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