Karlsruhe Series in Photonics & Communications, Vol. 12 Luca Alloatti High-Speed, Low-Power and Mid-IR Silicon Photonics Applications High-Speed, Low-Power and Mid-IR Photonics Applications Silicon Luca Alloatti Luca Alloatti High-Speed, Low-Power and Mid-IR Silicon Photonics Applications Karlsruhe Series in Photonics & Communications, Vol. 12 Edited by Profs. J. Leuthold, W. Freude and C. Koos Karlsruhe Institute of Technology (KIT) Institute of Photonics and Quantum Electronics (IPQ) Germany High-Speed, Low-Power and Mid-IR Silicon Photonics Applications by Luca Alloatti Dissertation, Karlsruher Institut für Technologie (KIT) Fakultät für Elektrotechnik und Informationstechnik, 2012 Impressum Karlsruher Institut für Technologie (KIT) KIT Scientific Publishing Straße am Forum 2 D-76131 Karlsruhe www.ksp.kit.edu KIT – Universität des Landes Baden-Württemberg und nationales Forschungszentrum in der Helmholtz-Gemeinschaft Diese Veröffentlichung ist im Internet unter folgender Creative Commons-Lizenz publiziert: http://creativecommons.org/licenses/by-nc-nd/3.0/de/ KIT Scientific Publishing 2013 Print on Demand ISSN 1865-1100 ISBN 978-3-7315-0056-8 HighϣSpeed, LowϣPower and MidϣIR Silicon Photonics Applications Zur Erlangung des akademischen Grades eines DOKTOR-INGENIEURS der Fakultät für Elektrotechnik und Informationstechnik des Karlsruher Instituts für Technologie genehmigte DISSERTATION von Dipl.-Phys. Luca Alloatti aus Turin, Italien Tag der mündlichen Prüfung: 20.12.2012 Hauptreferent: Prof. Dr. sc. nat. Juerg Leuthold Korreferenten: Prof. Dr.-Ing. Dr. h. c. Wolfgang Freude Prof. Dr.-Ing. Gert F. Trommer Table of Contents Table of Contents ...................................................................................................................... i Abstract (German) ................................................................................................................... v Preface ..................................................................................................................................... vii Achievements ........................................................................................................................... ix 1 Theoretical Background ............................................................................................. 1 1.1 Silicon-Organic Hybrid (SOH) ElectroǦOptic Modulator ............................................ 1 1.1.1 Motivation ....................................................................................................... 1 1.1.2 Pockels Effect .................................................................................................. 2 1.1.3 Bandwidth of a Modulator .............................................................................. 5 1.1.4 Driving Voltage ............................................................................................... 6 1.2 Interaction Factors in a HighǦIndexǦContrast Waveguide ............................................ 8 1.2.1 Excitation of Modes by Localized Currents .................................................... 8 1.2.2 Generation of a Guided Optical Wave by SecondǦOrder Nonlinear Mixing 10 1.2.3 Attenuation of a Guided Optical Wave ......................................................... 11 1.3 MetalǦInsulatorǦSemiconductor (MIS) Model ............................................................ 13 1.3.1 Definition of the Model ................................................................................. 13 1.3.2 Electron and Hole Densities for Different Temperatures and Gate Fields ... 16 2 HighǦSpeed SiliconǦOrganic Hybrid (SOH) Modulators ...................................... 19 2.1 Introduction ................................................................................................................. 19 2.2 42.7 Gbit/s Electro-Optic Modulator in Silicon Technology ..................................... 19 2.2.1 Abstract ......................................................................................................... 19 2.2.2 Introduction ................................................................................................... 20 2.2.3 SOH Approach .............................................................................................. 20 2.2.4 The Vision ..................................................................................................... 21 2.2.5 The Fabricated Device .................................................................................. 23 2.2.6 Device Characterization ................................................................................ 24 2.2.7 Discussion and Conclusion ........................................................................... 25 2.2.8 Appendix ....................................................................................................... 27 2.3 100 GHz Silicon-Organic Hybrid Modulator ............................................................. 29 2.3.1 Abstract ......................................................................................................... 29 2.3.2 Introduction ................................................................................................... 29 2.3.3 SOH modulator ............................................................................................. 30 2.3.4 Device fabrication and characterization ........................................................ 31 2.3.5 Discussion and conclusion ............................................................................ 33 2.3.6 Appendix ....................................................................................................... 33 ii Table of Contents 3 SecondǦOrder Nonlinear SiliconǦOrganic Hybrid (SOH) Waveguide ................. 35 3.1 Abstract ....................................................................................................................... 35 3.2 Introduction ................................................................................................................. 35 3.3 The Device Concept .................................................................................................... 37 3.4 PhaseǦMatching .......................................................................................................... 38 3.5 Power Levels and Conversion Efficiencies ................................................................ 40 3.6 Conclusion .................................................................................................................. 42 3.7 Appendix ..................................................................................................................... 43 4 SiliconǦOrganic Hybrid (SOH) PhaseǦShifters with Liquid Crystal Cladding ... 45 4.1 Abstract ....................................................................................................................... 45 4.2 Introduction ................................................................................................................. 45 4.3 Design and Fabrication ............................................................................................... 46 4.4 Device Characterization .............................................................................................. 47 4.5 Results ......................................................................................................................... 47 4.6 Conclusions ................................................................................................................. 48 4.7 AC Driving Signal ...................................................................................................... 49 5 Optical Absorption in Silicon due to Charge Inversion/Accumulation ............... 51 5.1 Abstract ....................................................................................................................... 51 5.2 Introduction ................................................................................................................. 51 5.3 Results ......................................................................................................................... 52 5.4 Supplemental information ........................................................................................... 59 6 Summary and Outlook ............................................................................................. 61 Appendix ................................................................................................................................. 63 Recipe for inǦHouse Fabrication of Silicon Rib Waveguides .............................................. 63 Fabrication of Electrodes ..................................................................................................... 65 Vias for Contacting Accumulation/Inversion Layers at Temperatures close to 0 °K .......... 67 Impedance and Propagation Loss from a Vector Network Analyzer (VNA) Measurement 68 Matlab Code for Numerical Integration of MIS Equations .................................................. 70 Sellmeier Equations for Crystalline Silicon and Silicon Dioxide ........................................ 72 Refractive Indices of Si and SiO2 ......................................................................................... 73 Table of Symbols .................................................................................................................... 75 Calligraphic Symbols ..........................................................................................................