Theory and Design of Phononic Crystals for Unreleased CMOS-MEMS Resonant Body Transistors

Resonant body transistors (RBTs) are solid state, actively sensed microelectromechanical systems (MEMS) resonators that can be implemented in commercial CMOS technologies. With small footprint, highQ, and scalability to gigahertz frequencies, they form basic building blocks for radio frequency (RF) front-ends and timing applications. Toward the goal of seamless CMOS integration, this paper presents the design and implementation of phononic crystals (PnCs) in the back-end-of-line (BEOL) of commercial CMOS technologies with bandgaps in the gigahertz frequencies to be used for enhanced acoustical confinement in CMOS-RBTs. Lithographically defined PnC dimensions allow for bandgap engineering, providing flexibility in resonator design, and allowing for multiple frequencies on a single chip. The theoretical basis for analyzing generic PnCs is presented, with focus on the special case of implementing PnCs in CMOS BEOL layers. The effect of CMOS process variations on the performance of such PnCs is also considered. The analysis presented in this paper establishes a methodology for assessing different CMOS technologies for the integration of unreleased CMOS-MEMS resonators. This paper also discusses the importance of uniformity of the acoustical cavity in the nonresonant dimension and its effect on overall resonator performance. A PnC implementation in IBM 32-nm silicon on insulator (SOI) BEOL layers is demonstrated to achieve 85% fractional-bandgap ~4.5-GHz frequency. With better energy confinement, the proposed CMOS-RBTs achieve a quality factor Q of 252, which corresponds to 8× improvement over the previous generation RBTs, which did not include PnCs. The presented devices have a footprint of 5 μm × 7 μm. This paper concludes with a discussion of the properties required of a CMOS technology for high performance RBT implementation.

[1]  Steven G. Johnson,et al.  Perturbation theory for Maxwell's equations with shifting material boundaries. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  S. Bhave,et al.  The resonant body transistor. , 2010, Nano letters.

[3]  Steven G. Johnson,et al.  Adiabatic theorem and continuous coupled-mode theory for efficient taper transitions in photonic crystals. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  A. Grill.  Porous pSiCOH Ultralow-k Dielectrics for Chip Interconnects Prepared by PECVD , 2009 .

[5]  Dana Weinstein,et al.  GAN MEMS RESONATOR USING A FOLDED PHONONIC CRYSTAL STRUCTURE , 2014 .

[6]  J. Larson,et al.  Ultra-miniature high-Q filters and duplexers using FBAR technology , 2001, 2001 IEEE International Solid-State Circuits Conference. Digest of Technical Papers. ISSCC (Cat. No.01CH37177).

[7]  C. Koh.  Generalized phononic networks : of length scales, symmetry breaking and (non) locality : "controlling complexity through simplicity" , 2011 .

[8]  C. Kittel.  Introduction to solid state physics , 1954 .

[9]  C. Dupre,et al.  Resonant-body silicon nanowire field effect transistor without junctions , 2012, 2012 International Electron Devices Meeting.

[10]  S. Cunningham,et al.  Challenges and Solutions for Cost-effective RF-MEMS Packaging , 2007, 2007 32nd IEEE/CPMT International Electronic Manufacturing Technology Symposium.

[11]  Xiao-Xing Su,et al.  Large bandgaps of two-dimensional phononic crystals with cross-like holes , 2011 .

[12]  Weileun Fang,et al.  Temperature coefficient of frequency modeling for CMOS-MEMS bulk mode composite resonators , 2015, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control.

[13]  M. Soljačić,et al.  Coupling, scattering, and perturbation theory: Semi-analytical analyses of photonic-crystal waveguides , 2003, Proceedings of 2003 5th International Conference on Transparent Optical Networks, 2003..

[14]  Tsu-Jae King Liu,et al.  Technologies for Cofabricating MEMS and Electronics , 2008, Proceedings of the IEEE.

[15]  R. Aigner,et al.  Advancement of MEMS into RF-filter applications , 2002, Digest. International Electron Devices Meeting,.

[16]  J. Tromp.  A Coupled Local‐Mode Analysis of Surface‐Wave Propagation In A Laterally Heterogeneous Waveguide , 1994 .

[17]  A. Ionescu.  Resonant body transistors , 2010, 68th Device Research Conference.

[18]  Dana Weinstein,et al.  Switchable piezoelectric transduction in AlGaN/GaN MEMS resonators , 2013, 2013 Transducers & Eurosensors XXVII: The 17th International Conference on Solid-State Sensors, Actuators and Microsystems (TRANSDUCERS & EUROSENSORS XXVII).

[19]  G. Roeck,et al.  Wave propagation in layered dry, saturated and unsaturated poroelastic media , 1998 .

[20]  L. Buchaillot,et al.  Electromechanical Transconductance Properties of a GaN MEMS Resonator With Fully Integrated HEMT Transducers , 2012, Journal of Microelectromechanical Systems.

[21]  M. Belyansky,et al.  High performance 32nm SOI CMOS with high-k/metal gate and 0.149µm2 SRAM and ultra low-k back end with eleven levels of copper , 2006, 2009 Symposium on VLSI Technology.

[22]  K. J. Gabriel,et al.  Post-CMOS processing for high-aspect-ratio integrated silicon microstructures , 2002 .

[23]  D. Weinstein,et al.  Phononic crystals for acoustic confinement in CMOS-MEMS resonators , 2014, 2014 IEEE International Frequency Control Symposium (FCS).

[24]  A. Semlyen,et al.  Rational approximation of frequency domain responses by vector fitting , 1999 .

[25]  F. Ayazi,et al.  Effect of phonon interactions on limiting the f.Q product of micromechanical resonators , 2009, TRANSDUCERS 2009 - 2009 International Solid-State Sensors, Actuators and Microsystems Conference.

[26]  Cheng-Syun Li,et al.  Advanced CMOS–MEMS Resonator Platform , 2012, IEEE Electron Device Letters.

[27]  M. Rais-Zadeh,et al.  HEMT-based read-out of a thickness-mode AlGaN/GaN resonator , 2013, 2013 IEEE International Electron Devices Meeting.

[28]  B. Djafari-Rouhani,et al.  Theory of acoustic band structure of periodic elastic composites. , 1994, Physical review. B, Condensed matter.

[29]  W.D. Brown,et al.  Challenges in the packaging of MEMS , 1999, Proceedings International Symposium on Advanced Packaging Materials. Processes, Properties and Interfaces (IEEE Cat. No.99TH8405).

[30]  Sylvain Ballandras,et al.  Trapping and guiding of acoustic waves by defect modes in a full-band-gap ultrasonic crystal , 2003 .

[31]  Hermann A. Haus,et al.  A variational coupled-mode theory for periodic waveguides , 1995 .

[32]  O. Ambacher,et al.  AlGaN/GaN-based MEMS with two-dimensional electron gas for novel sensor applications , 2008 .

[33]  K. Boustedt,et al.  Fundamental requirements on MEMS packaging and reliability , 2002, 2002 Proceedings. 8th International Advanced Packaging Materials Symposium (Cat. No.02TH8617).

[34]  G. Piazza,et al.  1 GHZ phononic band gap structure in air/aluminum nitride for symmetric lamb waves , 2011, 2011 IEEE 24th International Conference on Micro Electro Mechanical Systems.

[35]  Acoustic Bragg reflectors for Q-enhancement of unreleased MEMS resonators , 2011, 2011 Joint Conference of the IEEE International Frequency Control and the European Frequency and Time Forum (FCS) Proceedings.

[36]  B. Djafari-Rouhani,et al.  Acoustic band structure of periodic elastic composites. , 1993, Physical review letters.

[37]  Steven G. Johnson,et al.  Photonic Crystals: Molding the Flow of Light , 1995 .

[38]  R. Olsson,et al.  Silicon carbide phononic crystals for high f.Q micromechanical resonators , 2010, 2010 IEEE International Ultrasonics Symposium.

[39]  Jean-Pierre Berenger,et al.  A perfectly matched layer for the absorption of electromagnetic waves , 1994 .

[40]  Zohaib Mahmood,et al.  Resonant Body Transistors in IBM's 32 nm SOI CMOS Technology , 2014, Journal of Microelectromechanical Systems.