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Few Electron Paramagnetic Resonances Detection On FEW ELECTRON PARAMAGNETIC RESONANCES DETECTION TECHNIQUES ON THE RUBY SURFACE By Xiying Li Submitted in partial fulfillment of the requirements For the degree of Doctor of Philosophy Dissertation Adviser: Dr. Massood Tabib-Azar Co-Adviser: Dr. J. Adin Mann, Jr. Department of Electrical Engineering and Computer Science CASE WESTERN RESERVE UNIVERSITY August, 2005 CASE WESTERN RESERVE UNIVERSITY SCHOOL OF GRADUATE STUDIES We hereby approve the dissertation of ______________________________________________________ candidate for the Ph.D. degree *. (signed)_______________________________________________ (chair of the committee) ________________________________________________ ________________________________________________ ________________________________________________ ________________________________________________ ________________________________________________ (date) _______________________ *We also certify that written approval has been obtained for any proprietary material contained therein. Table of Contents TABLE OF CONTENTS ................................................................................................................................. II LIST OF FIGURES ...................................................................................................................................... IV ABSTRACT............................................................................................................................................... VII CHAPTER 1 INTRODUCTION .................................................................................................................1 1.1 STUDY OBJECTIVES.....................................................................................................................2 1.2 HIGHLY LOCALIZED EVANESCENT MICROWAVE MICROSCOPIC PROBE TECHNIQUES ..........3 1.3 ELECTRON SPIN...........................................................................................................................5 1.4 THE MAGNETIC SUSCEPTIBILITIES ............................................................................................9 REFERENCES............................................................................................................................................12 CHAPTER 2 ELECTRON PARAMAGNETIC RESONANCE (EPR) .................................................14 2.1 ABSORPTION LINE SHAPES .......................................................................................................14 2.1.1 Lorentzian Type Line Shapes...............................................................................................15 2.1.2 Gaussian Type Line Shapes .................................................................................................16 2.1.3 EPR Absorption Line Shapes...............................................................................................18 2.2 CLASSIC EPR DETECTION TECHNIQUES...................................................................................19 2.2.1 Microwave Cavity .................................................................................................................21 2.2.2 Magnetic Field Modulation..................................................................................................23 2.2.3 Frequency Modulation.........................................................................................................31 3+ 2.3 MATHEMATICAL MODEL OF CR ION IN AL2O3 EPR.............................................................32 2.4 LARMOR FREQUENCY................................................................................................................40 2.5 EPR SENSITIVITY......................................................................................................................40 REFERENCES............................................................................................................................................42 CHAPTER 3 MICROSTRIP RESONATOR ...........................................................................................45 3.1 MICROSTRIP TRANSMISSION LINE RESONATOR......................................................................45 I 3.2 MAGNETIC MICROSTRIP PROBE TUNING.................................................................................49 3.3 SYSTEM OVERALL Q FACTOR...................................................................................................51 3.4 MICROWAVE REFLECTIVE COEFFICIENT..........................................................................................53 REFERENCES............................................................................................................................................59 CHAPTER 4 EPR SINGLE POINT MEASUREMENT.........................................................................61 4.1 THEORETICAL BACKGROUND...................................................................................................61 4.2 MEASUREMENT APPARATUS.....................................................................................................63 4.2.1 Magnetic Field Modulation Coil..........................................................................................64 4.2.2 Concept of the Circulator.....................................................................................................65 4.2.3 Phase Sensitive Detector (PSD) ...........................................................................................66 4.3 EPR REAL TIME DETECTION.....................................................................................................69 4.4 COMPARISON OF EXPERIMENTAL AND THEORETICAL LINE SHAPES .......................................71 4.5 THE EPR EMM PROBE SENSITIVITY.......................................................................................74 4.5.1 Background Noise ................................................................................................................74 4.5.2 The Spin-Spin Relaxation Time...........................................................................................74 4.5.3 The Total Number of Spins..................................................................................................75 4.5.4 The Minimum Number of Spins ..........................................................................................76 REFERENCES............................................................................................................................................77 CHAPTER 5 EPR MEASUREMENT ON THE RUBY SURFACE ......................................................79 5.1 SINGLE POINT SURFACE EPR DETECTION ..............................................................................79 5.2 EPR SURFACE SIGNAL ANALYSIS.............................................................................................82 5.2.1 The Total Number of Spins near the Surface......................................................................84 5.2.2 The Minimum Number of Detectable Spins near the Surface............................................86 5.3 COMPARISON BETWEEN THE SURFACE EPR AND ENCLOSED EPR ........................................87 5.4 MAGNETIC FIELD DISTRIBUTION .............................................................................................88 REFERENCES............................................................................................................................................90 CHAPTER 6 CONCLUSIONS AND FUTURE APPLICATIONS OF EPR.........................................91 6.1 SUMMARY OF THE EPR MEASUREMENT ON THE RUBY SURFACE AND FUTURE WORKS ........91 II 6.2 APPLICATIONS OF SURFACE EMM EPR ..................................................................................94 6.2.1 Quantum Computing............................................................................................................95 6.2.2 Defects in Material ...............................................................................................................95 6.3.3 Aging Process Detection.......................................................................................................96 REFERENCES............................................................................................................................................97 APPENDIX A 3-D SCHRÖDINGER EQUATION....................................................................................99 APPENDIX B MAGNETIC DIPOLE MOMENT ...................................................................................103 APPENDIX C THE ATOMIC FORCE MICROSCOPY (AFM) .............................................................106 REFERENCES..........................................................................................................................................107 III List of Figures Figure 1-1 Magnetic Dipole and Electric Dipole EMM Probe 4 Figure 1-2 Stern’s-Gerlach’s Experiment Illustration 5 Figure 1-3 Zeeman Effects for single electron 8 Figure 1-4 Magnetic Susceptibility of Different Material 9 Figure 1-5 LCR measurement of a Solenoid Coil with Ruby Sample 11 Figure 2-1 Normalized Lorentzian type and Gaussian Type Line Shapes 15 Figure 2-2 First Derivatives of Gaussian and Lorentzian Type Line Shapes 17 Figure 2-3 EPR First Derivative Line Shape 18 Figure 2-4 The Classic CW EPR Setup 20 Figure 2-5 Microwave Magnetic and Electric Fields in a Rectangular Cavity 22 Figure 2-6 Magnetic Field Modulation Detections 25 Figure 2-7 Phase Sensitive Detector Input Voltage Waveform 27 Figure
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