Defect engineering of silicon based 2 d phononic crystals

DEFECT ENGINEERING OF SILICON BASED TWO-DIMENSIONAL PHONONIC CRYSTALS WANG NAN (B.Eng (Hons.), NUS) A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2013 DECLARATION I hereby declare that this thesis is my original work and it has been written by me in its entirety I have duly acknowledged all the sources of information which have been used in the thesis This thesis has also not been submitted for any degree in any university previously Wang Nan July 7, 2013 i ACKNOWLEDGEMENTS With the completion of this thesis, a wonderful four-year journey has come to an end, with a lot of fond memories left behind I would like to express my sincere gratitude to the following people who have helped me during this four-year journey Firstly, I would like to thank my thesis advisors, Prof Lee Chengkuo, Prof Moorthi Palaniapan and Prof Kwong Dim-Lee My greatest thanks go to Prof Lee Chengkuo, my main advisor, for his patience and valued guidance throughout my research He has graciously given some of his valuable time up for consultation and discussion, to impart his knowledge and valuable insight towards the progress of my research work He has also provided many valuable references and research tips which have helped me immensely This thesis would never be possible without his guidance and support Many thanks also go to my co-advisors, Dr Moorthi Palaniapan and Prof Kwong Dim-Lee, for their continuous support in the completion of my Ph.D research work Special thanks go to Prof Hsiao Fu-Li, for inspiring me to enter the world of phononic crystals with his knowledge on the fundamental theory, for his valuable help on various numerical calculations and modelling, and for his ii suggestions and discussions when replying to the reviewers‟ comments during the journal manuscript submission process Special thanks also go to Dr Tsai Ming-Lin, for his help, discussions and guidance on various complicated microfabrication processes I would like to express my deep thanks and appreciation to Mr Soon Bo Woon, for his time and help on the microfabrication of the batches of devices reported in this thesis The days and nights we spent together in the cleanrooms will be an everlasting part of my memory I would also like to acknowledge the fabrication support from the Institute of Microelectronics (IME), A*STAR, Singapore and the help from all my dear group mates from the Centre for Integrated Circuit Failure Analysis and Reliability (CICFAR), NUS, as well as people who helped me in one way or another Last but not least, my special thanks go to my family: my loving parents and wife, who have always been supporting me during the entire course of my four-year journey iii CONTENTS DECLARATION i ACKNOWLEDGEMENTS ii CONTENTS iv SUMMARY ix LIST OF TABLES xii LIST OF FIGURES xiii LIST OF SYMBOLS AND ABBREVIATIONS xxvi CHAPTER 1: INTRODUCTION 1.1 General introduction 1.2 Theoretical background 1.2.1 The Bravais Lattice and the unit cell 1.2.2 The Reciprocal Lattice and Brillouin Zone 1.2.3 Bloch theorem and the energy band theory 1.3 Literature review 1.3.1 PnC with different material compositions 1.3.1.1 Solid inclusions in solid background 1.3.1.2 Air inclusions in solid background 11 1.3.1.3 Vertical pillars on top of a substrate 13 1.3.2 PnC with different geometry 14 1.3.2.1 3-D PnC substrate 15 1.3.2.2 2-D PnC slab 17 iv 1.3.2.3 1.3.3 1-D PnC strip 17 Applications of various PnC devices with defects introduced 18 1.3.3.1 Waveguides 18 1.3.3.2 Resonators 20 1.4 Motivation and objective 21 1.5 Organization of thesis 23 CHAPTER 2: METHODS FOR NUMERICAL CALCULATION28 2.1 Introduction 28 2.2 Introduction on finite-element-method (FEM) modelling techniques 29 2.3 Numerical methods of pure PnC band gap calculation using COMSOL Multiphysics software 31 2.3.1 Governing equations 31 2.3.2 Subdomain settings 33 2.3.3 Boundary conditions 36 2.3.4 Meshing and equation solving 37 2.4 2-D PnC slab band gap optimization 38 2.5 Numerical methods for modelling defected PnC using COMSOL Multiphysics software 40 2.5.1 Calculation of the defected band structure of the PnC resonator with linear defects introduced in an otherwise perfect PnC 44 2.5.2 Calculation of the transmission spectra of the PnC resonator with linear defects introduced in an otherwise perfect PnC 47 2.5.3 Calculation of the steady-state displacement profiles of the PnC resonator with linear defects introduced in an otherwise perfect PnC 50 2.6 Conclusions 53 v CHAPTER 3: MICROFABRICATION PROCESS AND TESTING SETUP 55 3.1 Introduction 55 3.2 Detailed fabrication steps for devices in current work 56 3.2.1 AlN deposition and patterning 58 3.2.2 Top Al electrode deposition and patterning 61 3.2.3 PnC structure formation by DRIE through the silicon device layer 62 3.2.4 Backside release by DRIE of silicon substrate and RIE of the BOX layer 64 3.3 Processing outcome 66 3.4 Testing setup and procedure 74 3.5 Conclusions 79 CHAPTER 4: PHONONIC CRYSTAL WITH FABRY-PEROT TYPE OF DEFECTS 81 4.1 Introduction 81 4.2 Design approach 85 4.3 SEM images of the microfabricated cavity-mode PnC resonator based on Fabry-Perot types of defects 86 4.4 Testing results 88 4.5 Numerical simulations and discussions 91 4.6 Conclusions 96 4.7 Discussions on improved designs 97 vi CHAPTER 5: PHONONIC CRYSTAL WITH CENTRAL-HOLE DEFECTS 101 5.1 Introduction 101 5.2 Design approach 102 5.3 SEM images of the fabricated PnC with central-hole defects 105 5.4 Testing results 107 5.5 Numerical simulations and discussions 112 5.6 Conclusions 121 CHAPTER 6: PHONONIC CRYSTAL WITH DEFECTS OF REDUCED CENTRAL-HOLE RADII 122 6.1 Introduction 122 6.2 Design approach 124 6.3 SEM images of the fabricated PnC with defects of reduced central-hole radii 127 6.4 Testing results 129 6.5 Numerical simulations and discussions 136 6.5.1 Calculation of the defected band structure 136 6.5.2 Calculation of steady-state displacement profiles 143 6.6 Conclusions 149 CHAPTER 7: PHONONIC CRYSTAL WITH ALTERNATE-HOLE DEFECTS 151 7.1 Introduction 151 vii 7.2 Design approach 153 7.3 SEM images of the fabricated PnC with defects of reduced central-hole radii 157 7.4 Testing results 158 7.5 Numerical simulations and discussions 164 7.6 Conclusions 176 CHAPTER 8: CONCLUSIONS AND FUTURE WORK 178 8.1 Conclusions on current work 178 8.2 Recommendations for future work 181 BIBLIOGRAPHY 183 LIST OF PUBLICATIONS 194 viii SUMMARY The propagation of acoustic waves or elastic waves in phononic crystals (PnCs) has been extensively studied during the past two decades PnCs are the acoustic wave equivalent of the well-known photonic crystals (PhCs), whereby the propagation of acoustic waves which falls into a certain frequency range (acoustic band gap) are completely forbidden in the PnC structure, which consists of a PnC lattice formed by a periodic array of scattering inclusions located in a homogeneous background material Moreover, by strategically engineering defects through removal or distortion of the scattering inclusions on an otherwise perfect PnC material, devices of different functionalities like resonators and waveguides can also be realised However, up to date, the defect engineering on an otherwise perfect PnC to form resonators is mostly focused on the line defects in the form of Fabry-Perot resonant cavities, in which the line defects are engineered by completely removing several rows of the scattering air holes at the centre of the PnC and in the directions perpendicular to the direction of wave propagation In this type of resonators, the performance in terms of the Q factors and the insertion loss cannot be good, due to the significant mismatch ix BIBLIOGRAPHY [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] M Sigalas and E N Economou, "BAND-STRUCTURE OF ELASTIC-WAVES IN 2-DIMENSIONAL SYSTEMS," Solid State Communications, vol 86, pp 141-143, Apr 1993 M S Kushwaha, P Halevi, L Dobrzynski, and B Djafarirouhani, "Acoustic band structure of periodic elastic composites," Physical Review Letters, vol 71, pp 2022-2025, Sep 27 1993 M S Kushwaha, P Halevi, G Martinez, L Dobrzynski, and B Djafarirouhani, "Theory of acoustic band structure of periodic elastic composites," Physical Review B, vol 49, pp 2313-2322, Jan 1994 S Benchabane, A Khelif, J Y Rauch, L Robert, and V Laude, "Evidence for complete surface wave band gap in a piezoelectric phononic crystal," Physical Review E, vol 73, p 065601, Jun 2006 I El-Kady, R H Olsson, and J G Fleming, "Phononic band-gap crystals for radio frequency communications," Applied Physics Letters, vol 92, p 233504, Jun 2008 A Khelif, F L Hsiao, A Choujaa, S Benchabane, and V Laude, "Octave Omnidirectional Band Gap in a Three-Dimensional Phononic Crystal," IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control, vol 57, pp 1621-1625, Jul 2010 S Mohammadi, A A Eftekhar, A Khelif, W D Hunt, and A Adibi, "Evidence of large high frequency complete phononic band gaps in silicon phononic crystal plates," Applied Physics Letters, vol 92, p 221905, Jun 2008 S Mohammadi, A A Eftekhar, A Khelif, H Moubchir, R Westafer, W D Hunt, and A Adibi, "Complete phononic bandgaps and bandgap maps in two-dimensional silicon phononic crystal plates," Electronics Letters, vol 43, pp 898-899, August 2007 Y Pennec, B Djafari-Rouhani, H Larabi, J Vasseur, and A C Hladky-Hennion, "Phononic crystals and manipulation of sound," Physica Status Solidi C, vol 6, pp 2080-2085, 2009 J O Vasseur, P A Deymier, B Chenni, B Djafari-Rouhani, L Dobrzynski, and D Prevost, "Experimental and theoretical evidence for the existence of absolute acoustic band gaps in two-dimensional solid phononic crystals," Physical Review Letters, vol 86, pp 3012-3015, Apr 2001 T T Wu, L C Wu, and Z G Huang, "Frequency band-gap measurement of two-dimensional air/silicon phononic crystals using layered slanted finger interdigital transducers," Journal of Applied Physics, vol 97, p 094916, May 2005 183 [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] H M Lavasani, R Abdolvand, and F Ayazi, "A 500MHz Low Phase-Noise A1N-on-Silicon Reference Oscillator," in Custom Integrated Circuits Conference, 2007 CICC '07 IEEE, 2007, pp 599-602 S Ryder, K B Lee, X F Meng, and L W Lin, "AFM characterization of out-of-plane high frequency microresonators," Sensors and Actuators a-Physical, vol 114, pp 135-140, Sep 2004 D Joachim and L Liwei, "Characterization of selective polysilicon deposition for MEMS resonator tuning," Journal of Microelectromechanical Systems, vol 12, pp 193-200, 2003 L Khine and M Palaniapan, "High-Q bulk-mode SOI square resonators with straight-beam anchors," Journal of Micromechanics and Microengineering, vol 19, Jan 2009 K Wang, A C Wong, and C T C Nguyen, "VHF free-free beam high-Q micromechanical resonators," Journal of Microelectromechanical Systems, vol 9, pp 347-360, Sep 2000 L Yu-Wei, L Sheng-Shian, X Yuan, R Zeying, and C T C Nguyen, "Vibrating micromechanical resonators with solid dielectric capacitive transducer gaps," in Frequency Control Symposium and Exposition, 2005 Proceedings of the 2005 IEEE International, 2005, pp 128-134 S Pourkamali, A Hashimura, R Abdolvand, G K Ho, A Erbil, and F Ayazi, "High-Q single crystal silicon HARPSS capacitive beam resonators with self-aligned sub-100-nm transduction gaps," Journal of Microelectromechanical Systems, vol 12, pp 487-496, 2003 G K Ho, R Abdolvand, A Sivapurapu, S Humad, and F Ayazi, "Piezoelectric-on-silicon lateral bulk acoustic wave micromechanical resonators," Journal of Microelectromechanical Systems, vol 17, pp 512-520, Apr 2008 G Piazza, P J Stephanou, and A P Pisano, "Piezoelectric aluminum nitride vibrating contour-mode MEMS resonators," Journal of Microelectromechanical Systems, vol 15, pp 1406-1418, Dec 2006 G Piazza, P J Stephanou, and A P Pisano, "Single-chip multiple-frequency AlN MEMS filters based on contour-mode piezoelectric resonators," Journal of Microelectromechanical Systems, vol 16, pp 319-328, Apr 2007 C T C Nguyen, "MEMS technology for timing and frequency control," Ultrasonics, Ferroelectrics and Frequency Control, IEEE Transactions on, vol 54, pp 251-270, 2007 R H Olsson and I El-Kady, "Microfabricated phononic crystal devices and applications," Measurement Science & Technology, vol 20, p 012002, Jan 2009 C Kittel, Introduction to Solid State Physics, 8th ed.: John Wiley & 184 [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] Sons, Inc, 2005 R H Olsson, I F El-Kady, M F Su, M R Tuck, and J G Fleming, "Microfabricated VHF acoustic crystals and waveguides," Sensors and Actuators A: Physical, vol 145, pp 87-93, Jul-Aug 2008 A Khelif, B Aoubiza, S Mohammadi, A Adibi, and V Laude, "Complete band gaps in two-dimensional phononic crystal slabs," Physical Review E, vol 74, p 046610, Oct 2006 T Gorishnyy, C K Ullal, M Maldovan, G Fytas, and E L Thomas, "Hypersonic phononic crystals," Physical Review Letters, vol 94, p 115501, Mar 2005 Y Lai and Z Q Zhang, "Large band gaps in elastic phononic crystals with air inclusions," Applied Physics Letters, vol 83, pp 3900-3902, Nov 2003 S Mohammadi, A A Eftekhar, W D Hunt, and A Adibi, "Demonstration of large complete phononic band gaps and waveguiding in high-frequency silicon phononic crystal slabs," in 2008 IEEE International Frequency Control Symposium, 2008, pp 768-772 M Gorisse, S Benchabane, G Teissier, C Billard, A Reinhardt, V Laude, E Defay, and M Aid, "Observation of band gaps in the gigahertz range and deaf bands in a hypersonic aluminum nitride phononic crystal slab," Applied Physics Letters, vol 98, p 234103, Jun 2011 J C Hsu, "Effects of elastic anisotropy in phononic band-gap plates with two-dimensional lattices," Journal of Physics D-Applied Physics, vol 46, p 015301, Jan 2013 J F Zhao, R Marchal, B Bonello, and O Boyko, "Efficient focalization of antisymmetric Lamb waves in gradient-index phononic crystal plates," Applied Physics Letters, vol 101, p 261905, Dec 2012 Y Achaoui, A Khelif, S Benchabane, L Robert, and V Laude, "Experimental observation of locally-resonant and Bragg band gaps for surface guided waves in a phononic crystal of pillars," Physical Review B, vol 83, p 104201, Mar 2011 A Khelif, Y Achaoui, S Benchabane, V Laude, and B Aoubiza, "Locally resonant surface acoustic wave band gaps in a two-dimensional phononic crystal of pillars on a surface," Physical Review B, vol 81, p 214303, Jun 2010 T.-T Wu, Z.-G Huang, T.-C Tsai, and T.-C Wu, "Evidence of complete band gap and resonances in a plate with periodic stubbed surface," Applied Physics Letters, vol 93, p 111902, 2008 M A Al-Lethawe, M Addouche, A Khelif, and S Guenneau, "All-angle negative refraction for surface acoustic waves in 185 [37] [38] [39] [40] [41] [42] [43] [44] [45] [46] [47] pillar-based two-dimensional phononic structures," New Journal of Physics, vol 14, p 123030, Dec 2012 M Oudich, M Senesi, M B Assouar, M Ruzenne, J H Sun, B Vincent, Z L Hou, and T T Wu, "Experimental evidence of locally resonant sonic band gap in two-dimensional phononic stubbed plates," Physical Review B, vol 84, p 165136, Oct 2011 A Khelif, Y Achaoui, and B Aoubiza, "In-plane confinement and waveguiding of surface acoustic waves through line defects in pillars-based phononic crystal," AIP advances, vol 1, p 041404, Dec 2011 Y Pennec, B Djafari-Rouhani, H Larabi, J O Vasseur, and A C Hladky-Hennion, "Low-frequency gaps in a phononic crystal constituted of cylindrical dots deposited on a thin homogeneous plate," Physical Review B, vol 78, p 104105, Sep 2008 R Pourabolghasem, A Khelif, A A Eftekhar, S Mohammadi, and A Adibi, "Phononic bandgaps in silicon plate with metallic pillars," Electronics Letters, vol 48, pp 1147-U180, Aug 2012 A Khelif, Y Achaoui, and B Aoubiza, "Surface acoustic waves in pillars-based two-dimensional phononic structures with different lattice symmetries," Journal of Applied Physics, vol 112, p 033511, Aug 2012 B Graczykowski, S Mielcarek, A Trzaskowska, J Sarkar, P Hakonen, and B Mroz, "Tuning of a hypersonic surface phononic band gap using a nanoscale two-dimensional lattice of pillars," Physical Review B, vol 86, p 085426, Aug 2012 N Fang, F Wu, X Zhang, H Zhong, and Z Mu, "Acoustic band gaps in three-dimensional CsCl-type periodic liquid composites," Solid State Communications, vol 148, pp 267-270, 2008 X Zhang, Z Liu, Y Liu, and F Wu, "Elastic wave band gaps for three-dimensional phononic crystals with two structural units," Physics Letters A, vol 313, pp 455-460, 2003 D Yudistira, Y Pennec, B D Rouhani, S Dupont, and V Laude, "Non-radiative complete surface acoustic wave bandgap for finite-depth holey phononic crystal in lithium niobate," Applied Physics Letters, vol 100, p 061912, Feb 2012 L Y Wu and L W Chen, "Acoustic band gaps of the woodpile sonic crystal with the simple cubic lattice," Journal of Physics D-Applied Physics, vol 44, p 045402, Feb 2011 Y C Wen, J H Sun, C Dais, D Grutzmacher, T T Wu, J W Shi, and C K Sun, "Three-dimensional phononic nanocrystal composed of ordered quantum dots," Applied Physics Letters, vol 96, p 123113, Mar 2010 186 [48] [49] [50] [51] [52] [53] [54] [55] [56] [57] [58] [59] Y.-Z Wang, F.-M Li, K Kishimoto, Y.-S Wang, and W.-H Huang, "Wave band gaps in three-dimensional periodic piezoelectric structures," Mechanics Research Communications, vol 36, pp 461-468, 2009 L F Wang and K Bertoldi, "Mechanically tunable phononic band gaps in three-dimensional periodic elastomeric structures," International Journal of Solids and Structures, vol 49, pp 2881-2885, Oct 2012 R Sainidou, B Djafari-Rouhani, and J O Vasseur, "Elastic properties of finite three-dimensional solid phononic-crystal slabs," Photonics and Nanostructures - Fundamentals and Applications, vol 6, pp 122-126, 2008 C Goffaux, J Sanchez-Dehesa, and P Lambin, "Comparison of the sound attenuation efficiency of locally resonant materials and elastic band-gap structures," Physical Review B, vol 70, p 184302, Nov 2004 S Yang, J H Page, Z Liu, M L Cowan, C T Chan, and P Sheng, "Ultrasound Tunneling through 3D Phononic Crystals," Physical Review Letters, vol 88, p 104301, 2002 S X Yang, J H Page, Z Y Liu, M L Cowan, C T Chan, and P Sheng, "Focusing of sound in a 3D phononic crystal," Physical Review Letters, vol 93, p 024301, Jul 2004 F L Hsiao, A Khelif, H Moubchir, A Choujaa, C C Chen, and V Laude, "Acoustic wave band gaps in triangular and honeycomb lattice 2D ultrasonic crystals," in 2006 IEEE Ultrasonics Symposium, Vols 1-5, Proceedings, ed, 2006, pp 669-672 Z G Huang and Z Y Chen, "Acoustic Waves in Two-Dimensional Phononic Crystals With Reticular Geometric Structures," Journal of Vibration and Acoustics-Transactions of the ASME, vol 133, p 031011, Jun 2011 W Kuang, Z Hou, and Y Liu, "The effects of shapes and symmetries of scatterers on the phononic band gap in 2D phononic crystals," Physics Letters A, vol 332, pp 481-490, 2004 Y Liu, X Z Sun, and S T Chen, "Band gap structures in two-dimensional super porous phononic crystals," Ultrasonics, vol 53, pp 518-524, Feb 2013 M Oudich and M B Assouar, "Complex band structures and evanescent Bloch waves in two-dimensional finite phononic plate," Journal of Applied Physics, vol 112, p 104509, Nov 2012 Z Zhan and P Wei, "Influences of anisotropy on band gaps of 2D phononic crystal," Acta Mechanica Solida Sinica, vol 23, pp 181-188, 2010 187 [60] [61] [62] [63] [64] [65] [66] [67] [68] [69] [70] [71] V L Zhang, C G Hou, H H Pan, F S Ma, M H Kuok, H S Lim, S C Ng, M G Cottam, M Jamali, and H Yang, "Phononic dispersion of a two-dimensional chessboard-patterned bicomponent array on a substrate," Applied Physics Letters, vol 101, p 053102, Jul 2012 B Djafari-Rouhani, J O Vasseur, A C Hladky-Hennion, P Deymier, F Duval, B Dubus, and Y Pennec, "Absolute band gaps and waveguiding in free standing and supported phononic crystal slabs," Photonics and Nanostructures - Fundamentals and Applications, vol 6, pp 32-37, 2008 Z Hou and B M Assouar, "Modeling of Lamb wave propagation in plate with two-dimensional phononic crystal layer coated on uniform substrate using plane-wave-expansion method," Physics Letters A, vol 372, pp 2091-2097, 2008 Z L Hou, X J Fu, and Y Y Liu, "Calculational method to study the transmission properties of phononic crystals," Physical Review B, vol 70, p 014304, Jul 2004 A Khelif, B Aoubiza, S Mohyammadi, A Adibi, V Laude, and Ieee, "Hypersonic band gaps in two-dimensional piezoelectric phononic crystal slabs," in 2005 IEEE Ultrasonics Symposium, Vols 1-4, ed, 2005, pp 65-68 A Khelif, P A Deymier, B Djafari-Rouhani, J O Vasseur, and L Dobrzynski, "Two-dimensional phononic crystal with tunable narrow pass band: Application to a waveguide with selective frequency," Journal of Applied Physics, vol 94, pp 1308-1311, Aug 2003 G Wang, X Wen, J Wen, L Shao, and Y Liu, "Two-Dimensional Locally Resonant Phononic Crystals with Binary Structures," Physical Review Letters, vol 93, p 154302, 2004 T T Wu, Z G Huang, and S Lin, "Surface and bulk acoustic waves in two-dimensional phononic crystal consisting of materials with general anisotropy," Physical Review B, vol 69, p 094301, Mar 2004 Z L Hou and B M Assouar, "Numerical investigation of the propagation of elastic wave modes in a one-dimensional phononic crystal plate coated on a uniform substrate," Journal of Physics D-Applied Physics, vol 42, p 085103, Apr 2009 N Gomopoulos, D Maschke, C Y Koh, E L Thomas, W Tremel, H J Butt, and G Fytas, "One-Dimensional Hypersonic Phononic Crystals," Nano Letters, vol 10, pp 980-984, Mar 2010 A.-C Hladky-Hennion, C Granger, J Vasseur, eacute, ocirc, me, and M de Billy, "Propagation of elastic waves in one-dimensional periodic stubbed waveguides," Physical Review B, vol 82, p 104307, 2010 N Aravantinos-Zafiris and M M Sigalas, "Bandgaps in phononic strip waveguides," Journal of Applied Physics, vol 111, p 123516, 188 [72] [73] [74] [75] [76] [77] [78] [79] [80] [81] [82] Jun 2012 F C Hsu, C I Lee, J C Hsu, T C Huang, C H Wang, and P Chang, "Acoustic band gaps in phononic crystal strip waveguides," Applied Physics Letters, vol 96, p 051902, Feb 2010 Y Pennec, B D Rouhani, C Li, J M Escalante, A Martinez, S Benchabane, V Laude, and N Papanikolaou, "Band gaps and cavity modes in dual phononic and photonic strip waveguides," AIP advances, vol 1, p 041901, 2011 V L Zhang, F S Ma, H H Pan, C S Lin, H S Lim, S C Ng, M H Kuok, S Jain, and A O Adeyeye, "Observation of dual magnonic and phononic bandgaps in bi-component nanostructured crystals," Applied Physics Letters, vol 100, p 163118, Apr 2012 Y Cheng, J Y Xu, and X J Liu, "One-dimensional structured ultrasonic metamaterials with simultaneously negative dynamic density and modulus," Physical Review B, vol 77, p 045134, Jan 2008 D Nardi, M Travagliati, M E Siemens, Q Li, M M Murnane, H C Kapteyn, G Ferrini, F Parmigiani, and F Banfi, "Probing Thermomechanics at the Nanoscale: Impulsively Excited Pseudosurface Acoustic Waves in Hypersonic Phononic Crystals," Nano Letters, vol 11, pp 4126-4133, Oct 2011 X L Su, Y W Gao, and Y H Zhou, "The influence of material properties on the elastic band structures of one-dimensional functionally graded phononic crystals," Journal of Applied Physics, vol 112, p 123503, Dec 2012 X F Zhu, X Y Zou, B Liang, and J C Cheng, "One-way mode transmission in one-dimensional phononic crystal plates," Journal of Applied Physics, vol 108, p 124909, Dec 2010 F.-L Hsiao, A Khelif, H Moubchir, A Choujaa, C.-C Chen, and V Laude, "Waveguiding inside the complete band gap of a phononic crystal slab," Physical Review E, vol 76, p 056601, Nov 2007 N K Kuo, C J Zuo, and G Piazza, "Microscale inverse acoustic band gap structure in aluminum nitride," Applied Physics Letters, vol 95, p 093501, Aug 2009 K Nai-Kuei, Z Chengjie, and G Piazza, "Demonstration of inverse acoustic band gap structures in AlN and integration with piezoelectric contour mode wideband transducers," in 2009 IEEE International Frequency Control Symposium Joint with the 22nd European Frequency and Time forum, 2009, pp 10-13 K Nai-Kuei and G Piazza, "Evidence of acoustic wave focusing in a microscale 630 MHz Aluminum Nitride phononic crystal waveguide," presented at the 2010 IEEE International Frequency Control 189 [83] [84] [85] [86] [87] [88] [89] [90] [91] [92] [93] [94] Symposium (FCS), 2010 N.-K Kuo and G Piazza, "Fractal phononic crystals in aluminum nitride: An approach to ultra high frequency bandgaps," Applied Physics Letters, vol 99, p 163501, 2011 K Nai-Kuei and G Piazza, "Ultra high frequency air/aluminum nitride fractal phononic crystals," in Frequency Control and the European Frequency and Time Forum (FCS), 2011 Joint Conference of the IEEE International, 2011, pp 1-4 K Nai-Kuei and G Piazza, "1 GHZ phononic band gap structure in air/aluminum nitride for symmetric lamb waves," in Micro Electro Mechanical Systems (MEMS), 2011 IEEE 24th International Conference on, 2011, pp 740-743 Y W Gu, X D Luo, and H R Ma, "Low frequency elastic wave propagation in two dimensional locally resonant phononic crystal with asymmetric resonator," Journal of Applied Physics, vol 105, p 044903, Feb 2009 M Ziaei-Moayyed, M F Su, C M Reinke, K El, and R H Olsson, "Silicon carbide phononic crystals for high f.Q micromechanical resonators," in IEEE Ultrasonics Symposium (IUS), 2010, pp 162-166 M Ziaei-Moayyed, M F Su, C Reinke, I F El-Kady, and R H Olsson, "Silicon carbide phononic crystal cavities for micromechanical resonators," in IEEE 24th International Conference on Micro Electro Mechanical Systems (MEMS), 2011, pp 1377-1381 F C Hsu, T T Wu, J C Hsu, and J H Sun, "Directional enhanced acoustic radiation caused by a point cavity in a finite-size two-dimensional phononic crystal," Applied Physics Letters, vol 93, p 201904, Nov 2008 C Y Huang, J H Sun, and T T Wu, "A two-port ZnO/silicon Lamb wave resonator using phononic crystals," Applied Physics Letters, vol 97, p 031913, Jul 2010 F Li, J Liu, and Y H Wu, "The investigation of point defect modes of phononic crystal for high Q resonance," Journal of Applied Physics, vol 109, p 124907, Jun 2011 S Mohammadi and A Adibi, "Waveguide-Based Phononic Crystal Micro/Nanomechanical High-Q Resonators," Journal of Microelectromechanical Systems, vol 21, pp 379-384, Apr 2012 S Mohammadi, A A Eftekhar, and A Adibi, "Support loss-free micro/nano-mechanical resonators using phononic crystal slab waveguides," presented at the 2010 IEEE International Frequency Control Symposium (FCS), 2010 S Mohammadi, A A Eftekhar, W D Hunt, and A Adibi, "High-Q 190 [95] [96] [97] [98] [99] [100] [101] [102] [103] [104] [105] micromechanical resonators in a two-dimensional phononic crystal slab," Applied Physics Letters, vol 94, p 051906, Feb 2009 S Mohammadi, A A Eftekhar, A Khelif, and A Adibi, "A high-quality factor piezoelectric-on-substrate phononic crystal micromechanical resonator," in 2009 IEEE International Ultrasonics Symposium (IUS), 2009, pp 1158-1160 A Sato, Y Pennec, T Yanagishita, H Masuda, W Knoll, B Djafari-Rouhani, and G Fytas, "Cavity-type hypersonic phononic crystals," New Journal of Physics, vol 14, p 113032, Nov 2012 T T Wu, C H Hsu, and J H Sun, "Design of a highly magnified directional acoustic source based on the resonant cavity of two-dimensional phononic crystals," Applied Physics Letters, vol 89, p 171912, Oct 2006 A Khelif, A Choujaa, B Djafari-Rouhani, M Wilm, S Ballandras, and V Laude, "Trapping and guiding of acoustic waves by defect modes in a full-band-gap ultrasonic crystal," Physical Review B, vol 68, p 214301, Dec 2003 A Khelif, S Mohammadi, A A Eftekhar, A Adibi, and B Aoubiza, "Acoustic confinement and waveguiding with a line-defect structure in phononic crystal slabs," Journal of Applied Physics, vol 108, p 084515, Oct 2010 M Oudich, M B Assouar, and Z Hou, "Propagation of acoustic waves and waveguiding in a two-dimensional locally resonant phononic crystal plate," Applied Physics Letters, vol 97, p 193503, Nov 2010 J O Vasseur, A C Hladky-Hennion, B Djafari-Rouhani, F Duval, B Dubus, Y Pennec, and P A Deymier, "Waveguiding in two-dimensional piezoelectric phononic crystal plates," Journal of Applied Physics, vol 101, p 114904, Jun 2007 S Benchabane, A Khelif, A Choujaa, B Djafari-Rouhani, and V Laude, "Interaction of waveguide and localized modes in a phononic crystal," Europhysics Letters, vol 71, pp 570-575, Aug 2005 Y Achaoui, A Khelif, S Benchabane, and V Laude, "Polarization state and level repulsion in two-dimensional phononic crystals and waveguides in the presence of material anisotropy," Journal of Physics D-Applied Physics, vol 43, p 185401, May 2010 Z J He, X C Li, J Mei, and Z Y Liu, "Improving imaging resolution of a phononic crystal lens by employing acoustic surface waves," Journal of Applied Physics, vol 106, p 026105, Jul 2009 A Khelif, A Choujaa, S Benchabane, B Djafari-Rouhani, and V Laude, "Guiding and bending of acoustic waves in highly confined phononic crystal waveguides," Applied Physics Letters, vol 84, pp 191 [106] [107] [108] [109] [110] [111] [112] [113] [114] [115] [116] [117] [118] [119] 4400-4402, May 2004 T C Wu, T T Wu, and J C Hsu, "Waveguiding and frequency selection of Lamb waves in a plate with a periodic stubbed surface," Physical Review B, vol 79, p 104306, Mar 2009 T T Wu, Y T Chen, J H Sun, S C S Lin, and T J Huang, "Focusing of the lowest antisymmetric Lamb wave in a gradient-index phononic crystal plate," Applied Physics Letters, vol 98, p 171911, Apr 2011 J H Oh, I K Lee, P S Ma, and Y Y Kim, "Active wave-guiding of piezoelectric phononic crystals," Applied Physics Letters, vol 99, p 083505, Aug 2011 M W Nygren, "Finite Element Modeling of Piezoelectric Ultrasonic Transducers," 2011 B A Auld, Acoustic Fields and Waves in Solids New York: Wiley, 1973 E Hecht, Optics, ed San Francisco: Addison Wesley, 2002 S Pourkamali, G K Ho, and F Ayazi, "Low-Impedance VHF and UHF Capacitive Silicon Bulk Acoustic Wave Resonators - Part I: Concept and Fabrication," IEEE Transactions on Electron Devices, vol 54, pp 2017-2023, 2007 Z Y Liu, X X Zhang, Y W Mao, Y Y Zhu, Z Y Yang, C T Chan, and P Sheng, "Locally resonant sonic materials," Science, vol 289, pp 1734-1736, Sep 2000 E Yablonovitch, "INHIBITED SPONTANEOUS EMISSION IN SOLID-STATE PHYSICS AND ELECTRONICS," Physical Review Letters, vol 58, pp 2059-2062, May 1987 S John, "STRONG LOCALIZATION OF PHOTONS IN CERTAIN DISORDERED DIELECTRIC SUPERLATTICES," Physical Review Letters, vol 58, pp 2486-2489, Jun 1987 P Lalanne and J P Hugonin, "Bloch-wave engineering for high-Q, small-V microcavities," IEEE Journal of Quantum Electronics, vol 39, pp 1430-1438, Nov 2003 M W McCutcheon and M Loncar, "Design of a silicon nitride photonic crystal nanocavity with a Quality factor of one million for coupling to a diamond nanocrystal," Optics Express, vol 16, pp 19136-19145, Nov 2008 C Lee, J Thillaigovindan, C C Chen, X T Chen, Y T Chao, S H Tao, W F Xiang, A B Yu, H H Feng, and G Q Lo, "Si nanophotonics based cantilever sensor," Applied Physics Letters, vol 93, p 113113, Sep 2008 V Laude, Y Achaoui, S Benchabane, and A Khelif, "Evanescent Bloch waves and the complex band structure of phononic crystals," 192 [120] [121] [122] [123] [124] Physical Review B, vol 80, p 092301, Sep 2009 V Romero-Garcia, J V Sanchez-Perez, S Castineira-Ibanez, and L M Garcia-Raffi, "Evidences of evanescent Bloch waves in phononic crystals," Applied Physics Letters, vol 96, p 124102, Mar 2010 M Hirsekorn, "Small-size sonic crystals with strong attenuation bands in the audible frequency range," Applied Physics Letters, vol 84, pp 3364-3366, Apr 2004 C Goffaux and J Sanchez-Dehesa, "Two-dimensional phononic crystals studied using a variational method: Application to lattices of locally resonant materials," Physical Review B, vol 67, p 144301, Apr 2003 T F Krauss, "Slow light in photonic crystal waveguides," Journal of Physics D-Applied Physics, vol 40, pp 2666-2670, May 2007 F L Hsiao, A Khelif, H Moubchir, A Choujaa, C C Chen, and V Laude, "Complete band gaps and deaf bands of triangular and honeycomb water-steel phononic crystals," Journal of Applied Physics, vol 101, p 044903, Feb 2007 193 LIST OF PUBLICATIONS Journals and Letters Nan Wang, Fu-Li Hsiao, J M Tsai, Dim-Lee Kwong, Moorthi Palaniapan, and Chengkuo Lee, “Fano Resonance in High-Q Phononic Crystal Slab Based Micromechanical Resonators with Reduced Mode Mismatch”, IEEE Transactions on Nanotechnology, under review Nan Wang, Fu-Li Hsiao, Moorthi Palaniapan, and Chengkuo Lee, “Experimental and numerical investigation of two-dimensional phononic crystal resonators with additional holes in the cavity”, Sensors and Actuators A: Physical, under review Huicong Liu, You Qian, Nan Wang and Chengkuo Lee, “An in-plane nonlinear MEMS electromagnetic energy harvester”, IEEE/ASME Journal of Microelectromechanical Systems, under review Nan Wang, Fu-Li Hsiao, J M Tsai, Moorthi Palaniapan, Dim-Lee Kwong, and Chengkuo Lee, “Numerical and experimental study on silicon microresonators based on phononic crystal slab with reduced central-hole radii”, J Micromech Microeng., 23 (2013) 065030 Huicong Liu, Bo Woon Soon, Nan Wang, Cho Jui Tay, Chenggen Quan, and Chengkuo Lee, “Feasibility study of a 3-D vibration-driven electromagnetic MEMS energy harvester with multiple vibration modes”, J Micromech Microeng., vol 22, no 12, 125020, 2012 194 Nan Wang, Fu-Li Hsiao, J M Tsai, Moorthi Palaniapan, Dim-Lee Kwong, and Chengkuo Lee, “Investigation on the Optimized Design of Alternate-Hole-Defect for 2-D Phononic Crystal Based Silicon Microresonators”, J Appl Phys., vol.112, 024910, 2012 Nan Wang, J M Tsai, F L Hsiao, B W Soon, D L Kwong, M Palaniapan, and Chengkuo Lee, “Micromechanical Resonators Based on Silicon Two-dimensional Phononic Crystals of Square Lattice”, IEEE/ASME Journal of Microelectromechanical Systems, vol 21, no 4, pp 801-810, 2012 Nan Wang, F.L Hsiao, M Palaniapan, and Chengkuo Lee, “Silicon two-dimensional phononic crystal resonators using alternate defects”, Appl Phys Lett 99, 234102, Dec 2011 Nan Wang, J M Tsai, F L Hsiao, B W Soon, D L Kwong, M Palaniapan, and Chengkuo Lee, "Experimental Investigation of a Cavity-Mode Resonator Using a Micromachined Two-Dimensional Silicon Phononic Crystal in a Square Lattice," IEEE Electron Device Letters, vol 32, pp 821-823, Jun 2011 Reviewed Conference Proceedings and Presentations Nan Wang, Min Tang, Fu-Li Hsiao, Chong Pei Ho , Moorthi Palaniapan, Dim-Lee Kwong and Chengkuo Lee, “Experimental verification of phononic crystal slab based silicon microresonators”, Optical MEMS & Nanophotonics 2013, Kanazawa, Japan, 18-22 August 2013 (Accepted) 195 Nan Wang, Fu-Li Hsiao, J.M Tsai, Moorthi Palaniapan, Dim-Lee Kwong and Chengkuo Lee, “Experimental demonstration of fano resonance in microfabricated phononic crystal resonators based on two-dimensional silicon slab”, International Conf on Materials for Advanced Technologies (ICMAT 2013), Singapore, Jun 30 – Jul 5, 2013 Huicong Liu, You Qian, Nan Wang, and Chengkuo Lee, “Study of the wideband behavior of an in-plane electromagnetic MEMS energy harvester”, The 26th IEEE International Conference on Micro Electro Mechanical Systems (IEEE MEMS 2013), pp 829-832, Taipei, Taiwan, Jan 20-24, 2013 Nan Wang, Fu-Li Hsiao, J.M Tsai, Moorthi Palaniapan, Dim-Lee Kwong and Chengkuo Lee, “Experimental demonstration of fano resonance in microfabricated phononic crystal resonators based on two-dimensional silicon slab”, the 5th IEEE International Nanoelectronics Conference (INEC 2013), Singapore, Jan - 4, 2013 Nan Wang, J.M Tsai, F L Hsiao, M Palaniapan, B W Soon, Dim-Lee Kwong, and Chengkuo Lee, “Experimental study of microresonators based on silicon phononic crystal slab with alternate defects”, the 6th Asia-Pacific Conference of Transducers and Micro/Nano Technologies (APCOT 2012), Nanjing, China, July – 11, 2012 Nan Wang, Fu-Li Hsiao, Moorthi Palaniapan, and Chengkuo Lee, “Development of Microfabricated Phononic Crystal Resonators Based on Two-dimensional Silicon Slab”, 7th IEEE International Conference on Nano/Micro Engineered and Molecular Systems (IEEE NEMS 2012), p 144-148, Kyoto, Japan, Mar 5-8, 2012 Nan Wang, J M Tsai, Fu-Li Hsiao, B.W Soon, Dim-Lee Kwong, Moorthi Palaniapan, and Chengkuo Lee, “Experimental Demonstration of Microfabricated Phononic Crystal Resonators Based on Two-dimensional 196 Silicon Plate”, Defence, Science & Research Conf (DSR 2011), Singapore, Aug 3-5, 2011 Nan Wang, F.L Hsiao, M Palaniapan, J.M Tsai, J.B.W Soon, D.L Kwong, and Chengkuo Lee, “A Novel Micromechanical Resonator Using Two-dimensional Phononic Crystal Slab”, International Conf on Materials for Advanced Technologies (ICMAT 2011), Singapore, Jun 26 – Jul 1, 2011 Nan Wang, Fu-Li Hsiao, Moorthi Palaniapan, and Chengkuo Lee, “Design and characterization of Microfabricated Silicon Slab Based Phononic Crystal Resonators”, IEEE, The 8th International Conf on Networked Sensing Systems (INSS 2011), Penghu, Taiwan, Jun 12-15, 2011 10 Huicong Liu, Takeshi Kobayashi, Nan Wang, Cho Jui Tay, Chenggen Quan, and Chengkuo Lee, “Piezoelectric MEMS energy harvesting mechanism for collecting energy from low frequency vibrations - Toward self-powered wireless sensor networking”, IEEE, The 8th International Conf on Networked Sensing Systems (INSS 2011), Penghu, Taiwan, Jun 12-15, 2011 11 Bo Li, Fu-Li Hsiao, Nan Wang, and Chengkuo Lee, “Microcantilever photonic crystal sensor with dual nano-ring resonator, The 5th Asia-Pacific Conference on Transducers and Micro-Nano Technology (APCOT 2010), July 6-9, 2010, Perth, Australia 197 ... Fabry-Perot type of defects introduced of L = 2a (b) – (d) Schematic drawings of the supercells of the PnC resonators of L=2a with defects of various reduced central-hole radii (r’), (b) r’ =2? ?m, (c)... simulations and discussions 1 12 5.6 Conclusions 121 CHAPTER 6: PHONONIC CRYSTAL WITH DEFECTS OF REDUCED CENTRAL-HOLE RADII 122 6.1 Introduction 122 6 .2 Design approach... type of defects introduced of (a) L=2a (b) L=3a (c) L=4a 92 Figure 4.7: Steady-state displacement profiles of the cavity-mode PnC resonators with Fabry-Perot type of defects introduced