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1 MEMS ELECTROTHERMAL ACTUATORS IN GUIDED AND UNGUIDED FOURIER TRANSFORM SPECTROSCOPY SYSTEMS By SEAN ROBERT SAMUELSON A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2013
2 2013 Sean Robert Samuelson
3 To my m other and f ather
4 ACKNOWLEDGEMENTS I would like to thank my advisor, Dr. Huikai Xie for his guidance and support throughout the pursuit of my PhD. His openness to res earch in diverse forms allowed a varied experience set and a large range of proficiencies to come to fruition during this involved pursuit. Our common interest in finding understanding in the unknown has been my pleasure to share. I would also like to than k the additional members of my committee: Dr. Robert Moore, Dr. Fan Ren, and Dr. Jiangeng Xue Further, a large amount of time has been spent in fabrication at the Nanoscale Research Facility and as I learned fabrication procedures and refined my craft I b enefited greatly from the expert advice of Dr. Brent Gila, Alvin Ogden, Bill Lewis, and David Hayes. Without their assistance my cleanroom work would not have been as rewarding. Further, they provided insight to holistic structure and function for research and its applicability. I would also like to thank my lab colleagues. With Lei Wu I advanced my cleanroom skills and gained practical perspective on approaching design. Sagnik Pal engaged me with good conversation both on topics dealing with rese arch purs uits and those of an interpersonal character. I would also like to thank Kemiao Jia, Jingjing Sun, Victor Tseng, Xiaoyang Zhang, Jiping Li, Can Duan, and Ray McClure Further, I would like to thank my parents for their continued support and positive perspe ctive. Their character and resolve were inspirational to me when I did not feel such qualities within me.
5 TABLE OF CONTENTS Page ACKNOWLEDGEMENTS ................................ ................................ ............................... 4 LIST OF TABLES ................................ ................................ ................................ ............ 7 LIST OF FIGURES ................................ ................................ ................................ .......... 8 LIST OF A BBREVIATIONS ................................ ................................ ........................... 12 ABSTRACT ................................ ................................ ................................ ................... 14 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .... 16 1.1 What is FTS ................................ ................................ ................................ ...... 16 1.2 MEMS in FTS ................................ ................................ ................................ ... 18 1.3 Waveguides for Scanning and FTS Applications ................................ .............. 18 1.4 Research Goals in Context ................................ ................................ ............... 19 1.5 Dissertation Overview ................................ ................................ ....................... 20 2 DISCUSSION OF PRIOR ART ................................ ................................ ............... 23 2.1 MEMS Micromirrors ................................ ................................ .......................... 23 2.2 Miniaturized FTS ................................ ................................ ............................... 27 2.2.1 Research Review ................................ ................................ ................... 27 2.2.2 Commercial Review ................................ ................................ ............... 29 2.3 Waveguides ................................ ................................ ................................ ...... 30 2.4 Summary of General Prior Art ................................ ................................ ........... 33 3 ELECTROTHERMAL LADDER ACTUATOR MICROMIRROR .............................. 35 3.1 Prior Work ................................ ................................ ................................ ......... 35 3.2 Electrothermal Actuation Principl es ................................ ................................ .. 38 3.3 Ladder Actuator Design ................................ ................................ .................... 40 3.4 Large scan range Vertical Micromirror Based on the FDSB Ladder Actuator ... 42 3.5 Actuator Bimorph Design and Optimization ................................ ...................... 43 3.6 Ladde r Actuator Mirror Design and Simulation ................................ ................. 46 3.6.1 Actuator Variation ................................ ................................ .................. 47 3.7 Ladder Actuator Micromirror Fabrication ................................ ........................... 48 3.8 Ladder Actuator Micromirror Passive Physical Characteristics ......................... 50 3.9 Ladder Actuator Micromirror Active Performance Characteristics .................... 51 3.9.1 Piston Actuation ................................ ................................ ..................... 51 3.9.2 Tuned Piston Actuation ................................ ................................ .......... 53 3.9.3 Piston Resonance Measurements in the Nonlinear Region ................... 55
6 3.9.4 Piston Resonance Measurements in the Linear Region ........................ 56 3.10 Device Shortcomings ................................ ................................ ...................... 57 3.11 Summary ................................ ................................ ................................ ........ 58 4 ELECTROTHERMAL MICROMIRROR MESH ACTUATOR ................................ .. 79 4 .1 Design and Caveats ................................ ................................ .......................... 79 4.2 Parameter Selection and Simulation ................................ ................................ 81 4.3 Mesh Actuator Micromirror Fabrication ................................ ............................. 83 4.4 Mesh Actuator Micromirror Characterization ................................ ..................... 84 4.4.1 St atic Micromirror Characteristics ................................ .......................... 85 4.4.2 Dynamic Micromirror Characteristics ................................ ..................... 86 4.4.3 Piston Resonance Tests ................................ ................................ ........ 88 4.5 Fabrication Caveats and Considerations ................................ .......................... 89 4.6 Summa ry ................................ ................................ ................................ .......... 91 5 FOURIER TRANSFORM SPECTROSCOPY ................................ ....................... 102 5.1 Primary System Advantages ................................ ................................ ........... 102 5.2 Primary Sources o f Error ................................ ................................ ................ 103 5.3 System Design ................................ ................................ ................................ 106 5.4 Optical System Construction ................................ ................................ ........... 109 5.5 Electrical Drive and Acquisition System Design and Interfacing ..................... 111 5.6 Data Processing Configuration ................................ ................................ ....... 113 5.7 Experimental Data Processing with Ladder Actuator Micromirror ................... 117 5.8 Improved Experimental Data Processing with Ladder Actuator Micromirror ... 119 5.9 Experimental Data Processing with Mesh Actuator Micromirror ..................... 121 5.10 Novel Piston Resonance Testing ................................ ................................ .. 123 5.11 Summary ................................ ................................ ................................ ...... 126 6 WAVE GUIDES ................................ ................................ ................................ ..... 155 6.1 Waveguide Background ................................ ................................ .................. 155 6.2 Design of Multimorphs ................................ ................................ .................... 157 6.3 Fabrication ................................ ................................ ................................ ...... 160 6.4 Characterization ................................ ................................ .............................. 161 6.5 Summary ................................ ................................ ................................ ........ 162 7 CONCLUSION AND FUTURE WORK ................................ ................................ .. 171 7.1 Research Accomplishments ................................ ................................ ........... 172 7.2 Future Work ................................ ................................ ................................ .... 172 LIST OF REFERENCES ................................ ................................ ............................. 174 BIOGRAPHICAL SKETCH ................................ ................................ .......................... 184
7 LIST OF TABLES Table Page 3 1 Thermal and mechanical properties of multimorph materials. ............................ 78 3 2 ISC layer thicknesses for actuators ................................ ................................ .... 78 3 3 Section lengths of ISC actuator for ladder actuat or micromirror ......................... 78 4 1 Section lengths of ISC actuator sections for mesh actuator micromirror .......... 101 5 1 Low spectral resolution dataset characteristics. ................................ ............... 1 54 5 2 Higher spectral resolutio n dataset characteristics for ladder actuator micromirror. ................................ ................................ ................................ ...... 154 5 3 Spectral resolution dataset character istics for mesh actuator micromirror. ...... 154 6 1 ISC layer thicknesses for common process waveguide actuators .................... 170 6 2 Section lengths of ISC actuator sections for waveguide actuator. .................... 170
8 LIST OF FIGURES Figure Page 1 1 Basic FTS system in Michelson interferometer configuration with OPD marked in blue, dashed arrows. ................................ ................................ .......... 22 2 1 Micromirror array for OPA applications. ................................ ............................. 34 3 1 Fabricated micromirror with DRIE CMOS MEMS process. ............................... 60 3 2 Large tilt 1D mirror. ................................ ................................ ............................ 60 3 3 Tilt insensitive FTS setup. ................................ ................................ ................. 61 3 4 Piston LSF micromirror. ................................ ................................ ..................... 61 3 5 SEMs of ISC based micromirror. ................................ ................................ ....... 61 3 6 Multimorph showing close up of all layers where layer 1 is the top of the multimorph stack. ................................ ................................ ............................... 62 3 7 ISC actuator structure. ................................ ................................ ....................... 62 3 8 3D FEM models of the stacked FDSB. ................................ .............................. 63 3 9 Ladder actuator mirror. ................................ ................................ ....................... 64 3 10 FEM simulation of the two primary resonance modes of the ladder actuator micromirror. ................................ ................................ ................................ ....... 64 3 11 Complete cross section of S shaped multimorph with all layers. ........................ 65 3 12 Plot of vertical displacement as a function of aluminum thickness at 300K. ....... 65 3 13 Radius of curvature for second oxide bimorph layer at 300K. ............................ 66 3 14 Vertical displacement of ladder actuator with four ISC actuators versus uniform temperature differential inputs for multimorph and bimorph simplification. ................................ ................................ ................................ ...... 66 3 15 FEM as bimorph and analytic as full multimorph comparison for displacement of actuator as a function of temperature differentia l. ................................ ........... 67 3 16 Three segments of S shaped bimorph for downward initial displacement. ......... 67 3 17 Upward actuated ladder actuator micromirror fabrication process. ..................... 68 3 18 Downward actuated ladder actuator micromirror fabrication process. ............... 69
9 3 19 Upward ladder actuator SEMs. ................................ ................................ ........... 70 3 20 Downward ladder actuator SEMs. ................................ ................................ ...... 71 3 21 Displacement and tilt angle versus applied voltage at 0.1V increments. ............ 73 3 22 Tilt angle and recorded ac voltage applied to all actuators for piston motion. .... 73 3 23 Optical angle versus voltage for a single actuator for ladder actuator device. .... 74 3 24 Quasi static displacement in millihertz frequency measured in interferometric setup. ................................ ................................ ................................ .................. 74 3 25 Micromirror piston actuation frequency response over the range 50Hz to 1240Hz. ................................ ................................ ................................ .............. 75 3 26 Vibrometer results for micromirror. ................................ ................................ ..... 76 3 27 Micromirror piston actuation frequency response in linear region. ...................... 77 3 28 Boxed sections showing electrical short. ................................ ............................ 77 4 1 Mesh actuator resistance configu ration. ................................ ............................. 92 4 2 Vertical displacement of segment L 1 for varying aluminum thickness. ............... 92 4 3 Vertical displacement of the multimorph mesh actuator from temperature inputs. ................................ ................................ ................................ ................. 93 4 4 Mesh actuator simulated in FEM software. ................................ ......................... 93 4 5 Full mirror simulation for mesh actuator micromirror. ................................ ......... 94 4 6 First resonant piston mode ................................ ................................ ................. 94 4 7 Second resonant rotational mode pair ................................ ................................ 94 4 8 Process flow for downward actuated mesh actuated micromirror. ...................... 95 4 9 SEMs of mesh downward actuator. ................................ ................................ .... 96 4 10 Single axis displacement versus voltage for mesh actuator micromirror. ........... 97 4 11 Displacement for all actuators and current draw for driving voltage. .................. 98 4 12 Optical Angle versus voltage for single actuator. ................................ ................ 98 4 13 Piston resonance for mesh actuator micromirror in nonlinear region. ................. 99
10 4 14 Piston resonance of mesh actuator micromirror in linear region. ........................ 99 4 15 Device layer undercut and mirror plate etch through from backside. ................ 100 4 16 Undercut at actuator connection to substrate. ................................ .................. 100 4 17 Fabrication caveats in multimorph construction ................................ ................ 101 5 1 Full FTS system layout. ................................ ................................ .................... 128 5 2 Misalignment in system. ................................ ................................ ................... 129 5 3 Mirror tilt in system. ................................ ................................ .......................... 130 5 4 Alternate system design retaining unknown signal and isolated reference signal. ................................ ................................ ................................ ............... 131 5 5 Interference patterns with com bined beams. ................................ .................... 131 5 6 Far field beam overlap . ................................ ................................ .................... 132 5 7 Power scaled driving waveforms. ................................ ................................ ..... 132 5 8 First general iteration of FTS system. ................................ ............................... 133 5 9 Final iteration of FTS system. ................................ ................................ ........... 134 5 10 Alternate view of final FTS configuration. ................................ ......................... 135 5 11 General structure of electrical portion of FTS system. ................................ ...... 136 5 12 Signal generation in detail ................................ ................................ ................ 136 5 13 Alternate view of signal generation ................................ ................................ ... 136 5 14 Generated interferograms with white Gaussian noise. ................................ ..... 137 5 15 Interferograms with noise filtered in the frequency domain. ............................. 138 5 16 The spectrums of the generated data. ................................ .............................. 139 5 17 Raw, unfiltered interferograms from FTS system. ................................ ............ 140 5 18 Displacement calculated for equal temporal spacing. ................................ ....... 141 5 19 Filtered, dc offset nulled, and displacement calculated. ................................ ... 142 5 20 Spectrums for low spectral resolution datasets. ................................ ............... 143 5 21 Raw interferograms for increased ladder actuator OPD. ................................ .. 144
11 5 22 Optical path difference versus voltage for increased ladder actuator OPD. ..... 145 5 23 Reference spectrum with background for increased ladder actuator OPD. ...... 145 5 24 Unknown spectrum for increased ladder actuator OPD. ................................ ... 146 5 25 Raw interferogram for mesh actuator. ................................ .............................. 147 5 26 Optical path difference for mesh actuator micromirror. ................................ ..... 148 5 27 Spect rums with mesh actuator micromirror. ................................ ..................... 149 5 28 Actuation of ladder actuator micromirror with no resonance. ............................ 150 5 29 Piston resonance mode for ladder actuator. ................................ .................... 151 5 30 Subharmonic piston resonance mode for ladder actuator micromirror for 1/3 subharmonic in nonlinear micromirror response region. ................................ ... 152 5 31 Standard response for actuator micromirror in linear region. ............................ 153 6 1 Planar waveguide construction of infinite extent in z and y directions. ............. 164 6 2 Thickness of aluminum for segment L 1 ................................ ............................ 164 6 3 Waveguide structure. ................................ ................................ ........................ 164 6 4 FEM simulations of full actuated waveguide device. ................................ ........ 165 6 5 Modal analysis of actuating waveguide. ................................ ........................... 166 6 6 Fabrication process flow for actuated waveguide. ................................ ............ 167 6 7 SEMs of actuating waveguide device. ................................ .............................. 168 6 8 Displacement as a function of voltage. ................................ ............................. 169
12 L IST O F ABBREVIATIONS BOE Buffered Oxide Etch BOX Buried Oxide BS Beamsplitter CTE C oefficient of Thermal Expansion DOF Degree of Freedom DRIE Deep Reactive Ion Etching FDSB Folded Dual S shaped Bimorph FTIR : Fourier Transform Infrared Spectroscopy FTS Fourier Transform Spectroscopy HFF High Fill Factor ISC Inverted Series Connected LIGA Lithography Electroplating and Molding LSF Lateral Shift Free LVD Large Vertical Displacement MEMS Microelectromechanical Systems MZI Mach Zehnder Interferometer OPA Optical Phased Arrays OPL Optical Path Length OPD Optical Path Difference OCT Optical Cohe rence Tomography PECVD Plasma Enhanced Chemical Vapor Deposition PSD Position Sensitive Detector RIE Reactive Ion Etch ing SEM S canning Electron Microscope
13 SCS Single Crystal Silicon SOI Silicon On Insulator TTP Tip Tilt Piston
14 Abstract of Dissertation Pr esented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy MEMS ELECTROTHERMAL ACTUATORS IN GUIDED AND UNGUIDED FOURIER TRANSFORM SPECTROSCOPY SYSTEMS By Se an Robert Samuelson August 2013 Chair: Huikai Xie Major: Electrical and Computer Engineering Fourier Transform Spectroscopy is a method of determining material composition and concentration in both laboratory and field environments. Miniaturization of t his technology enables a spectrometer to function onsite and permit s rapid environmental analysis. Microelectromechanical systems provide a means for a spectrometer to move from the macro to micro scale. Two micromirrors are designed, fabricated, and chara cterized. The first micromirror is based on electrothermal actuation and presented to facilitate a micro spectrometer. The design is a ladder actuator that provides strong piston displacement characteristics with ultra low tilt The device performance yield s strongly linear motion and a large fill factor. The second micromirror is also based on electrothermal actuation and is designed to increase reliability of the device and facilitate a microspectrometer The design is a mesh actuator with large fill facto r that yields large vertical displacement. A microspectrometer is designed and implemented with fabricated ladder actuator and mesh actuator micromirror s in a benchtop prototype configuration The system is constructed for all main design considerations as follows: optical system ;
15 micromirror; mirror drive and data acquisition; and data processing. The full system is demonstrated by acquiring an unknown interferogram and calibration interferogram with different data sets and differen t spectral resolutions w ith both designed micromirrors Additionally, the system is used in micromirror characterization to determine piston resonance of different micromirrors. Finally, a ctuated waveguides are designed, fabricated and characterized. These devices are designed to wards use in guided wave spectroscopy and fiber scanning applications. The designs are a proof of concept and demonstrate large vertical displacement of the non actuating waveguide in concert with the displacement of the actuators. Overall, micromirrors ha ve been designed, fabricated, and characterized. The ladder actuator micromirror and mesh actuator micromirror has been demonstrated in a designed and constructed spectroscopy system with successful spectrum generation from unknown interferograms. The spec troscopy system has also been utilized for mirror characterization to determine piston resonance. Finally, actuated waveguides have been designed fabricated, and characterized.
16 CHAPTER 1 INTRODUCTION Microelectromechanical Systems ( MEMS ) are an enabling technolo gy that, through the prism of m iniaturization permits macro scale systems to move into the micro scale. It is a heady concept to view all of the ways that MEMS has benefited different technical domains. From optical switches  and OCT endoscopes  to OPA systems  MEMS has provided wide reaching and significant transformation of implementation methodologies of varied technological fields. Another area t hat MEMS promises to provide significant change is in the field of Fourier transform spectroscopy ( FTS ) Such a system has the ability to provide real time detection of chemical weapons and environmental hazards  which is amplified in its usefulness if the system capable of conducting such analysis is pocket sized and able to be carried in hand. The focus of this research is to successful ly implement an FTS system in miniaturized form. To that end, electrothermally actuated micromirrors are employed to enable this miniaturization. Additionally, the FTS system is designed to interface effectively with the micromirror to optimize miniaturiza tion and effective mirror utilization. Waveguides are also created with the intent of a proof of concept that may be applied to fiber scanning applications and FTS system usage In this chapter MEMS is addressed in a general sense and directed to micromirr ors, FTS is discussed and directed towards miniaturization, waveguides are mentioned in successful uses, benefits to society is specifically highlighted, and research objectives are outlined. 1.1 What is FTS Fourier transform s pectroscopy (FTS) is implemented via an instrument that has spectral information encoded such that the intensity distribution is recorded concurrently
17 through a single detector at all frequencies  Optical interference can be defined as the superposition of electromagnetic waves. These superimposed waves, when incident on a detector may collect the intensity distribution for production of an interferogram, which is a re cord of the output signal as the superimposed waves are varied. The consequences of such a system are profound and applicable to many different areas. Some of these include accurate measurements of distances, displacements and vibrations; additionally, stu dies of gas flows and plasmas; and laser frequency measurements are some of the applications of FTS systems  Narrowing focus again, the infrared region provides robust and well established applications for spectroscopy which include quantitative analysis of complex mixtures and investigation of dynamic systems  Additionally, biological and biomedical spectroscopy finds strong applications in infrared spectroscopy. The key component of an FTS system is the component that varies optical path length (OPL) where n(l) is the localized refractive index of the medium as a function of physical distance l along the physical path L in Eq uation 1 1. ( 1 1 ) From this equation, optical path difference (OPD) may be considered as the differential between the maximum and minimum OPL multiplied by two as in Equation 1 2. ( 1 2 ) The basic structure of an amplitude division interferometer demonstrating this principal is in the form of the traditional Michelson interferometer (Figure 1 1). An increase in OPD provides improved spectral resolution which determines the ability of the system to resolve features. It signifies the difference for example, between
18 three peaks blurring into one and three sharply defined peaks. Further, this figure provides context for the equations as they relate to an FTS system. The determination of the OPD provides the single greatest piece of insight into the caliber of an FTS system and co nsequently supplies the direction of inquiry for the use of MEMS in the design, namely: to determine the manner of effectively generating the largest OPD. 1.2 MEMS in FTS T here are two primary approaches to the direction or orientation of the research determin ed as follows: to increase OPD through a change in the physical path without changes in refractive index or to provide variation in the l ocalized refractive index while constraining changes in physical path. When changing the physical path is considered, t he approach strongly supports a solution that involves a micromirror. This fits as a logical extension from the manufacture of such devices on the macro scale where major systems use mirrors  I t further fits the first impulse to miniaturize what works on the macro scale. There has been much research on micromirrors for FTS applications  Advancement in terms of aperture increase, displacement increase, and tilt decrease are all factors that can be improved upon in optimizing a micromirror for this application. Prior gro up work has developed an inverted series connected (ISC) actuator  that is strongly suited to the design constraints presented and will the basis for this directed approach to OPD generation for FTS application. 1.3 Waveguides for Scanning and FTS Applications For the approach where refractive index will be varied, waveguides are a requirement. By guiding the waves we have the potential to co ntrol the refractive index of the medium precisely at all points along the guided optical path of light Prior work on Mach Zehnder interferometers (MZI) which are also amplitude division interferometers,
19 shows the ability to implement waveguide based int erferometers with more common fabrication materials  On the path to such a development, it is useful to verify the material qualitie s in the fabrication process are conducive and s ufficient to the production of e ffective waveguides for guiding light with out excessive loss or scattering from defects Scanning waveguides has been accomplished in the past with keeping light guided for def lection up to 1400m using silicon waveguides  and proof of suspended waveguide fabrication of InP waveguides  Further, successful biochemical detection has been recorded for monolithically fabricated MZI systems. The waveguide is fabricated in a common process fl ow to be actuated by external forces from electrothermal actuators with the mechanical displacement demonstrated as a stepping stone to an actuated single crystal waveguide core for practical functionality 1.4 Research Goals in Context From these noted effort s the purpose of this work comes to open question. The multitudinous uses of an FTS system come back to mind such as use in biological and biomedical spectroscopy. To speak to a present concern, r apid detection of chemical and biological agents is strong ly applicable to many sectors. One such sector is in medicine where such a system may reduce health care cost and improve quality of life [ 4] Another is the use of a portable system to aid in detection of biowarfare agents to protect against bioterrorism or to detect improvised explosive devices (IEDs) composed of such raw industrial chemicals as nitric acid, diesel fue l, ammonium nitrate and sugar  Optical spectroscopy, when combined with a spectral library can quickly identify the presence of biological and chemical ag en ts in these cases and others  Enabling technology to improve these areas with ease of use via dramatic reduction in size and cost ha s the power to enhance the safety and welfare of citizens
20 1.5 Dissertation Overview In this dissertation there are seven chapters. The first chapter addresses the introduction and motivation for the following research. Preliminary background and motivation in a present day, immediate context is provided. The second chapter presents a comprehensive literature review. First, MEMS is addressed and more specifically, micromirrors and the different actuation methodologies are given treatment. After, FTS systems ar e addressed in the varieties of miniaturizations that have been undertaken for FTS systems and spectrometers in general. Finally, waveguides are discussed both in terms of successful implementations on substrate and also actuated. The third chapter presen ts the ladder actuator micromirror. The theoretical underpinnings of electrothermal actuation are addressed. Then, the precursors to the current design are addressed in detail. Thereafter, the new design is addressed with justification, design constraints, fabrication, and characterization. The fourth chapter presents the mesh actuator micromirror. The design parameters with caveats and benefits are discussed. The fabrication is addressed in detail and characterization is also undertaken. Finally, a sectio n covering pitfalls in fabrication is noted. The fifth chapter discusses the FTS system and its theoretical design, including data processing. The control system is described in detail along with the optical setup. The system with the two MEMS mirror desi gns in place is addressed for novel characterization methods and for the use as a spectrometer to determine signal wavelengths and spectral limited linewidths of in system sources
21 The sixth chapter discusses waveguides, the theoretical underpinnings of t he devices and the design choices and constraints The devices are described in fabricati on and characterization as well The seventh chapter discusses the work in summary and the future plan for the work for the optimization of efforts to further the FTS system and u tilize the waveguides in such a system along with micromirror enhancements
22 Figure 1 1. Basic FTS system in Michelson interferometer configuration with OPD marked in blue, dashed arrows.
23 CHAPTER 2 D ISCUSSION OF PRIOR ART MEMS has permitted the gr owth of multi billion dollar industries and has many varied successful devices in numerous applications. A ny device constructed in the micro scale obtains the appellation of MEMS. More to the point, micromirrors are a specific type of MEMS that has widespr ead application in optical systems. These device are used in OPA applications  OCT  and general beam steering  Further, such systems have been used to develop mi cro spectrometers and fabricate waveguides that are stationary as well as movable. 2.1 MEMS Micromirrors Micromirrors, a subsection of MEMS, are commonly defined by their actuation methodology. The devices can be actuated by methods that include the following main forms: electrothermal, electromagnetic electrostatic, and piezoelectric Piezoelectric actuation is one of the methods of creating movable micromirrors. A specific design by Liu et al. is capable of tip tilt piston motion (TTP) and capable of 27 m vertical displacement at piston mode resonance at 2.45kHz at 5V and 9.65 scan angle at 3.5kHz rotation mode resonance  The device employs the ISC structure inspired by prior electrothermal actuator design. Another piezoelectric mirror design with intended applications to dual screen projection systems provides 5.6 and 6.8 scan angles on the slow and fast axis re spectively when driven at 10Vac and at resonance with 7.168kHz and 9.126kHz, respectively  The device is not tuned for vertical dis placement, though this is not a design requirement. The two primary drawbacks in using piezoelectric devices is the lack of large vertical displacement and the need to operate at resonance, placing stringent performance requirements on the system.
24 Electrom agnetic actuation is another type of actuation that permits the creation of micromirrors. One design by Ji et al. is capable of scans of 8.8 in the horizontal and 8.3 in the vertical directions accomplished by radial magnetic field  The system scans at 19.1kHz and 19.7kHz for the slow vertical and fast horizontal scan, respectively, with an eye towards raster scanning applications  Another design is novel in its use of combdrives that are primarily used in the domain of electrostatic actuators to instead drive a mirror plate by electromagnetic actuation. This design uses a LIGA (Lithography Electroplating and Molding) process to create the combdrive actuator. The system is capable of producing up to 50m displacement  Designs commonly require the use of, as is the case in these designs, external components to provide the mag netic force to enable actuation An application for an electromagneti c actuator is 3D virtual tactile displays, although the specific work does not utilize a MEMS device as the actuator  Another desig n displays both multiferroic behavior with response of a cantilever to either an electric or magnetic field that yields displacement up to around 0.6 m at 15V or 0.04T for a cantilever of length of 300m  Other electromagnetic devices can utilize diaphragms which are able to deflect 30um dynamically at 1Hz and statically at 15um; the packaged structure enables integration of the perma nents magnet in a core substrate and an actuator substrate with the diaphragms  Another electromagnetic actuator incorporates plana r microcoils with thick nickel iron core fabricated on a silicon wafer  Magnetic actuation is achieved in a clear form with a nickel coated plate and a polysilicon torsion bar that yields up to 80 static angular deflection; the system also employs electrostatic clamping with the substrate  An electromagnetic micromirror achieves up to 9
25 deflection angle at 2mT; the device is designed to be used in an endoscopic probe with the planar coil integrated into the endoscope  with a previously reported mirror aperture of 0.65mm  Ultimately, the magnetic actuator commonly requires operation at resonance to provide sufficient displacement and also re quires external components to actuate a single crystal silicon (SCS) based device design Electrostatic actuators are a strongly char acterized actuation methodology that has many successful implementations Many papers address design considerations for electrostatic actuators, such as torsional micromirrors with parallel plate design  An example of micromirrors produced with electrostatic actuation is a device designed for vertical displacement that is capable of achieving a range of 1.2m under 60V through the use of combdrives  Another design uses unidirectional actuator with hinges to prop up large mirrors for applications such as a bar code scanner  The device is capable of rotation up to 28 in optical range and positioned with precision of 0.038 statically  Another device that rotates along a single axis from substrate is capable of achieving 2.1 maximum angular rotation at 200V with combdrive actuation  A device designed for 2 D scanning utilizing a split frame gimbaled combdrive design requires high precision DRIE etchin g but yields, under dynamic operation, 11.8 at 1.18kHz and 8.8 2.76kHz for the outer and inner axis, respectively  Further, the device is designed for use in micro endoscopes. Another combdrive design that is intended to control the phase of directed light is capable of 9 optical scanning at approximately 150V and 7.5 m piston motion at approximately 110V under static actuation  Ultimately, electrostatic actuators are strongly suited to scanning applications and although piston displacem ent is possible, only in plane actuation
26 relative to the substrate is feasible for producing very large piston motion  Some combdrive designs include res onant scanners with hinges for frame assembly and electrostatic comb drives that can achieve 28 optical scan angle at 42V and can operate at a resonant frequency of 3.28kHz with a mirror plate of 200m250m  More complex designs can ach ieve 2D scanning. Such a device uses gimbaled structures with angular vertical combdrive actuators to achieve 6.2 at 55Vdc on both axes  Electrothermal actuators are another common type of actuation for multiple applications. One application is in optical coherence tomography ( OCT ) where large tilt is desirable. In such an environment, an ISC designed mirror is capable of achieving 46 scan angle at 4.8V and a piston displacement of approximately 325m for use in a micro endoscope  Another electrothermal design again intended for use in micro endoscopes is capable of 32 scanning angle at 12mW, as well as piston motion of up to 121m again at 12m W  Electrothermal designs have also been successful in OPA applications with HFF micromirrors from Wu et al.  and Jia et al.  The micromirror array for OPA applications by Wu et al. is a 44 array that permits a fill factor of 54% and 200 m piston actuation and tip tilt scanning of 18 at 4.5V using the LSF LVD actuator structure (Figur e 2 1)  These electrothermal actuators also have uses as micro grippers [3 7] and in fiber actuation  Another application as noted previously is EOCT probe use. One such instance is with an electrothermally actuated micromirror capable of 11 deflection at under 2V; additionally, the probe is assembled on a silicon substrate base that provides electrical traces for interfacing with the micromirror  Electrothermal actuators have
27 been modified as well to function as curved multimorphs with scan range up to 0.68V at 60  with extensive analysis  An additional application is a latching bistable mic roswitch allowing both on and off conditions in non actuating conditions  An electrothermal actuator with an electromagnetic actuat or for a hybrid approach allows 1.5 at 12mW for vertical electrothermal scan and 10 at 1Vac for horizontal electromagnetic scan  A folded electrothermal actuator provides 34 at around 20mW input power  Electrothermal actuation can also be used in adjusting t he shape of micromirror optical cavities where higher order modes may be suppressed with tuning current  Another example of electrot hermal actuation is a dual axis micromirror capable of achieving approximately 9 at less than 2.3V  2.2 Miniaturized FTS There are se veral systems that have been designed as full system designs, excepting the source and detector  Further, there are also discrete mi cromirrors that have been designed with the express purpose of functioning for FTS purposes, namely large piston displacement and low tilt to reduce and ideally eliminate fringe loss  2.2.1 Research Review First, self contained or bench top spectrometers will be discussed. One system has an integrated silicon beam splitter that uses an electrostatic combdrive actuator to move a maximum of 25m at 150V The sidewalls are smoothed by oxide deposition and etching for smoothing. Additionally, the system is designed for infrared operation with center wavelength of around 1500nm  Another integrated FTS system is a product of LIGA fabrication. In this system, the only component not present on the device is the source The electromagnetic
28 actuator consists of wound coils that provid e 54m of effective displacement at 12mW and is also designed for operation in infrared around 1500nm  An advantage to this system c an be considered as allowing the use of some pre existing components like the beamsplitter without having to increase the size of the system. Another design of significant quality is a wavefront division spectrometer based on lamellar grating interferomete r. The grating is modulated by combdrive actuation that is able to achieve 73m displacement  Another system utilizing this technol ogy is shown  Overall these systems have attractive characteristics but are diffraction based systems and are limited in practicabil ity for wavelength ranges as a result of physical design and also require ultra precise fabrication. In addition to these generally contained systems, there are also micromirrors fabricated independently for eventual integration into a system. To begin th ere is a combdrive actuator with in plane actuation that provides 38.5m of effective displacement achieved at 10Vac and 15Vdc applied This design utilizes sidewalls for the mirror surface as in the combdrive based system mentioned earlier  Another design allows out of plane displacement by staggering combdrives to elevate the mirror plate This allows 200m displacement under 40V at 5 kHz resonance but requires the mirror be placed in a vacuum cham ber held at 100 Pa  A progression from the same group yielded an e lectrostatic based micromirror based on pantograph lever design The cumulative design is capable of 500m displacement at 50Pa at 50V and 80m at 40V at atmosphere  Additional work relating to these designs and building to the final pantograph structure is presented in progressive works
29 under the umbrella of a European Union 7th framework project known as MEMFIS in    and  All these actuators e mploy the method of moving mirror plates to function as reflective surfaces for light in a FTS system and are, barring any strong nonlinearity, relevant to FTS in terms of piston motion used to generate OPD. An early portable system implementation and asso ciated considerations to such a system can be seen in  A magnetic actuation method used in Michelson and lamellar grating applicatio ns can achieve up to 250m with static deflection though white light acquisition was limited to 20 m in Michelson interferometer configuration  A thermally tunable grating varied by the strong temperature dependence of the refractive index of nitrobenzene the intensity is collected as a function of the heating element  Another spectrometer involves complete assembly of a spectrometer on silicon benchtop that is oriented by micro positioners and auto alignment through feedback from a charge coupled device for sy stem arm misalignment  Another design utilizes dovetailed bearing surfaces in silicon to allow arbitrarily large range, demonstrated at 10cm range  Additional systems have been demonstrated for novel Fabry Perot systems for shear stress systems  and a transparent spectrometer  Overall, t he displacement and the driving signal requirements are the most relevant characteristics of these devices. 2.2.2 Commercial Review There are several commercial systems that are portable and do not require samples be brought into a laboratory en vironment for testing. One such device is the Agilent portable FTIR 4100 ExoScan. The device is 7lb and is 6.75 in 4.68 in 8.81 in  Add itionally, a handheld computer is required that docks with the system This
30 handheld computer is 5.00 in 2.94 in 0.81 in and weighs 6.3oz. Additionally, the system is a Michelson interferometer and provides a maximum of 4cm 1 maximum resolution and a wavenumb er range of 4000 650cm 1 The stated application of this system is to measure samples too large to move to a lab and to address tasks such as verifying composite material integrity or determining if a polymer is properly cured. The structure of the device is a durable plastic casing with a grip for holding the device and a button on the grip to trigger an acquisition. Attached to the end closest to the user is a smartphone style device the handheld computer that interfaces with the interferometer and prese nts the results of the triggered scans, with interactive settings modification. Another portable commercial system is called ThermoScientific TruDefender FT. This system is 7.8 in 4.4 in 2.1 in and weights 2.9lb  The system is also a Michelson interferometer with a wavenumber range of 4000 650cm 1 with a maximum resolution of 4cm 1 ; notable is the identical ratings of the two commercial devices in terms of wavenumber range and maximum resolution. The stated applications of this system are to function as a rapid, field based system for identification of materials such as solvents and lubricants as well as narcotics and in customs inspect ion applications The device structure provides a rubberized case in a handheld format with a sample interface port at the end oriented away from the user. The interface buttons and display are integrated into the case with the interferometer, in contrast to the ExoScan. 2.3 Waveguides Fabricated waveguides permit the guiding of waves such that the directionality and optical path may be precisely controlled. The primary interest is, as with the actuators driving micromirrors, the OPD that can be generated with the devices in question such as with modulation of guided light  To wit, a variable OPD is most
31 explicitly achievable through loca lized changes in refractive index that is a direct result of the photoelastic effect. One such example of this is the fabrication of rib/ridge waveguides that function as a Mach Z e hnder stress sensor The system uses InP based structures for waveguides and has up to 90 phase shift, which is primarily limited due to large coupling loss  Another example of a waveguide that utilizes the photoelastic effect for use in arrayed waveguide gratings discusses birefringence and polarization dependent wavelength shifts. Two structures are con sidered including a single mode and pedestal structure Additionally, polarization wavelength shift is fo und to be less than 0.01nm and stress distributions are accurately determined  Further study on the elasto optic coefficients of Ga N are addressed in  Aside from waveguides utilizing the photoelastic effect, there is also work in actuating and movable configurat ions An example of this is an electrostatically actuated waveguide with a silicon core and a simple fabrication process with a loss rate of less than 1.8dB cm 1  Another movable waveguide structure is mentioned that is based on a similar process. This waveguide also has 1.8dB cm 1 propagation loss with a polarization dependence of 0.5dB  This design is capable of 1400 m deflection amplitude generated with electrostatic actuation with a cantilever of 3400 m  There are additional waveguides that have been successfully fabricated to give additional background to the materials and methods of fabrication, as well as the characteristics that one can expect with these materials Additionally, certain aspects of a waveguide system such as coupling methods need to be investigated, such as a 45 micromirror embedded in a single mode waveguide with a mirror backing of ultraviolet
32 resist  Waveguides are fabricated with Y branch and S bend waveguides with analysis of bend loss  Further designs allow waveguides splitters with low loss S bend connectors with waveguide cores consisting of SU 8 polymer  Additional designs are a silicon based waveguide characterizing evanescent waves and reflection modes  and an evanescent waveguide sensor for titanium dioxide waveguides  Fiber optic displacement sensors are also used with a tapered planar waveguide demonstrating a shift in resonance wavelength  Suspended waveguides are used a s displ acement sensors with a nitride waveguide which can be used with actuators  Fiber to planar waveguide couplers can be utilized to m easure optical properties such as that of a thin metal, which functions as a metal cladding  or for thermo optic effect of a polymer film with metal cladding  A silicon wavegui de with an optical microswitch with a gold coated mirror plate electrostatically actuate d to permit or limit propagation  Another switching application also may be applied for modulation with a silicon waveguide  Arrayed waveguide grating multiplexers with integrated turning mirror also with silicon core waveguides address loss and crosstalk, as wel l as polarization sensitivity  Mach Zehnder interferometric systems can be used as sensors with magneto optic modulation on silicon on insulator ( SOI ) waveguides  and with SU 8 waveguides  Additional advantages of waveguides is the possibility of monolithic integration of LED and photodetectors for applications such as near infrared biosensors  or CMOS compatible processes  Waveguides with metal cla dding can also be used for propagation with waveguide surface plasmon coupled modes  Waveguides also find application in Bragg grati ngs as strain sensing elements for optical mechanical accelerometers 
33 Overall, there is a practical constraint on materials that may be utilized. They must generally be limited to strongly available resources as the characterization of material for suitability is its own research and such, silicon, silicon dioxide, and nitride are the main focuses for use in waveguides. 2.4 Summary of Gene ral Prior Art In this chapter all main literature has been reviewed for waveguides, actuated waveguides, micromirrors and FTS systems. There is additional material that stems from the direct derivation of the micromirror structures researched in this work but they will be addressed in the buildup and design of the micromirrors. With this literature review, a broad perspective is given that entails the different possibilities and pursuits that are possible in attempting to create a scanning waveguide and a miniaturized FTS system.
34 Figure 2 1. Micromirror array for OPA applications. A) Fill factor 32%. B) Fill factor 54%. C) Single mirror sub aperture. D) Single LSF LVD actuator  B A C D
35 CHAPTER 3 ELECTROTHERMAL LADDER ACTUATOR MICROMIRRO R The first approach to creating an FTS system in an unguided medium is to construct a movable mirror. This is set to be accomplished by electrothermal micromirrors. The justification for this comes from the large dis placement, lack of reliance on external components to the device, and low driving voltage. It is true that power consumption is high compared to other actuation methodologies. However, it is not a critical component for the intended use of the micromirror when compared to the other requirements and thus the opportunity cost may be deemed to be acceptable In this chapter, prior work building up to the ISC design from in lab effort is addressed. Then, previous collaborative ISC design is discussed. The under pinnings of electrothermal actuation are presented for the full multimorph and also the bimorph simplifications The device is then conceptually constructed by design choices. Analytic and FEM analysis are addressed. The devices are then fabricated and cha racterized in terms of static and dynamic characteristics. Finally, the device resonant modes are determined and piston resonance modes are investigated in a novel approach for the nonlinear and linear regions of the device response curve. 3.1 Prior Work There is a continuous stream of effort bringing the state of electrothermal actuators from the directly derived prior work to the state from which this work develops. To trace this line, one of the first work s was an electrothermal micromirror intended for 2 D scanning using a DRIE CMOS MEMS process. The actuator is composed of oxide and aluminum with a poly silicon heater that enables up to 40 rotation angle with 8mA This chapter is based in part on 
36 on the mirror actuators and 11mA on the frame actuators in Figure 3 1(a)  The next step in development is to use two separate actuator groupings again with a mirror and frame actuator for large vertical displacement that also follows a DRIE CMOS MEMS process  The system is capable of actuating up to 200m at 6V  The principle of LVD actuation in this context is to produce equal angular rotation in the two actuating groups. As a variant, this device can have the mirror plate modified to hold a photoresist microlens with a focal length of 188m  The next work in progression of the electrothermal design is the subst itution of the poly silicon heater for a platinum heater. This change results in increased robustness and increased actuation in the 1 D device (Figure 3 2(a)) The actuation of the device is 124 at 12.5Vdc  The inverted series connected (ISC) bimorph is first demonstrated with a separate platinum heater between the bimorphs and the substrate  The next advancement is the lateral shift free (LSF) LVD micromirror. The process is refined to a combined surface and bulk micromachining batch process. Again using the p latinum heater, the results of the design are 620 m vertical displacement at 5.3Vdc with a reported tilt of 0.7 and lateral shift of 10m  Finally, the ISC actuator has the platinum heater integrated into the bimorph proper to form a multimorph structure  This ref inement permits a range of 480m at less than 8V and scan range for each axis of 30 for an LSF actuator design  Further LSF designs have varied devices such as 900m vertical displacements with less than 1.5 untuned tilt  a 10mm aperture device moving up to arou nd 500m in the vertical direction  OCT endoscopic probe applications  and the LSF LVD FTS design 
37 There have been a number of dif ferent electrothermal actuators developed in the lab where this research is conducted with a strong orientation towards large vertical displacement The first attempt at LVD was capable of 200m at 6V as previously mentioned  This design was followed by LSF LVD designs which were used in a tilt insensitive FTS  The prior in lab FTS system is based on this piston motion micromirror (Figure 3 4 (b)) used in a tilt insensitive FTS configuration (Figure 3 3) For the tilt insensitive setup, t he effective displacemen t peaked at 308m before falling strongly outside the linear region and was most consistent for 131m displacement A simulation of the tilt insensitive setup designed to compensate the 1.7 tilt present in the mirror with fully tuned d riving signals is fo und in Figure 3 3 (b ) with a schematic found in Figure 3 3 (a). A photo of the setup is also provided in Fig ure 3 3 (c) The micromirror employed has its tilt compensated in this setup. However, this signifies that the two signals from the different paths are matched, there is nothing to prevent the tandem travel of the beams across the surface of the detector as the micromirror actuates. Additionally, this configuration requires precise tuning of the driving signal to the actuators of the micromirror and as t he resistances of the actuators drift, there is no compensation for the actuators where the tilt can strongly vary and increase in a nonlinear fashion such that tuning is not consistent through the range of actuation Finally, there is significant bulk add ed to this setup with the tilt insensitive components The LSF electrothermal actuator provides for very large displacement but has the drawback of amplifying errors in the actuator by amplifying these errors via the frame that accompanies each actuator. T he other developed actuator design is the inverted S
38 curve ( ISC ) and this design also works to provide theoretically pure vertical displacement. The latest iteration of this actuator is found in  and illustrated in Figure 3 5 The design in this version is well defined with 46 optical angle and 340m vertical displacement  It represents a strong general base from which to work. 3.2 Electrothermal Actuation Principles To begin, since the work will continue what was begun with the prior tilt insensitive FTS design, the groun dwork for electrothermal actuation must be addressed. Stresses in a multimorph beam generate displacement, which may be divided into the intrinsic and extrinsic stresses in the multimorph where in is intrinsic stress and ex is extrinsic stress. Equivalently, intrinsic stress encompasses in_PT intrinsic strain mismatches caused by processing temperature change and in_other represents all other factors, which are approximately constant afte r fabrication  Finally, ex_JH represents the extrinsic stress induced via Joule heating in Eq uation 3 1. ( 3 1 ) The intrinsic stresses mentioned above provide the initial dc offset that is seen in all SEM s and the extrinsic stress provided by Joule heating interacts such that increased Joule heating serves to reduce the curl of the multimorphs ba ck to the orientation of pre release (towards the substrate). To fully characterize the extrinsic stress of the multimorph, equations summarized in a work by Weinberg are of great assistance  The m ain equation is given in Equation 3 2 ( 3 2 )
39 In this equation M is the external moment and F a is externally applied axial force. Both of these values are commonly considered zero for basic calculations of radius of curvature R To complete the list of variab les as follows: i is the CTE, E i modulus, A i is the area, z i is the position of the neutral axis with respect to an arbitrary reference, and I i is the moment of inertia with i in the variables signifying the i th layer. Additionally, with the beam much wider th an the thickness and isotropic, the Young's modulus can be substituted as in Equation 3 3  ( 3 3 ) These equations enable analytic solutions for the full multimorph to determine radius of curva ture and include both adhesion and insulation layers, in addition to the primary bimorph and Joule heating layers. The use of SiO 2 and Al as the primary layers of the multimorph stem from the large difference in the CTEs while still maintaining sufficient application in electrothermal actuation. Additionally, Pt is used as the layer that facilitates Joule heating and also motivates the use of the other main layer of oxide insulation between Pt and Al. The final material is Cr, which is used as an adhesion layer between oxide and metal layers for Al and Pt. This is mentioned now as the general structure of the multimorph going forward with the relevant material properties g iven in Table 3 1 The values given in the table are obtained from the material database in COMSOL and provided in the software package expressly for thin films used in MEMS design  Although the multimorph is the true manner of calculating the radius of curvature, a bimorph provides reasonable accuracy and can function for back of the envelope calculations This is feasible through Eq uation 3 4 and Equation 3
40 6 where layer index 1 is the bottom and layer index 2 is the top of the bimorph. Also, r T is the radius of curvature, T is the temperate change, is the CTE difference (Equation 3 5 ), and T is the curvature coefficient given in Eq uation 3 6 ( 3 4 ) ( 3 5 ) ( 3 6 ) When following this simplification of the m ultimorph, the equations for bimorphs allows a calculation of the radius of curvature for a beam that is simple while remaining acceptably accurate for initial verification, when multimorph analysis is not available 3.3 Ladder Actuator Design The basic concep tualization of the electrothermal actuator is based on a folded dual S shaped bimorph (FDSB) ele ctrothermal actuator design to achieve large displacement at low drive voltage  The FDSB is constructed of tw o separate ISC actuators ( Figure 3 7 (a)) that are conne cted by a joint or hinge ( Figure 3 8(a )). The fundamental principle of electroth ermal actuation is to induce a temperature change through Joule heating which is generated by applying an electrical current to a resis tor built in the bimorph. As a result of this heating, the difference of therma l stresses from different coefficients of therma l expansion (CTEs) between the two primary l ayers of the bim orph results in bending of the cantilevered structure. In the case of the ISC design, the primary layers are aluminum and silicon dioxide. The core of this actuator design is the S shaped bimorph or ISC ( Figure 3 7 (a)), which consists o f th ree sections L 1 L 2 and
41 L 3 which contain the followin g thin film bimorph layers of Al/SiO 2 SiO 2 /Al/SiO 2 and SiO 2 /Al respectively. The initial position of this beam, after release from the si licon substrate on which it is fabricated, will demonstrate the S shaped structure as shown in Figure 3 7 (b) which is given via FEM simulation in COMSOL  Section L 1 generates initial upwar d cur vature while L 3 generates downward curvature since Al h as much larger CTE than SiO 2 This curvature in the active bimorph sections will deform upon temperature change. This deformation is motion from the initial displacement that occurs as the natural stat e of the device. The intrinsic stress developed during thin film growth or deposition is the source of this stress yielding initial position. In addition to these active sections, L 1 and L 3 section L 2 provides an overlap that protects the junction between the two active sec tions and also provides approximate self compensation of thermal stra in for an effectively straight section between the two active sections ( Figure 1(b)) In this design, section L 1 and L 3 may 0 leading to zero tilt at the tip of the bimorph or may have different angles leading to out of plane torque that may be compensated by symmetric topology of actuators around the mirror plate A hinge is implemented that is of the same structural composition as L 2 the approximately self compensated section, and joins two S curves to form an FDSB actuator. This actuator structure results in an approximately pure vertical displacement. In order to further increase the verti cal displacement, two FDSB actuators are connected in series to form a ladder actuator ( Figure 3 8 (b)). With R o1 and R o3 signifying the initial radius of curvature of L 1 and L 3 respectively ( Figure 3 8 (a)), the initial displacement of the FDSB ladder actua tor can be expressed as follows:
42 ( 3 7 ) in which , and o is the tip angle of one bimorph section where o =L 1 /R o1 While these equations are able to determine the initial displacement of the actuator structure, an analytical model for the induced strain actuator structure can determine the radii of curvature o f the separate sections where thermal stress is the only contribution to the induced strain for a given temperature differential   3.4 Large scan range Vertical Micromirror Based on the FDSB Ladder Actuator After establishing the ladder actuator structure, the i ntegration of the actuator into a cohesive micromirror device can be realized. The mirror is structured with three stacked pairs of ladder actuators evenly spaced on a mirror edge and symmetric with the opposing edge on a single axis with the alternate axi s without actuators. When all actuators are actuated with a common driving signal, the idealized response of pure vertical displacement as the mirror plate moves towards the device substrate occurs. This is the desired response and can be seen where a mirr or plate under actuation experiences a displacement entirely from idealized Joule heating. Using symmetric actuators on the sides of the actuator axis of the mirror helps to balance any resulting out of plane torque and such effects are minimized in pursui ng pure piston motion, when optimizing driving signal for the actuators. Further, the premise of having three actuators on each side of the mirror was intended to provide tight control of the alignment of the mirror plate to incident light. This intent is the impetus to add the central actuators on each side of the actuator axis, resulting in the topology in Fig ure 3 9
43 3.5 Actuator Bimorph Design and Optimization The primary components of the actuator are the bimorph layers of SiO 2 and Al. However, there are a dditional layers in the actuator that qualifies as a multimorph. These different layers include thin SiO 2 and Cr layers that function as insulation and adhesion layers. Finally, there is a Pt layer that functions as a heater to allow greater Joule heating uniformity and is the impetus for the insulation layer of SiO 2 between the Al and Pt. Although these layers are contributory to the actuator structure and classify it as a multimorph as shown in accurate detail in Figure 3 11 the primary functional layers remain that of the bimorph The full multimorph stack can be determined in analytic solutions and verified in experimental results with bimorph components used as a simplification in FEM simulation Further, the residual stress of the thin films contribut ing to initial curling is primarily from the intrinsic thermal stress of the high temperature deposition of PECVD SiO 2 layers at 300C during device fabrication. The initial curling, as resulting from intrinsic stress, is countered by Joule heating from el ectrical current flow, and as curling relaxes, actuation occurs. To restate the intended optimization of the micromirror, it is desired to reduce tilt and to provide large piston actuation. In previous ISC designs, analytic equations have been used to opti mize thin film thicknesses  This process is followed here using the equations by Weinberg  as opposed to those formulated by Lobontiu  The first action is to optimize the thicknesses of the multimorph layers. Selecting section L 1 the thickness of aluminum, the only layer contiguous through the entire actuator structure, will be considered. Keeping in mind that the bimorph contributes st rongly to the overall actuator displacement characteristic  the other layer in this length L 1 or greatest importance is the first oxide layer. The value for this thickness is fixed at 1m in
44 order to achieve sufficient beam displacement and rigidity. Further, the insulation layers for oxide and Cr are fixed Pt is also fixed at 0.2m to be sufficiently thick and provide sufficient dimensi ons for resistive values but not be overly thick to significantly affect performance as the contribution for the bimorph in the multimorph is predicated on thinner layers supplementing the primary bimorph layers. With these values fixed, the analytic equa tion is graphed with the input of varying thicknesses of the aluminum layer and the corresponding displacement for the segment L 1 at 300K, to simulate initial displacement conditions on release. This chosen condition results from the high temperature depos ition process of the PECVD oxide. The graph that indicates a range of aluminum amenable to maximal displacement optimization is shown in Figure 3 12. The plot indicates that there is a maximal displacement of 12.26m at around 0.98m thickness. For 1m, t he displacement is given as 12.25m and is the selected thickness that also satisfies the need f or beam rigidity. The next step involves selection of the second primary oxide layer. This is determined by finding the maximal radius of curvature of the compe nsated sandwich structure between the two active lengths, which is ideally perfectly straight. Finding the largest achievable radius of curvature, the thickness of the second oxide thickness is determined to be 1.5 8 m (Figure 3 13) T his thickness is, howe ver, thicker than desirable for the oxide layer. In order to avoid excess intrinsic stress across the wafer that leads to bowing of the wafer, a thickness of 1.4m is selected. Now, the radius of curvature is determined for all sections and with the lengt h of L 1 set, the length of L 3 can be found by equating angles of the two active sections as in Equation 3 8. ( 3 8 )
45 The equation permits design of the micromirror to have no moment out of plane with equal angles for the active sections. The caveat is that this does not hold for different temperatures. However, the res ult of this equation is 197m for L 3 at 300K. Continuing, if topology is intelligently designed, then the out of plane moment can be compensated by actuators symmetric around the micromirror. Additionally, the lengths of the actuators must be reduced in th e interest of design orientations explained shortly in regards to sensitivity. As such, this constraint is not utilized in this design. T he thickness optimization s are recorded from the analytic solutions as shown in Table 3 2 A plot of the ladder actuato r as a multimorph and simplified bimorph with four three section ISC actuators stacked, is given in Figure 3 14 for a range of temperatures, which is relevant as temperature differentials and equivalent displacement generated as a result. Previous ISC des igns have, in FDSB configuration, taken up the majority of each mirror side  In these designs, very large displacement can occur, s uch as 480m in  but with excess undesired tilt under piston actuation. To address this, the ISC design must be optimized. To that end, single bimorph  which can be utilized as an approximate guideline for de sign constraints. ( 3 9 ) In Eq. (2) the variables are as follows: thermal response angle from Joule heating T ; average temperate rise as a result of Joule heating ; curvature coefficient of the bimorph combination r ; coefficient of thermal expansion from the top layer 1 and 2 ; and bimorph length L b From this equat ion it is found that the angular responsivity is directly proportional to the length of the bimorph in question. Reducing the bimorph
46 lengths for each section by approximately 60% over the previous designs allows a significant and proportional reduction in angular responsivity, which strongly reduces sensitivity to signal nonlinearities and allows piston motion, when properly driven, to be the pure system output. It is understood that there is more out of plane torque than selecting optimized lengths as in  However, this is a consequence of reducing responsivity. The function of this optimization is to reduce responsivity for all active s ections of the FDSB and consequently reduc e sensitivity to driving signal such that the actuat ors are more precisely controlled so practical signal generation yields controllable stepping in the submicron range Actuator stiffness is another critical aspec t of mirror design as it informs robustness. It has been demonstrated that the compensating section of the actuator structure increases robustness of the actuator  From this understanding, the overlap has been increased as a proportion of the S shaped structure. This yield s an increase in overlap section to strengthen the actuator structure, which leads to an increase in device rigidity a nd vertical stiffness, all facets of a robust actuator and, by extension, a robust micromirror. These improvements lower susceptibility of the mirror to rotation or breakage, which yields significant benefit for an intentionally mobile, piston actuating mi rror. The tradeoff of such gains is requisite reduction in multimorph length, and in turn reduced actuation range with section lengths given in Table 3 3 This has been handily addressed by stacking the FDSB actuators as illustrated in Figure 3 8 (b). 3.6 Ladde r Actuator Mirror Design and Simulation An aperture of 1.0mm is chosen to account for the requirement of optical imaging applications. The device size is 1.9mm1.9mm. This corresponds to a high fill factor of 28%, which is achieved by minimizing the device sidewalls as much as practicable.
47 Additionally, the mirror plate thickness will be defined by the device layer thickness, which is chosen to be 40m. The full mirror design is simulated via FEM simulation in COMSOL  The first mode is obtained and found to be a piston resonance mode present at 841Hz in Figure 3 10 (a). This result is positive as piston resonance will not adversely a ffect piston motion at higher frequencies and will in fact be an aid in increasing displacement for a given driving signal. The second mode is a rotational mode on the off actuator axis an d is present at 1132Hz in Figure 3 10 (b). A full mirror FEM simulati on is conducted to determine the displacement of the mirror. In the simulation, a temperature difference of 300K is shown with a displacement of 116m. This is compared to the analytic solution for the full multimorph which show s a value of 85.1 m at 300K The agreement is closest at lower temperatures with a difference of approximately 10m. At the largest difference of approximately 30m, the temperature is highest. These results are presented in Figure 3 15 for bimorph structures of oxide and aluminum i n the FEM and a full multimorph analytic solution 3.6.1 Actuator Variation There are two variations of the actuator structure defined by the initial displacement of the stacked FDSB on release. The variety already m entioned and represented in Figure 3 7 (a) is a n ISC actuator that has initial upward vertical displacement relative to the device layer on an SOI wafer. To generate downward initial displacement, the first oxide layer is placed in the position of L 3 an d retains its prior length (Figure 3 16 ). In the s ame manner, L 1 now is composed of a l uminum and the second oxide layer, while also retaining its prior length (Figure 3 16 ). In this manner, the initial displacement is downward on release. This allows for the unique feature of increasing the aperture of th e mirror and hiding the bimorphs underneath the increased
48 mirror plate and the mirror plate interacting with incident light is the bottom of the device layer that interfaced with the buried oxide (BOX)   Additionally, the mirror now remains within the substrate walls during the entire range of actuation and thus reduces the volume occupied by the device. The thicknesses are consistent for the two different types of actuators and these values are represented in Table 3 2 3.7 Ladder Actuator Micromirror Fabrication The fa brication of the ladder actuator devices follows a multi step process on a single silicon on insulator (SOI) wafer that encompasses a combined surface and bulk micromachining process. This process follows, generally, with variations, the process previously reported in  and  Two separate process flows are required to fully describe the different devices that express upward and downward piston motion actuation. Despite these different process flows, both devices are fabricated simultaneously on a single SOI wafer. Stem ming from this commonality, the steps in Figure 3 17 and Figure 3 18 are concomitantly described from steps (a) through (e). The differentiation in these steps stems from the ordering of the multimorphs from the device sidewall inward to the mirror plate, where the downward actuator is described in Figure 3 18 and the upward actuator is described in Figure 3 17 To begin, a clean SOI wafer is obtained. The wafer utilized for the fabricated devices possesses the following features: a 40m thick device layer, a 2m buried oxide (BOX) layer, and a 400m handling layer. On this wafer, 1m of PECVD SiO 2 is deposited and patterned by a buffered oxide etch (BOE) on the frontside of the wafer ( Figure 3 17 (a) and Figure 3 18 (a)). The use of the BOE is intended to pro vide a smooth slope for actuator fabrication consistency. An adhesion layer, which is not shown in the diagram, of 0.05m PECVD SiO 2 is added to the frontside of the wafer. Platinum is sputtered for
49 0.2m and then patterned via lift off for the purpose of Joule heating in the multimorph structure s ( Figure 3 17 (b) and Figure 3 18 (b)). PECVD SiO 2 is deposited for 0.2m and patterned by dry etch in a reactive ion etching (RIE) system. This layer functions as the thermal isolation in the multimorphs and is patt erned to provide contact opening on the bond pads of the device ( Figure 3 17 (c) and Figure 3 18 (c)). Aluminum is evaporated for 1.0m and patterned by lift off to form a portion of the actuator as well as the traces ( Figure 3 17 (d) and Figure 3 18 (d)). The final PECVD SiO2 layer is deposited and patterned through an RIE dry etch to complete the actuator structure ( Figure 3 17 (e) and Figure 3 18 (e)). After this step the application of the combined process flow varies between device designs. For the downward actuated mirror a frontside de ep reactive ion etch (DRIE) through the device layer to the BOX is performed ( Figure 3 18 (f)). For the upward actuator, the device is fully coated with photoresist (PR) and no etch is performed. At this point in the process, the frontside of the wafer is coated in PR and a carrier wafer is attached and hard baked for both processes ( Figure 3 17 (f) and Figure 3 18 (g)). Next, for both processes, the process wafer is bulk silicon etched in the DRIE through the handling layer to t he BOX ( Figure 3 17 (g) and Figure 3 18 (h)). With the carrier wafer still attached, the BOX is dry etched to removal in an RIE ( Figure 3 17 (h) and Figure 3 18 (i)). After this step the carrier wafer is removed and die level is reached ( Figure 3 17 (i) and Fig ure 3 18 (j)). For downward actuating devices in Fig ure 3 18 (k), small groups of wafers are attached to a carrier wafer and E Beam aluminum is deposited to form the mirror surface for 0.2m. For the final release of the devices, either type of device is mou nted on a carrier wafer with thermal release tape. These carrier wafers are
50 loaded into the DRIE and subjected to a combination of anisotropic silicon trench etching an d isotropic undercut etching. The steps are combined to recess the Si surrounding the ac tuators with anisotropic etching. Next, isotropic undercut removes Si from the actuators, most directly targeting the Si that would remain attached to the underside of the actuators, which is the focal point in this portion of the release process to avoid strong reduction in initial displacement. After final release, the devices, by intrinsic stress, are at initial position. 3.8 Ladder Actuator Micromirror Passive Physical Characteristics The two different device designs have been fabricated and a specifically detailed in SEMs that show the final state of the devices after final release for downward actuated devices in Figure 3 20 (a) and upward actuated devices in Figure 3 19 (a). The mirror plate in Figure 3 20 (a) consists of the 40m thick silicon device layer for the purposes of optical flatness. In Figure 3 20 (b) the initial downward displacement of the actuators can be clearly seen and the recessing of the mirror plate is also observable. A close up of the ladder actuator is shown in Figure 3 20 (c) and the e tching of the mirror plate is seen as a consequence of the anisotropic and isotropic release steps. It is also visible that the inner portion of the mirror plate is un etched due to the etch mask on its surface but that the height of the mirror plate is si gnificantly reduced elsewhere. This demonstrates the need for a thick device layer not only for the optical flatness of the mirror plate but also the significant sacrificial etching required for final release. Ideally a mirror plate would be made of a devi ce layer that has at least 60m thickness. The reason for retaining the etch mask stems from providing a strong connection point for the actuators to the mirror plate. In Figure 3 19 (a) the full, released device is seen for an upward actuating device. As i n Figure 3 19 (b), the basic sections of the micromirror are
51 shown and clear distinction is made between the mirror plate, actuators, substrate, and bond pads on sub strate. The final SEM is Fig ure 3 19 ( c ) that shows the visible materials in the devices. The visible materials include SiO 2 Al, and Si; embedded Pt for Joule heating is located between oxide layers and is not visible. The footprint of both styles of devices is the same at 1.9mm1.9mm. The mirror plate for the upward actuated device is 1.02mm1. 02mm, which yields a fill factor of 28%. The mirror plate for the downward actuated device, discounting the tabs at the corners of the larger rectangular mirror plate, has a mirror surface of 1.47mm1.32mm which results in a fill factor of 54%, which is si gnificantly more than previous single aperture designs  From this design the individual ladder actuators have an average resistance of 25 ohms with each individual ladder actuator capable of being driven through a distinct driving signal. The majority of resistance values are close to 25 ohms but some have had larger variation up to 35%. This can be attributed to process variation in dev ice fabrication. Additionally, the initial release displacement for the mirror plate is around 98m across multiple devices. This is lower than the simulated result but can also be attributed to process variation and over etching. The primary factor contri buting to over etching is the need to remove all silicon from the underside of the bimorphs. Without achieving this, the actuator i s strongly reduced in range, which is the prime justification for over etching as needed 3.9 Ladder Actuator Micromirror Active Performance Characteristics 3.9.1 Piston Actuation The dc response of the device ( Figure 3 18 ) is measured by an Olympus BX51 microscope and a Quadra Chek 200 geometry measuring system. From this setup, the mirror can step in piston motion through 90m with a si gnal ranging from 0 to 1.2V dc
52 ( Figure 3 21 ). The observed linearity results from the reduced angular responsivity and the strong mechanical coupling of the ladder actuators. The reduced travel in this setup is due to tying all actuators to the same signal which, without tuning significantly reduces range as lower resistance actuators are susceptible to burnout and breakage. The maximum current draw of the complete device is 252mA. In addition to the displacement measurements, the tilt through the entire dc piston actuation range is measured. The maximum recorded tilt angle in this uncompensated driving signal is 0.25 during the entire dc piston actuation range on the actuator axis in Figure 3 21 Additionally, there was no measureable off actuator tilt with this experimental setup. This results in a tilt reduction of 85% over the previous electrothermal piston, low tilt micromirrors used in FTS applications  For ac measurements, the micromirror is mounted on an optical breadboard for precise spacing from a 2D position sensitive detector (PSD). The driving signal ranges from 0.7 to 1.1V at 0.33Hz. The signal is un tuned and so does no t adjust for layer thickness mismatch in the actuators from fabrication or for release step undercut of the sidewall and mirror edges. For a practical, un optimized ac driving signal, the mirror produces a maximum of 0.22 tilt on the actuator axis and 0.0 97 on the off actuator ax is as measured via the PSD ( Figure 3 22 ). Despite the explicit intent of the ladder actuator being vertical displacement with low tilt; it is informative to test the angular scanning capability of the device to gain a holistic per spective of the capabilities of the micromirror. To that end, the micromirror angular scanning testing setup was constructed by having a HeNe laser incident on the mirror surface to form a right angle with the reflected light incident on graph paper. A
53 wav eform generator was attached to the actuators on one array, on a single side of the micromirror. An oscilloscope was also attached to record the waveform. Driving the micromirror with a triangle waveform, the driving signal was slowly incremented and the c orresponding increase in scan of the beam across the graph paper at 100Hz which form s a visually unbroken line across the graph paper was recorded The results of this test are shown in Figure 3 23 The results indicate that a single axis is capable of g enerating an optical angle of around 12 across the actuator axis. 3.9.2 Tuned Piston Actuation To provide more insight into the vertical displacement initially demonstrated for a common driving signal in Figure 3 21 tuned systems should be considered. Such re sults provide valuable insight, as there is a significant reduction in the range of pure piston motion if there is significant variation in the resistance of a device, which is informative of the capabilities of the device under practical constraints. It i s most expedient to consider signal application in terms of peak power as that is the measurement that indicates the peak signal a resistor can absorb before burnout. To address this issue, two aspects are combined. First, a custom system is created to pro vide arbitrary waveforms to drive each individual actuator, and tune the waveforms in relation to the other actuators in terms of power. Second, the system is placed in a custom interferometry setup, in the configuration of a traditional Michelson interfer ometer. The custom waveforms provide scaled signal that, without sectional scaling, is in the arrangement of a triangle waveform with arbitrary peak and offset duration. Thereafter, sections denoted by segments of the period are scaled in terms of power t o counter the changing resistance and thermal time constants of the individual resistors.
54 This is most expediently determined from measuring resting resistances and progressing through experimental determination of tilt of the mirror in pure piston motion by viewing the misalignment of the interferometer system in the far field through the range of actuation in a quasi static motion. After this procedure, displacement determined by interference fringes incident on a silicon based photodetector is recorded a long with temporally concomitant driving signal. Thus, a submicron level of accuracy is capable of being obtained to measure displacement as a function of voltage. One actuator has been used to p rovide the voltage axis in Figure 3 24 with the displacement provided by processing the raw interferogram recorded by the custom system. In Figure 3 24 the chart contains a slight curve at the low end indicative of Joule heating This indicates that in a quasi static state where the micromirror in question is driven at millihertz, the heating of the actuator is linearly related to displacement except at the lower end with a nonlinear characteristic There is, however, a noticeably slower velocity at the lower voltages in a drive signal for the first few microns. This is not as pronounced when the device is provided with an offset but is still present in the raw interferogram where there is a compression of the velocity to uniformity through the first microns of motion, and subsequently thereafter but at significantly reduced levels. As initially illustrated in Figure 3 21 the micromirror demonstrated the characteristic of a strongly linear displa cement as a function of voltage As the error bars in Figure 3 21 demonstrate, an alt ernate approach, as that in Figure 3 2 4 is necessary. In this manner, the results of Figure 3 21 are reinforced and the nonlinear region of the response curve of the device can be clearly seen whereas it was hidden within the margin of error in Figure 3 21 With these results, the characterist ics of the
55 device are further enforced as providing ultra low tilt and being favorably responsive to signal shaping throughout the piston range. 3.9.3 Piston Resonance Measurements in the Nonlinear Region Piston resonance is difficult to be visually identified. In this work, the interferometric setup is used to measure piston resonance. Actuating over a small range of 0.1V peak to peak with no dc offset, approximately 0.5m of mechanical range or vertical displacement is achieved. When piston amplitude at low dri ve frequency is the same as that of the drive signal. As the drive frequency increases to the piston resonance, the piston amplitude, z p becomes large and is greate multiple fringes will appear in the detector signal. The number of peaks is equal to 2z p 1 The full range of frequency response with the piston resonance frequency or first resonant mode experimentally determined to be at 828Hz is shown in Figure 3 25 This chart demonstrates piston resonance with a Q of approximately 32. Compared to the simulated piston resonance of 841Hz, there is close agreement. The slight variation can be attributed to process variation and additional contribution o f the multimorph versus bimorph modeling of the ladder actuator structure. Further, to determine the second resonant mode, the mirror is driven at 1V and the frequency is varied until resonance is discovered. This resonance is shown as a piston motion actu ator demonstrating an angular scanning pattern on a flat surface illuminated by the system with the detector removed in the far field. By this method, the second resonance mode or off actuator axis rotational mode is found at 1104Hz. Here, there again clos e agreement with the simulated result of 1132Hz. These results indicate that the design constraints have surpassed the frequency response over previous
56 designs where 406Hz was the torsional mode peak and was also the first resonant mode  As an additio nal note for the results in Figure 3 25 are the additional peaks at 414Hz, 276Hz, and 207Hz, which can be explained, respectively, as 1/2, 1 /3, and 1/4 subharmonics of piston resonance at 828Hz. This is the initial interpretation of the results in the nonlinear region. As shown in Figure 3 25 at small piston motion range with zero dc offset the response is within the nonlinear region 3.9.4 Piston Resonance Measurements in the Linear Region The previous piston resonance tests were conducted with zero dc offset and only a n ac component. T his signifies testing in the nonlinear section of the displacement curve of the device. Testing must also occur i n the linear region to assure that nonlinear effects are not skewing the testing results with the micromirror. However, it is pertinent to note that the results of measuring half lambdas are open to a level of visual interpretation, which is noted further in section 5.10. The interpretation that has been consisten tly employed is to consider cosine waves only when clearly independent and not modulated on another signal. With this choice, it is important to refine the interpretation by comparing to an establi shed measurement technique for determining resonant modes. The mainstream resource that is used for comparison is a laser vibrometer With the vibrometer system, t he micromirror is driven first with a single source divided across the actuators of 0.24Vac with no off set for the result in Figure3 26 (a). The resonant mode is found at 828.8Hz, which is strongly in agreement with the prior result in Figure 3 25 Additionally, there is significant noise at other frequencies apart from the rise associated with th e resonant mode peak. Driving with the same 0.24 Vac and adding an offset of 2V dc pr oduces the result in Figure 3 26 (b). This is much cleaner with noise
57 present only at low and high frequencies. The most important item to note is that the only resonance is the main piston resonance and no subharmonics are visible. The peak frequency is only slightly reduced at 826.3 Hz With this information, the micromirror is tested in the custom interferometer setup in the linear region as shown in Figure 3 2 7 The microm irror was tested from 50Hz to 1 0 00Hz. The system demonstrated excess noise that made discernment of the detector signal difficult. As a result, the setup was modified to add a lens for beam broadening and a pinhole to isolate the center part of the central fringe. With the output of the pinhole immediately incident on the photodiode, the system was tested with 716mVdc offset and 17mVac. The results of the system show a system with noisy signal up to around 200Hz. There is a slight dip before a rise to 261Hz with a Q of 5, which can be interpreted as the last section of noise in the system. After this, the baseline displacement is consistent until reaching the resonant peak of 782Hz. This peak has a Q of 19. During in system testing, the resonant frequency is found to be decreased with increased dc offset, which is the rationale for the lowered resonant peak in this testing case. The constructed frequency plot in Figure 3 27 fits much closer with the general structure of the vibrometer plot as a reference guid e for visual interpretation of the custom interferometer in system results 3.10 Device Shortcomings There is an overarching shortcoming in the design of the device. At the point in between the stacked actuator s as demonstrated in Figure 3 28 there is a short. The tolerance between the platinum and aluminum layers is below the minimum feature size of the masks and it is left more or less to chance if the platinum and aluminum will come into direct contact. If functioning as intended, the resistance, with platin um electrical
58 m wou ld be 72 ohms as in Equation 3 10 However, the result, instead of having eight ISC sections in series, has usually only two for a resistance closer to 18 ohms ( 3 10 ) This error in design causes the actuators to be much more difficult to control with ultra low resistance and also reduces overall range by reducing the effectiveness of the platinum heater. Such an oversight can be easily corrected, but remains an issue for this iteration of devices 3.11 Summary This chapter introduced the prior work for LSF LVD devices and introduced the ISC actuator. The ISC actuator was characterized with background information on the theoretical underpinnings of bimorph functionality with a mind to simplifying assumptions and the cost of such assumptions. Further, the ISC was developed into FDSB and fi nally into a ladder actuator. The ladder actuator was discussed as to its design parameters and choices were vetted. The fabrication process was discussed in detail with mention of caveats in the process flow. Next, released devices were discussed for both types of devices and given meaningful performance characteristics that discussed the ultra low tilt of belo w 0.25 and large piston displacement of 90m of the system under untu ned driving signals Next, the devices were characterized further with quasi s tatic displacement discussed in the context of function within the FTS system. Also with the FTS system, the devices were tested for piston resonance characteristics in both the nonlinear and linear regions of device operation where the piston resonance mo de and subharmonics were determined. A short discussion of
59 device shortcomings to round out the holistic character of the device was the final aspect to discuss for the ladder actuator micromirror.
60 Figure 3 1. Fabricated mic romirror with DRIE CMOS MEMS process. A) Previous iteration of full mirror. B) LVD mirror. C) LVD closeup  Figure 3 2. Large tilt 1D mirror. A) Full mirror. B) Substrate to actuator closeup with platinum heater. C) Actuator to mirror plate close up  A B C A B C
61 Figure 3 3. Tilt insensitive FTS setup. A) S chematic of tilt insensitive F TS. B) Simulation showing tilt compensation. C ) picture of setup with CCR (corner cube retroreflector), PD (photodiode), BS ( beamsplitter), LS (light source), FM (fixed mirror) and MM (movable MEMS micromirror)  Figure 3 4. Piston LSF micromirror. A ) LSF structure d iagram. B ) SEM of piston motion device for tilt insensitive FTS  Figure 3 5. SEMs of ISC based micromirror. A) Mirror surface side. B) Actuator side. C) Close up of actuator. D) thin film detail  A C B D A B A B C
62 Figure 3 6. Multimorph showing close up of all layers where layer 1 is the top of the multimorph stack. Figure 3 7. ISC actuator structure. A) Three seg ments of S shaped bimorph. B) Vertical displacement on release. L 1 L 2 L 3 SiO 2 Al A H o 3 H o2 H o1 o B z i F a M SiO 2 Pt Al
63 Figure 3 8. 3D FEM models of the stacked FDSB A) L adder actuator with stacked FDSB half segment. B) Full ladder actuator Mirror plate connection FDSB bimorph elements Substrate connection Hinges A 4H o 2H o 2H o R o3 R o1 B
64 Figure 3 9. Ladder actuator mirror. Figure 3 10. FEM simulation of the two primary resonance modes of the ladder actuator micromirror A) F irst resonant mode. B) S econd resonant mode 1.02mm 1.02mm 116m Stacked FDSB Mirror Plate SiO 2 Al Si A B
65 Figure 3 11. Complete cross section of S shaped multimorph with all layers. Figure 3 12. Plot of vertical displacement as a function of aluminum thickness at 300K.
66 Figure 3 13. Radius of curvature for second oxide bimorph layer at 300K. Figure 3 14 Vertical displacement of ladder a ctuator with four ISC actuators versus uniform temperature differential inputs for multimorph and bimorph simplification
67 Figure 3 15 FEM as bimorph and analytic as full multimorph comparison for displacement of actuator as a function of temperature differential. Figure 3 16 Three segments of S shaped bimorph for downward initial displacement
68 Figure 3 17 Upward actuated ladder actuator micromirror fabrication process. A) Oxide deposition and patterning B) Pt deposition and liftoff C) Oxide deposition and contact opening D) Al deposition and liftoff E) Oxide deposition and patterning F) Carrier wafer frontside attachment G) Backside bulk silicon etch H) Backside BOX etch I ) Carrier wafer removal J) Multistep silicon etch for final release A B C D E F G H I J SiO 2 Al Pt Si PR
69 Figure 3 18 Downward actuated ladder actua tor micromirror fabrication process A) Oxide deposition and patterning B) Pt deposition and liftoff C) Oxide deposition and contact opening D) Al deposition and liftoff E) Oxide deposition and patterning F) Silicon etch through device layer G) Carrier wafer frontside attachment H) Backside bulk silicon etch I) Backside BOX etch J) Carrier wafer removal K) Backside metal deposition L) Multistep silicon etch for final release A B C D E G H I J K SiO 2 Al Pt Si PR L F
70 Figure 3 19 Upward ladder actuator SEM s. A) T he mirror surface o f the upward actuated device. B) SEM of an actuator arr ay with raised mirror plate C) Close up of central ladder actuator Bond Pads A ctuators Mirror Plate Substrate A B
71 Figure 3 19 Continued Figure 3 20 Downward ladder actuator SEM s. A) T he backside mirror surface of the downward actuated device B) Frontside of full mirror. C) Close up of ladder actuator for downward actuated device Aluminum Silicon Dioxide Substrate Silicon S idewall Mirror Plate C Recessed Mirror Plate Surface A
72 Figure 3 20 Continued Bond Pads Hidden Actuators Substrate Bond Pads B Ladder Actuator (hidden bimorphs) Bond Pads Mirror P late C
73 Figure 3 21 Displacement and tilt angle versus applied voltage at 0.1V inc rements Figure 3 22 Tilt angle and recorded ac voltage applied to all actuators for piston motion.
7 4 Figure 3 23 Optical angle versus voltage for a single actuator for ladder actuator device. F igure 3 24 Quasi static displacement in millihertz frequency measured in interferometric setup.
75 Figure 3 25 Micromirror piston actuation frequency response over the range 50Hz to 1240Hz.
76 Figure 3 2 6 Vibrometer results for micromirr or. A) No dc component B) With dc component. A B
77 Figure 3 2 7 Micromirror piston actuation frequency response in linear region. Figure 3 2 8 Boxed sections showing electrical short. Overlap section
78 Table 3 1 Thermal an d mechanical properties of multimorph materials. Materials CTE ( ) (10 6 /K) ( E ) (GPa) Ratio( v ) Thermal conductivity ( k ) (W/m*K) SiO 2 0.5 70 0.17 1.4 Al 23.1 70 0.35 237 Pt 8.8 168 0.38 71.6 Cr 4.9 279 0.2 93.7 Table 3 2 IS C l ayer t hicknesses for a ctuators Adhesion SiO 2 SiO 2 (1st) Pt Heater Insulation SiO 2 Cr Al SiO 2 (2nd) 0.05 1.0 0.2 0.2 0.01 1.0 1.4 Table 3 3 Section lengths of ISC a ctuator for ladder actuator micromirror Upward ISC (m) Downward ISC (m) L 1 =102, L 2 =22 and L 3 =56 L 1 =56, L 2 =22 and L 3 =102
79 CHAPTER 4 ELECTROTHERMAL MICROMIRROR MESH ACTUATOR In addition to the ladder actuator structure, another actuator has been devised with a focus towards FTS system applications as well as reliability This device is fully designed and all parameters for design are derived and given. FEM models are develop ed for actuation verification and resonant modes. The devices are fabricated and verified in operation for both static and dynamic characteristics. Additionally, the system is used in an interferometer setup to determine resonance for the nonlinear and lin ear regions Finally, potential fabrication issues are addressed that can appear in the complex fabrication process. 4.1 Design and Caveats There are several characteristics of the mesh actuator device th at were intended to be improved in terms of reliability To increase reliability, several improvements to the ISC actuator structure are considered in practical terms. As the design on which the mesh actuator is based is the ISC actuator structure, r obustness is addressed in terms of the overlap reg i o n of the b imorph, which allows for increased vertical stiffness and to guarantee a strong connection between the active regions both mechanically and in terms of electrical connectivity by the sloped transition region  The use of the overlap region has been used in many prior ISC designs as in   and  and is utilized here as well. Additionally, for the regions of the actuator, namely inverting, compensated, and non inverting the same sequencing is retained The key difference is in two respects. To begin there is doubling of the ISC secti ons so that the S curves are matched by identical S curves. These complementary lengths are redundant to allow robust actuators that can survive burnout and still function, albeit at reduced
80 capacity as long as the failure is not at one of the short joine d segments of the device This concept is inspired from prior designs that have been used in high fill factor array applications  F urther, the purpose of the pairs of ISC sections is to attempt to provide greater mechanical stability in actuation so as to reduce environmental noise on the nanometer scale in affecting the mirror plate position, a concept best verified in application to an FTS system, an excellent manner of measuring nanometer scale mirror characteristics with in system operation. Further, two common failure points in the ISC design are in terms of the compensated segment of the ISC actuators and the hinges connecting th e ISC actuators to form the FDSB. These failure points are most often expressed when a device is weakened by suboptimal conditions such as overetching of exposed oxide layers during device final release or with contamination between thin film layers in the multimorph For the previously unaddressed hinges, the structures within the mesh actuator structure have a fixed point at the overlap of the mirrored ISC overlaps. Consequently there are significant lengths on the order of 25m of compensated sections s pread ing out from this central overlap point. This is used to add robustness and rigidity to the device in terms of reducing the likelihood of mechanical failure and increasing vertical stiffness and increasing the strength of the hinge connection between ISC actuators, as addressed in part in  The prime benefit to overlapping the platinum heater at the hinge is that only one ISC segment will fail without affecting others; however, the downside, is that the ISC actuators are in parallel as illustrated in Figure 4 1. Th is ultimately yields the result of 2R as in Equation 4 1. Further, calculating R for each ISC segment and considering
81 plat m, R is found to be 20.5 ohms and shown in Equation 4 2. This is not an optimal result and although power consumption is not effected by such as result, variation due to fabrication defects and release steps invites sma ll variances in resistance that become significant variations. Thus, signal drive tuning becomes even more critical ( 4 1 ) ( 4 2 ) 4.2 Pa rameter Selection and Simulation Fabricated on the same wafer as the ladder actuator and utilizing the same optimized thickness parameters, the parameters have already been selected. Even so, it is informative to follow the same procedure as that utilized in using the analytic equations by Weinberg  Using the pre selected length of L 1 the varying thickness plot of aluminum with the other fixed thickness layers of the stack show s a maximum displacement at 0.97m of 72.99m. With this, 1m of aluminum is selected with negligible loss of displacement to 72.93m (Figure 4 2) Next, the maximum radius of curvature is obtained for the app roximately compensated overlap segment by determining the second main oxide layer that completes the definition of the bimorph layers ; the thickness is determined to be optimized at 1.58m. In order to reduce stress on the wafer, this thickness is reduced to 1.4m as in the previous micromirror design. The final step is again to optimize the angles of the active sections to be equal for no out of plane torque as in Equation 3 8. This is still only valid for the temperature at which the equivalency is determ ined such that the equivalency for L 3 with a length of 138m would place L 1 at 197m, for approximate release conditions at 300K intrinsic
82 stress. This is passed over for a greater length and thus greater displacement while creating symmetric actuator place ment in the micromirror topology to compensate any out of place torque. The thickness parameters determined again and common to a single mask set can be found in Table 3 2 For the length parameters of the device, the optimized lengths are given in Table 4 1. The results of the full ISC device assuming identical mesh displacement as configured with the full multimorph stack can be plotted for displacement at various temperature displacements as in Figure 4 3. Additionally, the plot shows the bimorph plot wi thout the effect of platinum or thermal isolation layers. The difference is notable and the differential grows from approximately 61m at 100K to 154m at 300K. The plot shows temperature differentials from 100K to the theoretical initial displacement from residual stress due to the estimated high temperature PECVD deposition of oxide at 300K. For the topology of the device, each actuator is joined to the mirror plate at the center point of each side and there is a mesh actuator on each side of the mirror p late. This is to allow full tip tilt piston motion ability for the device. Additionally, as a downward actuating device, the aperture is 1mm from the frontside and when utilizing the backside of the device layer as the mirror surface achieves 1.3mm apertur e. With these parameters, first the actuator itself may be simulated. This is shown in Figure 4 4 with key features highlighted to show redundant ISC actuators and robust hinges. Beyond the actuator simulation, a full device simulation is accomplished to a id in viewing topology and structure. The device with actuators as bimorphs of oxide and aluminum is actuated under a temperature differential of 250K and achieves a
83 displacement of 261m (Figure 4 5) Of note, the range is reduced versus the original ISC design without mesh characteristics. This is, not due to heating characteristics as the simulation assumes uniform heating but is rather due to the structure of the hinge in the actuator. This indicates that the hinge is less deformable and should retain a more uniform shape throughout the range of actuation In addition to the displacement simulation, resonance simulation is also accomplished. The first resonant mode is piston mode and is found to be at 441Hz (Figure 4 6 ). The second resonant mode is a pai r for rotational mode at 714.6Hz(Figure 4 7 ). 4.3 Mesh Actuator Micromirror Fabrication The mesh actuator micromirror follows a similar process to the downward ladder actuator micromirror in Figure 3 18 Additionally, the devices are fabricated on the same waf er as the ladder actuator micromirrors. The process is a multi step process on a SOI wafer that utilizes surface and bulk micromachining processes. A clean SOI wafer is selected. The wafer possesses the following features: a 40m thick devices layer, a 2m BOX layer, and a 400m handling layer. On the wafer, 1m of PECVD SiO 2 is deposited and patterned by a BOE on the frontside of the wafer (Figure 4 8 (a)) The use of wet etch in this step allows a slope that promotes electrical path continuity that dry etc h does not facilitate. An adhesion layer, not shown in the diagram, of 0.05m PECVD SiO 2 is added to the frontside of the wafer. Platinum is then sputtered for 0.2m and patterned via lift off for the purpose of Joule heating in the multimorph structure (F igure 4 8 (b) ) PECVD SiO 2 is deposited for 0.2 m and patterned by dry etch in RIE system for thermal isolation in multimorphs. Further, the patterning provides contact openings on the bond pads of the device (Figure 4 8 (c)). Aluminum is evaporated for 1.0 m and patterned by lift off to form a portion of the actuator and electrical traces on the
84 substrate (Figured 4 8 (d)). The final PECVD SiO 2 layer is deposited and patterned by an RIE dry etch which completes the multimorph structure (Fi gure 4 8 (e)). A fron tside anisotropic silicon trench etch in the DRIE defines the mirror plate for the b ackside mirror plate (Figure 4 8 (f)). Next, the frontside of the wa f er is coated in P R and a carrier wafer is att ached and hard baked (Figure 4 8 ( g )). The backside of the p rocess wafer is bulk silicon etched by DRIE through the handling layer to the BOX, which functions as an etch stop (Figure 4 8 ( h )). With the BOX exposed, the oxide is etched in the RIE (Figure 4 8 ( i )). Next, the carrier wafer is removed and d ie level is ac hieved (Figure 4 8 ( j )). Metal is now deposited on the backside of the mirror plate wi th 0.2m of aluminum (Figure 4 8 (k)). For the final release of the devices, the devices are mounted on a carrier wafer with thermal release tape. The carrier wafers are lo aded into the DRIE and etched with anisotropic and isotropic undercut etching. After release of the devices from the thermal tape, the devices are in final re leased configuration (Figure 4 8 (l)). 4.4 Mesh Actuator Micromirror Characterization The downward act uated mesh actuator has been fabricated and specifically detailed in SEMs demonstrating the final configuration of the device. The fu ll mirror is shown in Figure 4 9 (a). Detail of a full mesh actuator is shown in Figure 4 9 (b) and a close up of the dual IS Cs and mesh hinge are shown with the exposed materials of the actuator labeled: SiO 2 and aluminum; the sidewall also s hows exposed silicon (Figure 4 9 (c)). The device footprint is 1.78mm1.78mm and the frontside mirror plate aperture is 1.06mm1.06mm, wher eas the mirror plate aperture on the backside of the mirror plate is 1.33mm1.38mm. This yields a fill factor of 35.7% and 55.98%, respectively. The initial displacement of the devices is consistently centered around 249m. This is reduced from the 319m d isplacement achieved with the optimized design without
85 redundant ISCs and meshed hinges  The primary contribution here is the rigidity of the meshed hinge. Prior hinge designs allowed greater bending and twisting to allow full displacement for ISC initial displacement. However, the meshed hinge does not allow this deformation and thus reduces initial displacement. The average resistance s for the device have been found to vary between 14 ohms and 24 ohms, which are consistent, factoring in process variation, with the calculated resistance. T he average current draw per resistor is 45mA and the maximum voltage is averaged to 1.6V. Thus, the average power draw for each resistor is 72mW and 288mW for all four actuators in the device. It may be noted the overall power consumption matches strongly with the determined power consumption of the ladder actuator device. The overlap can be explained i n the commonalities of the system, the current path for the two devices is almost exactly matched at approximately 1640m overall length, which provides the rational for the strong power consumption overlap. 4.4.1 Static Micromirror Characteristics The testing o f the device also extends to determination of displacement and angular characterization. The pure displacement tests are conducted on an Olympus BX51 microscope and a Quadra Chek 200 geometry measuring system With one axis of actuators actuating, the micr omirror is able to achieve 90m at 1.4V. The passive axis functions as a force as a spring to counteract the motion of the active axis generating the displacement by applied voltage. Under these conditions, range is expected to be reduced from all actuator s under driving signal. The results of this test are presented in Figure 4 10 In addition, all actuators are actuated under a common drive signal that is supplied by a dc voltage power supply with sufficient current. The results under these
86 conditions an d tested with the same microscope and geometry measuring system yields a maximum displacement of 145m at 1.8V in Figure 4 11 Under this method of actuation there is still a range of about 100m less than the initial displacement of 249 m. This large disp lacement from the substrate can be attributed to the greater rigidity in the mesh actuator hinge. In addition to the displacement, current is given for each recorded displacement, showing a value of 143mA across all four actuators at the maximum displaceme nt of 145m for 1.8V. The power is lower than the noted average as this is a separate device, and exhibits variation in a peak power consumption of 257mW versus the average of 288mW 4.4.2 Dynamic Micromirror Characteristics Beyond displacement, achievable optic al angle is determined for the micromirror. The device is configured so the HeNe laser is incident on the micromirror and reflects onto graph paper while forming a ninety degree angle with the incident light. With this setup a func tion generator drives a s ingle actuator of the micromirror to determine the common angle for each individual actuator that can be generated where a full axis is effectively a doubling of the optical scan angle from a single actuator under tuned driving signal conditions. The maxim um angle achievable under normal scanning at 100Hz without resonant mode effects yiel ds about 16 at 2.7V (Figure 4 12 ). The mirror was tested by incrementing the driving voltage by 0.1V and recording a new datapoint when a change on the graph paper was vi sually discernable. The error bars are for 1, which is approximately equivalent to centimeter on the graph paper. A notable feature of the mesh actuator is that the mirror may be driven beyond safe voltage such that burnout conditions occur, the mirror w ill destroy one actuator section but the device is still functional with the redundant signal path and ISC actuator section. Although such a
87 feature is not an optimal device characteristic change and undoubtedly effects resonance and performance characteri stics, the device is still functional and can continue to perform effectively until replacement in a hypothetical system. As it stands, such a characteristic was directly observed under several instances testing different devices past the safe voltage leve ls for operation. Upon burnout, denoted by fluctuation in measured current and changing in the optical scan angle characteristic, multiple devices demonstrated the ability to function sufficiently so as to continue scanning patterns. In determining the sec ond resonant mode or angular resonant mode the mirror is driven at 1V and the frequency is varied until resonance is discovered. Th e resonance is observable as a strongly amplified angular actuation When moving the driving frequency toward the resonant m ode, increasing frequency near the resonant peak causes an increase in the amplitude signal to a maximal scanning angle at angular resonance. By this method, alternate to that utilized in de ter mining the angular mode for piston actuation, the second resona nce mode is found at around 533 Hz in the linear region of actuation Agreement versus the simulated result of 714.6Hz is not close, and does not find good agreement as was the case for the piston actuator micromirror previously examined The difference can be attributed more to process variation from the device on the outer quarter of the wafer, as well as undercut in release. Additional contribution is from the dc offset of the driving voltage, which reduces resonant frequency. Finally, contribution to thi s disparity can also be connected to the use of the multimorph versus bimorph modeling of the mesh actuator structure in the FEM software package
88 4.4.3 Piston Resonance Tests In addition to the above static and dynamic tests, piston resonance is an important ch aracteristic of the micromirror, especially for the intended application of the device to piston motion. As with the ladder actuator micromirror, t he constructed interferometric setup is used to measure piston resonance. The small range of actuation is 0.1 V peak to peak with no dc offset that yields approxim ately 0.5m of mechanical range in the form of vertical displacement of the micromirror The frequency response plot is shown in Figure 4 13 The first resonant mode or piston resonance mode is found to be at 386Hz with a Q of approximately 5.5 This mode is compared to the simulated mode of 441Hz. The difference can be attributed as in the discussion of the second resonant mode to process variation from the device on the outer quarter of the wafer and un dercut o n release. Additionally, simulation in the FEM software of the multimorph versus bimorph contributes to the disparity. In addition to the primary piston resonance mode, there are subharmonics present as well in the nonlinear region. The subharmonic s present are 1/2 and 1/3 at 191Hz and 129Hz respectively. The subharmonic of 191Hz is only slightly shifted from the expected 1/2 subharmonic of 193Hz. These subharmonics are not generally expected but are clearly present in the testing of multiple device s. It is important to mention that these characteristics are clearly noted while the device is being operated in the nonlinear region of the response curve of the device. As such, it is important to test the device again in the linear region. Testing the d evice in the linear region is accomplished with a strong dc offset and a small ac component. This is accomplished with 512mVdc and 18mVac for approximately one half lambda of actuation for each rise and, separately, fall of the
89 triangle waveform of the ac component of the driving signal. The results of this modified driving signal results in a piston resonance mode that is determined to reside at a peak that encompasses the frequencies from 345Hz through 349Hz (Figure 4 14 ) The broader peak of the resonanc e is of note; further, the Q factor is now 12, which although still lower than the ladder actuator is approximately 2.2 times larger than the Q factor present in the nonlinear region. Additionally, the reduced Q factor over that of the upward ladder actua tor can be primarily attributed to the recessed nature of the mirror plate such that its full range of actuation is within the substrate sidewalls. Additionally, all subharmonics are absent from the chart. From the mesh actuator, it is noted that the subha rmonics or strong modulated noise are present in the nonlinear region, whereas, the primary piston mode harmonic is the only peak present in the linear region. Further, unlike the ladder actuator micromirror, there was no additional system modification req uired to test the device in the linear region as the system response was clean until the peak rise began for the resonant mode for piston motion. 4.5 Fabrication Caveats and Considerations There are several considerations for fabrication that can improve or ne gatively affect the character of the devices. First, the primary concern for the devices is undercut. Depending on the configuration of the device, undercut can be so severe that even some bond pads or electrical traces can be compromised for functionality This can be seen in a more extreme case in Figure 4 15 were the device is viewed from the backside In this case there are two items of note. First, above the handling layer is the device layer which is seen to be severely undercut. Further, this can, if there is strong optimization of high fill factor; and illustrate the compromise of electrical trace integrity.
90 Further, there is weakening of the actuator connections to the substrate as in Figure 4 16 which references the devices fabricated for EOCT app lications as in  Ultimately, this negative effect can be countered by either a more conservative design of the sidewalls in terms of gr eater design tolerances smaller final release batches, and /or a manner of reducing exposed metal in the DRIE for etch steps to promote greater etch uniformity The best compromise is to create a more conservative sidewall and reduce device counts in relea se batches. Also illustrated in Figure 4 15 is the thinning of the expanded mirror aperture for the backside mirror surface. This is again a consequence of overetching in the final release steps. This SEM contains a micromirror with a device layer of 40m. This can most effectively be countered by the use of thicker device layers, the value of which should optimally range between 60m and 80m in order to provide ample sacrificial thickness for release without etching through the mirror plate and reducing t he backside mirror aperture to that of the frontside mirror aperture. The only practical downside to the thicker mirror plate is lowering of the resonant frequencies. The second concern is in the form of the structural integrity of the layers that constitu te the multimorph. Two concerns can be noted in Figure 4 17 First, the width of the platinum is less than other layers; this contributes to the phenomenon of voiding, as demonstrated in the SEM, which is potentially an issue for long term reliability of t he device. It is possible that an annealing step could combat this, but this may be rendered less practical as a consequence of the lower melting point of aluminum at 660C. Second, the peeling of the 20nm chromium adhesion layer can be due to contaminatio n in deposition, or more likely, etching in the long term final release steps. These issues
91 do not stop the device from functioning, but are considerations for long term reliability and optimization of fabrication processes. 4.6 Summary This chapter addressed mesh actuator design concept s and parameter selection. The device was designed analytically and its improvements in reliability in terms of robustness and rigidity were based off of improvements to and combinations of prior ISC designs. The device was furt her simulated both for displacement and resonant modes. The device fabrication procedure was discussed and the device results after release were detailed. Further, the device was characterized for piston motion under single axis and dual axis actuation con ditions Optical scanning capabilities were determined as well, inclusive of the angular scanning resonant mode The device was also analyzed in a novel interferometric system for piston resonance in the nonlinear and linear regions of device operation. Fi nally, caveats and considerations in fabrication for the most prominent aspects were considered as they interact with design considerations and constraints
92 Figure 4 1. Mesh actuator resistance configuration. Figure 4 2. Vertical displacement of se gment L 1 for varying aluminum thickness.
93 Figure 4 3. Vertical displacement of the multimorph mesh actuator from temperature inputs. Figure 4 4. Mesh actuator simulated in FEM software. Robust hinge Redundant ISC Mirror plate Substrate SiO 2 Al
94 Figure 4 5. Full mirror simulation for mesh actuator micromirror. Figure 4 6. First resonant piston mode Figure 4 7. Second resonant rotational mode pair Mirror Plate 261m SiO 2 Al
95 Figure 4 8. Process flow for downward actuated mesh actuated micromirror A) Oxide deposition and patterning B) Pt deposition and liftoff C) Oxide deposition and contact opening D) Al deposition and liftoff E) Oxide deposition and patt erning F) Silicon etch through device layer G) Carrier wafer frontside attachment H) Backside bulk silicon etch I) Backside BOX etch J) Carrier wafer removal K) Backside metal deposition L) Multistep silicon etch for final release A B C D E G H I J K SiO 2 Al Pt Si PR L F
96 Figure 4 9. SEMs of mesh downward actuator. A) Fu ll mirror. B) Full actuator C) Close up of mes h and dual ISCs Mirror P late A Bondpad Mirror P late Mesh H inge B
97 Figure 4 9. Continued Figure 4 10. Single axis displacement versus voltage for mesh actuator micromirror. Aluminum Mesh H inge Oxide C
98 Figure 4 11. Displacement for all actuators and current draw for driving voltage. Figure 4 12. Optical A ngle versus voltage for single actuator.
99 Figure 4 13. Piston resonance for mesh actuator micromirror in nonlinear region. Figure 4 14. Piston resonance of mesh actuator micromirror in linear region.
100 Figure 4 15. Device layer undercut and mirror p late etch through from backside. Figure 4 16. Undercut at actuator connection to substrate.
101 Figure 4 17. Fabrication caveats in multimorph construction Table 4 1 Section l engths of ISC a ctuator s ections for mesh actuator micromirror Downward ISC ( m ) L 1 = 252 L 2 =20 and L 3 =1 38
102 CHAPTER 5 FOURIER TRANSFORM SPECTROSCOPY FTS is implemente d most simply and compactly with a Michelson interferometer In the device, a beam of radiation from a source is divided into two paths by a beam splitter where one path is reflected after the same consistent optical path length while the second path is va ried in displacement for the generation of the OPD. These two beams recombine and the variation of intensity of the beam emerging from the interferometer is measured by the detector as a function of path differe nce. This system is illustrated in Figure 5 1 (a). In Figure 5 1 (b) we see the optical feedback reference portion of the system. This is implemented to account for the majority of nonlinearities inherent in even well designed commercial system s 5.1 Primary System Advantages It is informative to discuss the advantages of an amplitude division system such as is found in Fig ure 5 1 The two primary advantages are known as the multiplex or advantage encompasses the ability of the FTS to measure all resolution elements at all times. With spectra measured in the same time at the same resolution, optical throughput and efficient signal to noise ratio ( SNR ) will exceed a grating spectrometer by where M is given as the number of res olut ion elements in the spectrum. If is the resolution and is the maximum retardation of the interferome ter the relation is given in Equation 4 1. From this definitio n, is the maximum wavenumber, is th e minimum wavenumber in Equation 5 2  ( 5 1 )
103 ( 5 2 ) The throughput advantage states that more radiation can be passed between the source and the detector for each resolution element. The maximum optical throughpu t of a Michelson interferometer based FTS system is given by I and effective area of the interferometer mirrors given by A m in Eq uation 5 3  ( 5 3 ) For a grating spectrometer, with throughput G slit height h effective area of grating A g focal length of the collimating mirrors f and grating constant a in Equation 5 4  ( 5 4 ) Comparing Equation 5 3 and Equation 5 4, the advantage of the Michelson based system without change to the grating or beamsplitter increases as the square of the wavenumber for the ratio I / G 5.2 Primary Sources of Error Taking the correction of nonlinearities into account, these are the primary sources of error in the system and primarily stem from the movable mirror as follows: beam divergence, mirror misalignment and nonlinear velocity. Beam divergence is determined by the maximum solid angle in steradians that can be tolerated beyond which self apodization occurs. T his is a result of misalignment in the system and is not dependent on tilt in the mirror under actuation. As such, it is the only major source of error that does not hang exclusively on the movable mirror. Misalignment of the device or rather, the frame of the mirror and not the mirror plate; an improperly aligned source;
104 or misalignment of a fixed mirror are examples of error stemming from this situation. Additionally, misalignment of the sources also introduces this type of error and is represented in the hypothetical illustration in Figure 5 2(a). Additionally, a close up of the movable mirror and the misalignment angle present under the movable mirror is shown in Figure 5 2(b). max in Equation 5 5 the equation incidence  ( 5 5 ) If beam divergence does occur, a mono chromatic source will indicate this by showing attenuation. To provide perspective, if a maximum wavenumber of 15800cm 1 is used and an OPD of 55.6cm 1 is available, a maximum solid angle of 0.0221 steradians is the maximum allowable solid angle before att enuation becomes manifest in the interferogram, from a purely ideal perspective. Possibly the most important of the main three sources of error for MEMS devices is mirror misalignment. This source of error is entirely dependent on the MEMS mirror and is un avoidable on commercial macro systems and is certainly unavoidable in this context (Figure 5 3) Determining the tilt angle with a beam diameter D in centimeters, the maximum allowable tilt before loss of frin ge modulation occurs is Equation 5 6  ( 5 6 ) To provide perspective with a maximum wavenumber of 15800cm 1 and a beam diameter of 1.02mm (aperture limited), a tilt of no more than 0.0018 is permissible before effects of misalignment begin to take effect. Generally, a rule of thumb can be
105 used that loss of fringe modulation does not occur until the optical path difference between the center and radial rays is x is approximately 0.1 misalignment or more The third and final main source of error is nonlinear mirror velocity. If a system is run in a step scan fashion then velocity is not a concern. However, if a rapid scan system can be implemented, the increase in speed is worthy of extra effort. A rapid scan system can generally be considered as faster than 0.1cms 1 If this approach is taken then a proper sampling rate t samp must be considered that satisfies the Nyquist Shannon sampling theorem Equation 5 7. ( 5 7 ) Regardless of the mirror actuation system, there is a slowdown and speedup of the mirror wherein there is not a uniform velocity. However, that is not the case with a micromirror as constant velocity is never reached. As such, it is beneficial to be able to ignore the effect of nonlinear velocity. This may be accomplished via the imple mentation of a reference laser as in Figure 5 1(b). By this method, the ideal approach involves triggering of sampling through optical feedback over the reference laser interference pattern, tr iggered at the maximum and minimum intensities or zero crossing s This way, if a HeNe laser was used with 633nm wavelength and the broadband source in infrared had a center wavelength at 1550nm, sufficient data points are available from only sampling at the maximum intensity of the HeNe interference pattern to reconst ruct the broadband signal. Additionally, with optical feedback, mirror tilt can be corrected. If a solutions will solve the three main problems inherent in an FTS system.
106 5.3 Syste m Design The concept of the system is to have a reference signal to allow accurate sampling. Such a system is shown in Figure 5 1. There is an alternate approach to this and it is shown in Figure 5 4. In this system, a dichroic filter is used to isolate th e HeNe reference laser to allow simultaneous sampling of the unknown and the reference signal. This provides sufficient information to reconstruct a spectrum even under strongly non ideal situations. When dealing with unknown signals that do not include sp ectral information in the wavelength of the reference laser, such as another distinct source in the visible region it is possible to add a dichroic filter on the detector, D2, to remove the signal so that only a constant phase shift differentiates the acq uired reference signal from the unknown signal. First, the system must be properly aligned. This requires that the system achieves extremely low to no misalignment and also is aligned within the coherence lengths of the system sources Alignment can be ac hieved by viewing the combined signals in the output arm of the interferometer. With spots from the separate beams combined and overlapping, there are effectively two patterns that can be observed. The first pattern is given in Figure 5 5(a). This pattern indicates misalignment in the system and requires realignment of the system. The process is situational ly dependent as to the correct procedure, but upon successful completion, will yield a result like that in Figure 5 5(b). In this manner, with the movabl e mirror at rest, the system will be aligned and within coherence length This is straightforward with laser references such as the HeNe laser as the coherence length is up to 410 4 cm  Although not utilized in this setup, when using short coherence sources, it is desirable to include a white light source that allows true zero path difference ( ZPD ) to be determined at peak interfer en ce
107 intensity. Any inherent error for alignment may be mitigated with phase correction which takes into account the constant error of misalignment and is included during post processing or data processing The error contribution from system alignment is not sufficient to cause the system to fall out of ali gnment over the course of use as long as the system remains unperturbed from external forces. This system is not ideally isolated, but can be considered to remain properly positioned for the duration of a single session when using the system. Next, one must consider tilt of the movable mirror or micromirror when under actuation. If the mirror falls out of alignment, the recorded interference or interferogram will show attenuation and a quick falloff and y ield unusable information or noise recorded in the interferogram. To counter this, with electrothermal actuators, as those used in the system, it is possible to tune the waveforms to counteract misalignment. The process t o accomplish this is to first align the system as above. After this, actuate the device for the desired displacement in terms of power scaling by the resting resistances While continuing to watch the interference pattern in the far fie ld with the detector removed, the fixed mirror spot wil l remain fixed while the movable mirror will shift. This can be seen in three selected instances during micromirror driving. The points show maximal misalignment in the driven range in Figure 5 6(a), misalignment in Figure 5 6(b) and alignment at Figure 5 6(c). Generally, voltage can be used to determine the response of the mirror in terms of displacement. If, however, there is large variation in resistance, it is better to think in terms of power as in Equation 5 8. ( 5 8 )
108 In this manner the square of voltage can be related to the resistance for a common power applie d to the actuators The process in tuning the driving signal is to first measure the resting resistances. Then scale voltage in relation to equivalent power driving each resistor, though voltage is the generated driving signal. Thereafter, observe movement in the far field and record the direction of drift of the micromirror spot. This corresponds to the actuator characteristics in terms of Joule heating. Determine changes in resistance for power scaling, thereby tuning the drive to reduce tilt. An example of this system is shown in a hypothetical tuned result in Figure 5 7. In this manner, the ladder actuated micromirror with the ability to be driven with six discrete waveforms, can be actuated in a power tuned form. Further the mesh actuated micromirror ca n be driven in the same manner with four discrete waveforms. This system cannot overcome all issues however. If there is a significant difference in resistance, such as by 40%, then there will be a large reduction in achievable pure piston displacement. Th us, this approach works in all situations but cannot overcome all device limitations, such as large actuator mismatches leading to reduced pure piston motion. For the waveforms given, the horizontal axis is in terms of the number of discrete voltage levels or data points. As such, there is no strict relationship to the temporal interval of the period. This will be addressed when discussing the creation of the waveform generation equipment. The final component goes beyond initial system alignment and calibr ation of the micromirror. It addresses non uniform system velocity. In this manner, the first consideration is the open loop repeatability of the micromirror under consistent driving conditions. It is found that there is strong agreement between cycles or periods in
109 repetition. However, this only holds over a few thousand iterations before variations begin to be noticeable and recalibration becomes necessary. Although this is a large amount for some requirements, no two iterations are consistent on a nanome ter scale, which is the relevant scale for this system. As such, it is not sufficient to record a reference interferogram and then record the unknown interferogram in separate cycles. As such, it is required to collect both interferograms at the same time. This necessitates the system as in Figure 5 4, which when combined with proper data processing, permits proper calibration of the system for an acquisition of a spectrum. 5.4 Optical Sy stem Construction The system that was ultimately used went through several iterations. Two specific forms capture the general progression of the system. First, there is the form of the system w h ere a single detector is used. It is presented in Figure 5 8. In the system, there is the basic Michelson interferometer setup with a fi xed mirror (FM), a movable mirror (MM), a beamsplitter (BS), and a detector (D1). Further, there is a second beamsplitter used to couple in the two light sources, in this case a HeNe laser with at 633nm and a green laser diode with 532nm for center wavelen gths. As a note about the movable mirror, the mirror is the ladder actuator micromirror in this image The device is bonded to a dual in line package (DIP) adaptor by silver epoxy and then wire bonded to connect the device pads to the pins of the DIP adapt or. This adaptor is then placed in the breadboard section mounted as in Figure 5 8 where signal wires are added. The primary shortcoming of this system is the ability to acquire only one interferogram at a time. In theory, the reference laser could be remo ved from the interferogram by subtracting out the known quantity essentially as background signal However, this is not practicable as the micromirror provides nonlinear velocity in a manner that is not
110 repeatable. Consequently, it is necessary to not assu me any character of the interferogram. This makes the system with a single detector not a practical choice. To alleviate the issues in the previous system iteration, an alternate approach was proposed and implemented The first impulse was to follow the de sign as in Figure 5 1. This, however, requires access to the backside of the mirror plate and thus requires more specialized adaptors for the micromirror. While not an issue on its own, the increase in system bulk is sufficiently negative as to motivate an alternate approach as that in Figure 5 4. The implementation is given in Figure 5 9. The first note is the addition of a third beamsplitter. The second detector (D2) detects all signals unfiltered and provides the unknown interference signal. The first d etector (D1) has a dichroic filter that passes wavelengths centered on red laser light. This way, an isolated but temporally concomitant signal can be recorded to provide full calibration. Additionally, if the unknown signal is not to include the reference HeNe, then another dichroic filter can be added to remove that signal from the incident beam. The only caveat to this system is the further division of incident intensity on the detectors. This can be an issue for systems with low intensity sources, but i s not strictly an issue for high power sources. Further, the shortcoming can be countered by using a higher sensitivity detector. An alternative view of the setup is seen in Figure 5 10 to allow a clearer view of the second detector (D2), mounted in this m anner to reduce system size as much as possible. The setup of the system is accomplished in the same manner that signal optimization is achieved, by viewing beam overlap in the far field with a broadened spot size. In this manner, when true interference fr inges are observed,
111 this is the point of alignment of the system. Generally, a detector is removed for alignment and then replaced after alignment is completed. 5.5 Electrical Drive and Acquisition System Design and Interfacing The penultimate segment of the s ystem design is the construction of the signal generator and the data acquisition segment, or the electrical segment of the system. To begin, the general structure of this portion of the larger system is as in Figure 5 11. In this system, there is the USB 1608FS from Measurement Computing which is a prebuilt data acquisition system (DAQ) which permits acquisition of analog signals, which in this case constitutes: both detector signals and a driving signal line. The DAQ comes with a robust library that perm its continuous acquisition. The general flow of the code used to control the USB based system is as follows: 1. Initialize DAQ for number of analog channels, sample rate, and data points per cycle. 2. Configure files to hold data 3. Library call to continuous acqui sition function for real time acquisition to binary files 4. Convert binary files to spreadsheets with comma delimiters Following this procedure, the data may be collected when needed. For the signal generation, Figure 5 12 shows the relationships as in Figu re 5 11 but with more detail for signal generation. The dotted outline of the UM232R utilizes a USB to USART bidirectional bridge from FTDI using the FT232R integrated circuit ( IC ) This system comes with a pre established library and allows the microcontr oller to interface with the PC. However, this is not strictly necessary and can be omitted if a proper lookup table is already loaded into the microcontroller. The microcontroller is an MSP430f169 and interfaces with the sample and hold LF398N, which is a monolithic IC. Next, the signal is
112 passed to an op erational amp lifier or opamp configured as a unity gain buffer amplifier to provide sufficient power to the micromirror, which the sample and hold IC is incapable of providing. A clearer picture of the disc rete components is provided in Figure 5 13. The microcontroller which is programmed entirely in assembly, functions in the following manner: 1. Initialize general system including initializing external 8MHz crystal 2. Initialize internal microcontroller digital to analog converter (DAC), timer, and USART 3. Enable interrupt service routines ( ISRs ) 4. T imer ISR outputs individual waveform data, one data point per channel in rapid succession 5. Still in ISR, CH CS in Figure 5 13 set high to allow sample and hold IC to hold proper value for proper channel. 6. (Optional) with USART, enter ISR to record byte transfers to known array size allowing call to FLASH write subroutine to permanently store updated information. Following this procedure, the signal generator is fully funct ional. An additional note, the sample and hold IC uses a 0.01F external capacitor, which is acceptable for a sample rate below 3kHz. Otherwise, the connects remaining are for supply and ground lines. The final note refers to the waveforms previously gener ated as demonstrated in Figure 5 7. Now, the sample rate that determines the trigger for the ISR is defined by a value set in the code of the microcontroller. To determine the frequency of the periodic waveform at output from the buffer amplifier, the foll owing can be used (Equation 5 9): ( 5 9 ) The value 8MHz is def ined by the external crystal, off microcontroller, in the system, samples are the number of data points in Figure 5 7 or 550 in that case, channels is the
113 number of channels outputting or six for a ladder actuator micromirror, and hexValue defines an arbitrary value for setting frequency. Thus, the given example with hexValue of 8191 in decimal provides a frequency of 0.296Hz. 5.6 Data Processing Configuration Signal collection, when triggered by a reference signal for the microcontroller will collect an interfero gram record that can be corrected through established means. In this way, if S( ) represents the interferogram record and B( ) represents the spectrum then in Equation 5 10 t he general equation for generating the spectrum from the interferogram record is given where the reverse is true in Equation 5 11 ( 5 10 ) ( 5 11 ) There is more to the conversion than this to adjust fo r inherent errors in any system with several well established pattern s th at have been sequence d in the past as in  and  However, the use of the system with a micromirror is less standard with the significant nonlinearity of the movable micro mirror. As a consequence, the approach requires strong explanation. To facilitate this, ideal d ata is constructed and used to demonstrate the system. Further, the data relatively resembles the non ideal results presented later to lend further credence to such results. First, obtain the reference and unknown interferograms. This is accomplished by dr iving the micromirror by a tuned driving signal in the form of an arbitrary periodic waveform as in Figure 5 7. The theoretical simulation involves a traversal of 25.58 m OPD, which is 12.79 m in terms of physical distance. This result for the HeNe referen ce signal is shown in Figure 5 14(a). Additionally, the combined signal is composed of the
114 HeNe and the green laser with the red laser having a signal four times as strong as defined by the peak to peak amplitude. This is represented in Figure 5 14(b). As a note white Gaussian noise is added with a SNR of 5dB to the generated signals Second, the interferograms are filtered in the frequency domain for any known noise modulated on the actual signal. This is accomplished by a transform into the frequency dom ain and performing a boxcar function multiplication with the transformed signal. The selection may be tuned by experimentation to find an acceptable tradeoff to remove noise before effecting true signal. After, the signal is properly transformed back into the time domain. The result of this is seen by Figure 5 15(a) for the reference interferogram and Figure 5 15(b) for the unknown signal. Third, the peaks must be located and a maximum selected for the start point of the data set. The signals are also cente red in the vertical axis around the zero level to remove excess dc in the spectrum. With the reference signal known and data points re corded at even temporal spacing, t he displacement can be determined in the travel between valleys and peaks and then betwe en peaks and valleys, iterating forward until the last data point. With both interferograms recorded concomitantly, it is possible to apply exactly the values obtained with the reference interferogram to the unknown interferogram. This is not represented i n the constructed signal but will be discussed further in the real datasets. Fourth, the data is apodized with a symmetric Gaussian window The consequence of this is a reduction in side lobe amplitude. However, there is a reduction in theoretical resoluti on for a given maximum OPD. With a rectangular window applied, the same as an interval less than infinity  the approximate best wavele ngth resolution
115  is in Equation 5 12. The other method of determination of best resolution achievable can be determined from generati ng comparable ideal simulated data to compare to the experimental results. ( 5 12 ) Fifth the result is padded to the data with zeros to form 2 19 values for a Fast Fourier Transform (FFT) permitting large numbers of bins for refined viewing of the data characteristics so that the data is not lost in binning for the sma ller data set sizes that can occur. Sixth, after the FFT, the Mertz phase correction method is applied  This method involves obtainin g the phase angle as in Equation 5 13 and then applying to the real and imaginary components of the transformed interferogram ( 5 13 ) ( 5 14 ) Seventh the spectrum is obtained and demonstrated in the final graphs of the simulated data set with the reference spectrum in Figure 5 16(a) and the unknown spectrum in Figure 5 16(b). For the reference spectrum, the peak is at 15800cm 1 wh ile the peaks of the unknown spectrum are 15800cm 1 and 18700cm 1 for the red and green lasers, respectively, which corresponds to the generated data sets. To determine the effect of apodization functions, it is important to determine the effects on spectr al resolution. Using the Gaussian windowing, the effect on spectral resolution can be clearly defined as the full width at half height (FWHH) of a lineshape given by Equation 5 15 where is the retardation or maximum OPD 
116 ( 5 15 ) Without factoring in the effect of the apodization function, the FWHH is given as 1 cm 1 and the lineshape reaches the wavenumber axis at ( ) 1 cm 1 Consequently, the difference at lower spectral resolutions is not significant and can be ignored if needed in initial analysis. Having completed a discussion of the data processing method ology and providing a worked example, it is now possible to clearly move through experimentally determined data sets. Before beginning the discussion of experimental data processing, the photodiode in the system needs to be addressed. This also informs the choice for the simulated data and the ratio of the re d to green sources of four The ratio stems from the responsivity of the photodetector, which is a Thorlabs FDS100 photodiode. The output voltage for the photodiode can be expressed as in E quation 5 16  ( 5 16 ) For the equation, P is the incident light power, is the responsivity of the photodiode, and R L is the load resistor. With the load resistance consistent for different sources, the incident light power and responsivity are variable for the sources. For the HeNe laser source used, the power is 10mW and the responsivity is approximately 0.4A/W. Further, for the green laser diode, the power is 3mW and the responsivity is approximately 0.3A/W. With these values, the ratio of red to green sources can be established to be approximately 4.44. This value is the motivation for the ratio of four for red to green in the generated data. The other main effect on the system for source ratios in an interferogram and consequently spectrum is misalignment in system, specifically from
117 the source coupling into the system. These two factors will be considered when noting the source ratios in the following spectrums 5.7 Experimental Data Processing with Ladder Actuator Micromirror With the results above, it is now possible to apply these techniques to data obtained through experimental means in the established system I n the following, the FTS system described above is combined with a ladder actuator micromirror and driven by a calibrated waveform using the waveform generation techniques described. The first data set s are shown as the raw interferograms as recorded from the silicon photodetector with the horizontal axis representing the equal temporal spacing. Additionally, the noise is unfiltered and dc offset is not corrected in Figure 5 17(a) and Figure 5 17(b) The envelope is unambiguously represented here as the in system micromirror moves through the full OPD. In this data, the mirror at rest is fully perpendicular to the incident light and tilts through the actuation. However, signal is still present clearly through the entire range of actuation and thus there is n o excess loss of signal. Without the tuned driving signal, the mirror would have fallen out of alignment after only several microns of displacement. The next step in processing the results is filtering in the frequency domain, removal of dc offset and calc ulating the equivalent displacement in terms of the equally space d temporal sampling. The displacement is also determined in these steps and is given in Figure 5 1 8 The displacement is given here as a function of voltage of one driving signal. It is impor tant to keep in mi nd that the displacement is OPD, where OPD is twice the physical displacement of the mirror. With these steps completed the next step is to remove any duplicates in the strongly oversampled data set. Next, the equally spaced displacement is generated as a
118 vector. At this point, a P iecewise Cubic Hermite Interpolating Polynomial ( pchip ) function is generated from the voltage recorded interferogram and the nonlinearly spaced displacement calculated from the evenly spaced temporal sampling. Then the evenly spaced displacement is used to interpolate the corresponding voltage for said even displacement from the converted data The key component of concomitant sampling of the reference with the unknown interferograms come s into play here where the displacement results determined in Figure 5 18 hold for both interferograms. Applying pchip to both interferograms gives the result as seen for the reference signal in Figure 5 19(a) and the unknown signal in Figure 5 19(b). N ext an N point symmetric Gaussian window is generated that corresponds to the data sets above. After apodizing the results from Figure 5 19, the data is padded for 2 19 total data points as discussed in the generated data proof of concept. Now, the FFT is completed and the Mertz ph ase correction is taken. After, the wavenumber axis is generated from the displacement axis With conjugate symmetric dat a for the real valued inputs not included in the chart t he results are shown for the reference signal in Figure 5 20(a) and for the unk nown signal Figure 5 20(b). The results of the system are important to consider in terms of center wavelength for the two sources, as well as the line shape of the individual signals. The results of these relevant metrics are presented in Table 5 1. The pri mary consideration for this dataset is the small OPD that defines the dataset. In the table, the first relevant data is the theoretical FWHH defined for the OPD and the apodization function. The experimental FWHH is determined for the two separate signals and the difference of the
119 two datapoints defining the FWHH are listed in terms of the variation from ideal and experimental. Finally, the center wavelength is given for both signals. For the reference signal or HeNe laser, there is good agreement with the theoretical FWHH. However, there is significant broadening of the lineshape for the green laser diode. This can be primarily attributed to the extremely short dataset and the great signifigance of any error for even a half lambda. With such errors there ca n be close error peaks in the closeness of sidelobes that are merged with the central, true peak. This error is primarily introduced in the conversion from the temporal domain to the spatial domain and the subsequent interpolation required to generate even ly spaced datapoint s for the FFT. The last main consideration is the ratio of the two sources and the loss in the system versus the ratio in the spectrum. The ratio from the experimental dataset is 5.6. Comparing this to the detector ratio of 4.44, the dis crepancy can be primarily attributed to green laser error when coupling the source into the system with the less efficient clamp for the laser housing. 5.8 Improved Experimental Data Processing with Ladder Actuator Micromirror From this initial data collection of smaller OPD, the driving signal of the ladder actuator micromirror is refined further and larger OPD is achieved This larger displacement provides better spectral resolution and further demonstrates the capabilities of the system. The raw interferogra m of the reference signal and the unknown signal is given in Figure 5 21. The interferograms demonstrate the use of the tuned signal drive very clearly. The envelope of the signal shows attenuation as the mirror tilts out of alignment and as the driving si gnal is tuned for the change in the response of the micromirror, the mirror begins to move back into alignment as the ac
120 component of the signal increases. The last section of the interferogram shows a reduced amplitude but a still valid signal. The proces s of filtering in the frequency domain and signal dc offset nulling leads to the conversion from the temporal to spatial domains and the resulting calculation of the displacement of the micromirror through the interferogram. This displacement is recorded i n terms of OPD in Figure 5 22. With the increased OPD, the resulting res olution will be improved This is demonstrated in the spectrum of the reference signal in Figure 5 23. The notable aspect of the spectrum is the presence of signal surrounding the HeNe laser peak. This d erives from one main source. That source is the background signal from overhead lighting in the laboratory testing environment that was present during the collection of this dataset. Additionally, a peak is present at 3.1552 10 4 cm 1 whi ch is a harmonic of the reference source peak wavenumber The unknown spectrum is found in Figure 5 24(a) with a closeup in Figure 5 24(b). The background is still present in this spectrum, having been collected concomitantly with the reference signal. Add itionally, the alignment of the green laser is shown to be e xceptionally good in this setup G enerally, the alignment of the green laser, determined by the coupling of the green and red lasers into a common path through a beamsplitter is limited in capturi ng all the green laser diode possible by the aperture of the micromirror. In this case, the aperture is more diffraction limiting as with both the red and green laser than in terms of the misalignment of the green laser whereby more signal is lost to the d ip package on which the micromirror is mounted. In this case, the ratio of the two peaks is approximately 5.2. Considering again the
121 detector ratio of 4.44 for the different signals and the minor misalignment introduced when coupling the two sources into t he system with the third beamsplitter, the result is close to the anticipated ratio. The results of the spectral data are summarized in pertinent points in Table 5 2. The FWHH of the experimental data results are similar this time, in contrast to the low s pectral resolution dataset previously described. However, the FWHH is larger than the expected result. This is primarily attributed to the interpolation, as before. The issue stems again from the need to interpolate the inconsistent spacing in the spatial domain as a result of temporal sampling. This allows broadening of the peaks under slightly shifted frequencies from interpolation that are not resolvable at these resolutions. The center wavelengths are in strong agreement with the previous results, varyi ng less than a half of a nanometer, denoting that the predominate signal is strongly oriented around the true signal although broadening does o ccur from the spatial sampling. 5.9 Experimental Data Processing with Mesh Actuator Micromirror The previous interfer ogram data sets were obtained with the ladder actuator micromirror. This mirror functions well in the quasi static range and is able to maintain a set displacement under such conditions Even though affected by environmental characteristics such as vibrati on and air currents in the form of noise in the interferogram the response characteristic of the micromirror is still clearly present under quasi static driving signal. The mesh actuator micromirror allows larger vertical displacement and the potential for rapid scanning usage. The methodology for tuning the driving signal for the device is to first tune the waveforms for the individual actuators in quasi static actuation. After, the frequency can be increased and data is then collected.
122 Since it becomes mu ch more difficult to visually interpret the interferogram at the faster velocity charac teristic of the micromirror, signal becomes more effectively interpreted in the spectrogram. The noise inherent in the micromirror actuating at such a faster speed is se en in the raw interferograms for the reference an d unknown signals in Figure 5 25 Velocity is noted to significantly vary over the range of actuation an d is demonstrated in Figure 5 25 (a). The signal is filtered in the frequency domain and the dc offset i s nulled. After this, the displacement is determined from the reference signal for conversion from the temporal to t he spatial domain in Figure 5 26 After interpolating the spatial data to an equal spacing distribution the spectrums can be obtained with apodization and phase correction. The results of this process yields Figure 5 27 with the reference and unknown signals. Using the mesh actuator successfully at higher frequencies opens the path to even higher frequencies and builds on the work with the la dder actuator that enabled the directly observable construction of a functional methodology for obtaining a spectrum, which can be obscured in the raw interferograms collected at higher frequencies. Additionally, t he noise seen in Figure 5 27 (b) of the unk nown spectrogram is a result of high er cutoff for frequency filtering due to faster mirror scanning Th e noise in the signal is from environmental effects on the mirror plate in terms of tilt and position at the nanometer scale, which results in random bac kground noise to appear in the spectrum The results of the spectrums are summarized in Table 5 3. As with the other spectral data, there are broader experimental FWHH versus the theoretical best case results. This remains primarily attributable to the err or introduced in interpolation that allows the broadening of the peaks by, as is the case in this dataset, by 2.1nm and
123 2.4nm for the red and green peaks, respectively. Triggering the data collection for evenly spatially separated points is the clear solut ion to this error source and is feasible and practicable when drawing on the FTS system developed in this work. It is also clear that the developed mesh actuator micromirror is capable of producing effective spectrums as the movable mirror in FTS systems. This is a strong validation of the reliability motivated design choices that have helped robustness and stability to achieve effective use in the traditional Michelson interferometer FTS system setup. The ratio of the red to green source recorded in the in terferogram is 8.5. Comparing this to the photodetector ratio of 4.44 and the previous two experimental results with ratios in the range of five, this result is closer to a half of the anticipated green laser diode source in the spectrum. As noted in the s ystem setup pictures, the HeNe laser is fixed in a sound and effectively constant orientation. For the green laser diode, the mount for the laser diode housing is prone to movement when working on the system. The source can be realigned but slight system m isalignment can lead to large loss of signal, as discussed in the theoretical background. This is the primary source of error which increased the ratio in favor of the red laser signal over that of the green laser diode source. With these results, a functi onal FTS system has been devised that permits the clear determination of unknown inputs. The system is functionally prepared to add a white light source to assist in determination of true ZPD ; from there, infrared sources may be incorporated for work with practical sample determination. 5.10 Novel Piston Resonance Testing There is another practicable application of the FTS that has been utilized. This application is the testing of piston resonance for micromirrors As discussed in the preceding chapters, most no tably in sections 3.9.3, 3.9.4, and 4.4.3, this is an approach
124 to determining piston resonance. The method is to place the micromirror in the system and drive it over one to two half lambdas. This very small actuation range will ideally remain constant exc ept at resonance peaks In practice, noise is also a notable characteristic of the micromirror most notable in the lower frequency region. The default actuation is shown in Figure 5 28 Here approximately 1.5 half lambdas constitute a half period of the dr iving signal. In this plot, the signals were affected by electrical noise in the system setup such that a post processing filter was used to reduce noise and aid in readability of the plots but not modify the true signal. This was accomplished with a smoot hing function in the form of a generalized moving average Savitzky Golay filter. It is notable that the detector signal is not ideal and commonly the rising slope and falling slope of the drive signal do not exhibit the same characteristic response from mi cromirror are recorded on the photodiode The consequence of this is that some level of interpretation is required for the number of half lambdas present for a given frequency. The methodology employed is that a full period of the approximate co sine wave c an be counted as a half lambda. If there is modulation on another wave, this is not considered to be an independent peak and is considered noise. It is important to note that t his may be true in some instances and incorrect in others such that interpretat ion, as noted, comes into effect As in section 3.9.4, the response from a commercial vibrometer may be used to aid interpretation. As part of this chart reading, t he re is a greater resemblance to co sine waves that are not modulated noise in the nonlinear region at frequencies that correspond with 1/2 and 1/3 frequencies of the main resonant mode This has led to the interpretation of subharmonics in the nonlinear region. Additionally, a baseline of half lambdas must be chosen, which is most
125 effectively sel ected by the most common half lambda count outside resonance. When a harmonic or subharmonic is encountered in the nonlinear region of the mirro r response curve there is a significant increase in displacement and subsequently an increase in interference p eaks. This is seen in Figure 5 30 Here approximately 13.5 half lambdas a present at this 1/3 subharmonic at 276Hz in the nonlinear region of the micromirror response curve as in Figure 5 2 2 from 0V to around 0.35 V The next chart provides a vi sual represe ntation in system for determining piston resonance from the nonlinear region with the primary piston resonance mode at 828Hz is Figure 5 29 (a) At this frequency there are 48 half lambdas. In the linear region, the resonance is found at 782Hz in Figure 5 29 (b) and the signal is much cleaner and easier to determine that there are 9.5 half lambdas. This is a novel application of the FTS system and allows a difficult problem of determining true piston resonance with an elegant solution. It is primarily useful for determining the presence of piston modes in the system because it does not permit knowledge of the type of response for other resonant modes but if FEM simulation indicates the approximate location of the non piston resonant mode and its type, the lo ss of fringing effects in the system can indicate the pre sence of such a mode which is most effective when used with larger non resonant travel of the mirror For example, the presence of a rotational mode will lose interference fringing effects and will indicate the effect of a no n pison mode resonance. This is likely less efficient for the determination of the resonance of a tilt mode as driving at large voltages will induce a significant tilt and alternate approaches are more efficient such as the meth ods used to determine the mesh and ladder actuator micromirror rotational modes
126 The work of testing piston resonance in the nonlinear range risks the presence of modes of the micromirror that are not naturally occurring in the linear range, which is the p rimary range of operation. These extra modes are the subharmonic resonant modes. As such, the piston resonance tests were conducted in the linear region after being conducted in the nonlinear region. It was discovered that the ladder actuator micromirror s howed noteable noise at lower frequencies and a miniaml peak at the frequency that corresponded to the 1/3 subharmonic, which may be seen as the boundary of the low frequency noise range Additionally, the mesh actuaor micromirror no longer exhibited any s ubharmonics, only the piston resonance mode An example of the mesh actuator micromirror actuation in the linear region is shown at 200Hz in Figure 5 31 (a) while that of the ladder actuator response is given in Fi gure 5 31 (b) for the same 200Hz 5.11 Summary An FTS system has been developed and implemented. The MEMS micromirror s with ladder actuators and mesh actuators h ave been incorporated into the system with a robust optical portion that permits simultaneous acquisition of a reference and unknown spectrum. A complex arbitrary waveform generator has been created to provide custom driving signal s to tune the actuation of the micromirror for strongly piston oriented motion. Additionally, a system was developed to accomplish data processing for the system to coun ter practical error constraints. Further, a sample signal was generated and the algorithms for data processing were applied as a proof of concept. Next, the system was verified with successful experimental data processing for separate data sets for the lad der actuator micromirror The system was also verified with successful spectrum generation with the mesh actuator micromirror. Finally, a novel application of
127 the FTS system is introduced to use the system to determine piston resonance modes of micromirror s and testing is addressed in both the nonlinear and linear regions
128 Figure 5 1. Full FTS system layout A) Infrared subsystem. B) R eference laser system for optical feedbac k. A B
129 Figure 5 2. Misalignment in system. A ) Source misalignment. B) Closeup of misalignment effects on movable mirror. A B MM Movable Mirror FM Fixed Mirror BS Beamsplitter S1 Source D1,D2 Detector DF Dichroic Filter
130 Figure 5 3. Mirror tilt in system. A) Full system with mirror tilt. B) Alternate mirror tilt in single dimension. A B MM Movable Mirror FM Fixed Mirror BS Beamsplitter S1,S2 Sources D1,D2 Detector DF Dichroic Filter
131 Figure 5 4. Alternate system design retaining unknown signal and isolated reference signal. Figure 5 5. Interference patterns with combined beams. A) Misaligned beams. B) Aligned beams. A B MM Movable Mirror FM Fixed Mirror BS Beamsplitter S1,S2 Sources D1,D2 Detector DF Dichroic Filter
132 Figu re 5 6. Far field beam overlap. A) Full misalignment. B) Intermediate misalignment. C) Alignment. Figure 5 7. Power scaled driving waveforms. A B C
133 Figure 5 8. First general iteration of FTS system. MM Movable Mirror FM Fixed Mirror BS Beamsplitter S1,S2 Sources D1,D2 Detector DF Dichroic Filter BS BS S 1 S 2 FM MM D1
134 Figure 5 9. Final iter ation of FTS system. MM Movable Mirror FM Fixed Mirror BS Beamsplitter S1,S2 Sources D1,D2 Detector DF Dichroic Filter D1 DF S1 S2 FM MM D2 BS BS BS
135 Figure 5 10. Alternate view of final FTS configuration BS BS BS S 1 S 2 FM MM D2 DF BS D1 MM Movable Mirror FM Fixed Mirror BS Beamsplitter S1,S2 Sources D1,D2 Detector DF Dichroic Filter
136 Figure 5 11. General structure of electrical portion of FTS system. Figure 5 12. Signal generation in detail Figure 5 13. Alternate view of signal generation
137 Figure 5 14. Generated interferograms with white Gaussian noise. A) HeNe reference. B) Combined signals. A B
138 Figure 5 15. Interferograms with noise filtered in the frequency domain. A) Reference signal. B) Unknown signal. B A
139 Figure 5 16. The spectrums of the generated data. A) Reference spectrum. B) Unknown spectrum. A B
140 Figure 5 17. Raw, unfiltered interferograms from FTS system. A) Reference interferogram. B) Unknown interferogram. B A
141 Figure 5 18. Displacement calculated for equal tem poral spacing.
142 Figure 5 19. Filtered, dc offset nulled, and displacement calculated. A) Reference signal. B) Unknown signal. B A
143 Figure 5 20. Spectrums for low spectral resolution datasets. A) Reference spectrum. B) Unknown spectrum. B A
144 Figure 5 21. Raw interferograms for increased ladder actuator OPD A) Reference interferogram. B) Unknown signal interferogram. B A
145 Figure 5 22. Optical path difference versus voltage for increased ladder actuator OPD Figure 5 23. Reference spectrum with background for increased ladder actuator OPD
146 Figure 5 2 4 Unknown spectrum for increased ladder actuator OPD A) Full Spectrum. B) Closeup of red and green peaks. A B
147 Figure 5 25 Raw interferogram for mesh actuator A) Reference signal. B) Unknown signal. A B
148 Figure 5 26 Optical path difference for mesh actuator micromirror.
149 Figure 5 27 Spectrums with mesh actuator micromirror. A) Reference spectrum. B) Unknown spectrum. B A
150 Figure 5 28 Actuation of ladder actuator micromirr or with no resonance.
151 Figure 5 29 Piston resonance mode for ladder actuator. A) Micromirror in nonlinear region. B) Micromirror in linear region. B A
152 Figure 5 30 Subharmonic piston resonance mode for ladder actuator micromirror for 1/3 subharmo nic in nonlinear micromirror response region.
153 Figure 5 31 Standard response for actuator micromirror in linear region. A) Mesh actuator response at 200Hz. B) Ladder actuator response at 200Hz A B
154 Table 5 1 Low spectral resolution dataset characte ristics. Theoretical FWHH (cm 1 ) Experimental FWHH (cm 1 ) Ideal Difference (nm) Experimental Difference (nm) Center red 472.3 504 18.4 20.8 632.4 green 472.3 966 13.8 27.4 532.7 Table 5 2 Higher spectral resolution dataset characteristics for ladder actuator micromirror. Theoretical FWHH (cm 1 ) Experimental FWHH (cm 1 ) Ideal Difference (nm) Experimental Difference (nm) Center red 174.4 392 7.1 15.7 632.8 green 174.4 384 5 10.9 532.9 Table 5 3 Spectral resolution dataset character istics for mesh actuator micromirror. Theoretical FWHH (cm 1 ) Experimental FWHH (cm 1 ) Ideal Difference (nm) Experimental Difference (nm) Center red 206 334 11.3 13.4 632.6 green 206 399 5.9 8.3 532.3
155 CHAPTER 6 WAVEGUIDES Guided waves are the other approach that may be taken to accomplish the go al of generating sufficient OPD for u se in an FTS system This method involves a path length that is influenced not only by the physical distance for light to traverse but also the refractive index of the medium of propagation. In this manner, light is able to achieve greater path difference in a gui ded medium than the unguided atmosphere for equivalent physical distances Further, there is strict control of the path of light through the medium, enabling a strongly compact system. The work here demonstrates a fabricated waveguide capable of la rge range vertical displacement that can be adapted to refractive index changes and also finds use in fiber scanner applications. 6.1 Waveguide Background As the importance of refractive indexes are known for the propagation of optical light as waves, the mode s that are permitted to propagate and more importantly the cutoff wavelength needs design constraints to take into account the tolerance for this shift. This may be addressed succinctly when considering an asymmetric waveguide, defined by n 1 being very muc h less than n 3 as refractive indices labeled in Figure 6 1 where n 2 is the intended medium of the propagating waves and the layers are infinite in extent in the z and y directions. From this waveguide, when configured asymmetrically, a single equation may be used to determine the difference in refractive indices required between n 3 and n 2 in order for a certain mode to propagate Equation 5 6  This chapter is based in part on 
156 ( 5 1 ) In this equation m is the mode number where m = 0 is the vacuum wavelength of the desired wavelength, and t is the thickness of layer n 2 Further, it is possible to verify that prior propagation modes remain defined under changes in refractive indices. Beyond this determination of propagation modes it is possible to utilize the equation with changes in localized refractive index These changes are generated by stress in the waveguide that may be created through bending and curling of the waveguide by a mechanically coupled actuator, such as with the ch osen electrothermal actuator. For the equations that establish the relationship between stress and change s in localized refractive index as follows: x polarized light with x as the localized refractive index; x as t he x direction stress component; y as the y direction stress component; z as t he z direction stress component; and C 1 and C 2 as pho toelastic constants. These parameters define Equation 5 2 as given in  and  ( 5 2 ) Then, for y polarized light with n y as the localiz ed refractive index Equation 5 3 is given in  and  ( 5 3 ) To complete the understanding of t hese equations, C 1 and C 2 must be fully defined. For photoelastic constant C 1 and C 2 P 11 and P 12 are Pockels coefficients which are the only still und efined variables in Equation 5 4 and Equation 5 5 
157 ( 5 4 ) ( 5 5 ) Finally, it is possible to define the bir efringence at localized indi ces as follows in Equation 5 6 ( 5 6 ) As long as these values can be determined which are primarily provided by stress tensors from FEM software, it is possible to incorporate knowledge of simple bimorphs to provide the means to generate stresses in the waveguides and thus shift the refractive i ndex. These bimorphs, or more accurately, multimorphs will be developed in the next section. When using such a method, one must make sure that the changes in the localized refractive indices continue to propagate and do not decouple light from the waveguid e, which incorporates Equation 5 1 to assure this does not occur. With the methods covered in this section it is possible to determine the variation in refractive index from changes in stress in a given material that may be characterized with Pockels coeff icients. 6.2 Design of Multimorphs To design the multimorphs utilized in actuating the waveguide, the ISC actuator is selected again as it provide large displacement at low driving voltages and large vertical displacement. The ISC actuator is selected exclusiv ely. No FDSB actuator structure is utilized, so there is no hinge or symmetric ISC construction. In this manner, the un actuated waveguide tracks in the same spatial manner as the electrothermal actuator In optimizing the characteristics of the multimorph for optimal displacement
158 while retaining rigidity, t he same procedure as followed to optimize the multimorphs with the ladder actuator and mesh actuator are applied. First, the section L 1 which is defined from the substrate connection of the actuator to the overlap or compensated region known as L 2 is optimized for the thickness of aluminum at 300K, as driven by the intrinsic stress from the PECVD oxide during deposition. The thickness is determined to be at maximum for 0.98 m thickness for 25.67m verti cal displacement, which is close to 1m thickness for 25.65m vertical displacement (Figure 6 2). In the next step, maximizing the radius of curvature of the overlap section to approximate a straight section, the thickness of the second oxide layer constit uting the bimorph is determined to be optimized at 1.58m. In order to reduce stress on the wafer, this thickness is reduced to 1.4m as in the micromirror design s to reduce the stress on the wafer. The final step is optimization of matching the angles of the active sections for L 1 and L 3 With 148 m, the matched condition is 211 m. However, it is desired to generate an unmatched condition so that the curve of the ISC is titled above parallel with the substrate. In this manner, the weight of the mirror plat e that leads to drooping can be compensated by this additional curvature. The thickness parameters as determined can be found in Table 6 1 For the length parameters of the device, the optimized lengths are given in Table 6 2 The next task is developing t he waveguide structure. In the case of this device, the waveguide must be fabricated from the thicknesses that are available from other, constraining processes. As has been noted, the devices constructed share a common fabrication process flow Consequentl y, the waveguide structure that has been selected is as shown in Figure 6 3.
159 The bottom cladding of platinum was a choice intended to protect the oxide from undercut roughing during final release of the actuator and waveguide structures. The consequence of this is that the platinum will absorb some of the energy of the propagating waves. Additionally, for the short distance of the waveguide, totaling approximately 420m, it is not critical t hat the propagating wave is not partially absorbed by metal claddin g or that the wave propagates in a higher loss evanescent mode. Additionally, as is noted and will be noted in fabrication, the oxide core is composed of oxide deposited through PECVD deposition which constitutes the second oxide layer of the bimorph and the thermal isolation layer for a total thickness of 1.6m This assures that the material is not single crystal silicon (SCS) and the polarization state of the waves may shift. Consequently, these constraints are not critical as a proof of concept for the actuating waveguide structure, but it suffices to permit this structure to demonstrate the feasibility of such a design. This employs all characteristics required for a waveguide employed in the movable arm of the FTS system. It also, with an unfixed end, can perform the function of an integrated waveguide scanner. The designed device is simulated to show the actuation of the full device and the movement of the un actuated waveguide. This is demonstrated in Figure 6 4. The full device is shown in Figure 6 4(a) where the waveguide is in the center and the 98m displacement is generated by 200K temperature differential There is a noted droop in the waveguide but the device still actuates vertically by a large displacement and a smaller relative lateral shift A closeup of the droop of the waveguide relative to the actuators is presented in a closeup in Figure 6 4(b). Further, modal analysis is
160 conducted with the first res onant mode out of plane at 306Hz in Figure 6 5 (a) The second resonant mode or rotational mode is found at 1550Hz in Figure 6 5 (b). 6.3 Fabrication The waveguide actuator micromirror follows a similar process to the ladder actuator micromirror and mesh actuator micromirror Additionally, the devices are fabricated on the same wafer as the micromir rors. The process is a multi step process on a SOI wafer that employs surface and bulk micromachining processes. A clean SOI wafer is selected with the following components : a 40m thick device layer, a 2m BOX layer, and a 400m handling layer. On the waf er, 1m of PECVD SiO 2 is deposited and patterned by a BOE on the frontside of the wafer (Figure 6 6(a)). The use of wet etch in this step creates a slope that enables unbroken electrical path that dry etch does not. An adhesion layer that is not shown in t he process flow of 0.05m PECVD SiO 2 is deposited on the frontside of the wafer. Platinum is sputtered for 0.2m and patterned through lift off for Joule heating in the multimorph structure (Figure 6 6(b)). PECVD SiO 2 is deposited for 0.2m and dry etch pa tterned in the RIE system to provide thermal isolation in the multimorphs and provides contact openings on the b ond pads of the device (Figure 6 6(c)). Aluminum is evaporated for 1.0m and patterned by lift off for the actuator and substrate electrical tra ces (Figured 6 6(d)). The final PECVD SiO 2 layer is deposited and patt erned by an RIE dry etch as the final thin film layer of the multimorph structure (Figure 6 6(e)). The frontside of the wa f er is spin coated in P R and a carrier wafer is attached and har d baked (Figure 6 6( f)). The p rocess wafer is bulk silicon etched by DRIE through the handling layer to the etch stop BOX (Figure 6 6( g )). The exposed BOX is etched in the RIE (Figure 6 6( h )). Die level is reached when the carrier wafer is removed (Figure 6 6( i )). T he devices are mounted on a carrier wafer with
161 thermal release tape and loaded into the DRIE to be etched with anisotropic and isotropic undercut etching. After release of the devices from the thermal tape, the devices are in released configurati on (Figure 6 6( j )). 6.4 Characterization On final release of the device, t he initial displacement of the mirror plate is 217m. The actuator pair resistances are 52 ohms each which is close to the theoretical value of the pair resistances calculated to be app roximately 48 ohms each The maximum voltage for the device before burnout is 1.2V. The maximum power consumption for the device per actuator pair is 75mW at peak power. This results in a consumption of 225mW for the full device with three actuator pairs. The released device is shown in Figure 6 7. The full mirror is shown in Figure 6 7(a) and the mirror plate connected to the waveguide is shown in Figure 6 7(b). The wa ve guide is centered relative to the full device with actuators immediately on either side of the waveguide. The connection to the mirror plate presents no unexpected results. Further, the mirror plate is sized to present an easy location on which to focus for characterization. It is possible to reduce the mirror plate size as the only strict r equirement for the actuated waveguide is to provide a solid, unbendable section connecting the actuators and waveguide to a common plane. In Figure 6 7(c) a closeup is provided of an unanticipated feature. The waveguide is separated from the platinum cladd ing at the interface with the substrate. This separation occurs on the release of the device which indicates that the metal oxide interface is not sufficient to overcome the mechanical force that causes separation of the thin film layers Correcting this issue is best accomplished by replacing the platinum cladding with air such that the oxide core is susceptible to superficial roughing but would
162 not encounter interface changes at an unpredictable length along the waveguide at the point of peel off. The di splacement of the device from a driving signal in terms of voltage is shown in Figure 6 8 where the maximum displacement is 56m at 1.2V The waveguide actuate s over around 26% of the initial displacement. This is attributeable to the external force suppli ed by the actuator pairs that is required to generate displacement of the non actuating waveguide. An additional character of the displacement is the strong vertical displacement The lateral displacement of the device is under 5m through the full range o f actuation During actuation, the waveguide slides along the substrate through a range of less than 5m and remains in continuous, direct interface with the substrate of the device The other noteable aspect of the device is the difficulty of a waveguide propagation test. A prism would be used but interaces with the other exposed oxide of the actuators that are only 18m from the waveguide symmetric from the center line of the waveguide on both sides. This problem can be addres sed by either DRIE or KOH etc h ing a location for a fiber core to abut the waveguide to assure light propagation into the fabricated waveguide exclusively 6.5 Summary In this chapter the theoretical underpinnings of an electrothermally actuated waveguide are discussed, as well as the cons iderations for the waveguide structure. From this, a structure is designed and simulated to show a waveguide that is capable of vertical scanning. The device fabrication is discussed. The device is then discussed for released devices in terms functionality and shortcomings. Improvements are also discussed and the theoretical discussion addresses the next progression of this preliminary, successful device fabrication and testing. Th e device provides interesting
163 potential applications for displays as well as a proof of concept for future design use in a guided wave FTS system and other refractive index varying applications
164 Figure 6 1. Planar waveguide construction of infinite extent in z and y directions. Figure 6 2. Thickness of aluminum for segment L 1 Figure 6 3. Waveguide structure. t op cladding: air core: oxide bottom cladding: Pt
165 Figure 6 4. FEM simulations of full actuated waveguide device. A) Full simulation. B) Section with actuators and waveguide closeu p. waveguide 98m actuators mirror plate actuator length 410m SiO 2 Si Al Pt A waveguide actuators mirror plate SiO 2 Si Al Pt B
166 Figure 6 5. Modal analysis of actuating waveguide. A) First resonant mode. B) Second resonant mode. B A
167 Figure 6 6. Fabrication process flow for actuated waveguide. A) Oxide deposition and patterning B) Pt deposition and liftoff C) Oxide deposition and contact opening D) Al deposition and liftoff E) Oxide deposition and patterning F) Carrier wafer frontside attachment G) Backside bulk silicon etch H) Backside BOX etch I) C arrier wafer removal J) Multistep silicon etch for final release A B C D E F G H I J SiO 2 Al Pt Si PR
1 68 Figure 6 7. SEMs of actuating waveguide device. A) Full device. B) Mirror plate to waveg uide C) Waveguide to substrate mirror plate waveguide bondp ads actuator pair A waveguide actuator pair mirror plate B
169 Figure 6 7. Continued Figure 6 8. Displacement as a function of vo ltage. waveguide actuator pair platinum cladding oxide core C
170 Table 6 1 ISC l ayer t hicknesses for common process waveguide a ctuators Adhesion SiO 2 SiO 2 (1st) Pt Heater Insulation SiO 2 Cr Al SiO 2 (2nd) 0.05 1.0 0.2 0.2 0.01 1.0 1.4 Table 6 2 Section l engths of ISC a ctuator s ections for waveguide actuato r. Downward ISC ( m ) L 1 = 148 L 2 =20 and L 3 = 252
171 CHAPTER 7 CONCLUSION AND FUTURE WORK Thi s work addresses efforts with micromirrors, spectroscopy systems, and actuated waveguides. This effort begins with the overarching goal of approaching FTS systems and MEMS de vices that are capable of enabling miniaturization of FTS system s This encompasses direct creation of a system and the enabling MEMS technology in the form of two distinct micromirrors. Further, actuated waveguides provide an alternate approach for this g oal and this approach is investigated with preliminary and promising results. The ladder actuator is constructed to achieve strong vertical displacement with ultralow tilt The device also allows precise positional control of the mirror plate on the submic ron scale This allows the device to function under quasi static actuation and effectively generate signal in an FTS system that is not subsumed by noise. The design of the micromirror also provides a strong basis for expansion of mirror aperture and incre ases in displacement. The mesh actuator is designed to increase reliability of the symmetric ISC design. This design creates redundant ISC sections to increase stability of the device under actuation. Also, the micromirror contains a hinge that is intended to increase robustness and rigidity of the device. An FTS system is completely design and implemented. This includes the electrical, optical subsystem, and post processing systems. In this system, the micromirrors developed in this work are used to genera te spectrums of unknown light sources at different OPDs and used to determine piston resonance of the micromirrors.
172 Finally, an actuated waveguide device is designed and fabricated. The device demonstrates the ability to produce large vertical displacement and effectively actuates a fabricated waveguide with potential applications to FTS systems and fiber scanning. 7.1 Research Accomplishments Th is work accomplished the following: 1. Design and fabrication of ladder actuator micromirror capable of achieving 90m d isplacement with 0.25 tilt in un tuned piston motion. 2. Design and fabrication of mesh actuator micromirror capable of achieving 145m vertical displacement and a fill factor of up to 55.98%. 3. Design and implementation of FTS system using above micromirrors with the following subsystems: optical subsystem based on Michelson interferometer ; electrical subsystem providing arbitrary waveform generation for a de monstrated six discrete channel system ; and post processing subsystem including data acquisition and da ta processing of temporally collected data. 4. Successful spectrum generation in full FTS system with ladder actuator micromirror for OPD of 21.5m and 58.21m. 5. Successful spectrum generation in full FTS system with mesh actuator micromirror for OPD of 49.35 m. 6. Use of FTS system to test ladder actuator micromirror and mesh actuator micromirror for piston resonance in the nonlinear and linear regions of the device response. 7. Design and fabrication of an actuated waveguide capable of achieving 56m actuated verti cal displacement. 7.2 Future Work With the successes that this work has achieved, there are several promising paths for future work. These paths are for the following: micromirrors, FTS system, and actuated waveguide. For micromirrors there are several improve ments that can be made. First, the ladder actuator s and mesh actuators have yielded significant advantages that allow an
173 FTS system to function effectively. However, there needs to be an increase in range for the micromirrors without compromising the advan tages of these specific micromirrors. For the FTS system, there is a main area that requires effort. There should be work on optical feedback in the system. There needs to be a way to automatically control the drift of the mirror. This eliminates manual tu ning that remains consistent over a sufficient time but invariably requires correction over multiple experiments. The actuated waveguide can be improved by using a single crystal source for the core. Further, a core with well defined Pockels coefficients i s ideal. Finally, a design with a clear location to place a fiber core to abut the fabricated waveguide is critical to allow practical use of the device.
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184 BIOGRAPHICAL SKETCH Sean Robert Samuelson obtained his Bachelor of Science, Master of Science, and Doctor of Philosophy all in Electrical and Computer Engineering from the University of Florida. During his doctoral studies he worked in the Biophotonics and Microsystems Laboratory within the Interdisciplinary Microsystems Group at the University of Florida. His w ork has encompassed the design and fabrication of multiple micromirror devices and actuated waveguides that have been utilized in OCT, FTS, photoacoustic and other imaging applications Upon completion of his dissertation, he has contributed to over 18 re sea rch publications conference papers, and patents.