Polarization Studies of Coupled Quantum Dots A thesis presented to the faculty of the College of Arts and Sciences of Ohio University In partial fulfillment of the requirements for the degree Master of Science Swati Ramanathan November 2007 2 This thesis titled Polarization Studies of Coupled Quantum Dots by SWATI RAMANATHAN has been approved for the Department of Physics and Astronomy and the College of Arts and Sciences by Eric A. Stinaff Assistant Professor of Physics and Astronomy Benjamin M. Ogles Dean, College of Arts and Sciences 3 Abstract RAMANATHAN, SWATI , M.S., November 2007, Physics and Astronomy Polarization Studies of Coupled Quantum Dots (91 pp.) Director of Thesis: Eric A. Stinaff This thesis examines photoluminescence spectra and polarized photoluminescence spectra of coupled semiconductor quantum dots. Previous results on the polarization memory of charge states in single quantum dots have demonstrated that different excitonic charge states have identifiable polarization signatures [1,2,3]. Our results indicate that coupled quantum dots have similar polarization signatures to single quantum dots. New studies on polarization memories of anticrossing regions in coupled quantum dots were undertaken, and polarization memories of anticrossing lines were tracked through the anticrossing region. Preliminary results indicate that the polarization memory of anticrossing lines shows a marked decrease with bias, reaches a minima at the centre of the anticrossing region, and then starts increasing again. This work helps in the identification of spins, a necessary first step towards achieving spin control in quantum dots for the production of qubit states for quantum processing, and lays the groundwork for the production of entangled photon pairs. Approved: _____________________________________________________________ Eric A. Stinaff Assistant Professor of Physics and Astronomy 4 Acknowledgements I would like to thank my advisor, Dr. Eric Stinaff, without whose constant guidance and mentoring, this thesis would not have been possible. His unwavering support and willingness to clear my doubts and misconceptions is greatly appreciated. Thanks to his excellent instruction, the unfamiliar field of condensed matter physics is not so unfamiliar to me anymore. His extremely high theoretical and experimental standards have inspired and helped me to raise my own standards. As a beginner in the field, that is probably the most important thing I could have ever learned. I would like to thank my lab partners, Kushal Wijesundara, Mauricio Garrido, Anna Opitz, and Ru Zhang for their willingness to help, to share lab resources, and for helping keep a light hearted atmosphere even in the midst of serious data taking. I would finally like to thank my family for their love and encouragement, which was undiminished even by the long distance. I dedicate this thesis to one of my favorite people in the world, my grandfather. 5 Table of Contents Abstract....................................................................................................................... 3 Acknowledgements..................................................................................................... 4 List of Tables .............................................................................................................. 8 List of Figures............................................................................................................. 9 List of Graphs ........................................................................................................... 11 Chapter 1: Introduction............................................................................................ 12 1.1. Outline.................................................................................................... 13 1.2. Semiconductor Physics .......................................................................... 14 Chapter 2: Theory of Quantum Dots ....................................................................... 17 2.1. From Bulk to Lower Dimensions .......................................................... 17 2.2. Quantum Wells ...................................................................................... 18 2.3. Quantum Wires ...................................................................................... 18 2.4. Quantum Dots ........................................................................................ 19 2.5. Applications of Quantum Dots .............................................................. 21 Chapter 3: Growth Techniques ................................................................................. 25 3.1. Self Assembled/Stranski-Krastanow Technique.................................... 26 3.2. MOCVD................................................................................................. 28 3.3. MBE....................................................................................................... 29 3.4. Colloidally Grown QDs ......................................................................... 31 3.5. Comparison of Growth Techniques....................................................... 32 6 Chapter 4: Optical Properties of Quantum Dots....................................................... 34 4.1. Introduction............................................................................................ 34 Chapter 5: Photoluminescence Spectroscopy .......................................................... 37 5.1. Introduction............................................................................................ 37 5.2. Experimental Setup................................................................................ 38 5.2.1. Sample............................................................................................. 38 5.2.2. Lab Description .............................................................................. 38 5.3. Single Quantum Dots............................................................................. 41 5.3.1 Inference of Charge State of Single Quantum Dots......................... 42 5.3.2 Binding Energy ................................................................................ 43 5.4. Coupled Quantum Dots.......................................................................... 46 Chapter 6: Polarization Studies................................................................................. 50 6.1 Introduction............................................................................................. 50 6.2. Working Principle of Liquid Crystal Retarder....................................... 54 6.3. Polarization Memory ............................................................................. 54 6.4 Exchange Interactions............................................................................. 56 6.4.1. Isotropic Exchange ......................................................................... 57 6.4.2. Anisotropic Exchange ..................................................................... 57 6.5. Anticrossing in Positive Trion ............................................................... 59 6.6. Applications of Polarization Studies...................................................... 60 7 Chapter 7: Data and Results...................................................................................... 66 7.1. Anticrossing A ....................................................................................... 68 7.2. Anticrossing B ....................................................................................... 72 7.3. Anticrossing C ....................................................................................... 74 Chapter 8: Conclusion and Future Directions........................................................... 78 References................................................................................................................. 80 Appendix A............................................................................................................... 88 Appendix B ............................................................................................................... 89 Appendix C ............................................................................................................... 91 8 List of Tables Table 1: Experimental Details Aperture A ……………………………….………..68 Table 2: Anticrossing A, Line 1……………………………………………...….…68 Table 3: Anticrossing A, Line 2………………………………………………...….70 Table 4: Experimental Details Aperture B…………………………………..……..72 Table 5: Anticrossing B, Line 2……………………………………………..……..72 Table 6: Experimental Details Aperture C……………………………………....…74 Table 7: Anticrossing C, Line 1……………………………………………..….….74 Table 8: Anticrossing C, Line 2………………………………………………....…76 9 List of Figures Figure 1.1. Band Structure and Energy Gap of a Material ............................................. 16 Figure 2.1. Density of States of Bulk, Quantum Well, Quantum Wire, Quantum Dot .. 17 Figure 2.2. InAs band structure with electron and hole in C and V bands. .................... 19 Figure 2.3. Detection of antibodies using quantum dots ................................................ 22 Figure 3.1. Strain relaxation leading to S-K self-assembled growth .............................. 27 Figure 3.2. MOCVD grown quantum dots ..................................................................... 28 Figure 3.3. MBE grown InAs/GaAs dots........................................................................ 30 Figure