
the sensing axis of the accelerometer under examination. A sinusoidal excitation was
applied using the shaker table and the responses of both the accelerometers are shown in
the captured image in Figure 4.20. The single-axis accelerometer and the reference
accelerometer were mounted such that the standard accelerometer experienced an axial
load but the single-axis accelerometer experienced an off-axial load.
It was noticed that the output of the accelerometer was not a sinusoid as the
accelerometer under examination experienced an off-axis load. The average amplitudes of
the output of the accelerometer under examination were measured under different
acceleration values and the slope of the plotted curve shown in the Figure 4.21 gives the
106
Chapter 4
cros-axis sensitivity of the device. The off-axial sensitivity of the accelerometer under
examination was measured as 1.08 mV/g which is ~ 4% of the axial sensitivity.
Standard Accelerometer
SOIMUMPs Single-axis Accelerometer
Figure 4.20: Dynamic response of both the accelerometers where the standard
accelerometer experiences an axial load and the single-axis accelerometer experiences an
off-axial load.
Off-axial sensitivity ~ 1.08 mV/g
R2 = 0.959
Figure 4.21: The off-axial sensitivity curve for the packaged single-axis accelerometer.
4.9 Closure
In this chapter, we showed that it is helpful to append a Displacement-amplifying
Compliant Mechanism (DaCM) with a capacitive accelerometer consisting of a proofmass with a suspension and sensing combs. It is noted that mechanical noise is usually
lower than electronic noise. Hence, increasing sensitivity through mechanical
107
Chapter 4
amplification helps improve the resolution of the device. Furthermore, even though a
large natural frequency implies high stiffness and little motion of the proof-mass, we have
been able to achieve a change in capacitance that is detectable even with an off-the-shelf
ASIC that has a low gain. Another important conclusion of this work is that between the
two accelerometers with and without a DaCM but occupying the same footprint area, the
one with the DaCM has higher sensitivity by a factor of about 6.5. This net amplification
was not reported in two other works that reported mechanical amplification. Furthermore,
the die-level characterization showed that there is an amplification of more than 11
between the output (i.e., the sensing side) and input sides of the DaCM in the fabricated
device. Noise and damping can be improved through vacuum-packaging of the device.
108
Chapter 5
Development of a dual-axis low-g capacitive
in-plane accelerometer with two dacms
Summary
In addition to the two case studies presented in the chapter 3 that show the advantages of
using DaCMs in single-axis in-plane accelerometers and the development of a single-axis
wide-band capacitive micromachined accelerometer in Chapter 4, we present here the
development of a dual-axis in-plane capacitive accelerometer with two DaCMs. This
chapter contains the design of the dual-axis accelerometer followed by the fabrication,
characterization, packaging and testing of the device to further demonstrate the
effectiveness of DaCMs in micromachined accelerometers.
5.1 A Dual-axis accelerometer
A dual-axis accelerometer is designed to sense both the orthogonal components of
acceleration along any arbitrary direction in a plane. It requires two independent motions
of the proof-mass. This can be achieved by designing a suitable mechanism that is
capable of de-coupling the motion in one orthogonal axis from the other.
5.2 De-coupling of the in-plane axes
De-coupling can be achieved by arranging four sliding joints as shown in Figure 5.1a.
The arrangement works perfectly if the design of the sliding joints offers zero axial
stiffness and infinite cross-axial stiffness, but this is not so in practice. The design shown
in Figure 5.1b uses the compliant equivalents of sliding joints to obtain de-coupling
among the axes [129]. The design has symmetry with eight folded-beam suspensions
replacing the sliding joints in a monolithic compliant design. This arrangement is used for
creating a compliant XY stage. The arrangement provides isolation of the stage (i.e., the
stage moves along only one direction when it is actuated in that direction) and isolation of
109
Chapter 5
the actuator (i.e., when the stage is actuated in one direction, the location of the other
actuator remains unaffected).
(a)
(b)
Figure 5.1: (a) A schematic showing two independent actuations of the proof-mass using
the XY flexure mechanism, (b) A parallel arrangement of an XY Stage.
Here, we use the de-coupling mechanism for the purpose of sensing. That is, the
stage is used as the proof-mass whose motion is sensed. The folded beam suspensions
allow the proof-mass to move along the direction of the applied acceleration in the plane
of actuation whereas the ports X and Y move by the respective X and Y components of
the displacement of the proof-mass in that plane. The actuation of the ports X and X do
not undergo any disturbance when the device is actuated along the Y direction and vice
versa.
5.3 Mechanical design of the dual-axis accelerometer
The dual-axis accelerometer contains a de-coupling mechanism that acts as a proof-mass
and de-couples the X and Y components of the applied acceleration. As stated earlier, the
de-coupling mechanism consists of a set of folded beam suspension units, a portion of
inertial mass and four ports of actuation. A good feature of the mechanism is that the
inertial mass is allowed to move in the direction of the applied acceleration, whereas the
sensing ports move only along the X and Y axes. That is, motion along an arbitrary inplane direction is mechanically decomposed into two orthogonal in-plane directions, X
and Y. Thus, the displacements at the X and Y ports of the mechanism are equal to the
110
Chapter 5
corresponding X and Y components of the proof-mass displacement. Two DaCMs were
designed to be incorporated in the dual-axis accelerometer design. One DaCM is attached
to Port X and the other is attached to Port Y. The other two ports are connected to
capacitive combs that can later be used for electrostatic actuation and force-feedback if
the device is operated in a closed-loop. Capacitive combs are also attached to the output
ends of the DaCMs where the amplified axial displacement components of the proof-mass
will be sensed. For capacitive sensing, we add sense-combs with considerable mass to the
ports, which disturbs the perfect de-coupling arrangement of Figure 5.1b under the bodyforce arising because of the applied acceleration. In particular, the sense-combs tend to
rotate about the out-of-plane axis warranting an additional suspension that limits this
rotation. But the use of this additional folded beam suspension increases in-plane stiffness
and thus reduces the in-plane sensitivity. Figure 5.2a shows the schematic of the sensing
element with 12 folded-beam suspensions [130] and two inverting DaCMs. This special
configuration retains decoupling of the two axes even after appending the inverting
DaCMs, the sense-comb, and the external suspensions at the sensing ports of both axes as
opposed to de-coupling layout of the XY stage shown in Figure 5.1b. It may be noted that
there is a direct correspondence between the configuration of the schematic in Figure 5.2a
and that of the designed device layout in Figure 5.2b. De-coupling ensures low cross-axis
sensitivity because the input in one direction does not affect the other.
In addition to achieving de-coupling of the two axes with the special configuration
of Figure 5.2a and displacement amplification, the inverting DaCM was designed to have
low stiffness along the intended axis and high stiffness along the cross axes. The
stiffness-matched inverting DaCM was again obtained using the stiffness map-based
selection method described in the Section 2.4.4.
The design of the dual-axis accelerometer shown in Figure 5.2b is symmetric
about the X and Y axes. The thickness of the entire device was chosen as 25μm because
the device was planned to be fabricated using the SOIMUMPs process. The minimum
feature size chosen is 6 μm and the sense-gap is 4 μm. The total size of the designed
accelerometer is 8.5 mm × 8.5 mm along with a proof-mass that is as big as 3mm × 3
mm. The design is deliberately conservative because we chose a multi-user fabrication
process.
111
Chapter 5
Sense-comb
Proofmass
Proof-mass
Y
Actuatingcombs
X
Folded-beam
suspensions
Comb-drive
DaCM
(a)
Sense-comb
DaCM
Anchor
Anchor
Proof-mass
Anchor
Anchor
Actuating
-combs
(b)
Figure 5.2: (a) The schematic and (b) the layout of a dual-axis capacitive lateral
accelerometer with a decoupling mechanism and two inverting DaCMs.
112
Chapter 5
5.4 Modeling and analysis
The design of the dual-axis accelerometer with two DaCMs in two orthogonal directions
can be represented as two identical single-axis accelerometers with DaCMs mounted
orthogonally to each other. Thus, the lumped mass and stiffness values of the dual-axis
accelerometer will be the same along both the axes. Therefore, analytical modeling and
an FE analysis of the accelerometer along one axis can be used to predict the response of
the accelerometer in the other axis.
5.4.1 Design of the DaCM
All the lumped parameters of the accelerometer with the DaCMs are found using the
stiffness map-based selection method as discussed in previous chapters. The optimized
design of the DaCM used in the accelerometer was found using this method. The lumped
stiffness and mass values of the accelerometer including the DaCMs are given in Table
5.1.
Table 5.1
Lumped parameters of the dual-axis in-plane accelerometer
Parameters
Values
Suspension stiffness  ks  and mass  ms  of
23 N/m and
the actuation side
0.58 × 10-6 kg
Stiffness of the external suspensions  kext 
0.08 N/m and
and mass of the sense-comb  mext 
0.0155 × 10-6 kg
24.14 N/m and
k ci and kco values of the DaCM
32.32 N/m
4.98 × 10-8 kg and
mci and mco values of the DaCM
5.35 × 10-10 kg
Geometric amplification  n  of the DaCM
113
-6.44
Chapter 5
5.4.2 Analysis of the mechanical design
In this section, an analysis of the mechanical element of the dual-axis accelerometer is
done using both the analytical model and the finite element method.
5.4.2.1 Analytical modeling
The SML model of an accelerometer with a DaCM is given in section 2.4.3. The
performance specifications (e.g., static displacement sensitivity and first in-plane natural
frequency) found using analytical expressions in Eqs. (35) and (37) and 3D FE analysis
using COMSOL multiphysics are given in Table 5.2. The Net Amplification values and
the figure of merit values are also given in Table 5.2
Table 5.2
Performance specifications of the dual-axis accelerometer
Specifications
Analytically estimated
FE result
Static displacement sensitivity
0.594 µm/g
0.586 µm/g
First
1007.5 Hz
1030.56 Hz
(both axes)
(both axes)
Net Amplification (NA)
1.56
1.53
Figure of Merit (FOM)
23.8
24.57
two
in-plane
modal
frequencies (without damping)
5.4.2.2 Finite element analysis
Figure 5.3 shows a simulated image where static 1g acceleration in the form of a body
force is applied along both the X and Y axes. It is worth noticing that the proof-mass
moves along the resultant direction of the applied acceleration but the outputs of the
DaCMs move only along the intended axes. It can also be seen that though the DaCMs
amplify the displacement from their inputs to their outputs by a certain factor, the
direction of the displacement is reversed. The first three modes of vibration of the dualaxis in-plane accelerometer with DaCMs simulated using COMSOL Multiphysics are
shown in Figure 5.4a-c. The identical values of the first two modal frequencies ensure
structural symmetry along both the axes.
114
Chapter 5
Proof-mass
3 mm × 3 mm
Y
X
Figure 5.3: Simulated image of the dual-axis in-plane accelerometer with two DaCMs
under 1 g body-load along both the axes. The decoupling mechanism decouples the
applied acceleration into its corresponding axial components and the two DaCMs amplify
the displacement of the proof-mass along both the axes.
The base capacitance (Cbase ) of the sense comb is analytically estimated to be
0.977 pF. Assuming the circuit gain K to be 2 V/pF, the design values of the axial
voltage sensitivity of the accelerometer can be found by using Eq. (5) to be 0.572 V/g.
In order to find the NA value using FE simulation, a similar type of a dual-axis
accelerometer is designed without any DaCM but the proof-mass size is increased to 3.76
mm × 3.76 mm (See Figure 5.5) to make the footprint of the accelerometer the same as
the dual-axis accelerometer with DaCMs. The effective in-plane stiffness  k s  and the
effective mass  mpm  of this accelerometer design are computed as 23.14 N/m and 0.896
× 10-6 kg respectively. The static displacement sensitivity of the accelerometer without
the DaCM is found to be 0.382 µm/g and the first two modal frequencies are also
simulated to be at 808.85 Hz and 808.93 Hz. These two modes are in-plane modes with
almost the same frequency of vibration along both the X and Y axes. The analytically
115
Chapter 5
estimated and FE simulated values of NA are found to be 1.56 and 1.53 respectively.
Thus, the improvement of sensitivity by the use of mechanical amplifiers (DaCMs) can be
estimated as more than 50% along with an enhancement of operational bandwidth by
about 25%.
(a)
1031 Hz
(b)
1031 Hz
(c)
1533 Hz
Figure 5.4: (a-c) First three modes of vibration of the dual-axis accelerometer with
DaCMs. It can be seen that the first two modes are in-plane modes with an identical
frequency whereas the third mode is an out-of-plane mode at a higher frequency.
116
Chapter 5
Proof-mass
3.76 mm × 3.76 mm
Figure 5.5: Simulated image of a dual-axis accelerometer without any mechanical
amplification under 1 g body-load along both the axes. The accelerometer occupies the
same footprint area as the design with two DaCMs. Thus, the accelerometer contains a
larger proof-mass compared to that of the design with DaCMs.
5.5 Fabrication and prototyping
The dual-axis in-plane accelerometer was also fabricated using the Silicon-on-insulator
Multi-user MEMS Process (SOIMUMPs) [123]. A few optical and SEM micrographs of
the fabricated device are shown in Figure 5.6a-e.
(a)
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Chapter 5
(b)
(c)
(d)
(e)
Figure 5.6: (a-c) Optical micrographs (top view) of the fabricated dual-axis
accelerometer die, (d-e) Tilted SEM images of the device showing parts of the DaCM and
the sense-comb present in the accelerometer.
5.6 Die-level characterization
The die-level dynamic measurements on the fabricated dual-axis accelerometer with
DaCMs were also performed using POLYTEC MSA 500. The time response, frequency
response and step response of the device were captured optically using the equipment and
analyzed to study the dynamic behavior of the device.
5.6.1 Measurement of the geometric amplification of the DaCMs
The fabricated device was actuated by applying an alternating voltage  Vac  of 5 V over a
DC bias
 Vdc 
of 5 V on the actuating combs along both the axes separately. The
actuation frequency was set at 100 Hz. The magnitude of displacements at both the proofmass and the sense-comb along both the axes were measured and plotted in Figure 5.7.
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Chapter 5
The geometric amplification  n  , which is the ratio of the displacement at the sense-comb
attached to the output end of the DaCM to the displacement at the proof-mass attached at
the input end of the DaCM, measured as -6.24 approximately. A phase difference of 180º
between the proof-mass and sense-comb displacements confirms that the DaCM is of an
inverting type that reverses the direction of displacement from its output port to its input
port.
0.143 µm
0.892 µm
n = - 0.892 0.143
 -6.24
Figure 5.7: Time vs. Displacement plot, captured by a Laser Doppler Vibrometer, of the
input and output ports of the DaCMs present in the dual-axis accelerometer along both the
axes. The displacement amplification by the DaCMs can be measured by taking ratios of
the displacement amplitudes at any time at the output and input ports of the DaCMs.
5.6.2 Measurement of in-plane frequency response
The device was again actuated electrostatically along both the axes using an alternating
voltage of 3 V over a DC bias of 5 V with the frequency varying from 10 Hz to 1500 Hz.
The amplitudes of the displacement of the sense-comb along both the X and Y axes at
each frequency step were recorded and plotted using software called a Planar Motion
Analyzer (PMA) version 2.6. The in-plane frequency responses along both the axes of the
device are shown in Figure 5.8a. The frequency response of the input side, i.e., the
actuation side can also be observed in the figure. Experimentally obtained in-plane modal
119
Chapter 5
frequencies were found to be 920 Hz for the X-axis and 918 Hz for the Y-axis. An
average value of the absolute geometric amplification  n  of 6.2 was extracted from the
Bode plot. The phase response in also given in Figure 5.8b. The 3dB bandwidth of the
accelerometer was measured to be approximately 505 Hz for both the axes.
n~
(a)
(b)
Figure 5.8: Experimentally obtained Bode plot (Displacement amplitude in (a) and Phase
in (b)) of the accelerometer showing the frequency response of the device at both the
input and output of the DaCMs.
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Chapter 5
5.6.3 Study of the step-response of the device
The step-response of the fabricated accelerometer was obtained by actuating the device
using a DC voltage of 10 V in the form of a square pulse along both the axes at the same
time. As the device was actuated, both the displacement of the proof-mass at the actuation
side and the sense-comb at the output of the DaCMs along both the axes were captured
optically and then plotted with respect to time to achieve the step response of the device
shown in Figure 5.9.
The dynamic behavior of the device was extracted from the step response of the
device by finding the damping ratio  of the response using Eq. (17), where, Z1 and Z 2
are the two consecutive peaks of the damped oscillation of the sensing side. The measure
value of  is 0.2118. The measured value of the time constant of the damped oscillation
 d was 1.087 ms. The Quality factor Q was also found using Eq. (11) as 2.36. It may also
be noted that the damping can be easily measured from the response of the sensing side
rather than from that of the actuation side as the sensing side moves more than the latter
because of the presence of the DaCMs.
Z1 = 0.4438 µm
Z 2 = 0.1138 µm
Figure 5.9: Experimentally obtained step response of the accelerometer captured using
Laser Doppler Vibrometer to study the dynamic behaviour of the device along both the
axes.
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Chapter 5
5.7 Die-to-die hybrid packaging
The fabricated accelerometer was packaged along with a commercially available
universal capacitance readout ASIC die MS3110D [126]. A hybrid die-to-die System-inPackage (SiP) technique was adopted to package the device inside a hybrid ceramic
package. A custom-designed Low Temperature Co-fired Ceramic (LTCC) substrate was
used as the base for both the micromachined device and the interface electronic ASIC
dies shown in Figure 5.10a. Electrical connections are routed by screen printing of silver
paste on the LTCC substrate. Conductive silver epoxy was used to perform die-tosubstrate attachments and non-conductive epoxy was used to attach the ceramic substrate
to the package. All the electrical connections between the accelerometer die to the
capacitance extraction ASIC dies and between the ASIC dies to the contact pads on the
LTCC substrate were established by performing thermosonic ball-to-wedge gold wire
bonding. Figure 5.10b shows an optical image of the accelerometer wire-bonded to the
capacitance extraction ASIC dies. An evaluation board was designed and fabricated for
testing the packaged accelerometer.
5.8 Testing and calibration
Both static and dynamic calibration were performed on the packaged dual-axis
accelerometer. Static calibration was performed by mounting the packaged accelerometer
on a vertical turn-table while dynamic calibration was performed by mounting the device
on a vibration shaker. The experimental setup showing the packaged device on the turntable is shown in Figure 5.11a. During the static calibration, the turn-table was rotated
precisely to vary the applied acceleration on the device, whereas the platform of the
shaker table was excited at 20 Hz for different values of g. Both the open-loop static and
dynamic response of the packaged device are shown in Figure 5.11b. The static
sensitivity was measured as 580 mV/g and 589 mV/g while the dynamic sensitivity was
found to be 762 mV/g and 778 mV/g for the X and Y axes respectively. The difference
between the static and dynamic sensitivities could be because of the presence of the
overshoot in the dynamic response of the accelerometer. It can be noted that the measured
static axial voltage sensitivity closely matches the design value of the axial voltage
sensitivity (static) which is 572 mV/g for both the axes. The measured static and dynamic
linearity was found to be well within 2% of the full-scale output (FSO) along both the
axes. The cross-axis sensitivity of the packaged accelerometer was also measured by
122
Chapter 5
mounting the packaged accelerometer such that the acceleration due to gravity acted
perpendicularly to the measuring axis. The cross-axis sensitivity of the packaged dualaxis accelerometer was measured to be less than ±2% of the axial sensitivity for both the
axes as shown in Figure 5.12.
19 mm
19 mm
(a)
MS3110 die for Y axis
MS3110 die for X axis
Micromachined dual-axis accelerometer
(b)
Figure 5.10: (a) LTCC substrate developed for packaging the dual-axis accelerometer
with DaCMs, (b) Hybrid die-to-die packaging of a dual-axis accelerometer die along with
two MS3110 dies inside a ceramic flat pin package.
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Chapter 5
(a)
Static sensitivity along X ~ 580 mV/g
Static sensitivity along Y ~ 589 mV/g
Dynamic sensitivity along X ~ 762 mV/g
Dynamic sensitivity along Y ~ 778 mV/g
(b)
Figure 5.11: (a) Experimental setup for static calibration of the packaged dual-axis
accelerometer using a turn table. The MS3110 evaluation board was required only at the
beginning of the test to program the MS3110 ASIC dies. Once programmed, the
evaluation board was disconnected while testing. (b) Both the static and dynamic
calibration curves for the dual-axis accelerometer along the X and Y axes where the
sensitivities of the packaged dual-axis accelerometer can be found from the slope of the
calibration curves.
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Chapter 5
Figure 5.12: The off-axis sensitivity curve that is obtained by rotating the device while
keeping the sensitive axis horizontal.
5.9 Conclusion and closure
In Chapters 3 and 4, it was shown that a DaCM is useful in enhancing the sensitivity and
resonance frequency simultaneously, by design. In this chapter, it is demonstrated that the
same is possible for the dual-axis in-plane accelerometer. Two features contributed to
this: (i) the two-axes are de-coupled using a specially designed compliant suspension, and
(ii) DaCMs are mounted on both the axes. Modeling, design, fabrication, packaging, and
testing are all presented in this chapter.
The next chapter is focused on demonstrating a wide-band dual-axis accelerometer
without using amplifying mechanism.
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Chapter 6
Development of a dual-axis wide-band
accelerometer without mechanical
amplification
Summary
We report here the development of a wide-band (of the order of 6 - 8 kHz) capacitive
dual-axis micromachined accelerometer without using mechanical amplification. The
objective of the work presented in this chapter was to develop a tri-axial wide-band
accelerometer with a single proof-mass. Thus, we began with the development of a singleaxis and a dual-axis wide-band in-plane accelerometer. In Chapter 4, we presented the
development of a wide-band (~ 6 kHz) single-axis accelerometer. Later, we realized that
the bandwidth requirement could not be met using the DaCM beyond 6.5 kHz and, thus,
started designing a dual-axis accelerometer with a single proof-mass and without using
mechanical amplification. We have successfully designed and developed a wide-band
dual-axis micromachined accelerometers with a bandwidth of about 8 kHz. This work is
reported in this chapter. Also presented here is the design and the process flow for
fabricating a wide-band tri-axial accelerometer.
6.1 Acclerometer specifications
The specifications of a wide-band micromachined accelerometer are given in Table 6.1.
The striking feature of the specifications is that the required bandwidth of the
accelerometer is of the order of 8 kHz with a moderate sensitivity of 100 mV/g, which is
not available with commercial micromachined accelerometers at present. Commercially
available accelerometers with the specified bandwidth cannot meet the sensitivity
requirement. However, other specifications in Table 6.1 are not so stringent. So, if we
take the noise in the electronics as 1 mV, the expected resolution of the accelerometer is
10 milli-g. Despite this not-so-demanding resolution, it is a non-trivial design problem
because of the requirement of a very high bandwidth.
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Chapter 6
Table 6.1
Target specifications of the wide-band tri-axial accelerometer
Parameters
Values
Measurement range
±2g
Frequency response (3dB)
10 Hz to 10 kHz
Sensitivity
100 mV/g
Operating temperature
20 – 40 °C
Shock
10g
Transverse sensitivity
10 % FS
Sensitivity drift
0.3 (% / °C)
Supply voltage
3 – 10 V DC
Resonance frequency
30 kHz
With the given specifications of the tri-axial accelerometer, we started with the
design of a wide-band dual-axis in-plane accelerometer with a single proof-mass. The
plan for the development of a tri-axial wide-band accelerometer was to use the out-ofplane movement of the proof-mass to detect the acceleration along the out-of-plane
direction.
6.2 Mechanical design of the wide-band dual-axis accelerometer
Designing a wide-band dual-axis in-plane accelerometer involves a proper selection of
the suspension stiffness and the mass of the proof-mass. No DaCMs were used in the
design and development of the wide-band dual-axis accelerometer. As discussed in the
previous chapter, the design of the multi-axis accelerometer requires de-coupling of the
applied acceleration into its axial components. Thus, a suitable de-coupling mechanism
was used to de-couple the applied excitation into its axial components.
Here, as in Chapter 5, we use a de-coupling mechanism for the purpose of sensing.
The stage of the de-coupling mechanism is used as the proof-mass whose motion is
sensed. For capacitive sensing, we add sensing combs, which disturbs the perfect decoupling arrangement when the body-force of acceleration has components along both the
X and Y axes. The cross-axial sway of the capacitive combs can be prevented by using an
additional suspension. Such an arrangement presented in [130] is shown in Figure 6.1a. It
uses 12 folded-beam suspensions as opposed to the design of an XY stage proposed by
127
Chapter 6
Awtar 2003 [129] which uses eight folded-beam suspensions. This new arrangement
offers higher cross-axial and rotational stiffness, with respect to ports X and Y, compared
to the arrangement shown in Figure 6.1a.
The mechanical design of the dual-axis lateral capacitive accelerometer is shown
in Figure 6.1b. It may be noted that there is a direct correspondence between the
configuration of the schematic in Figure 6.1a and that of the device layout in Figure 6.1b.
It consists of a proof-mass along with de-coupling mechanism, four sets of sense-comb
fingers and four external suspensions. The mechanism has two ports, one along each axis.
Thus, two sets of sense-combs were attached to the proof-mass. One set of sense-combs
from each axis will be used for sensing while the other set in that axis will be used for
actuation along that axis.
The mechanism allows the proof-mass to move along any arbitrary direction in the
plane of actuation whereas ports X and Y move because of the respective X and Y
components of the displacement of the proof-mass in that plane. The actuation of the
ports X and X do not undergo any disturbance when the device is actuated along the Y
direction and vice versa.
The cross-axial sensitivity of a capacitive accelerometer is dependent on the total
displacement of the sense-combs due to a cross-axial load. Cross-axial displacement can
take place due to any unwanted rotation or planar motion in the cross-axial direction.
Appending comb-drives at ports X and Y increases the mass at those points and thus
makes them prone to cross-axial movement, and rotation about the z-axis in particular.
So, the twelve folded-beam suspensions are arranged in such a way that the cross-axial
stiffness and the rotational stiffness at ports X and Y become higher as compared to the
design shown in Figure 5.1b. A differential capacitance sensing technique has been
adopted in the design. Note that the stationary combs are not shown in Figure 6.1b.
External suspensions connected at the end of the sense-comb are designed to offer high
cross-axial stiffness and very low axial stiffness.
It can be seen that the design is symmetric about both the X and Y axes. The
thickness of the entire device was chosen as 50 μm. The minimum feature size was set at
4 μm and the sense-gaps at 3 μm. The total size of the designed accelerometer is 3.7 mm
× 3.7 mm along with a proof-mass that occupies a 1.2 mm × 1.2 mm footprint.
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Chapter 6
Folded beam
suspensions
Port Y
Port X
Port X
Proofmass
Y
Port Y
X
Folded beam
suspensions
(a)
Sense-combs
Sensecombs
Anchored
Proof-mass
Y
External
suspensions
X
(b)
Figure 6.1: (a) A modified configuration for improved de-coupling of the X-Y axes
[130], (b) Mechanical design of the dual-axis lateral capacitive accelerometer.
6.3 Design analysis
The 2D finite element structural analysis of the configuration shown in Figure 6.1b was
performed using COMSOL Multiphysics software by applying a 1 g static body-force
along the X axis and 0.5 g along the Y axis and finding the corresponding displacements
at both the ports shown in Figure 6.2. Port X shows a static deflection of 1.108 nm under
a 1 g load, whereas port Y moves by 0.554 nm under a 0.5 g body-force. As the sensecombs are attached to these ports, the axial displacement sensitivity of the sense-combs,
129
Chapter 6
i.e., the displacement per unit gravitational load
 d g 
is 1.082 nm/g, which
corresponds to a capacitance sensitivity of 0.5 fF/g. The first three modes of vibration are
obtained from the modal analysis, as shown in Figure 6.3a-b.
0.5g
1g
Figure 6.2: The FEA solution shows the response of the device on the application of
body-force along both the axes.
In the modal analysis, the first two in-plane modal frequencies were found to be
15.12 kHz, whereas the third mode is an out-of-plane mode with a frequency of 15.3 kHz.
The existence of the first three orthogonal modes of vibration at almost the same
frequency indicates that the design has almost identical stiffness along all the three axes
because the proof-mass is the primary contributor to the inertia here. The simulated inplane frequency response of the device is shown in Figure 6.3c. The 3 dB bandwidth of
the model is found to be approximately 8.27 kHz which is indicated in Figure 6.3c. An
ideal case with no damping is considered here for simplicity of the simulation.
The simulated cross-axial sensitivity of the accelerometer model was found to be
less than 4% by measuring the total cross-axial displacement of the sense-comb along one
axis when a known body-load was applied orthogonally to that axis. The simulation
shows a maximum stress of 0.344 MPa under a 10 g static body load.
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Chapter 6
15.12 kHz (in-plane)
15.12 kHz (in-plane)
Measures X and Y component of acceleration
(a)
15.3 kHz (out-of-plane)
(b)
Measures Z component of
acceleration
(c)
Figure 6.3: (a) First two in-plane modes of vibration, (b) the out-of-plane mode, and (c)
simulated frequency response of the device for both the axes.
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Chapter 6
6.4 Extension to tri-axial design
Figure 6.3b shows the third mode of the designed dual-axis accelerometer which is the
out-of-plane motion of the proof-mass. This mode is also found at 15.3 kHz. It can be
seen from Figure 6.3a-b that the designed dual-axis accelerometer is equally compliant in
all the three orthogonal axes. Thus, the third out-of-plane mode of the device could be
used to capture the Z-axis component of the applied acceleration, while the first two inplane modes capture the X and Y components of the applied acceleration. The in-plane
component of displacement of the accelerometer can be sensed by the differential sensing
combs placed at the X and Y ports of the device. Two capacitive electrodes, one each at
the top and bottom, are necessary to form a differential capacitance for the proof-mass.
This calls for a custom bulk-micromachining process as a multi-user process like
SOIMUMPs has provision for only one structural layer whereas this tri-axial device
would need two electrode layers equally spaced from the structural layer that contains the
proof-mass.
6.5 Fabrication and Prototyping
The designed dual-axis accelerometer was fabricated using a customized Silicon-onInsulator (SOI) based bulk-micromachining process. This process was designed to
develop tri-axial accelerometers with three equally-spaced silicon layers as required for
developing the designed tri-axial accelerometer. It is a process that involves an SOI wafer
anodically bonded to another single-crystal silicon layer with a gap of 2 µm. The
structural layer or the top silicon layer of the SOI wafer is used to pattern the dual-axis
accelerometer structure with the proof-mass and the folded-beam suspensions. The 2 µmthick buried silicon dioxide layer is used as a sacrificial layer. The substrate or handle
layer of the SOI wafer is used as the bottom electrode. The bonded silicon layer on the
top acts as the other electrode. The complete process was developed as a collaborative
research effort between Indian Institute of Science, Bangalore and ECS Partners at The
University of Southampton, UK. The entire process flow has two phases. In Phase-I, the
SOI wafer is processed to fabricate the dual-axis accelerometer. Phase-II involves the
process of bonding another processed silicon wafer on the top. Thus, Phase-II of the
process extends the dual-axis fabrication to a tri-axial accelerometer fabrication. Due to
unavoidable circumstances, Phase-II was not been carried out and thus the development
132
Chapter 6
ended up fabricating only a wide-band dual-axis accelerometer. The complete
microfabrication process used to fabricate the accelerometer is discussed next.
6.5.1 Microfabrication process
6.5.1.1 Phase-I
The process in phase-I started with an SOI wafer with 50-µm thick structural layer, 2 µmthick buried oxide (BOX) layer and 650 µm-thick substrate or handle layer. A thin layer
of silicon dioxide was deposited on top of the wafer using the PECVD technique. Then, a
positive photoresist was spin-coated over the deposited oxide layer. The photoresist was
photo-lithographically patterned using the first mask called “SOI”. This mask defines the
structure of the accelerometer. Reactive Ion Etching (RIE) was performed on the thin
layer of the deposited oxide. This patterned oxide layer was used later as the hard-mask to
define the structural layer of the accelerometer. Later, the photoresist was removed after
the RIE of the oxide layer. Then, the wafer was flipped and the backside of the SOI wafer
was also spin-coated with photoresist and then lithographically patterned using the second
mask called “BOTTOM ELECTRODE” to pattern the bottom electrode and anchor on
the 650-µm thick substrate. Deep Reactive Ion Etching was done on the 650-µm thick
substrate layer to define the anchor and the bottom electrode for the accelerometer using
the BOX as the etch stop. Then, the wafer was flipped again and the 50-µm thick device
layer was etched using the patterned oxide on the top side as a mask. This step defines the
structures of the dual-axis wide-band accelerometer on the device layer. Later, the
deposited oxide layer was also etched from the top side using wet etching. A dry HF
vapour release technique was used to release the structure partially by etching away the
buried oxide (BOX). It can be noted that only the combs and the suspensions were
released in this step but the proof-mass was partially released. A fully released device can
be realized if a rather longer dry etching of oxide is performed. A partial release of the
proof-mass was planned for Phase- II where an anodic bonding of another silicon wafer
had to be performed on the processed SOI wafer. The partial release of the proof-mass
can avoid possible stiction or collapse of the proof-mass during anodic bonding where a
large potential difference is applied across the wafer. As stated earlier, the fabrication
ended with the development of the dual-axis accelerometer. Thus, we received the diced
accelerometer dies with completely released proof-masses. Phase-II of the process flow is
also given here for future reference. The entire process flow for Phase-I of the
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Chapter 6
microfabrication process is shown in Figure 6.4a-l. Figure 6.4l gives a completely
released wide-band dual-axis accelerometer.
50 µm
2 µm
650 µm
(a)
(b)
(c)
(d)
Figure 6.4: (a-l) Phase-I of the custom SOI-based process flow to fabricate a bulk-
micromachined wide-band dual-axis accelerometer (Contd.)
134
Chapter 6
(e)
(f)
(g)
(h)
(i)
Figure 6.4: (a-l) Phase-I of the custom SOI-based process flow to fabricate a bulk-
micromachined wide-band dual-axis accelerometer (Contd.)
135
Chapter 6
(j)
(k)
(l)
Figure 6.4: (a-l) Phase-I of the custom SOI-based process flow to fabricate a bulk-
micromachined wide-band dual-axis accelerometer.
6.5.1.2 Phase-II
The processed wafer from Phase-I is used in Phase-II. A new 500-µm thick bulk single
crystal silicon wafer will also be used for the fabrication of the top electrode of the
accelerometer. A thin layer (2 µm) of silicon dioxide is to be deposited on both the sides
of the bulk silicon wafer followed by spin-coating and lithography of photoresist on the
top side using the third mask called “TOP ELECTRODE”. The photoresist is to be
removed after RIE of the deposited thin silicon oxide. The patterned bulk silicon wafer is
to be flipped and bonded on top of the patterned SOI wafer as shown in Figure 6.5d. The
deposited oxide layer at the back side of the bulk silicon wafer is to be lithographically
patterned using the fourth and final mask called “VIA” followed by a DRIE process step
to define the vias to access the electrodes on the device layer of the SOI wafer. This is
shown in Figure 6.5f. A final HF vapour release is to be performed to release the proofmass and the other partially released moving parts. Wire-bonding is to be performed
136
Chapter 6
during the packaging process through the vias. The cross-section of the final tri-axial
device is shown in Figure 6.5g.
(a)
(b)
(c)
(d)
Figure 6.5: (a-f) Phase-II of the custom SOI-based process flow to be followed to extend
the dual-axis accelerometer to a tri-axial accelerometer (Contd.).
137
Chapter 6
(e)
(f)
(g)
Figure 6.5: (a-f) Phase-II of the custom SOI-based process flow to be followed to extend
the dual-axis accelerometer to a tri-axial accelerometer.
138
Chapter 6
Using Phase-I of the process, the dual-axis accelerometers were fabricated. A
complete 6 inch mask was developed and sent for fabrication using the microfabrication
facility of ECS Partners at the University of Southampton, UK. The 6 inch mask layout is
shown in Figure 6.6. The yield of this process was almost 98% and the devices were
found to be visually correct after an initial microscopic inspection. A few scanning
electron microscope (SEM) images of the device are shown in Figure 6.7a-g. Figure 6.8
shows the fabricated and diced devices inside a Gel-Pack container before shipment.
Figure 6.6: A 6 inch mask layout containing designs of wide-band dual-axis
accelerometers. The same mask layout can also be used for the fabrication of tri-axial
accelerometers.
6.6 Die-level characterization
As discussed in the previous chapters, the die-level dynamic measurements of the
fabricated wide-band dual-axis accelerometer were also performed using POLYTEC
MSA 500. The device placed below the vibrometer was probed and then actuated
electrostatically using an alternating voltage of 4.6 V above a DC bias of 10.7 V by
placing the probes on the gold contact pads of the die. Here, we used one set of sensecombs from each axis as drive-combs and the voltage was applied on those drive-combs
which were used to actuate the device along both the axes during die-level testing.
139
Chapter 6
(a)
(b)
(c)
Figure 6.7: (a-g) Scanning electron microscope (SEM) images of the fabricated dual-axis
accelerometer showing different parts of the accelerometer (Contd.).
140
Chapter 6
(d)
(e)
(f)
Figure 6.7: (a-g) Scanning electron microscope (SEM) images of the fabricated dual-axis
accelerometer showing different parts of the accelerometer (Contd.).
141
Chapter 6
(g)
Figure 6.7: (a-g) Scanning electron microscope (SEM) images of the fabricated dual-axis
accelerometer showing different parts of the accelerometer.
Figure 6.8: The diced devices placed inside a Gel-pack container for shipment.
6.6.1 Extraction of the frequency response
In order to find the frequency response of the accelerometer, the frequency of the applied
voltage was swept from 10 Hz to 20 kHz with a step of 10 Hz. The in-plane frequency
response along both the axes of the device is shown in Figure 6.9a-b. The experimentally
obtained in-plane modal frequencies were found to be 14.28 kHz for the X axis and 14.32
kHz for the Y axis. The 3 dB bandwidth of the sensor was found to be approximately 8.5
kHz for both the axes. The quality factor, Q , of the dual-axis accelerometer was found to
be approximately 26.
142
Chapter 6
f =14.28
n
Amplitude (nm) vs. Frequency (kHz)
f1 =14.0 f 2 =14.54
Phase vs. Frequency
900 Phase change
(a) Frequency response along the X axis
f n =14.32
Amplitude (nm) vs. Frequency (kHz)
f1 =14.1 f 2 =14.65
Phase vs. Frequency
900 Phase change
(b) Frequency response along the Y axis
Figure 6.9: (a-b). Experimentally obtained frequency response of the device along X and
Y axis.
6.6.2 Study of the step-response
The step-response of the accelerometer was obtained by actuating the micromachined
dual-axis accelerometer electrostatically along both the axes. A DC voltage of 40 V in the
form of a step function with a sufficiently large period was applied at both the drivecombs to actuate the device. As the device was excited, the displacement of the sensecombs along both the axes was measured optically and then plotted with respect to time
to achieve the step response of the device. The measured step-response of the device for
143
Chapter 6
the X axis is shown in Figure 6.10a. The step response of the device along the Y axis is
also similar.
(a)
2.4  107  e 2044t
2.34  107  e 2064t
(b)
Figure 6.10: (a) Experimentally obtained response of the accelerometer due to a step
excitation (b) Exponential decay of the step response of the accelerometer along both the
axes.
The peak amplitudes of the damped oscillation were plotted with time to obtain the
exponential decay of the damped oscillation for both the axes. The rate of exponential
decay was found from the best fit exponential curve of the data shown in Figure 6.10b.
Using Eq. (17) the value of the damping factor,  , for the dual-axis accelerometer is
144
Chapter 6
found to be about 0.023. The average time constant of the damped oscillation,  d , is
found to be 77.9 µs. The value of the logarithmic decrement,  , is found using the Eq.
(17) to be 0.16.
6.7 Integration and Packaging
The method used to integrate and package a dual-axis accelerometer is slightly different
from the technique used to package a single-axis accelerometer. In the case of packaging
a single-axis accelerometer, a printed circuit board (PCB) with all the components
becomes an integrated part of the attached micromachined accelerometer die. The entire
PCB becomes unusable for any other die. However, during the integration and packaging
of the fabricated dual-axis accelerometer, a different technique was adopted. In this case,
the dual-axis accelerometer die was wire-bonded and packaged inside a 44-pin leadless
chip carrier (LCC) package. The package was so chosen that it exactly fitted the dual-axis
accelerometer die. The PCB with the capacitive signal conditioning circuitry for
accommodating MS3110 Universal capacitance extraction ICs, the power supply ports,
the output ports, the passive inductors and bypass capacitors for noise cancellation and
filtering was fabricated. The schematic diagram of the PCB is given in Figure 6.11a. The
PCB also contains a 44-pin LCC socket that can fit the 44-pin LCC package. The PCB
does not require any gold-plated pads as the accelerometer die was placed inside the 44pin LCC package and the package can be placed inside the socket that can tightly fit the
LCC packages. Thus, an operative PCB can be used for any number of packaged dualaxis accelerometers as the packaged accelerometers can be removed from the socket.
Figure 6.11b shows the image of the wide-band dual-axis accelerometer die packaged and
wire-bonded inside a 44-pin LCC package whereas Figure 6.11c shows the customdesigned PCB with the 44-pin LCC socket and a packaged accelerometer placed inside
the socket.
6.8 Testing and Calibration
The packaged wide-band dual-axis accelerometer was tested and calibrated by mounting
the packaged accelerometer along with the evaluation board on a LDS vibration shaker
table. The experimental setup with the packaged device on the shaker table is shown in
Figure 6.12. The shaker table was excited at different values of acceleration (from 0.05 g
to 1.5 g) at a given frequency. The output voltage from the accelerometer for both the
145
Chapter 6
axes were recorded and plotted to get the calibration curve along both the X and Y axes.
The open-loop response of the packaged device is shown in Figure 6.13. The measured
sensitivity was around 62 mV/g along both the axes for 100 Hz and 200 Hz. The crossaxis sensitivity of the packaged accelerometer was also measured by mounting the
packaged accelerometer such that the acceleration due to gravity acted perpendicularly to
the measuring axis. The cross-axis sensitivity of the packaged dual-axis accelerometer
was measured to be less than 5% of the axial sensitivity for both the axes.
(a)
(b)
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(c)
Figure 6.11: (a) Schematic of a PCB that contains two MS3110 ICs for both the X and Y
axes, power supply including the voltage regulator and the output ports, (b) The wideband dual-axis accelerometer wire-bonded inside a 44-pin LCC package, and (c) The
custom designed and developed evaluation board along with a packaged dual-axis
accelerometer.
Oscilloscope
Packaged
Accelerometer
LDS Shaker
Power supply units
Figure 6.12: An experimental setup to test the integrated and packaged dual-axis
accelerometer on a vibration shaker table.
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Figure 6.13: The calibration curve of the packaged dual-axis accelerometer at different
frequencies.
6.9 Conclusion
We present here the design and development of a dual-axis capacitive in-plane wide-band
micro-accelerometer for high-frequency applications. The device was designed using the
concept of an XY stage that can de-couple any in-plane motion into its axial components.
Here, we used a modified de-coupling mechanism for sensing acceleration in any
direction of plane. The decoupling mechanism was designed by arranging 12 folded-beam
suspensions in a specific way to achieve a high cross-axial and rotational stiffness.
Differential capacitive comb-drives were appended to the ports of the de-coupling
mechanism to sense the axial components of the applied acceleration.
This dual-axis accelerometer design can be extended into a tri-axial accelerometer
design as the first three simulated mode shapes indicates equal compliance of the device
along the three orthogonal axes. The third mode, i.e., the out-of-plane motion of the
proof-mass can be utilized to capture the Z-axis component of the applied acceleration.
This can only be achieved if two electrodes are placed at the top and bottom of the proofmass thus making a differential capacitance arrangement. This calls for a custom
microfabrication process as SOIMUMPs does not support more than one structural layer.
The custom bulk-micromachining process using an SOI wafer was designed and Phase I
of the process was completed.
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The dual-axis in-plane accelerometer was fabricated. The device was then
packaged along with MS3110 capacitance extraction ICs. A custom PCB was developed
to test the packaged devices. The measured sensitivity of the dual-axis in-plane
accelerometer was found to be 63 mV/g with a 3dB bandwidth of 8.5 kHz. The minimum
resovable capacitance acceleration by the accelerometer was found to be 15 milli-g
whereas the required specification was 10 milli-g. The quality factor of the device was
found to be about 26. Vacuum packaging might give a better quality factor along with
better voltage sensitivity and reduced damping. This work will be taken up later.
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Development of Meso-scale Spring-Steel
Accelerometers
Summary
This chapter deals with the work done on the development of meso-scale accelerometers
using spring steel as the structural material. We started the work with the design and
development of a single-axis meso-scale spring steel accelerometer with a DaCM.
Another single-axis accelerometer with the same footprint was also developed without
using a DaCM. Both the single-axis meso-scale accelerometers were tested and
calibrated with respect to a standard accelerometer. The dynamic sensitivity, frequency
response and the cross-axial sensitivity of both the accelerometers were measured and
compared. The test results reaffirm that an improved accelerometer in terms of sensitivity
and bandwidth is achievable using a DaCM and this claim is scale-independent. Also
presented in this chapter is the development of two dual-axis accelerometers. They use
two different de-coupling mechanisms. The most interesting feature of the first device is
the use of Li-ion batteries as the extra proof-mass while it acts as the power supply for
the Hall-effect sensors used for sensing the displacement. Thus, the first device becomes a
stand-alone sensor that can directly be used without the requirement of any external
power source. The second device is more compact in size as compared to the first device.
It also has a better cross-axis performance as compared to the first one. The use of spring
steel and off-the-shelf electronics make the sensors cost-effective and potential candidates
for a low-volume market.
7.1 Objective of the work
The development of meso-scale dual-axis accelerometers presented in this chapter fulfils
two objectives. The single-axis spring-steel accelerometer with a DaCM proves again that
the sensitivity and bandwidth of accelerometers can be improved simultaneously and thus
the trade-off between the sensitivity and bandwidth of the accelerometer can be avoided.
This part of the work also proves that the claim made in the previous sentence is also
scale and material independent, i.e., the use of a DaCM can be beneficial irrespective of
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the size and the material used to fabricate the accelerometers. The second part of work
presented in this chapter, i.e., the development of dual-axis spring steel accelerometers
establishes the viability of the use of spring steel for developing meso-scale cost-effective
sensors such as accelerometers for a small volume market.
7.2 Accelerometers in micro and meso scale
Commercially available micromachined accelerometers packaged in the form of ICs have
sizes of the order of a few mm to cm. But when it comes to the functionality of these ICs,
they cannot be operated as stand-alone units. They all require evaluation boards on which
the accelerometers are to be mounted or soldered along with other circuit components.
These circuit components are required for providing power supply ports, I/O ports and
also for the purposes of further signal conditioning such as filtering, analog to digital
conversion etc. Thus, the size of the microaccelerometer ICs along with their evaluation
boards becomes much bigger of the order of a few cm. An example of such a
commercially available accelerometer with its evaluation board is shown in Figure 7.1.
A micromachined
accelerometer IC
A micromachined
accelerometer with its
evaluation board
A meso-scale spring
steel accelerometer
Figure 7.1: Size comparison of a meso-scale spring-steel accelerometer with respect to a
commercially available micromachined accelerometer mounted on its evaluation board.
Also shown in the figure is a meso-scale spring steel accelerometer packaged
inside an acrylic casing along with two Li-ion batteries that supply power to its signal
conditioning electronics described later in this chapter. It can be seen that the developed
meso-scale accelerometer has comparable size. So, these meso-scale accelerometers can
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also be used for applications where these micromachined accelerometers are used
provided they meet sensitivity, bandwidth and other requirements. Furthermore, the unit
price for this type of commercially available accelerometer is of the order of a few 100s
of rupees. But, when it comes to evaluation boards, the cost is often 10-100 times the cost
of the IC chip for each piece. Therefore, in this chapter, we report the work done towards
the development of cost-effective meso-scale accelerometers using spring-steel that can
be used as a potential replacement for micromachined accelerometers where the
requirement for volume production is low. An introduction to meso-scale was given in
Chapter 1 along with the rationale for using spring steel for the development of mesoscale accelerometers.
7.3 Single-axis meso-scale spring steel accelerometers with and without
a DaCM
In this section, we present the development of meso-scale spring-steel single-axis
accelerometers. Two accelerometers, one aided with a DaCM and the other without it,
were designed. Both the accelerometers have the same foot-print. Thus, the accelerometer
which is aided with a DaCM has a smaller proof-mass compared to that of the
accelerometer without a DaCM. Both the accelerometers are designed, analyzed,
fabricated, packaged and tested.
7.3.1 Mechanical designs
Both the accelerometers contain a proof-mass suspended by four 10 mm long and 0.2 mm
wide beams. The size of the proof-mass in the accelerometer that contains a DaCM is 20
mm × 30 mm, whereas the proof-mass of the accelerometer without a DaCM is 20 mm ×
45.98 mm. The design was fabricated by machining a spring steel foil of 0.5 mm
thickness. The footprints of both the accelerometers were 40 mm × 46 mm. Extra masses
were added to the top and bottom of the 0.5 mm-thick spring-steel sheet by adding 2 mmthick spring-steel pieces cut in the size of their respective proof-masses. The
accelerometer with a smaller proof-mass is aided with a non-inverting type DaCM
designed using the stiffness-based selection map technique. The design procedure is the
same as discussed for the micromachined accelerometers designed in the previous
chapters of this thesis. The method is not included here to avoid repetition.
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The top-view of both the accelerometers along with their dimensions is shown in
Figure 7.2. It can be noticed from Figure 7.2 that the size of the proof-mass is larger in
the design without a DaCM than in the design with a DaCM while the footprint of both
the designs are the same. The 3D continuum models of the single-axis meso-scale
accelerometers that were used for a 3D finite element analysis were shown in Figure 7.3.
The minimum feature size for both the designs was set at 0.2 mm. The width of all the
beams of the DaCM and the beams used as proof-mass suspensions are kept at 0.2 mm
except for the beam at the output of the DaCM. This is 1.5 mm wide because a tiny diskmagnet is to be attached there. The motion of the disk magnet will be sensed by a Halleffect sensor which is used for sensing the displacement in the from meso-scale
accelerometers.
All the dimensions are in mm
Figure 7.2: The top view of the designs of the two meso-scale accelerometers along with
their dimensions. The left one is a single-axis meso-scale accelerometer with a DaCM
whereas the right one has no DaCM.
7.3.2 Analysis and performance comparison
A finite element analysis was performed using COMSOL Multiphysics [78] on the 3D
continuum models of both the designs shown in Figure 7.3. Both static and
eigenfrequency analyses were performed. The effect of geometric nonlinearity was taken
into account during all the analyses. Static displacement sensitivity and cross-axial
sensitivity were simulated for both the designs using a static analysis whereas the modal
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frequencies and modes of vibration were found using an eigenfrequency analysis. The
static analysis for both the designs is shown in Figure 7.4a-b.
(a)
(b)
Figure 7.3: The 3D model of (a) the single-axis meso-scale spring steel accelerometer
with a DaCM and (b) the one without a DaCM.
During the static analysis, a body load of 1 g is applied along the sensitive axis
(here the Y axis) and the displacements of the points of maximum displacement for both
the designs were measured. The output of the DaCM is the point of maximum
displacement for the design with a DaCM, whereas the maximum displacement occurs at
the proof-mass for the design without a DaCM. It is observed that the static displacement
sensitivity of the design with a DaCM is 92.4 µm/g and the same for the design without a
DaCM but with a larger proof-mass, is 66.6 µm/g. Thus, the simulated net amplification
(NA) achieved using the DaCM is 1.39. That indicates that, by design, an improvement of
39% in sensitivity is achieved using a DaCM.
The modes of vibration of both the designs were also simulated. The first four
simulated modes of the single-axis meso-scale accelerometer with a DaCM are shown in
Figure 7.5 whereas the modes of vibration of the design without a DaCM are shown in
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Figure 7.6. It can be seen that the first modes of vibration of both the designs are in-plane
modes. As we know, the first natural frequency involving in-plane motion of a device
decides the bandwidth of the device. The first natural frequency of the design with a
DaCM was found at 86 Hz while the same for the design without a DaCM is 61 Hz.
Therefore, an improvement of bandwidth by ~ 41% is achieved using a DaCM.
Maximum displacement at the
output of DaCM ~ 92.4 µm
1 g load along Y
(a)
Maximum displacement at the
output of DaCM ~ 66.6 µm
1 g load along Y
(b)
Figure 7.4: Static finite element analysis of (a) the single-axis meso-scale accelerometer
aided with a DaCM and (b) the one without a DaCM using COMSOL Multiphysics.
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163 Hz
86 Hz
301 Hz
455 Hz
Figure 7.5: The simulated first four modes of vibration of the single-axis meso-scale
spring steel accelerometer model with a DaCM.
61 Hz
133 Hz
239 Hz
375 Hz
Figure 7.6: The simulated first four modes of vibration of the single-axis meso-scale
spring steel accelerometer model without a DaCM.
The cross-axial sensitivity or the transverse sensitivity of the single-axis mesoscale spring-steel accelerometer with a DaCM is simulated using COMSOL Multiphysics
by applying an off-axial load of 1 g along the X-axis while the Y-axis is the sensitive axis
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for the accelerometer. The total displacement due to the cross-axial load of 1 g is
measured to be 0.3 µm at the output of the DaCM. Therefore, the simulated cross-axial
sensitivity of the accelerometer becomes approximately 0.3% of the axial sensitivity. The
simulated figure of the device with an off-axial load is shown in Figure 7.7.
Maximum off-axial displacement ~ 0.3 µm
1 g load
Figure 7.7: The deflection at the output of the DaCM due to the application of an cross-
axial load of 1 g applied along the X-axis of the device.
7.3.3 Prototyping
The designed meso-scale single-axis spring steel accelerometer was fabricated using
Wire-cut Electro-Discharge-Machining (EDM) (Make: Mechanica, Maxicute). The Wirecut EDM machine is shown in Figure 7.8a. The minimum feature that can be fabricated
using this machine is 0.2 mm whereas the minimum possible gap between two structures
is 1.5 mm. A 0.5 mm-thick spring-steel (EN J42/AISI 1080) foil was machined using
Wire-cut EDM to fabricate the shape of the accelerometer. Several holes were drilled
prior to Wire-cut EDM in order to thread the wire through the metal foil.
Steel blocks of 2 mm thickness were cut 1 mm smaller in size from all the edges of
the proof-masses of the respective designs using a CNC machine and were attached to the
top and bottom surfaces of the proof-mass on the accelerometers. The dimensions of the
steel blocks added to the existing proof-mass of the design with a DaCM are 18 mm × 28
mm × 2 mm whereas the same for the design without a DaCM are 43.97 mm × 18 mm ×
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2 mm. The machined parts of the accelerometer with a DaCM are shown in Figure 7.9.
The accelerometer structure machined using wire-cut EDM on a 0.5 mm-thick spring
steel foil is shown along with two 2 mm-thick steel blocks.
Figure 7.8: The Wire-cut Electro-Discharge-Machining facility at the Department of
Mechanical Engineering, Indian Institute of Science, Bangalore.
DaCM output port
Steel
block
DaCM
Figure 7.9: The machined parts of the spring-steel accelerometer with a DaCM before
manual assembly.
7.3.4 Signal conditioning using a Hall-effect proximity sensor
In this work, linear Hall-effect proximity sensors (Allegro A1395) were chosen to sense
the displacements of the moving parts of the accelerometers. The working principle of a
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Hall-effect sensor is that a potential difference arises across an electrical conductor,
transverse to the direction of the current in the conductor when the magnetic field is
perpendicular to the current. This is a non-contact proximity sensor. The output voltage of
the Hall-effect sensor changes as the magnetic field across the sensor varies.
Hall-effect
sensor IC
Neodymium
disk magnet
(a)
Hall-effect sensor IC
9.8 mm
13.8 mm
(c)
(b)
Figure 7.10: (a) Linear Hall-effect sensor and the Neodymium disc magnet, (b) Custom
PCB with the Hall-effect sensor soldered on it, (c) Calibration curve of the linear Halleffect sensor used for this work.
A linear Hall-effect sensor IC of size 2.0 mm × 3.0 mm × 0.75 mm with a microlead package (MLP/DFN) [131] and commercially available Neodymium (NdFeB) disc
magnets, shown in Figure 7.10a, with a 3 mm diameter and 1.5 mm thickness are used in
this work for displacement-sensing. The disk magnets were attached to the moving parts
of the accelerometers. For the design with a DaCM, the disk magnet was attached to the
output end of the DaCM, whereas it was attached to the proof-mass for the design without
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a DaCM. A custom-designed PCB, shown in Figure 7.10b, containing a Hall-effect sensor
was attached to the stationary part of the device at a distance of 4.5 mm from the magnet.
The magnetic field of the disk magnet was measured to be 3100 Gauss and the sensitivity
of the Allegro A1395 linear Hall-effect sensor is 10 mV/Gauss. The optimal distance of
4.5 mm was arrived from the calibration curve of the Hall-effect sensor, shown in Figure
7.10c, to operate it in a nearly linear region. Finally, the batteries, acting as extra proofmasses, are also connected to the PCBs containing the Hall-effect sensors through wires.
7.3.5 Integration and packaging
Two spring-steel blocks were attached to the top and bottom of the proof-mass to add
sufficient mass to the device. The entire assembly was performed manually and the
assembled parts were attached on an acrylic base. The disk-magnet was pasted on the
output end of the DaCM, whereas the PCB containing the Hall-effect sensor was placed
at a distance of 4 mm from the magnet.
7.3.6 Testing and calibration
The assembled device was placed on a vertical turn-table and rotated precisely. The
component of gravitational acceleration along the sensitive axis of the accelerometer
varies as the device rotates. The experimental setup for the static testing of the device is
shown in Figure 7.11.
PCB containing
Hall-effect sensor
Vertical
turn table
the
Assembled
accelerometer
Figure 7.11: The experimental setup for the static testing of a fabricated single axis
spring-steel accelerometer with a DaCM using a vertical turn-table.
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The output voltage of the accelerometer which was recorded as the device on the
vertical turn-table was rotated from -900 to 00, then from 00 to 900 with a step of 100. -900
corresponds to a position where the entire device is placed vertically with the DaCM
facing the ground whereas 900 corresponds to a position where the DaCM faces upwards
and is vertical. The horizontal placement of the device is designated by 00. Thus, the static
acceleration due to gravity acting along the sensitive axis varies from -1 g to 1 g. The
output voltage from the Hall-effect sensor was plotted to get the calibration curve of the
single axis spring- steel accelerometer with a DaCM. The measured value of sensitivity
was 71.4 mV/g from the static calibration curve shown in Figure 7.12. The noise present
in the signal was measured around 1 mV when the device was placed on a vibration
isolation table with the device caged within a conductive enclosure to reduce the 50 Hz
noise interference. Thus, the minimum detectable acceleration using a single-axis springsteel accelerometer with a DaCM becomes 14 milli-g.
Sensitivity = 71.4 mV/g
R2 error ~ 0.9932
Figure 7.12: Experimentally obtained calibration curve of a single-axis spring-steel
accelerometer with a DaCM.
7.4 Development of a dual-axis meso-scale spring-steel accelerometer
without mechanical amplification
Apart from developing single-axis meso-scale accelerometers with and without a DaCM,
we also report here the development of dual-axis meso-scale accelerometers without
mechanical amplification. Two dual-axis accelerometers were designed and fabricated
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with two different types of de-coupling mechanisms. Both the devices were fabricated,
assembled, packaged, and tested successfully.
7.4.1 First prototype of meso-scale dual-axis accelerometer
In this section, the development of the first prototype of a meso-scale dual-axis spring
steel accelerometer is presented. The design of the dual-axis accelerometer is discussed,
ans is followed by the prototyping of the device. The finite element simulation of the
mechanical component of the accelerometer is discussed. In this work, too, Hall-effect
based proximity sensors have been used for sensing the displacement of the proof-mass.
The Hall-effect sensors also require an external DC power supply to operate. For this
purpose, rechargeable Li-Ion batteries are used as in-built power sources to the Halleffect sensors. The batteries are used as part of the proof-mass of the accelerometer.
Finally, integration of the signal conditioning circuit with the prototype and packaging of
the device are also discussed along with the calibration and testing of the prototype.
7.4.1.1 Design
The design of the first prototype of the meso-scale dual-axis accelerometer uses the
design of a compliant XY stage discussed in Section 5.2 of Chapter 5. Here, we use it for
the purpose of sensing with required modifications to make it an accelerometer. Using the
XY stage, the proof-mass is allowed to move along any arbitrary direction in the plane of
the applied acceleration, whereas ports X and Y move by the respective X and Y
components of the displacement of the proof-mass in that plane. The modified version of
the XY stage used in the accelerometer is shown in Figure 7.13a. It has an overall
dimension of 73 mm × 73 mm × 0.5 mm. The proof-mass is the point of maximum
displacement for a conventional single-axis accelerometer. But, in this dual-axis
accelerometer design, ports X and Y are the maximum points of displacements along the
X and Y directions respectively. Thus, the displacement of the proof-mass along the X
direction can be captured by measuring the displacement at port X and at port Y.
Sensitivity is one of the most significant specifications of an accelerometer. The
stiffness of the folded beam suspension and the inertia of the proof-mass determine the
sensitivity of an accelerometer. Thus, for a given suspension geometry, the sensitivity can
only be improved by increasing the mass of the proof-mass. In this work, we have
enhanced the sensitivity of the accelerometer by attaching spring-steel blocks and Li-ion
batteries to the accelerometer proof-mass and thus increased the inertia of the
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accelerometer. The isometric view and the side view of the solid model of the device,
made in SolidWorks [132], are shown in Figure 7.13b-c respectively.
73 mm
Port Y
73 mm
Port X
(a)
Li-Ion Battery
Li-ion Battery
Li-Ion Battery
Steel
block
(c)
(b)
Figure 7.13: (a) A modified XY flexure used as a dual-axis accelerometer, (b) Isometric
view of the first prototype of a meso-scale dual-axis accelerometer with two Li-ion
batteries attached to the top and bottom of the metal proof-mass, (c) Side view of the
proposed device showing the arrangement to increase the proof-mass using Li-ion
batteries and steel blocks.
7.4.1.2 Finite element analysis of the design
A finite element analysis was performed using COMSOL Multiphysics software [78] on
both the 2D and 3D models of the designed device. Initially, a static, geometrically
nonlinear, elastic analysis was performed by applying the inertial force as a body force on
the mechanism without an extra proof-mass due to batteries. As can be seen in the finite
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element simulation result in Figure 7.14, the stage moves by exactly 30% in the Ydirection as compared to that in the X-direction because the applied acceleration is 0.3 g
in the Y-direction while it is 1 g in the X-direction. In the prototype, the magnets are
attached at the portions indicated as ports X and Y while the Hall-effect sensors were
attached to a fixed frame opposite to the magnets.
Port Y 2.89µm
Port X 9.64 µm
0.3g
1g
Figure 7.14: FE simulation showing the XY flexure mechanism de-coupling two
different input accelerations along its X and Y axes.
The cross-axial coupling is simulated to be approximately 0.6% of the axial
displacement which is quite good for an accelerometer application. A modal and
frequency response analysis was also performed on the 3D model of the accelerometer
along with the steel blocks and the batteries acting as the extra proof-mass. The
displacement characteristics are the same for ports X and Y as the structure is
geometrically symmetric about both the X and Y axes. The 3 dB bandwidth of the device
was simulated to be 20 Hz whereas the natural frequency is around 36.3 Hz. The
simulated frequency response (without damping) of the 3D model is shown in Figure
7.18b.
7.4.1.3 Prototyping
The designed meso-scale dual-axis spring steel accelerometer was fabricated using Wirecut EDM by cutting a 0.5 mm-thick spring-steel foil in the shape of the dual-axis
accelerometer shown in Figure 7.15.Two 2 mm-thick steel blocks were cut in the size of a
proof-mass using a CNC machine and were attached to the top and bottom surface of the
proof-mass on the accelerometer. The dimensions of each of the steel blocks added to the
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existing proofmass are 15.625 mm × 15.625 mm × 2 mm. In order to attach Li-ion
batteries of size 40.78 mm × 40.06 mm × 5.7 mm to the proof-mass, two acrylic cases,
serving as the housing for the batteries, were made using the CNC machine and attached
to the free surfaces of the top and bottom metal blocks. The attached batteries are elevated
by 2 mm from the de-coupling mechanism using those two 2 mm-thick steel blocks and
become a part of the proof-mass. Thus, the batteries are detachable from the proof-mass
and can be replaced after recharge whenever required.
Figure 7.15: The XY stage used for the first prototype of a dual-axis spring-steel
accelerometer realized on 0.5 mm thick spring steel foil using Wire-cut EDM.
7.4.1.4 Packaging and integration to Hall-effect sensors
As discussed in Section 7.4.1.1, the displacements of ports X and Y indicate the inertial
force felt by the proof-mass due to the applied acceleration along both the X and Y
directions. Linear Hall-effect proximity sensors [131] were used here to sense the
displacements of ports X and Y. Two disk magnets were attached to the X and Y ports of
the dual-axis accelerometer and two custom designed PCBs containing Hall-effect
sensors were attached to the fixed frame 4.5 mm away from the disk magnets.
An acrylic housing arrangement with top and bottom covers was fabricated using
CNC machining for the entire device. The device was placed inside the acrylic housing
and the final manual assembly, shown in Figure 7.16a-b, was performed using screws.
Windows were cut in the housing arrangement to take out the output leads from the PCBs
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containing the Hall-effect sensors. The overall dimensions of the packaged meso-scale
spring steel dual-axis accelerometer are 73 mm × 73 mm × 28.5 mm.
Li-ion battery
Port Y
Port X
(b)
(a)
Figure 7.16: (a) First prototype of a packaged meso-scale spring steel dual-axis
accelerometer with a yellow cover and (b) without a cover exposing the top Li-ion battery
acting as an extra proof-mass as well as a power source for the Hall-effect sensor at Port
Y.
7.4.1.5 Calibration and testing
The packaged meso-scale dual-axis spring-steel accelerometer was mounted on an LDS
shaker table which can vibrate within a specified range of acceleration and frequency. A
commercially available 3-axis analog milli-g accelerometer, made of ST Microelectronics
(Model: LIS3L02AS4) [128], was used as a reference accelerometer to calibrate the
meso-scale dual-axis accelerometer and control the shaker table. The experimental setup
is shown in Figure 7.17.
The shaker table along with the device under test was vibrated at different
frequencies with an amplitude of vibration of 0.2 g. An oscilloscope was used to record
the output of both the axes. The frequency response of the dual-axis accelerometer along
the X axis was obtained by plotting the output of the Hall-effect sensor, mounted along
the X axis of the accelerometer, with respect to the frequency of the applied acceleration.
The experimentally obtained frequency responses for both the X and Y axes are shown in
Figure 7.18a with the simulation curve superimposed on it. The experimentally achieved
first two in-plane natural frequencies of the accelerometer are 39.5 Hz and 52 Hz for the
X and Y axes respectively whereas the 3 dB bandwidth of the accelerometer is
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approximately 28 Hz for both the axes. It may be noted that the simulated first natural
frequency is 36.3 Hz along both the axes.
The shaker table along with the device under test was again vibrated at different
acceleration values varying from 25 milli-g to 0.7 g at a fixed frequency of 10 Hz. The
output of the sensor for both the X and Y axes was recorded and then plotted to get the
calibration curve of the meso-scale spring steel dual-axis accelerometer which is shown in
Figure 7.18b. The experimentally obtained sensitivity of the developed accelerometer is
78 mV/g and 102 mV/g approximately for the X and Y axes, respectively, with a
minimum detectable acceleration of 25 milli-g for both the axes. The measurements made
on the prototype showed significant asymmetry and lack of orthogonal de-coupling along
the two in-plane axes. This asymmetry was attributed to the imprecision in manual
assembly, the influence on Hall-effect sensing due to possible rotations of the heavy
proof-mass about the in-plane axes, and low out-of-plane stiffness.
Meso-scale
accelerometer Reference
accelerometer
Analog output display
Vibration
Shaker table
Figure 7.17: Experimental setup showing the developed first prototype of a meso-scale
dual-axis spring-steel accelerometer being calibrated with respect to a reference
accelerometer on a vibration shaker table.
Also shown in Figure 7.18b are the linear fits to the simulated data. It can be seen
that the simulation shows a sensitivity of about 140 mV/g. This discrepancy between the
simulation and the experiment is could primarily be due to the package, the casing that
holds the batteries, in particular. It is suspected that this is also the reason for the
asymmetric experimental data in the X and Y axes.
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Off-axial sensitivity was also measured by applying an off-axial load on the device
under test and measuring the output of the sensor with respect to the output of the sensor
when an axial loading is applied. Off-axial sensitivity is generally expressed in terms of
% of the axial sensitivity. The off-axial sensitivity of this accelerometer was measured to
be 13.09 % and 12.08 % for the X and Y axes, respectively.
Simulated bandwidth ~ 20 Hz
Experimental bandwidth ~ 28 Hz
(a)
(b)
Figure 7.18: (a) Plot showing the simulated and experimentally obtained frequency
response of the first prototype of the meso-scale dual-axis spring-steel accelerometer for
both the X and Y axes, (b) Plot showing experimentally obtained calibration curve of the
sensor for both the X and Y axes.
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7.4.2 Second prototype of a dual-axis meso-scale spring-steel accelerometer
In the second prototype of the meso-scale device, we present an alternative design of the
suspension and avoid attaching the batteries. Consequently, the size is also reduced
significantly. The changes are aimed at achieving better de-coupling of the two in-plane
axes. The new design and assembly are described next, and are followed by the
experimental results and concluding remarks.
7.4.2.1 Design
In addition to the reasons stated in the preceding section for the large discrepancy
between the sensitivities along the two in-plane axes of the first prototype, we suspect
that there is another reason. This has to do with the geometric complexity of the design
and the number of slender beam segments in it. As can be seen in Figure 7.13a, there are
eight folded-beam suspensions present and each folded-beam suspension contains four
beams. Any mismatch in the machining of these 32 beams would result in asymmetry.
Therefore, in this work, we consider another design shown in Figure 7.19. This design is
generally used in micro machined gyroscopes [133] to have a degenerate pair of natural
frequencies. The new design has only 16 beams, half of which are aligned with one inplane axis (labelled X-axis) and the other half along the Y-axis. A portion in the form of a
Swiss-cross (the plus sign) is at the centre in order to attach additional steel pieces of the
same shape on either side to act as the proof-mass. The circular holes indicate the
locations where the spring-steel foil will be first drilled in order to pass the wire in wirecut EDM. There are 12 holes in the interior. Thus, 12 cuts are made to create the 16
beams and the central plus-shaped portion for affixing the proof-mass. Four more holes in
the corners are made to enable assembly of the complete sensor. Two rectangular cuts at
the top and right side are meant for mounting the Hall-effect sensor and its custom-made
evaluation PCB.
7.4.2.2 Prototyping and Integration
A spring-steel sheet of 0.2 mm thickness was used to cut the suspension and the proofmass as per Figure 7.19. This was done on a wire-cut EDM system. The fabricated
spring-steel sheet is shown in Figure 7.20 on the left side. Each beam in it is 7 mm-long
and 0.25 mm wide. Smaller widths than 0.25 mm are possible but not reliably
reproducible. Micro EDM may be necessary to reliably achieve very small widths. It can
be noticed in Figure 7.20 that there is enough or a rigid portion along either axis to mount
169
Chapter 7
a permanent magnet opposite to which the Hall-effect sensors can be mounted. Shown
also in Figure 7.20, on the right side, is a plus-shaped steel piece, which was also cut
using wire EDM. This has a thickness of 2 mm. In order to add sufficient mass to the
proof-mass, two such pieces are needed to be mounted on each side of the spring-steel
sheet.
Port Y
Port X
Figure 7.19: Design of the suspension of the second prototype of an in-plane dual-axis
spring-steel accelerometer.
Figure 7.20: Wire-cut patterned spring-steel sheet with its suspension and provisions for
the mounting the proof-mass pieces, magnets, and Hall-effect sensors along with their
PCBs.
170
Chapter 7
As in our single-axis meso-scale accelerometer and first prototype of the dual-axis
meso-scale accelerometer, we used a Hall-effect sensor integrated circuit (IC) chip
(Allegro A1395) of size 2.0 mm × 3.0 mm × 0.75 mm with a micro-lead dual flat no-lead
(MLP/DFN) package [131] in this work. The magnets were affixed on the moveable
portions next to the rectangular cuts in the patterned spring-steel foil shown in Figure
7.20. A printed circuit board (PCB) was designed to accommodate the sensor IC and its
five leads onto solderable pads. Two such PCBs with the IC and soldered wires were
mounted on the non-movable frame next to the NdFeB magnets as can be seen in Figure
7.21. An acrylic casing was machined for the purpose of accommodating all the pieces.
Figure 7.21: The complete accelerometers in an acrylic casing with the IC on a PCB, two
extra plus-shaped masses attached on the spring-steel foil, the leads for taking the
readings. One PCB is seen at the top while the other is underneath and on the right side,
where the leads can be seen. There are another plus-shaped mass underneath on the other
side of the spring-steel foil.
A suitable distance of 4 mm was decided based on the calibration curve of the
Hall-effect sensor shown in Figure 7.10c. Thus, the PCBs were mounted at about this
distance. The voltage reading of the Hall-effect sensor is to be used as per this calibration
curve to arrive at the distance between the magnet and the sensor IC. As can be seen in
Figure 7.21, the entire assembly fits within a volume of 42 mm × 42 mm × 23 mm. Such
a size may be acceptable for some applications that demand cost-effective solutions for
small-volume markets.
171
Chapter 7
7.4.2.3 Testing and result
The assembled and integrated prototype was tested to obtain the dynamic response. The
experimental setup for measuring the dynamic response is shown in Figure 7.22. The
equipment used in this setup included a vibration shaker (LDS), a power supply, and an
oscilloscope. The accelerometer was mounted on the platform of the LDS shaker and then
vibrated. The output of the accelerometer was measured using an oscilloscope. Two
different types of experiments were carried out using this setup.
2nd generation
device
Response on the
Oscilloscope
LDS Shaker
Power
Supply Unit
Figure 7.22: Experimental setup for dynamic testing of the developed second prototype
of the meso-scale spring-steel accelerometer using an LDS shaker table.
The first experimental task was the extraction of the frequency response of the
developed sensor where the device under test was shaken at an acceleration of 0.5 g for
different frequencies starting from 10 Hz to 200 Hz. The output from the sensor was
measured and then plotted. The accelerometer was tested separately for the two axes. The
measured output is shown in Figure 7.23. Once again, it can be seen that the response
along both axes is almost the same. According to the experiment, it can be seen that the
first two resonance frequencies are about 33 Hz and 103 Hz.
The second experiment that was carried out was the dynamic calibration of the
device where it was vibrated at a fixed frequency of 10 Hz for different values of
acceleration starting from 0 to 1g for both the axes. The dynamic calibration curve for
172
Chapter 7
both the axes is shown in Figure 7.24 which shows that the sensitivity of the developed
meso-scale spring steel accelerometer is around 40 mV/g for both the axes.
Figure 7.23: Experimentally observed frequency response of the second prototype of a
meso-scale spring-steel accelerometer along both the axes.
Figure 7.24: Dynamic calibration curve of the second prototype of a meso-scale spring-
steel accelerometer along both the axes.
7.5 Conclusion and Closure
In this paper, we described the work done on the development of meso-scale
accelerometers made of spring steel and equipped with linear Hall-effect sensors. At the
beginning, a single-axis meso-scale accelerometer aided with a DaCM was designed.
173
Chapter 7
Also designed was a single-axis meso-scale accelerometer that did not contain a DaCM
but occupied the same footprint area. The second one contained a larger proof-mass
compared to the first one. The accelerometer with a smaller proof-mass and with a DaCM
was simulated to have 39% more sensitivity with 41% more bandwidth as compared to
the design without a DaCM. A single-axis spring-steel accelerometer with a DaCM was
fabricated using the Wire-cut EDM technique and assembled manually. The static
calibration of the fabricated accelerometer was performed by mounting the device on a
vertical turn-table and rotating it from -900 to 900. The sensitivity of the device was found
to be 71.4 mV/g with a minimum detectable acceleration of 14 milli-g. The cross-axial
sensitivity was found to be less than 1% of the axial sensitivity.
The first prototype of the dual-axis accelerometer uses a modified XY flexure
mechanism for de-coupling the input excitations in a plane into its orthogonal
components in that plane. The accelerometer was fabricated by cutting a 0.5 mm-thick
spring-steel foil using Wire-cut EDM. Two 40.78 mm × 40.06 mm × 5.7 mm Li-ion
batteries, used as power sources of the Hall-effect sensor, were also used as extra proofmasses of the accelerometer. Hence, the prototype of the accelerometer did not require
any external power supply to operate. The final assembly of the parts of the accelerometer
was performed manually and thus misalignment could not be avoided. The prototype was
mounted on a shaker table and then tested and calibrated with respect to a reference
accelerometer. It was observed that the accelerometer did not have similar characteristics
along both the axes because of misalignment during manual assembly, asymmetry in the
battery dimension, and an unequal distance between the moving disk magnet and the
Hall-effect sensor IC in both the X and Y axes. The experimentally observed in-plane
natural frequency was at 39.5 Hz for the X axis and 52 Hz for the Y axis whereas the 3
dB bandwidth was obtained at 28 Hz approximately for both the axes. The sensitivity of
the accelerometer was 78 mV/g and 102 mV/g for the X and Y axes respectively with a
minimum detectable acceleration of 25 milli-g. Though the prototype used a perfect decoupling mechanism, the sensor was quite sensitive along the transverse direction due to
asymmetric manual assembly. This can be improved further by the design of the
compliant suspension. This and other improvements will be taken up in our future work
to establish spring steel as a viable material for meso-scale applications.
By making the improved prototype of the second generation of spring-steel dualaxis in-plane accelerometers successfully, it has been shown here that it is indeed viable
174
Chapter 7
to have steel meso-scale accelerometers made only with workshop technology. The
improvements of the accelerometer are the size and near-perfect de-coupling of the
response along the two in-plane axes. The accelerometer presented in this paper has a
footprint of 40 mm × 40 mm and a thickness of less than 25 mm with space for encasing
the batteries. The sensitivity is 40 mV/g, which needs to be improved with modifications
in the design and incorporating mechanical amplifiers and other types of displacementsensing sensors. The ultimate goal of this work is to prove the viability of spring-steel
accelerometers that can compete with silicon devices.
175
Chapter 8
Conclusion and future scope
Large proof-mass, low stiffness of the suspension, small inter-finger-gap in capacitive
combs, high circuit gain of the interface electronics, and low damping help enhance the
sensitivity and resolution of micromachined capacitive accelerometers. But large proofmass and low stiffness decrease the resonance frequency and hence the bandwidth. Thus,
there is a trade-off present between the sensitivity and bandwidth of the accelerometers.
In this thesis, it is shown that mechanical amplification using Displacement-amplifying
compliant mechanisms (DaCMs) help increase both the sensitivity and resonance
frequency simulataneously without adding much noise to the system.
Two of the best single-axis accelerometers from the literature are used to show
that appending DaCMs to the existing designs enhances their sensitivity and resonance
frequency. An important point to note is that a DaCM occupies the space relieved by the
reduced proof-mass. Consequently, the overall footprint remains the same as that of the
original devices without the DaCMs reported in the literature. The method of designing
DaCMs uses a selection map-based interactive design technique that begins with userspecifications and accounts for practical considerations such as maximum stress and
minimum feature sizes.
A single-axis wide-band capacitive in-plane accelerometer equipped with a DaCM
was designed and fabricated. The DaCM used here is a non-inverting DaCM with high
geometric amplification of 11. The designed single-axis accelerometer was found to be
about 6.5 times more sensitive compared to a design with the same footprint and without
a DaCM. But it was also noticed that in the first in-plane natural frequency reduced due to
the presence of flexible parts in the DaCM. The designed device was fabricated using a
multi-user MEMS process, namely, SOIMUMPs. The fabricated device was tested at the
die level using Laser Doppler Vibrometer to extract the dynamic characteristics of the
device. Later, the device was packaged along with an off-the-shelf commercially
available universal capacitance extraction IC on a custom-designed gold-plated PCB. The
device was tested and calibrated dynamically by mounting it on a vibration shaker.
176
Chapter 8
A new low-g dual-axis capacitive in-plane accelerometer that includes two DaCMs
was designed, fabricated, integrated with electronics, packaged and tested successfully.
The main conclusions from the work are: (1) a monolithic dual-axis in-plane capacitive
accelerometer with a single proof-mass can be designed using a de-coupling mechanism
that can decompose an in-plane acceleration into its axial components; (2) a dual-axis
accelerometer with good sensitivity and bandwidth is feasible using a simple and
relatively conservative bulk-micromachining process if DaCMs are incorporated into the
design, as practically demonstrated here; and (3) a systematic and pragmatic selectionbased design method can be used to design DaCMs.
A dual-axis wide-band accelerometer was also designed without using mechanical
amplification. The design also uses a modified design of an XY stage that is used here as
a de-coupling mechanism for the purpose of sensing. It was observed that DaCMs are not
suitable for designing accelerometers with very high natural frequency of the order of 1015 kHz. This is because of the presence of softer springs with very low spring constants at
the output side of the DaCMs. The design of the wide-band dual-axis accelerometer was
microfabricated using a SOI-based process. It was found that the design has almost equal
compliance along all the three orthogonal directions. Therefore, this dual-axis
accelerometer design can also be extended to develop a tri-axial accelerometer if a few
more fabrication process steps are performed.
The main conclusions that can be derived from the work on development of mesoscale spring steel accelerometers are as follows: (i) the effectiveness of DaCMs in
simulataneous improvement of sensitivity and bandwidth is scale-independent. DaCMs
can also be used to develop sensitive accelerometers in the meso-scale using different
materials such as spring steel; and (ii) spring steel is a well suited material in the mesoscale and can be used to fabricate multi-axis meso-scale accelerometers.
The future work may consider the role of damping and noise when DaCMs are
appended to accelerometers. Packaging all the microfabricated accelerometers in vacuum
may be taken up in future. The effect of Brownian noise should be measured when
DaCMs are added in the accelerometers. A comparative study of thermal noise in a
micromachined accelerometer with a DaCM and without it needs to be carried out. The
overall noise of all the packaged accelerometers may also be measured in future. The
Phase-II of wide-band accelerometer development should be taken up to fabricate tri-
177
Chapter 8
axial wide-band accelerometer with a single proof-mass. All of these could not be
accomplished in this work due to unavailability of the necessary equipment.
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