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Pur due UniversityPur due e-PubsO pen Access hTheses4" 0))"- N umerical Simulation of Hydrogen Plasma inM pcvd ReactorD i HuangP urdue UniversityF ollow this and additional works at:% 5,. !+ .(&,0-!0""!0+,"* "../%".". -+., "*$&*""-&*$+))+*.hThi

s document has been made available through Purdue e-Pubs, a service of the Purdue University Libraries. Please contact epubs@purdue.edu for

!!&/&+*(&*#+-)/&+*R ecommended CitationH uang, Di, "Numerical Simulation of Hydrogen Plasma in Mpcvd Reactor" (2014).O pen Access hTheses. 441. 5,. !+ .(&,0-!0""!0+,"* "../%".". 0114

PURDUE UNIVERSITY

GRADUATE SCHOOL

Thesis/Dissertation Acceptance

Thesis/Dissertation Agreement.

Publication Delay, and

Certification/Disclaimer (Graduate School Form 32) adheres to the provisions of

Department Di Huang

NUMERICAL SIMULATION OF HYDROGEN PLASMA IN MPCVD REACTOR

Master of Science in Aeronautics and Astronautics

Alina Alexeenko

Timothy S. Fisher

Li Qiao

Alina AlexeenkoWayne Chen07/25/2014

i NUMERICAL SIMULATION OF HYDROGEN PLASMA IN MPCVD REACTOR

A Thesis

Submitted to the Faculty

of

Purdue University

by

Di Huang

In Partial Fulfillment of the

Requirements for the Degree

of

Master of Science in Aeronautics and Astronautics

August 2014

Purdue University

West Lafayette, Indiana

ii

ACKNOWLEDGEMENTS

I would like to express my deepest appreciation to my advisor, Dr. Alina Alexeenko for her supportive guidance, constant help, and kindness throughout my pursuit of my degree. I have the deepest appreciation for being given this great opportunity to complete this research with her as my advisor. I would like to thank my committee members, Professor Timothy Fisher and Professor Li Qiao, for their teaching and serving in my committee. I have great appreciation to Dr. Abbas Semnani at Birck Nanotechnology Center for his support and assistance in electromagnetic modeling. I would like to thank Professor Allen Garner at School of Nuclear Engineering for his support and assistance in utilizing COMSOL Multiphysics. I have great appreciation to my colleagues, Venkattraman Ayyaswamy, Arnab Ganguly, Andrew Weaver, Marat Kulakhmetov, Tony Cofer, Cem Pekardan, Devon Parkos, Siva Sashank, Israel Sebastiao, Andrew Strongrich, Bill O'Neill and Nikhil Varma. They gave me many opportunities for active discussion and persistent help throughout my research. iii

TABLE OF CONTENTS

Page

LIST OF TABLES .............................................................................................................. v

LIST OF FIGURES ........................................................................................................... vi

LIST OF SYMBOLS ....................................................................................................... viii

LIST OF ABBREVIATIONS ............................................................................................. x

ABSTRACT ....................................................................................................................... xi

CHAPTER 1. INTRODUCTION ................................................................................. 1

1.1 Background ............................................................................................... 1

1.2 Motivation ................................................................................................. 2

CHAPTER 2. ELECTROMAGNETIC SIMULATION .............................................. 4

2.1 Experimental System................................................................................. 4

2.2 Computational Domains ............................................................................ 6

2.2.1 3-D Computational Domain ................................................................7

2.2.2 2-D Computational Domain ..............................................................11

2.3 Boundary Conditions............................................................................... 12

2.3.1 Boundary Conditions for 3-D Model ................................................12

2.3.2 Boundary Conditions for 2-D Model ................................................14

2.4 Numerical Simulations and Results ........................................................ 14

2.4.1 3-D Numerical Simulation with ANSYS HFSS ...............................14

2.4.2 3-D Numerical Simulation with COMSOL Multiphysics ................15

2.4.3 2-D Axial Symmetric Simulation with COMSOL Multiphysics ......18

2.5 Assumptions Based on Simulation Results ............................................. 21

CHAPTER 3. PLASMA SIMULATION BASED ON FÜNER'S MODEL ............. 22

3.1 Introduction to the Plasma Model ........................................................... 22

3.1.1 Material Properties Modification Due to Plasma Effects .................23

3.1.2 Füner's Model of Electron Number Density .....................................24

3.1.3 Drift-diffusion Model of Electron Number Density .........................25

iv Page

3.1.4 Heat Transfer Model .........................................................................26

3.1.5 Coupling of Models ..........................................................................29

3.2 Computational Model of the Plasma Model ........................................... 32

3.3 Boundary Conditions of the Plasma Model ............................................ 32

3.3.1 Boundary Conditions of Heat Transfer Simulation ..........................32

3.3.2 Boundary Conditions of the Drift-Diffusion Equation .....................33

3.4 Simulation Results of the Plasma Model ................................................ 34

3.4.1 Results of the EM Simulations ..........................................................34

3.4.2 Results of the UDF ............................................................................38

3.4.3 Results of the Heat Transfer Simulation ...........................................45

3.5 Validity Tests for Standing Wave and Sinusoidal Oscillation Field

Assumptions ................................................................................................................. 48

3.5.1 Validity Test for Standing Wave Assumption ..................................48

3.5.2 Validity Test for Sinusoidal Oscillation Field Assumption ..............50

CHAPTER 4. CONCLUSIONS AND FUTURE WORK .......................................... 52

4.1 Conclusions ............................................................................................. 52

4.2 Future Work ............................................................................................ 53

LIST OF REFERENCES .................................................................................................. 55

VITA ................................................................................................................................. 61

v

LIST OF TABLES

Table .............................................................................................................................. Page

Table 2.1 3-D mesh statistic.............................................................................................. 17

Table 2.2 2-D mesh statistic.............................................................................................. 20

Table 2.3 The comparison of solutions from all models .................................................. 20

Table 3.1 Electron including reactions and associated constant parameters [30] ............. 23

Table 3.2 Comparison of the EM simulation results ........................................................ 38

Table 3.3 Comparison of the n

e simulation results ........................................................... 42

Table 3.4 Comparison of the T

e simulation results .......................................................... 45

Table 3.5 Comparison of the T

g simulation results .......................................................... 48 vi

LIST OF FIGURES

Figure ............................................................................................................................. Page

Figure 1.1 Illustration of plasma environment in AX5200S MPCVD reactor ................... 2

Figure 2.1 The experimental system ................................................................................... 5

Figure 2.2 Schematic diagram of the MPCVD reactor at two stage positions [24]............ 6 Figure 2.3 Models of rectangular waveguide and TE-TM wave convertor ........................ 9

Figure 2.4 Cross-section of the plasma region.................................................................. 10

Figure 2.5 3-D computational domain .............................................................................. 10

Figure 2.6 2-D computational domain .............................................................................. 12

Figure 2.7 3-D model in HFSS including port .................................................................. 13

Figure 2.8 Electrical simulation results (HFSS 3-D) ........................................................ 15

Figure 2.9 3-D mesh built by COMSOL .......................................................................... 16

Figure 2.10 3-D mesh element quality histogram ............................................................. 17

Figure 2.11 Electrical simulation result (COMSL 3-D) ................................................... 18

Figure 2.12 2-D mesh built by COMSOL ........................................................................ 19

Figure 2.13 2-D mesh element quality histogram ............................................................. 19

Figure 2.14 Electrical simulation results (COMSL 2-D) .................................................. 21

Figure 3.1 Comparisons of original RHS and approximation .......................................... 28

Figure 3.2 Loop of solvers ................................................................................................ 29

Figure 3.3 Flow chart of algorithm ................................................................................... 31

vii

Figure ............................................................................................................................. Page

Figure 3.4 BCs of heat transfer simulation ....................................................................... 33

Figure 3.5 BCs of drift-diffusion model ........................................................................... 34

Figure 3.6 EM simulation results for 500 W input power ................................................ 35

Figure 3.7 EM simulation results for 400 W input power ................................................ 36

Figure 3.8 EM simulation results for 300 W input power ................................................ 36

Figure 3.9 Field strength variations on susceptor surface and along reactor axis ............ 37

Figure 3.10 n

e simulation results for 500 W input power ................................................ 39

Figure 3.11 n

e simulation results for 400 W input power ................................................ 39

Figure 3.12 n

e simulation results for 300 W input power ................................................ 40 Figure 3.13 Electron density variations on susceptor surface and along reactor axis ...... 41

Figure 3.14 T

e simulation results for 500 W input power ................................................ 42

Figure 3.15 T

e simulation results for 400 W input power ................................................ 43

Figure 3.16 T

e simulation results for 300 W input power ................................................ 43 Figure 3.17 Electron temperature variations on susceptor surface and along reactor axis 44

Figure 3.18 T

g simulation results for 500 W input power ................................................ 46

Figure 3.19 T

g simulation results for 400 W input power ................................................ 46 Figure 3.20 Heavy species temperature variations on susceptor surface and along reactor

axis .................................................................................................................................... 47

Figure 3.21 Test result for standing wave, with both diffusion and mobility enabled ..... 49

Figure 3.23 Comparison of the diffusion term and mobility term .................................... 50

Figure 3.24 Test result for sinusoidal oscillation field ..................................................... 51

viii

LIST OF SYMBOLS

electrical field gas density 4 permittivity of vacuum magnetic field time 4 permeability of vacuum current density ae reaction rates ae threshold energy of reactions permittivity due to effects of plasma conductivity due to effects of plasma angular frequency of plasmaquotesdbs_dbs24.pdfusesText_30

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