Thin Film Adhesion and Morphology of Graphene on Undulated Electronic Substrates A Dissertation Presented by Guangxu Li to The Department of Mechanical and Industrial Engineering in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Mechanical Engineering Northeastern University Boston, Massachusetts February 2012 NORTHEASTERN UNIVERSITY Graduate School of Engineering Dissertation Title: Thin Film Adhesion and Morphology of Graphene on Undulated Electronic Substrates Author: Guangxu Li Department: Mechanical and Industrial Engineering Approved for Dissertation Requirement for the Doctor of Philosophy Degree Dissertation Advisor: Prof. Kai-Tak Wan Date Dissertation Reader: Prof. Sinan Müftü Date Dissertation Reader: Prof. Andrew Gouldstone Date Department Chair: Prof. Jacqueline Isaacs Date Graduate School Notified of Acceptance: Director of the Graduate School Date TABLE OF CONTENTS TABLE OF CONTENTS ........................................................................................... I LIST OF FIGURES .................................................................................................. V LIST OF TABLES .................................................................................................... X ABSTRACT ............................................................................................................ XI ACKNOWLEDGEMENTS .................................................................................. XIII CHAPTER 1 INTRODUCTION .......................................................................... 1 1.1 Introduction of adhesion ................................................................................... 1 1.1.1 Definition of adhesion ...................................................................................................... 1 1.1.2 Adhesion mechanisms ...................................................................................................... 3 1.1.3 Adhesion effects ............................................................................................................... 5 1.2 Review of solid adhesion .................................................................................. 8 1.2.1 Hertz contact theory ......................................................................................................... 8 1.2.2 JKR theory...................................................................................................................... 10 1.2.3 DMT theory .................................................................................................................... 12 1.2.4 Dugdale-Barenblatt-Maugis model ................................................................................ 13 1.2.5 Adhesion map for solids contact .................................................................................... 15 1.2.6 Other adhesion models ................................................................................................... 16 1.3 Review of thin film adhesion ......................................................................... 18 1.3.1 Peel test .......................................................................................................................... 19 1.3.2 Blister test ....................................................................................................................... 20 1.3.3 Punch test ....................................................................................................................... 23 1.4 Graphene and its adhesion property ............................................................... 24 1.5 Research objectives ........................................................................................ 28 1.6 Organization of the thesis ............................................................................... 29 i CHAPTER 2 THIN FILM ADHESION IN THE LONG RANGE INTERSURFACE FORCE ................................................................................... 31 2.1 New Tabor parameter ..................................................................................... 31 2.2 Punch test model ............................................................................................. 37 2.2.1 Rectangular film under pure stretching .......................................................................... 37 2.2.2 Rectangular film under pure bending ............................................................................. 53 2.2.3 Circular film under pure stretching ................................................................................ 55 2.2.4 Circular film under pure bending ................................................................................... 58 2.3 Pressurized blister model ................................................................................ 59 2.3.1 Rectangular pressurized blister under pure stretching ................................................... 59 2.3.2 Rectangular pressurized blister under pure bending ...................................................... 64 2.3.3 Circular pressurized blister under pure stretching .......................................................... 65 2.3.4 Circular pressurized blister under pure bending ............................................................ 69 2.4 Constrained blister model ............................................................................... 70 2.4.1 Circular constrained blister under pure stretching ......................................................... 70 2.4.2 Circular constrained blister under pure bending ............................................................ 75 2.4.3 Rectangular constrained blister under pure stretching ................................................... 76 2.4.4 Rectangular constrained blister under pure bending ...................................................... 79 2.4.5 Discussion ...................................................................................................................... 79 2.5 New adhesion map for thin film ..................................................................... 89 CHAPTER 3 HYSTERESIS OF LOADING AND UNLOADING A RIGID PUNCH TO A CLAMPED MEMBRANE .......................................................... 92 3.1 Rectangular film ............................................................................................. 92 3.2 Circular film ................................................................................................... 96 3.3 Discussion ....................................................................................................... 99 CHAPTER 4 MOLECULAR MECHANICS SIMULATION OF GRAPHENE-GRAPHENE ADHESION ..........................................................106 4.1 Molecular mechanics simulation method .....................................................106 ii 4.2 Young’ modulus and effective thickness of graphene .................................107 4.3 Adhesion energy of two graphene layers .....................................................116 4.4 Adhesion mechanics between graphene-substrate .......................................118 4.5 Adhesion mechanics between two graphene layers .....................................130 4.6 Misorientation effect to the adhesion property of graphene ........................133 CHAPTER 5 GRAPHENE ON ELECTRONIC SUBSTRATES .................136 5.1 Introduction ..................................................................................................136 5.2 Experiment ....................................................................................................139 5.2.1 Sample preparation ....................................................................................................... 139 5.2.2 Blister formation .......................................................................................................... 144 5.3 Model and Analysis ......................................................................................150 5.4 Discussion .....................................................................................................155 5.5 Graphene on other substrate materials .........................................................159 CHAPTER 6 CONCLUSION AND FUTURE WORK .................................161 6.1 Significant contributions and conclusions ....................................................161 6.2 Future work ...................................................................................................163 REFERENCES .....................................................................................................166 APPENDIX 1: MATHEMATICA PROGRAM FOR RECTANGULAR PUNCH TEST MODEL UNDER PURE STRETCHING ...................................................179 APPENDIX 2: MATHEMATICA PROGRAM FOR RECTANGULAR PUNCH TEST MODEL UNDER PURE BENDING ..........................................................183 iii APPENDIX 3: MATHEMATICA PROGRAM FOR CIRCULAR PUNCH TEST MODEL UNDER PURE BENDING ....................................................................186 APPENDIX 4: MATHEMATICA PROGRAM FOR RECTANGULAR PRESSURIZED BLISTER MODEL UNDER PURE STRETCHING ................190 APPENDIX 5: MATHEMATICA PROGRAM FOR RECTANGULAR PRESSURIZED BLISTER MODEL UNDER PURE BENDING .......................195 APPENDIX 6: MATHEMATICA PROGRAM FOR CIRCULAR PRESSURIZED BLISTER MODEL UNDER PURE STRETCHING ............................................200 APPENDIX 7: MATHEMATICA PROGRAM FOR CIRCULAR PRESSURIZED BLISTER MODEL