A dissertation presented to. the faculty of. the College of Arts and Sciences of Ohio University. In partial fulfillment

Transcription

1 Ultrafast Exciton Dynamics and Optical Control in Semiconductor Quantum Dots A dissertation presented to the faculty of the College of Arts and Sciences of Ohio University In partial fulfillment of the requirements for the degree Doctor of Philosophy Kushal Chinthaka Wijesundara June Kushal Chinthaka Wijesundara. All Rights Reserved.

2 2 This dissertation titled Ultrafast Exciton Dynamics and Optical Control in Semiconductor Quantum Dots by KUSHAL CHINTHAKA WIJESUNDARA has been approved for the Department of Physics and Astronomy and the College of Arts and Sciences by Eric A. Stinaff Associate Professor of Physics and Astronomy Howard Dewald Interim Dean, College of Arts and Sciences

3 3 Abstract WIJESUNDARA KUSHAL CHINTHAKA, Ph.D., June 2012, Physics and Astronomy Ultrafast Exciton Dynamics and Optical Control in Semiconductor Quantum Dots Director of Dissertation: Eric A. Stinaff Device miniaturization with advanced fabrication techniques has revolutionized the semiconductor industry along with innovative concepts of carrier spin, potentially important at the fundamental physical limits of scalability. For spin-based information processing, semiconductor coupled quantum dots (CQDs) provide excellent control in spin dynamics due to 3-D confinement, discrete energy levels, and optical orientation and coupling. The research presented in this dissertation investigates spin interactions and exciton relaxation channels in semiconductor CQDs measured through optical control and time-resolved experimental techniques. Our experiments involving photoluminescence (PL) and photoluminescence excitation (PLE) methods revealed effects arising from the structural properties of semiconductor nanostructures, including quantum rings and CQDs. High resolution PL measurements on positively charged exciton states demonstrated experimental evidence of isotropic exchange interaction. Controlling exchange interaction in different spin configurations is fundamental to quantum logic operations. Hence, polarization dependent PL experiments were executed and electric field tunable exchange interaction effects were reported on the neutral exciton states.

4 4 Next, time-resolved measurements were performed while pumping above the InAs wetting layer (WL) energy and probing below the WL to determine the dynamics of the optically generated electric field in CQDs. The observed, rapid onset of the optically generated electric field may provide the use of CQDs for optical switching applications. Finally, carrier relaxations in the CQDs were identified through the dynamics of the spatially indirect exciton state using a mode-locked laser excitation source and standard time-resolved single photon counting technique. Wave function distribution, carrier tunneling, and phonon scattering led to the observed lifetime and intensity modulations. With time-resolved PLE, bi-exponential lifetime decay revealed nonmonotonic phonon relaxations as a result of the structure factor of the CQDs. Furthermore, with resonant excitation, carrier tunneling into charged exciton states was also eliminated. These results demonstrated tunable exciton relaxation rates in CQDs, which are useful for quantum information, optoelectronics, and photonics applications. Approved: Eric A. Stinaff Associate Professor of Physics and Astronomy

5 5 I dedicate this dissertation to my family, who has always believed in the pursuit of academic excellence.

6 6 Acknowledgments Among many to whom I owe acknowledgments, first and foremost I would like to thank my advisor, Dr. Eric Stinaff, for his invaluable advice, encouragement, and support, which allowed me to pursue my diverse research interests. He always made time for inspiring scientific discussions and provided critical suggestions when reviewing my papers. His guidance and patience motivated me to work in an exciting research setting and to grow as an independent experimentalist. I would also like to acknowledge the rest of the members of my doctoral committee, Dr. Saw-Wai Hla, Dr. Alexander Govorov, and Dr. Jeffrey Rack, for taking their precious time to critique and provide invaluable feedback. I am grateful to our collaborators, Dr. Daniel Gammon and Dr. Allen Bracker at the Naval Research Laboratory, for providing us with high quality samples and their critique of manuscripts, thought-provoking questions, and critical suggestions. My sincere gratitude also goes to Dr. Sergio Ulloa and his student Juan Rolon, for providing theoretical insight and mathematical modeling to our experimental observations and being a part of our publications I believe I have learned a great deal through these collaborations. I would also like to express my appreciation to the members of the Stinaff research group, especially Mauricio Garrido, for sharing laboratory resources and fruitful discussions, and to Darshan Desai and current group members, for giving me the opportunity to work as a peer mentor.

7 7 I regard with great gratitude all the Professors in the Department of Physics and Astronomy at Ohio University, in particular Horacio Castillo, David Drabold, Alexander Govorov, Saw-Wai Hla, Alexander Neiman, Arthur Smith, David Tees, and Sergio Ulloa, who have taught me and provided me with a strong foundation in Physics at the graduate school. I wish to thank the technical staff, especially Jeremy Dennison, Doug Shafer, and Todd Koren, for helping us with every aspect in setting up the laboratory; Don Roth and Chris Sandford, for always being willing to share their knowledge and expertise; and Donald Carter, for lending high speed electronics which helped us to build time-domain experimental setups. Many thanks also go to the administrative staff, namely Tracy Inman, Ennice Sweigart, and Wayne Chiasson, for their help from the day I arrived, and for providing an accommodating environment within the department. I am grateful to my mother and father, for their unconditional love, support, and all of the sacrifices that they have made during my entire education. I would also like to thank my sister, who always encouraged me and supported me in all of my endeavors. Most importantly, I would like to thank my wife, Gayani, for her love and patience. She has always stood by me and inspired me to achieve my goals. Finally, many thanks to those who have funded my research and travel to participate in conferences, including NQPI program at Ohio University, Graduate Student Senate Travel Grant, Ohio University CMSS fellowship award, National Science Foundation (NSF DMR ), and Battelle Memorial Institute during the latter part of my research.

8 8 Table of Contents Abstract... 3 Dedication... 5 Acknowledgments... 6 List of Tables List of Figures Chapter 1 Introduction Semiconductor Nanostructures Layout of the Dissertation Chapter 2 Device Structure and Experimental Techniques Semiconductor Quantum Dots Device Fabrication Photoluminescence Coupled Quantum Dot Spectra Quantum Ring Luminescence Resonant Excitation Chapter 3 Temporal Response of the Optical Field in CQDs Photovoltaic Effects in Semiconductors Quasi-Pump Probe Experiment Temporal Response Chapter Summary... 49

9 9 Chapter 4 Electric Field Controlled Spin Interactions Optical Orientation Exchange Interaction and Exciton Fine Structure Polarization-Resolved Photoluminescence Electric Field Tunable Exchange Interaction Spin Effects of Charged Exciton States Control of the Electron-Hole Exchange Interaction Chapter Summary Chapter 5 Tunable Exciton Relaxations and Time-Resolved Spectroscopy Exciton Relaxation in Quantum Dots Luminescence Intensity Intensity Modulations Decay Rate Model Time - Correlated Single Photon Counting Exciton Lifetimes Resonant Excitation Theoretical Model Photon Correlation Measurements Chapter Summary Chapter 6 Conclusion References Appendix: Publications and Conference Presentations

10 10 List of Tables Table 2.1: Material parameters for GaAs and InAs at 300K Table 3.1: Extracted photon peak energies from gated photon counting technique...44

11 11 List of Figures Figure 2.1: (a) First Brillouin zone of the reciprocal lattice along with points with high symmetry (X, and L). (b) Calculated band structure of GaAs Figure 2.2: Density of states for 3-D and 0-D confinement Figure 2.3: Schematics of the coupled quantum dot fabrication process. (a) Selfassembled single InAs/GaAs QD layer. (b) Partially capped and annealed to truncate, which enables control of the bottom QD. (c) Strain induced stacking of the top dot to preferentially nucleate on the bottom dot along with height control (d). A filled state XSTM image is also depicted in (e)...29 Figure 2.4: (a) CQD device layer sequence. (b) Band edge diagram with applied electric field Figure 2.5: Emission from QD ensemble with inhomogeneous linewidths of ~ 50 to100 mev (red curve) along with homogeneous isolated single dot luminescence linewidths of few µev (blue spectral emission line) Figure 2.6: (a) CQD bias map with large field dependent inter-dot (indirect) excitons along with intra-dot (direct) transitions highlighted to identify 0 X, X, and X exciton states. Owing to the asymmetric nature of the CQD with a smaller top dot, results in anti-crossing signature are circled along with the characteristic X pattern. (b) Schematics of the large field dependent indirect transitions that red shifts in energy with applied field....33

12 Figure 2.7: Photoluminescence from ring-shaped nanostructure samples formed at (a) 350 C and (b) 450 C Figure 2.8: Schematics of the basic resonant excitation process Figure 3.1: (a) Band edge diagram of the CQD Schottky diode along with direct and indirect transitions. (b) Tunneling of electrons (holes) from top- T (bottom) to bottom-b (top) and creation of the optically generated electric field (OGEF). (c) OGEF associated shift in PL spectra monitored through indirect exciton Figure 3.2: Schematic representation of the quasi-pump probe setup. A modulated (250Hz) diode pumped solid states (DPSS) laser is used to generate the optical field while a CW laser is used to probe and monitor the indirect exciton Figure 3.3: Gated photon counting technique. Modulated laser excitation (250Hz) energy above WL and corresponding charging behavior of the optically generated electric field (OGEF) schematically shown in the top figure. (a) Gated photon counts measured by single photon counting module (SPCM) for different delay times (DL) with a fixed gate width (W). (b) Sample spectrum for a specific delay time and gate width Figure 3.4: Normalized relative photon counts corresponding to different delay times and a fixed gate width analogous to the decay of the optically generated electric field (OGEF) Figure 3.5: Temporal response of the optically generated electric field (OGEF). The decay of the OGEF is measured from the plot of photon peak energy with time delay in the gated photon counts. The inset shows

13 the turn-off of the negative triggering laser pulse relative to the decay of the OGEF Figure 3.6: Decay of the optically generated electric field with laser excitation above the WL for two different powers of P (0.3 mw) and 2P (0.6 mw). Inset shows the semi-logarithmic plot of the power dependence Figure 3.7: Generation rate of the optically created electric field along with the rising edge of the modulated laser pulse Figure 4.1: Schematic representation of the optical orientation process. With circular polarized light, specifically defined spin orientations of the electrons and holes are attained and identified in agreement with optical selection rules and device characteristics. Furthermore, detecting the orientation of the emitted light also reveals the associated spin states of the electron and hole pair Figure 4.2: Expected luminescence from circularly polarized excitation corresponding to (a) neutral exciton, (b) positively charged exciton, and (c) negatively charged exciton with associated spin configurations Figure 4.3: Schematic representation of the exciton fine structure due to exchange interactions Figure 4.4: Polarization-resolved photoluminescence setup to measure the degree of polarization Figure 4.5: (a) Schematic representation of direct and indirect excitons as a function of applied electric field along with relevant spin configurations. Band edge diagrams shown in (b) and (c) represent

14 14 the CQDs in a Schottky diode structure with larger bottom dot (B) and smaller top dot (T). The variation in the band edge diagram at high electric fields (b) shows hole level resonances along with electron wave function (blue) and symmetric (direct), anti-symmetric (indirect) hole wave functions (red). At low electric fields (c), overlap between the electron and the anti-symmetric hole wave function is decreased and more atomic like behavior can be observed Figure 4.6: (a) Photoluminescence spectra from the 4nm CQD structure. Spectral lines associated with exciton states are clearly indentified, including the inter-dot and intra-dot exciton states along with the anti-crossing signature highlighted in the squared region. (b) Polarization-resolved PL spectra for the neutral exciton state near anti-crossing region is acquired through excitation to the quasicontinuum wetting layer with σ+ polarized excitation and detected for both σ+ and σ polarizations. (c) Degree of circular polarization as a function of applied electric field evaluated from Equation 4.2 corresponding to the direct (open squares) and indirect (solid circles) exciton states Figure 4.7: Difference in the circular polarization percentage as a function of relative electric field, relative to the inter-dot and intra-dot neutral exciton states. At low relative electric fields a higher degree of circular polarization memory can be observed with 4nm barrier (squares) as opposed to the 2nm barrier (circles) CQD structure. This common trend in the degree of circular polarization is a consequence of reduced wave function overlap and the electron-hole exchange interaction with increase in the barrier separation....63

15 15 Figure 4.8: Origin of the "X" pattern in the singly charged exciton state. (a) Four possible recombination paths from the initial charged exciton to the ground state hole level. (b) Basic singly charged exciton spectral recombination signature without tunneling or spin effects Figure 4.9: (a) Identification of the singly charged trion state. (b) Spin fine structure of the positive trion along with spin states of XH and X L...66 Figure 4.10: The degree of circular polarization for the two spin states XH and X L Figure 4.11: (a) X, X fine structure doublet of the positive trion which arise H D LD due to the isotropic exchange interaction along with corresponding degree of polarization memory results (b)...69 Figure 4.12: Barrier dependence of the degree of circular polarization on X LD as a function of relative electric field Figure 4.13: Polarization dependent photoluminescence spectra as a function of applied electric field that tunes inter-dot and intra-dot excitons by ~ 14 mev as shown in the bottom panel along with a dip in the circular polarization memory of the indirect exciton is depicted in the top plot Figure 4.14: (a) Polarization memory dip coincident with ground state hole molecule. (b) Possible mechanism through mixing of hole states that enhances relaxation channels as illustrated in (c, d) Figure 4.15: Linearly polarized doublet with splitting energy analogous to the anisotropic exchange energy....74

16 Figure 4.16: Variation of the minimum at the polarization dip as a function of laser excitation energy Figure 5.1: Exciton states and intensity profiles. (a) Schematic representation of the exciton states. Rectangles represent the CQD strcuture with top (T) and bottom (B) quantum dots. The electron (e) tends to localize in the bottom dot while the holes (h) form molecular states (D and I), which results in both direct (X D ) and indirect (X I ) excitons. (b) Inset depicts the actual PL spectra associated with the anti-crossing region and the direct (X D ) and indirect (X I ) excitons, which are analogous to the schematic in (a). The main plot illustrates the Intensity profile of the two excitons. With an applied electric field relative to the anticrossing region, a decrease in indirect exciton intensity is prominent as opposed to the direct exciton intensity Figure 5.2: Photoluminescence spectra of the exciton states as a function of energy separation between indirect and direct excitons, relative to the neutral exciton anti-crossing Figure 5.3: Indirect exciton intensity modulations. (a) Measured normalized indirect exciton intensity to compensate for the overall increase in the PL intensity. (b) Indirect to direct exciton intensity ratio derived from the decay rates associated with non-resonant excitation. (c) PL spectra plotted as a function of exciton energy separation to clearly identify processes related with intensity modulations Figure 5.4: Possible mechanisms associated with the exciton decay process including phonon scattering and carrier tunneling to other exciton states. Indirect (I) and direct (D) exciton states decay radiatively with rates of R I and R D and the other charge states with R +. Phonon

17 assisted non radiative process is denoted by γ along with the tunneling to other exciton states through ν Figure 5.5: Schematic representation of the time correlated single photon counting (TCSPC) experimental setup. Excitation was provided by a mode-locked Ti:Sapphire laser (pulse width of ~ 1.5 ps operating at 80 MHz) attached to a high powered diode pumped solid state laser (CW-DPSS). From the avalanche photodiode (APD) and allied electronics [SYNC Synchronized laser diode pulse, TAC Time to amplitude converter, and MCA Multi channel analyzer] acquired lifetimes as illustrated in the bottom right plot. A photograph of the actual experimental setup is depicted in the top left corner Figure 5.6: Indirect exciton lifetime and intensity modulation for two different CQDs. (a) Indirect exciton lifetime behavior as a function of exciton energy separation. (b) Normalized intensity modulation associated with the indirect exciton. (c) PL spectra as a function of exciton energy separation between indirect (X I ) and direct (X D ) excitons relative to the anti-crossing energy. The blue stripe [(a), (b), (d), and (e)] highlights both intensity and lifetime minima that correspond to an exciton energy separation of ~ 6-8 mev. Dotted vertical lines represent the X-pattern signature and the onset of the singly charged exciton (X + ) along with its dominant effects shown by the gray shading in the top four plots. (f) PL spectra for a different CQD along with the lifetime and intensity profile are depicted in (d) and (e) respectively Figure 5.7: Schematic representation of the exciton states via spread of the electron and hole wave functions as a variable of energy separation. The prominent region for indirect exciton relaxation to trion states is shown in the shaded area of the plot....94

18 18 Figure 5.8: Indirect exciton relaxation to positively charged exciton (positive trion) state. (a) Indirect exciton state. (b) At high enough forward bias voltages, the electron can tunnel out to the substrate. Consequently, with reduced Coulomb energy, the top (T) dot hole tunnels into the bottom (B) dot. (c) Subsequent excitation results in creating an e-h pair in the B dot and generating the positively charged exciton state Figure 5.9: Normalized relative intensity of the indirect exciton and singly charged exciton (positive trion) states. "X" symbolizes the positve trion molecular anti-crossing signature that appears in the PL spectra as a function of exciton energy separation. Green doted vertical line represents the energy separation corresponding to both intensity and lifetime minimum that can be associated with other relaxation processes within the CQD system Figure 5.10: Bi-exponential behavior of the direct exciton lifetimes due to resonant laser excitation into the indirect exciton state as a function of exciton energy separation. The semi-log plot visualizes the time decays of the two exponents that correspond to both indirect exciton (lower slope) and direct exciton states (higher slope) Figure 5.11: (a) Extracted lifetimes I, D corresponding to indirect and direct excitons with resonant laser excitation. For comparison, indirect exciton lifetimes with non-resonant excitation are shown as a dotted line. In the resonant case, indirect exciton lifetimes tend to diverge up to 4 ns beyond generation of the trion state denoted by X and can be mapped from the PL plot (b)

19 19 Figure 5.12: (a) Recombination rates for the direct and indirect excitons and nonradiative contributions to the exciton lifetimes via phonon-mediated relaxation channels and trion formation rates extracted from the biexponential data. (b) PL spectra corresponding to the neutral exciton and positive trion states as a function of exciton energy separation Figure 5.13: Comparison between theoretical and experimentally extracted phonon relaxation rates. (a) Total phonon relaxation rate derived from the deformation potential (DP), piezoelectric effects (PZ), and phonon polarizations. Structure factor contour plots as a function of the exciton energy separation are illustrated, along with phonon wave vector dispersion in the inset. (b) Experimentally extracted phonon-mediated relaxation rates and exciton recombination rates. Accordingly, a clear agreement between theory and can be established Figure 5.14: Schematic representation of the Hanbury Brown-Twiss (HBT) interferometer type setup which can be used for both photon autocorrelation and cross-correlation experiments Figure 5.15: Photon correlation measurements illustrated through coincidences as a function of delay time. (a) Anti-bunching signature observed from cross-correlation between indirect and direct excitons. (b) Coincidence as a function of delay time for the neutral exciton and unknown higher energy state that was observed in one CQD aperture. Completely random cross-correlation elucidates exciton states arising from two different CQD apertures and validates the consistency of the reported tunable exciton relation rate measurements

20 20 Chapter 1 Introduction 1.1 Semiconductor Nanostructures The trend in miniaturization marked a new era in research and technology with the invention of the transistor [1] by Shockley, Bardeen, and Brattain, which made a historical breakthrough for semiconductors. With the advancement in micro fabrication techniques, transistors with higher switching rates were made possible; this resulted in a rapid change in electronics and the telecommunication industry. As predicted by Moore s Law [2], the exponential decrease in the device structure will result in the technology node reaching well below 10 nm within the next decade, at which point it will encounter fundamental physical limits. Thus, revolutionary concepts such as intrinsic spin properties of charge carriers need to be considered as a functional unit to satisfy underlying quantum mechanical effects at this device operating limit. Beyond technological applications, understanding theoretical concepts through device properties will provide invaluable insight into the development in many branches of semiconductor physics, including Atomic Physics, Quantum Statistics, and Quantum Information Processing. Besides bulk materials, technological advancements and theoretical concepts have also been explored on electronic structures of two dimensions. These quasi-two dimensional systems, known as quantum wells [3], had improved optical properties that

21 21 could be tuned by band-gap engineering [4] and attracted the attention of many research possibilities. Optical studies on these 2-D structures underlined the tremendously increased role of excitonic effects [5], which were found to be of great importance. However, with the notion of nanotechnology in mid 80 s research, endeavors were focused on the possibility of reducing the dimensionality to create 1-D quantum wires and 0-D quantum dot structures. A quantum dot or an artificial atom, being a nanostructure, confines charge carriers in all three spatial directions and owing to their structure, research has mainly concentrated on studying their optical and electrical properties [6,7]. Quantum dots have proven their viability in many technological applications, which include clean renewable energy sources via nanocrystals to provide white light phosphorescence [8] as well as efficient laser systems in the telecommunication industry that have succeeded to minimize temperature-sensitive output fluctuations [9]. In addition quantum dots have also provided valuable insight as diagnostic tools in bio-medical engineering and clinical perspectives [10]. Quantum dots may also help to realize potential next-generation quantum information processing and quantum computing schemes [11]. Among many possible implementation methods, spins in coupled quantum dots (CQDs) are considered to be useful as a candidate to provide quantum bits (qubits) as they can be initialized, manipulated, and measured through optical techniques. Therefore, identifying different spin configurations of excitons and their dynamical properties is indispensable. Thus, exploring this zero dimensional structure through polarization dependent photoluminescence, and time-resolved techniques will enable us to identify exciting

22 features of tunnel coupling, charge and spin state control, relaxation channels, and radiative lifetimes Layout of the Dissertation Physical properties of bulk zinc-blende crystal structures of GaAs and InAs semiconductors, along with quantum mechanical properties, including charge carrier confinement in low dimensions, are initially discussed in Chapter 2 of this dissertation. Next, device fabrication and the growth techniques related to CQD are summarized. Basic concepts including photoluminescence and photoluminescence excitation are illustrated. At the end of this chapter, PL is used to identify spectral lines resulting from various exciton states of the CQDs along with the initial results related to single Quantum Ring emissions. Comparable with potential shifts due to carrier ionization in quantum wells, the temporal response related to the optically generated electric field in CQDs is investigated for the first time, as presented in Chapter 3. A novel experiment involving the two color quasi-pump probe technique is introduced to measure the decay rate of the optical field while monitoring it through the large field sensitive indirect exciton state. Further discussion on carrier traps that may influence the optical field decay time is presented. Power dependent measurements on the optical field were also carried out to determine the influence from carrier density. This chapter concludes with a discussion of the frequency response on the onset of the optical field and its possible applications.

23 23 Chapter 4 explains optical orientation techniques to control exchange interactions that affect spin control in CQD systems. The generation of intra-dot and inter-dot transitions is discussed with overlap in carrier wave functions. A polarization-resolved experimental setup and measurements of the degree of circular polarization memory are presented. Initial results on spatial separation of the electron and the hole with applied field are used to alleviate the anisotropic part of the exchange interaction. Spin orientations within the fine structure of the singly charged positive trion states are highlighted. The spectrally-resolved fine structure doublet that arises due to isotropic exchange splitting is measured for the polarization memory. Exchange control in the fine structure doublet is recognized via the spectator hole in the top dot of the trion state; additional insight was gained through variation in the barrier between the two dots. The minimum in the degree of circular polarization in inter-dot exciton is described through the ground state hole mixing process. Resonant laser excitation is implemented to gain efficient relaxations and mitigate exchange interactions. Chapter 5 introduces time-resolved experiments including the details of the experimental techniques. For the first time, lifetime and intensity modulations in the spatially indirect exciton state along with the oscillatory phonon relaxations are reported in this chapter. At the lowest energy separation between the spatially indirect and direct exciton states, observed intensity and lifetimes of the neutral exciton are demonstrated with a basic carrier wave function overlap model. Both charging and phonon-mediated relaxations were incorporated to completely identify modulation in the exciton states. Modified time-resolved experiments via photoluminescence excitation (PLE) are

24 24 incorporated to alleviate the charging events. Resulted bi-exponential lifetimes are extracted through rate equations to quantify associated phonon rates. In addition, Hanbury Brown-Twiss type photon correlation experiments are introduced to identify the generation of the spatially direct exciton through the relaxation process in the inter-dot exciton. Detailed theoretical investigation is also presented to explain the observed phonon oscillatory relaxations that highlighted the influence on the structural parameters of the CQD. A complete review of the research achievements presented in this dissertation is discussed in Chapter 6.

25 25 Chapter 2 Device Structure and Experimental Techniques 2.1 Semiconductor Quantum Dots To understand the physical properties associated with quantum dots, a basic discussion of bulk semiconductor materials is presented where the electronic properties of such solids depend on their crystalline structure. QDs that are discussed in this dissertation were formed by InAs and GaAs that crystallized in the zinc-blende structure. The associated first Brillouin zone from the fcc reciprocal lattice along with the high symmetry points are illustrated in Figure 2.1(a). Figure 2.1: (a) First Brillouin zone of the reciprocal lattice along with points with high symmetry (X, and L). (b) Calculated band structure of GaAs (After P.Y. Yu and M. Cardona [12]).

26 From these crystalline structures, band diagrams are calculated, for example, through the pseudo-potential method [13]. Such a band structure diagram for GaAs is illustrated in Figure 2.1(b). The energy difference between the conduction band minimum 6 and valance band maximum 8 is the direct band gap energy of GaAs as illustrated in Figure 2.1(b). The valance band at 8 is degenerate for wave vector, k = 0. However, due to different effective masses of the holes (heavy and light), two different dispersion curves are observed for non-zero wave vector values. Furthermore, a split-off band 7 also exists due to the spin orbit coupling effect. Table 2.1 highlights basic material parameters for InAs [14,15] and GaAs [16]. 26 Table 2.1: Material parameters for GaAs and InAs at 300K. Parameter GaAs InAs Energy bandgap (ev) Lattice constant (nm) In quantized semiconductor structures, from envelope wave function and effective mass approximations, carrier motion can be expressed as depicted in Equation 2.1, along with effective mass, confinement potential, and carrier energy denoted by m *, V (r), and E respectively.

27 27 2 2m * 2 V ( r) ( r) E ( r) (2.1) The periodic part of the particle wave function (Bloch function) results in s-like and p-like wave functions for the conduction band electrons and valance band holes respectively. Moreover, the confinement effects lead to changes in the density of states of the semiconductors. For bulk materials and quantum dots density of states can be written as; 3 2 D Bulk 1 2m ( ) E (2.2) D ( ) 2 E QD E n n (2.3) Figure 2.2, illustrates, Energy vs. Density of states plot for bulk semiconductors and QDs. The observed singular density of states for electrons reveals that it s comparable to real atoms. Thus, distinctive properties associated with QDs can be investigated with optical spectroscopy. Figure 2.2: Density of states for 3-D and 0-D confinement.

28 Device Fabrication Different groups of semiconductors are grown in the Stranski-Krastanov (SK) growth mode [17], which exploits the self-assembly and provides a means of building nanoscale materials. Thus, using molecular-beam epitaxy (MBE) or metal-organic vapor phase epitaxy, high quality quantum dots can be grown. With InAs and GaAs quantum dots, the initial growth is a layer by layer process in the SK growth mode. The critical layer thickness of InAs (few monolayers) has been found by considering the growth as a first order phase transition [18]. The InAs islands are created beyond this critical thickness which results in an increase in the surface energy. However, the strain energy is limited by the island formation. Thus, the total energy can be minimized [19] for a critical InAs island size in the Stranski-Krastanov mode. As such no further process of etch or implantation is necessary since quantum dots are grown during the deposition, which is one of the advantages of employing the SK mode. This allows for a homogeneous surface with minimal defects from impurities while maintaining the interface morphology of quantum dots. The self-assembled InAs/GaAs single quantum dots grown by SK mode have provided numerous experimental results in identifying different spin and charge exciton states [20,21,22]. However, in order to investigate exchange coupling between spins and other important quantum mechanical properties applicable for spin-based information schemes [23], along with inter-dot exciton states that are widely discussed throughout this dissertation, fabricating and exploiting coupled quantum dots is necessary. Similar to the formation of single dots, coupled quantum dots are fabricated by introducing novel

29 29 techniques incorporated with the MBE mode that has been available to our research through a collaboration with the Naval Research Laboratory in Washington DC. Initially a self-assembled single InAs/GaAs layer is grown under the SK mode [Figure 2.3(a)] followed by a partial cap layer of GaAs as depicted in Figure 2.3(b). Using an indium flush method, the height of the first quantum dot layer is controlled by capping it off at a desired point (2-4 nm) [24]. Subsequently a thin GaAs layer is deposited (2-15 nm) on the capped layer of InAs, which acts as the tunnel barrier between the two quantum dots. Next, a second layer of InAs QDs are grown and the top dot height is controlled using the same technique of partial cap and anneal. Further, due to strain effects, the subsequent QD layer nucleates selectively on top of the first layer, which gives rise to the preferred CQD structure as schematically illustrated in Figure 2.3(c) and (d). A cross-sectional scanning tunneling microscopy (XSTM) image of the sample crosssection that has been cleaved in situ will provide both identification and the dimensionality of individual dots as illustrated in Figure 2.3(e). Figure 2.3: Schematics of the coupled quantum dot fabrication process. (a) Selfassembled single InAs/GaAs QD layer. (b) Partially capped and annealed to truncate, which enables control of the bottom QD. (c) Strain induced stacking of the top dot to preferentially nucleate on the bottom dot along with height control (d). A filled state XSTM image is also depicted in (e) (Courtesy of the Naval Research Laboratory).

30 30 This allows the application of an electric field along the growth direction. A charging sequence, along with different charged states and multi-exciton generation can be realized by the band edge representation of the CQD device as depicted in Figure 2.4 (b). Figure 2.4: (a) CQD device layer sequence (After M. Scheibner. et al., Phys. Rev. B 75, (2007) [25]). (b) Band edge diagram with applied electric field (After M. F. Doty. et al., Phys. Rev. B 78, (2008) [26]). Further, lithographically defined micron sized apertures are created on top of the sample surface via an aluminum shadow mask to optically probe and manipulate individual QDs. In conjunction with electric field control, precise optical mapping at the single dot level may provide insight into unique properties of CQDs. As depicted in Figure 2.5, typical single QD spectra probed via apertures falls within homogeneously broadened linewidths of a few µev as opposed to the inhomogeneously broadened

31 linewidths of ~ mev that arise due to simultaneous detection of QD with differed geometries. 31 Figure 2.5: Emission from QD ensemble with inhomogeneous linewidths of ~ 50 to100 mev (red curve) along with homogeneous isolated single dot luminescence linewidths of few µev (blue spectral emission line). Such high resolution spectral maps are indeed necessary to observe associated line shifts from charged excitons and multi-excitons that are on the order of a few mevs. 2.3 Photoluminescence With non-resonant laser excitation into the quasi-continuum of the InAs wetting layer, excitons are created when electrons are excited from the valance band to the conduction band, leaving behind holes. This excitation energy is created using a Ti: Sapphire laser operated in CW mode ( nm). After relaxation of the electron hole pairs to the lowest available energy states, recombination of the electrons and holes generates photons that can be used to map the charge and spin states of the QDs; this

32 32 process is defined as photoluminescence (PL). The detection of photoluminescence is made using Princeton Instrument s Trivista triple grating spectrometer with a maximum resolution ~0.006 nm (at 600nm) and 1100 g/mm in triple additive mode along with the CCD detector of more than 20% quantum efficiency over the wavelength range of 200 to 1050 nm. Furthermore, samples were kept at cryogenic temperatures using Advanced Research System s closed cycle cryostat to keep vibrations well below 5 nm and reduce phonon-assisted scattering events. Beyond the basic photoluminescence measurements, to gain insight into various processes such as carrier spin and relaxation dynamics that take place within the CQD systems, polarization and time-resolved experiments are discussed in detail in the following chapters of this dissertation Coupled Quantum Dot Spectra Mapping the charge and spin states is possible due to bias maps, which are three dimensional contour plots as shown in Figure 2.6(a), which represents the applied electric field, spectral energy, and PL intensity along the x, y, and z coordinates respectively. In CQD bias maps, weak electric field dependent intra-dot transitions are observed similar to the single dot spectra due to quantum confined stark effect. More importantly and unique to CQDs, largely field dependent inter-dot transitions are observed, which are a main focus throughout the dissertation, as these have been an essential tool in exploring many physical properties associated with the CQD system. Signatures associated with the spectral lines in single QDs have been clearly identified

33 33 and presented in the literature [20,27]. Likewise spectral lines from direct transitions in CQDs can be recognized, similar to single QDs, which arise due to recombination of electron and hole pairs from the same dot. The direct neutral exciton can be readily identified from the CQD bias map as it extends towards higher electric fields and extinguishes beyond a field when the carriers ionize. Following along the energy relative 0 to the neutral exciton ( X ), 2 mev above, the singly charged exciton or positive trion ( X ) is identified. The onset of the negative trion ( X ) can be identified ~ below 6 mev of the neutral exciton when the ground state electron is resonant with the Fermi energy. Figure 2.6: (a) CQD bias map with large field dependent inter-dot (indirect) excitons along with intra-dot (direct) transitions highlighted to identify 0 X, X, and X exciton states. Owing to the asymmetric nature of the CQD with a smaller top dot, results in anticrossing signature are circled along with the characteristic X pattern. (b) Schematics of the large field dependent indirect transitions that red shifts in energy with applied field.

34 34 In addition to these characteristic signatures that arise from Coulomb interaction energies, unique to CQDs are the inter-dot exciton states with large Stark shifts that red shift in energy due to the applied field as shown in Figure 2.6(b). The asymmetric nature of the CQDs that arise due to strain-enhanced nucleation, results in a smaller top dot and a larger bottom dot [28]. Thus, hole level anti-crossings [Figure 2.6(a)] are observed due to tunnel coupling of hole states as the hole wave function becomes delocalized over both dots. The characteristic X pattern can be observed at the rectangular highlighted area within the positive trion due to the anticrossing that takes place in both initial and final states, along with crossings. Details of the trion fine structure are discussed in section Quantum Ring Luminescence Analogous to QDs, carrier confinement and prevailing atomistic behavior of quantum rings has been widely discussed in the literature [29,30,31]. QRs exhibit carrier confinement in a periodic channel, along with unique dynamical properties due to its distinctive crater geometry at the middle region. Advancements in fabrication have allowed for the growth of low density semiconductor rings. Basic PL measurements on InGaAs quantum rings were obtained through collaboration with the University of Arkansas; for the contributions made on luminescence measurements, this resulted in the first peer-reviewed journal publication from our group [32]. The ring shaped InGaAs/GaAs nanostructures grown on GaAs substrate at different substrate temperatures, namely 350 C and 450 C, were excited with a CW,Ti-

35 35 Sapphire laser with 750 nm for the ensemble with 750 nm and 780 nm for single rings. The PL spectra for samples, (a) 350 C and (b) 450 C, revealed the InAs wetting layer and the quantum ring ensemble as depicted in Figure 2.7. Comparison of PL spectra of the wetting layer and the ensemble for samples grown at 350 C and 450 C, demonstrated that ensemble energy is similar for both samples, as opposed to the wetting layers. Due to the alloying of Ga in the crystallization process and thinner WL, luminescence from the 350 C sample shifted towards a lower energy as compared with the sample grown at 450 C. To observe single ring PL spectra, the spectrometer slit width was narrowed down and the CCD was binned such that a narrow vertical region was selected, which demonstrated a method for confocal spectroscopy as there were no sub-micron apertures to probe. Comparison of single ring spectra expresses the fact that the single rings reside at relatively higher energies in the low temperature grown sample [Figure 2.7(a)], while relative lower energy is favorable for the high temperature grown sample as depicted in Figure 2.7(b). Although a dramatic energy shift in ring energies was not observed, this may still account for the size difference that has been observed through AFM images for samples grown at 350 C and 450 C. The low energy shift in the single ring emission indicates that even after a capping procedure similar to that discussed in section 2.2, there may be an equilibrium size or shape for the quantum ring growth.

36 36 Figure 2.7: Photoluminescence from ring-shaped nanostructure samples formed at (a) 350 C and (b) 450 C (After J. H. Lee et al., Cryst. Grow. Des (2008) [32]). 2.4 Resonant Excitation In typical PL experiments, with non resonant excitation into the quasi-continuum wetting layer, electron and hole pairs are generated, which relax down to the ground state typically through energy transfer to the lattice vibrations; the recombination gives rise to observed PL. In resonant excitation, absorption takes place only when the excitation energy is resonant with an allowed quantized energy of the CQD, which can either be direct or indirect absorption. A schematic representation of the resonant excitation

37 process is illustrated in Figure 2.8, where it has been utilized in some of the discussed experiments in sections 4.6 and of the dissertation. 37 Figure 2.8: Schematics of the basic resonant excitation process.

38 38 Chapter 3 Temporal Response of the Optical Field in CQDs Semiconductor heterostructures have been used extensively for many optoelectronic applications. However, rapid progress has been focused on quantum dots as it integrates with many new technological applications. In particular, coupled quantum dots (CQDs) have revealed new possibilities due to their controllability in inter dot tunneling interactions. For example, in high frequency experiments, such as differential transmissions and electric field oscillations, complicated and specialized equipment is necessary to generate electric field modulations. In this chapter we focus on a novel approach to this by way of manipulating the applied electric field, through optical pumping of CQD wetting layers (WLs), and extracting its temporal response. 3.1 Photovoltaic Effects in Semiconductors Photoluminescence (PL) is one of the most important tools that has been used to investigate light matter interactions, which takes place in bulk and quantum confined semiconductor structures, through carrier recombination as noted in section 2.3. Besides PL measurements, there has also been considerable amount of work reported on photocurrent (PC) spectroscopy as a result of carrier ionization and tunneling. For example, in QD structures, device engineering (through GaAs n-i diodes) has enabled a novel approach to read-out information from a two-level system [33].

39 39 Additionally, early reports have indicated that carrier ionization in semiconductors results in potential shifts due to opposing effects between photo-voltage and build-in potentials [34]. Similarly, with precise laser excitation we can generate an optical field within the self-assembled InAs/GaAs CQD device structure and observe a shift in the field strength through PL spectra. Through laser excitation above the WL energy (~1445 mev) of the CQDs, e-h pairs can be generated and later recombine via direct or indirect transitions as shown in Figure 3.1(a), However, with an applied electric field, charges can build up and create an optically generated electric field, Figure 3.1(b). The charge accumulation will introduce an opposite field that results in a shift in PL spectra as depicted in Figure 3.1(c). Figure 3.1: (a) Band edge diagram of the CQD Schottky diode along with direct and indirect transitions. (b) Tunneling of electrons (holes) from top-t (bottom) to bottom-b (top) and creation of the optically generated electric field (OGEF). (c) OGEF associated shift in PL spectra monitored through indirect exciton (After K. C. Wijesundara et al., Mater. Res. Soc. Proc. 1208E, 1208-O05-02 (2010) [35] and M. Garrido et al., Appl. Phys. Lett. 96, (2010) [36]).

40 40 In addition, excitation above the WL energy has been shown to generate a shift of a few tenths of a Volt in the field dependent spectra of the CQDs as opposed to excitation below the WL energy [36]. However, a quantitative measure of the optical field generation rate was not taken into consideration. Therefore, to further the dynamics of the optically generated electric field, time-resolved experiments have yet to be explored. 3.2 Quasi-Pump Probe Experiment With a continuous wavelength (CW) laser excitation source, an optical field can be generated to compensate and overcome the applied electric field due to carrier interactions that take place within a CQD. As the spatially indirect exciton is much more sensitive to the applied electric field due to the large Stark shift of 0.74 mev/kv.cm -1, indirect exciton recombination can be used as a probe to measure the optical field within the device. Through time-resolved spectroscopy we can gain insight into the dynamics of the optically generated electric field within the CQD device. In order to measure the dynamics of the optical field, we modulated the optical field within the CQD and measured both rise and decay characteristics. To modulate above the WL energy and create optical field oscillations in the CQDs, we also had to continuously monitor the indirect exciton PL emission throughout the experiment. Therefore, to fulfill the above requirements a two color experiment (or a quasi-pump probe type experiment) was designed to quantify the optical field modulations within the CQDs. A modulated (250Hz), diode-pumped, solid-state (DPSS) laser was used as the pump source (532 nm), which generated the optical field through absorption above the

41 41 WL energy, while the continuous indirect PL was generated by below WL absorption. The schematic of the experimental setup is depicted in Figure 3.2. An avalanche photo diode (APD) - Perkin Elmer single photon counting module (SPCM) - was used in conjunction with a Stanford Research Systems, SR-400 photon counter to measure the photon counts. Figure 3.2: Schematic representation of the quasi-pump probe setup. A modulated (250Hz) diode pumped solid states (DPSS) laser is used to generate the optical field while a CW laser is used to probe and monitor the indirect exciton (After K. C. Wijesundara et al., Mater. Res. Soc. Proc. 1208E, 1208-O05-02 (2010) [35]). The highly field dependent spatially indirect exciton was monitored using a standard micro-pl setup. Here the excitation was provided using a near IR laser energy below the WL, which also acted as the probe. Next, to measure both the decay and rise time of the optically generated electric field (OGEF), we implemented the gated photon counting technique to identify photons of interest within a specific time interval through

42 42 the SPCM. With this technique, photons that are outside of the interested time interval can be discriminated. Figure 3.3 illustrates the process by which the gated photon counting is executed along with a sample spectrum. As demonstrated in Figure 3.3(a), once the optical field generation is triggered, and at a specified delay DLn, and at a gate width W, the SPCM only counts the photons within this gate time. Figure 3.3: Gated photon counting technique. Modulated laser excitation (250Hz) energy above WL and corresponding charging behavior of the optically generated electric field (OGEF) schematically shown in the top figure. (a) Gated photon counts measured by single photon counting module (SPCM) for different delay times (DL) with a fixed gate width (W). (b) Sample spectrum for a specific delay time and gate width (After K. C. Wijesundara et al., Mater. Res. Soc. Proc. 1208E, 1208-O05-02 (2010) [35]).

43 43 With triggered laser pulses, an equal number of gates are enabled at each count period, and for a specific gate delay, the peak wavelength of the spatially indirect exciton is monitored through the spectrometer scan as shown in Figure 3.3(b). Next, we varied the gate delay relative to the trigger of the laser pulse and repeated the above gated photon counting technique. For subsequent delay times (DL0, DL1 DLn), spectra were plotted as a function of photon count vs. energy as illustrated in Figure 3.4. Figure 3.4: Normalized relative photon counts corresponding to different delay times and a fixed gate width analogous to the decay of the optically generated electric field (OGEF) (After K. C. Wijesundara et al., Mater. Res. Soc. Proc. 1208E, 1208-O05-02 (2010) [35]). The peak photon count energy for each spectral scan as illustrated in Figure 3.4 was extracted and tabulated along with the corresponding delay times (Table 3.1). The entire time behavior of the OGEF decay was obtained through repeating the above procedure. Additionally, photon counts were measured with different gate widths when

44 44 determining the decay time constant in order to eliminate any possible influence of the gate width on the SPCM counts. Throughout the data analysis the peak counts had a signal to noise (S/N) ratio of more than 10. Since the S/N ratio was fairly high, a background subtraction or synchronous photon counting technique (analogs to lock-in detection with analog signals) was not required throughout the experiment. Table 3.1: Extracted photon peak energies from gated photon counting technique Delay DLn (ms) Peak energy (mev) Through the use of the positive edge of the modulated laser pulse and the gated photon counting technique, the experiment was extended to measure the generation rate of the OGEF. 3.3 Temporal Response To understand the charge carrier dynamics associated with the optically generated field within the CQD system, a photon count rate was necessary. Therefore, to obtain the temporal response, the peak photon counts and associated delay times were measured. For each of these individual data points the standard error was the source of error. Figure

45 illustrates the plot of individual peak photon counts as a function of the delay time; the data were fitted to a first order exponential decay function. From 8 sets of decay plots the average decay time constant was calculated to be μsec [35]. The negative edge of the laser pulse that triggered the OGEF is also shown in the inset of Figure 3.5. The negative edge of the laser pulse had a turn-off time of 2 3 μsec, which was much shorter than that of the decay rate of the OGEF. Thus, convolution effects were minimal on the measured temporal response. Figure 3.5: Temporal response of the optically generated electric field (OGEF). The decay of the OGEF is measured from the plot of photon peak energy with time delay in the gated photon counts. The inset shows the turn-off of the negative triggering laser pulse relative to the decay of the OGEF (After K. C. Wijesundara et al., Mater. Res. Soc. Proc. 1208E, 1208-O05-02 (2010) [35]). The optically created electric field is generated from the ionized electrons and holes that remain within the CQD device. Hence, the induced optical field will mainly

46 46 depend on the carrier trap densities at impurity sites. It also can depend on the carrier generation, tunneling, and recombination rates. However, for bulk GaAs and GaAs heterostructures, carrier generation, tunneling, and recombination rates have been reported to be on the order of a few hundred pico seconds up to the order of nano seconds, both in theory [37,38] and in experiments [39]. Therefore, the observed longer decay time of the optically generated field ( μsec) [35] can be attributed to the excitons ionizing and carriers trapping and remaining at impurity sites as well as at material boundaries within the device region of the Schottky structure. As depicted in our CQD device structure (Figure 2.4), these sites can be located at, for example, the AlGaAs/GaAs interface, doped or intrinsic GaAs interface, or the InAs WLs. To investigate the viability of the measured decay time of the optically generated electric field we also investigated its power dependence behavior. For this experiment the CQD was excited from above the WL laser excitation energy with two different powers of P (0.3 mw) and 2P (0.6 mw) respectively. The laser excitation power dependence of the decay of the optically generated field is depicted in Figure 3.6. With increased laser excitation power density, more and more electron hole pairs contributed to the OGEF. This can be observed through the photon peak energy variations associated with the first few data points (delay times ~ 0.0 μsec) corresponding to the laser powers of P and 2P as presented in the main plot of Figure 3.6. Conversely, the separation of the data points becomes smaller with increased delay time, which can be attributed to the charge-carrier tunneling out of the device region of the CQD structure.

47 47 However, from the inset of Figure 3.6, a linear separation between the photon peak energy for the two different laser excitation powers (P, 2P) indicated that the decay rate of the OGEF remained within the range of μsec [35]. Furthermore, this exemplifies that the number of electrons and holes created within the device does not affect the response time of the optically generated electric field. The power dependent measurements also indicate that the observed longer lifetime for the decay rate of the OGEF is mainly caused by the trapping of charge carriers at impurity sites within the Schottky diode system, or due to the trapping at material boundaries. Next, to determine the creation of the OGEF and its generation rate, the same experiment was carried out as discussed in section 3.2. Figure 3.6: Decay of the optically generated electric field with laser excitation above the WL for two different powers of P (0.3 mw) and 2P (0.6 mw). Inset shows the semilogarithmic plot of the power dependence (After K. C. Wijesundara et al., Mater. Res. Soc. Proc. 1208E, 1208-O05-02 (2010) [35]).

48 48 With laser excitation above the WL and carrier relaxations, an optical field can be generated. Hence, as we would expect a faster generation rate of the OGEF, the rising edge of the modulated laser pulse was considered and measurements were carried out with shorter, peak photon time delays (DL0, DL1 DLn). The resulting faster generation rate of the optical field and its behavior are represented in Figure 3.7. From the data analysis it was evident that the generation rate of the optically created electric field does seem to follow the rising edge of the modulated laser pulse. Hence, the generation rate of the OGEF is limited by the resolution of the experimental setup, which is equivalent to the rise time of the laser pulse (7 8 μsec) [35]. Figure 3.7: Generation rate of the optically created electric field along with the rising edge of the modulated laser pulse (After K. C. Wijesundara et al., Mater. Res. Soc. Proc. 1208E, 1208-O05-02 (2010) [35]).

49 49 However, the observed results signify that the OGEF has frequencies in the order of the MHz range, which are more applicable to electrical field modulating devices as opposed to the OGEF decay that falls within the khz range. 3.4 Chapter Summary Besides the use in spin manipulation and quantum information processing schemes, CQDs can be used in many opto-electronic applications. The feasibility of such an application was studied in this chapter. Using a non-resonant excitation above the WL energy, an optically generated electric field was identified within the CQD structure as described in the literature [36]. Using a gated photon counting technique, the associated temporal response of the OGEF was measured using a modulated laser excitation with energy above the WL, while continuously monitoring the PL through a CW laser that was below the WL energy. We observed a relatively longer decay time on the order of μsec [35] for the temporal response of the OGEF. This can be related to the trapping of carriers at material interfaces and impurity sites and was consistent with carrier lifetimes in III-V materials. Experiments associated with the variations in the laser power signified that the decay rate of the OGEF does not have an influence on the number of charge carriers generated within the device. The onset of the optically generated electric field was limited by the temporal resolution of the experiment (2.5 μsec) [35]. The observed results of the generation rate of the OGEF yielded a frequency response in the order of the MHz range, which can provide future applications for fast, non-contact, electric field modulation techniques. Results that have been presented in this chapter,

50 which were associated with the temporal response of the optically generated electric field in CQDs, are the original published work of Wijesundara et al., [35]. 50

51 51 Chapter 4 Electric Field Controlled Spin Interactions Recombination of electron-hole pairs from various excitonic states within the QD gives rise to PL and via bias maps on which we are able to identify various charge states associated with the CQD structure. Thus, PL experiments ensure identification of optical charge generation. However, for various applications, including quantum information processing, the ability to generate and control the spin states of excitons has attracted considerable attention. Optical pumping with circularly polarized laser excitation, along with spin manipulation, can be attained in the fine structure of the exciton states. In the strong quantization axis, degeneracy of the hole spin projection in sublevels is lifted due to the electron and hole exchange interaction that has been widely discussed in the literature [40]. By far the most attractive feature that differentiates the CQDs from single QDs is the strong electric field dependence of the neutral and singly charged indirect exciton states. The author s published, novel results on the electric field tunable exchange interactions [41], and spin effects on singly charged states [42], along with the ground state hole molecular effects on the inter-dot exchange interaction [43] are presented in this chapter.

52 Optical Orientation In charge tunable QDs, many efforts have been undertaken to investigate optical pumping of excitonic states through polarization-resolved measurements to determine correlations between excitation and polarization sensitive luminescence. Therefore, in order to better understand spin relaxation processes and probe the carrier spin states in CQDs, optical orientation techniques were utilized. In principle, the optical orientation approach demonstrates the angular momentum conservation between light and the crystal nanostructure. With resonant or non-resonant circular polarized laser excitation corresponding to either right or left circularly polarized light ( or ), photons of angular momentum of 1(units of ) are attained. When the CQDs are excited with such polarized excitation it conserves the angular momentum by producing photogenerated electron hole pairs while conserving the total spin. In the direct band gap semiconductor CQDs, electron states in the conduction band are twofold degenerate with a total angular momentum of J 1/ 2. The valance band hole states with the associated p-type Bloch wave character demonstrates fourfold degeneracy that gives rise to a total angular momentum of J 3/ 2 as illustrated in Figure 4.1. The angular momentum hh projections corresponding to the twofold degenerate heavy holes m 3/ 2 and the lh twofold degenerate light holes m 1/ 2 provide the sub bands related to the heavy and j light hole states. Furthermore, due to the compressive strain corresponding to the lattice mismatch between InAs and GaAs materials, and the structural confinement, the light hole sub band is shifted in energy and the heavy holes are predominant in the low energy j

53 states. Thus, the recombination of excitons comprising electrons and heavy holes, in agreement with optical transition selection rules, gives rise to the circularly polarized light of or as depicted in Figure Figure 4.1: Schematic representation of the optical orientation process. With circular polarized light, specifically defined spin orientations of the electrons and holes are attained and identified in agreement with optical selection rules and device characteristics. Furthermore, detecting the orientation of the emitted light also reveals the associated spin states of the electron and hole pair. Measuring the luminescence polarization, spin states of different excitons can be investigated through optical pumping as discussed above. To gain insight into the spin dependent interactions, we consider elementary charged excitons. Excitation into the quasi-continuum wetting layer with circularly polarized light would essentially generate electron and hole pairs with an electron spin of 1 and heavy hole spin of 2 3 that 2 conserves the angular momentum of 1. Some of the carriers would then relax and become trapped inside the QDs. However, in the relaxation process, spin of 1 2 electrons and unpolarized holes can prevail due to the relatively fast hole spin relaxation rate arising from the spin-orbit interaction within the valance band [44] of the confined

54 structure. Therefore, if the electron predominantly remains in a spin of 54 1 configuration, 2 0 neutral exciton ( X ) luminescence would be expected to be equivalent to the initial circularly polarized excitation ( ) as shown in Figure 4.2(a). With an initial ground state heavy hole, polarized excitation can create two paired holes in the positively charged exciton [positive trion ( X )] configuration [Figure 4.2(b)]. The expected PL polarization can be determined from the spin-down electron that results in the same helicity as the excitation. Figure 4.2: Expected luminescence from circularly polarized excitation corresponding to (a) neutral exciton, (b) positively charged exciton, and (c) negatively charged exciton with associated spin configurations. Optically pumping an initial isolated electron will result in a negatively charged exciton [negative trion ( X )] state as depicted in Figure 4.2(c) where the PL emission can be predicted from the hole spin state. However, due to efficient hole relaxations and

55 55 paired electron spins, the expected luminescence will be unpolarized. Beyond the expected luminescence from basic exciton configurations, experimental measures have provided further insight into the polarization effects, including polarization signatures associated with different charge states in single QDs that have been widely discussed in the literature [45]. To understand these observed results of exciton luminescence, the electron and hole exchange interactions that arise due to the structural anisotropy of the crystal is discussed in the next section. 4.2 Exchange Interaction and Exciton Fine Structure To better understand the origin of the expected polarized luminescence from exciton states, fundamentals of the electron-hole exchange interaction is explored. Qualitatively, the electron and hole exchange interaction arises due to the strain field that is present in the CQD structure. This lifts the heavy hole and light hole degeneracy along with the inversion asymmetries in the QD potential [46]. The exchange Hamiltonian can be presented along with group symmetry considerations as [47,48]: H EX 20 I zs z 1( I xs x I ys y ) 2 ( I xs x I ys y ) H0 H1 H2 (4.1) Where S S, S, S ) and I I, I, I ) denotes the total electron and hole spins ( x y z ( x y z respectively, and corresponding exchange splitting strengths are represented by. The isotropic part of the exchange interaction denoted by the first term, H 0 in the Hamiltonian, splits the fourfold degenerate exciton ground state by ~ 100eV, into two

56 doublets with total spins of 1 and 2 respectively as schematically illustrated in 56 Figure 4.3. The doublet with total spin of 1 is termed as a bright exciton as it couples with the light field conserving the angular momentum. The dark exciton (total spin of 2 ) results in non- radiative processes but is accessible through mixing with bright excitons [25]. The second term in the Hamiltonian ( H 1) denotes the anisotropic exchange energy corresponding to the bright excitons that splits the doublet 1 due to lowering the confinement symmetry (Piezoelectric effects [49,50]). This is opposed to the already lifted dark state doublet [51,52] 2, (Hamiltonian H 2 ). Thus, the circularly polarized x y excitation ( ) mixes the bright states into linearly polarized states (, ) corresponding to the anisotropic exchange interaction and splits them into a linearly polarized doublet (~ 10 ev). Figure 4.3: Schematic representation of the exciton fine structure due to exchange interactions.

57 57 When exchange interaction effects are considered, further insight can be obtained for the exciton states presented in Figure 4.2. The unpaired electron and hole in the neutral exciton, experiences a strong anisotropic exchange energy that wipes out the polarization memory resulting in a positively polarized luminescence. With two holes and an electron, the hole spins cancel out in the positive trion and the exchange energy is diminished, resulting in a positively polarized luminescence. Similarly for the negative trion with two paired electrons and a hole, the degree of polarization mainly depends on the spin configuration of the hole singlet state as the exchange energy is eliminated due to total spin zero electrons. As such, due to the anisotropy, the expected polarized luminescence from exciton states are in clear agreement with reported experimental observations [45]. 4.3 Polarization-Resolved Photoluminescence A polarization-resolved photoluminescence setup is constructed by introducing linear polarizers and liquid crystal retarders to the basic PL experiment. Initially linear polarized light is created by sending the CW laser beam through the linear polarizer with energy above the quasi-continuum wetting layer. Next, the desired circular polarized light necessary to excite the CQDs is generated using liquid crystal retarders. By varying the applied voltage given to the D3040 liquid crystal retarder, its effective birefringence and hence retardance can be varied, which is used to generate a phase shift of /4 or 3/4 to create or circularly polarized light. After the recombination process, the emitted light is sent through an analyzer system consisting of a second liquid crystal retarder and

58 a linear polarizer. This process verifies for both and 58 helicities and evaluates the degree of circular polarization of the emitted light that is dispersed by a 3-stage spectrometer and detected through a LN 2 cooled CCD as illustrated in Figure 4.4. To gain insight into the polarization signatures through measuring the rate at which unpaired photo-generated charge carrier spin flip occurs, the degree of polarization is determined from Equation (4.2) P ( I ( I I I ) ) (4.2) Here I ( I ) represents the intensity of ( ) polarization under polarized excitation. By varying the applied electric field given to the Schottky photodiode, polarization signatures associated with different exciton states that arise from the embedded CQDs can be monitored. Figure 4.4: Polarization-resolved photoluminescence setup to measure the degree of polarization.

59 Spin states of the excitons are denoted by B, T q X, with spin up or down electrons (, B T 59, ), holes (, ) in the bottom (B) or top (T) dot along with charge (q) throughout this chapter. 4.4 Electric Field Tunable Exchange Interaction As discussed in section 4.2, polarization-resolved PL results on neutral and singly charged exciton states arise as a consequence of anisotropic exchange interaction [45]. These results further exemplify that the polarized emission is uniquely determined by the unpaired carrier spin configurations. As a result one may alleviate the anisotropic exchange interaction effects through exclusion of the overall spin. A unique feature of the CQD structure is its ability to spatially separate the electron and hole as a function of an applied electric field as schematically depicted in Figure 4.5. This technique allows effective control of the overall exchange interaction rather than the spin elimination. In the n-doped CQD system, varying the electric field can attain hole levels in resonance, where the tunnel coupling of hole states results in the formation of molecular states that can be observed as unique anti-crossing signatures. The overlap between the electron wave function and the symmetric hole wave function creates the direct transitions, while the overlap of the electron wave function with the asymmetric hole wave function results in the generation of the indirect transitions.

60 60 Figure 4.5: (a) Schematic representation of direct and indirect excitons as a function of an applied electric field along with relevant spin configurations. Band edge diagrams shown in (b) and (c) represent the CQDs in a Schottky diode structure with larger bottom dot (B) and smaller top dot (T). The variation in the band edge diagram at high electric fields (b) shows hole level resonances along with electron wave function (blue) and symmetric (direct), anti-symmetric (indirect) hole wave functions (red). At low electric fields (c), overlap between the electron and the anti-symmetric hole wave function is decreased and more atomic-like behavior can be observed. At high electric fields, the hole levels become resonant, leading to enhancement of the symmetric and anti-symmetric molecular hole wave functions [Figure 4.5(b)]. Away from the anti-crossing region the holes can be predominantly localized on either the top or bottom dot, leading to indirect or direct excitonic states as schematically illustrated in Figure 4.5(c). Thus, varying the electric field leads to the tuning of the excitonic emission from inter-dot to intra-dot. Therefore, spatial separation of the electron and the hole provides a distinctive method to control the overall exchange interaction.

61 61 Next, polarization-resolved PL measurements were performed on neutral exciton states in order to determine the degree of circular polarization according to Equation 4.2. Using a basic PL spectral map, the different excitonic state spectral lines that are inherent to the CQD emission as depicted in Figure 4.6(a) were recognized, especially inside the squared region, where the indirect and direct transitions associated with the neutral exciton state were predominant. Figure 4.6(b) represents the polarization dependent photoluminescence spectra for the neutral exciton, and on the top, the polarization memory analysis from each point of the spectra denoted by dashed lines is depicted in Figure 4.6(c). From the analysis of the polarization dependent spectra it is evident that the degree of circular polarization memory corresponding to the direct transition demonstrates relatively lower polarization percentage values due to the strong exchange interaction in its direct configuration. At the anti-crossing region ~ kv/cm, the degree of circular polarization displays similar polarization percentage values for both indirect and direct transitions as evident by Figure 4.6(c). In the n-doped CQDs, molecular symmetric and anti-symmetric hole wave functions corresponding to the hole level molecular state observed at ~ kv/cm, have comparable amplitude in both dots. Therefore, direct configuration of the neutral exciton demonstrated an increased polarization percentage, whereas the polarization memory associated with the indirect configuration exhibits a reduced value. As the applied electric field is reduced, the wave function amplitude of the hole is shifted, which involves a change in the overlap of the electron-hole wave functions. This change results in reduced exchange interaction effects, which cause the indirect exciton transition to provide an increased degree of circular

62 62 polarization, manifested from the 4nm barrier CQD sample data, as depicted in Figure 4.6. Since the degree of circular polarization is influenced by the anisotropic exchange interaction, by experimentally tuning the electric field one can control the overall electron-hole exchange interaction [41]. Figure 4.6: (a) Photoluminescence spectra from the 4nm CQD structure. Spectral lines associated with exciton states are clearly indentified, including the inter-dot and intra-dot exciton states along with the anti-crossing signature highlighted in the squared region. (b) Polarization-resolved PL spectra for the neutral exciton state near anti-crossing region is acquired through excitation to the quasi-continuum wetting layer with σ+ polarized excitation and detected for both σ+ and σ polarizations. (c) The degree of circular polarization as a function of an applied electric field evaluated from Equation 4.2 corresponding to the direct (open squares) and indirect (solid circles) exciton states (After K. C. Wijesundara et al., Mater. Res. Soc. Proc. 1117E, 1117-J04-08.R1 (2009) [41]). Electric field tunable polarization-resolved measurements were extended to similar CQD structures with different barrier heights of 4 nm and 2 nm respectively.

63 63 Experimental parameters including laser power were kept constant while exciting into the quasi-continuum of the wetting layer. For the two different barrier CQD structures, hole level anti-crossings were observed at different applied electric fields due to structural variations and different tunneling strengths [53]. As such, hole level anti-crossing signatures were identified at kv/cm and kv/cm respectively for the 2 nm and 4 nm barrier CQD structures. To signify comparable results on the polarization-resolved PL, measurements were presented relative to the anti-crossing point of the two CQDs. Difference in the degree of circular polarization between the indirect and direct exciton states of the neutral exciton as a function of relative electric field is depicted in Figure 4.7 for the 2 nm (circles) and 4 nm (squares) barrier samples. Figure 4.7: Difference in the circular polarization percentage as a function of relative electric field, relative to the inter-dot and intra-dot neutral exciton states. At low relative electric fields a higher degree of circular polarization memory can be observed with 4nm barrier (squares) as opposed to the 2nm barrier (circles) CQD structure. This common trend in the degree of circular polarization is a consequence of reduced wave function overlap and the electron-hole exchange interaction with increase in the barrier separation (After K. C. Wijesundara et al., Mater. Res. Soc. Proc. 1117E, 1117-J04-08.R1 (2009) [41]).

64 64 Overall, the difference in the degree of polarization increase as a function of relative electric field with increasing barrier separation between the top and the bottom dot in the CQD structures is evident by the plot. For a given relative electric field, as the barrier between the top and the bottom dot is reduced, the overlap between the electron and the hole wave function increases due to the higher tunneling strengths. This results in a relatively higher exchange interaction for the lower barrier CQDs. These barrierdependent, polarization-resolved results further reveal the electric field controllable electron-hole exchange interaction effects. 4.5 Spin Effects of Charged Exciton States When the electric field is further reduced relative to the neutral exciton anticrossing, luminescence intensity variations are observed along with additional spectral lines associated with other charge states as depicted in Figure 4.6(a). Below 40 kv/cm, singly charged positive trion luminescence is observed due to charge carrier tunneling. Key to the detailed polarization signatures is the identification of an X shaped pattern within the singly charged positive trion state, which contains both crossings and anticrossing signatures [54]. This characteristic pattern can be identified from the higher energy lines of the positive trion and determining the 4 recombinations between the initial and final states as illustrated in Figure 4.8. The spin fine structure is observed as a result of exchange interactions and the detailed spectral pattern of the positive trion arises as a combined result of tunneling, exchange interaction, and the Pauli Exclusion Principle. The origin of the spin states associated with the fine structure splitting in the

65 optical spectra arises from kinetic hole-hole and electron-hole exchange interactions as discussed in the literature [25]. 65 Figure 4.8: Origin of the "X" pattern in the singly charged exciton state. (a) Four possible recombination paths from the initial charged exciton to the ground state hole level. (b) Basic singly charged exciton spectral recombination signature without tunneling or spin effects (After E. A. Stinaff, et al., Science 311, 636 (2006) [54]). In subsequent experiments, polarization dependent photoluminescence was utilized as a tool to probe the spin fine structure via detailed polarization signatures in singly charged positive trion states. Initially, the characteristic X pattern was identified as depicted in Figure 4.9(a) within the squared region where the spectra has been plotted relative to the intra-dot neutral exciton energy and anti-crossing electric field. In the zoomed region of the trion state, different spectral lines were identified from associated

66 spin states as illustrated in Figure 4.9(b), which is in agreement with results discussed in the literature [25]. 66 Figure 4.9: (a) Identification of the singly charged trion state. (b) Spin fine structure of the positive trion along with spin states of IEEE Nanotechnology 11, 887 (2011) [42]). XH and X L (After K. C. Wijesundara, et al., From the spin configuration associated with the positive trion state X patterned region, two spin states were identified as X H, X where the subscripts H, L correspond to L the relatively high and low energy states [42]. Polarization-resolved PL measurements were obtained in the fine structures of the singly charged positive trion. The degree of

67 circular polarization is evaluated according to Equation 4.2 and the observed circular 67 polarization percentage results for the spin states of X H, X are shown in Figure 4.10, L where the higher energy state revealed relatively larger circular polarization memory results as opposed to the low energy spin state. Figure 4.10: The degree of circular polarization for the two spin states XH and X L. From the above results, the lower energy state X L with the spin configuration of X,0, L can be thought of as a neutral exciton with a spectator hole in the top dot, hence the hole spins are not paired. This results in relatively higher anisotropic exchange energies similar to intra-dot exciton states, which gives rise to a low degree of circular polarization. Whereas from the higher energy state spin configuration of X,0,0 H, it is evident that the hole spin singlet states are formed and the degree of polarization depends on the unpaired electron, which results in relatively higher circular polarization percentages.

68 From the isotropic exchange interaction, the energy splitting associated with the spin fine structure of the singly charged positive trion state can be identified. Related spin 68 states are represented by X H X D X L X,0 and,0, H D D, L D respectively, for the lower and higher energy configurations of the spin fine structure doublet. The two spectral lines of the spin fine structure doublet are observed due to the high electric field dependent indirect transitions that arise from the associated spin configurations of the fine structure doublet and from the allowed recombination path via the electron and the hole in the top dot. In the spin fine structure doublet the electron and the top dot hole states have opposite spin configurations in agreement with the optical selection rules, which gives rise to the observed spectral lines as observed in Figure 4.11 whereas the energy splitting of the spin fine structure doublet is essentially determined from the isotropic exchange energy between the bottom dot electron and the hole states. However, bottom dot hole states exhibit either singlet (anti-parallel) or triplet (parallel) configurations with the top dot hole. Therefore, even without using a magnetic field, (which is normally used to mix the states and create dark exciton to be optically active), bright and dark exciton splitting can be measured directly via top dot hole state using optical techniques. Next, the degree of circular polarization was evaluated for the spin states X H X D,0, H D and X L X D,0, L D. From the circular polarization percentage results shown in Figure 4.11(b), an overall increase in the polarization memory can be observed for the fine structure doublet as a function of a relative electric field, relative to the intradot anti-crossing. Within the fine structure doublet, an applied electric field causes the

69 69 top dot hole to spatially separate and results in reduced exchange interaction energy. Therefore, the observed trend in circular polarization memory for the doublet is analogous to the inter-dot neutral exciton state as discussed in section 4.4 with a resident hole in the bottom dot. The inset in Figure 4.11(b) also indicates a relative increase in the degree of circular polarization memory for the fine structure doublet as a function of an applied electric field [42]. Moreover, this trend can be prominently observed through the difference in polarization memory for the doublet as depicted in the main plot of Figure 4.11(b). Figure 4.11: (a) X, X fine structure doublet of the positive trion which arise due to H D LD the isotropic exchange interaction along with corresponding degree of polarization memory results (b) (After K. C. Wijesundara, et al., IEEE Nanotechnology 11, 887 (2011) [42]). From the above plot it is evident that the circular polarization percentage is higher for the X LD state as compared to the higher energy component X H D. These observed

70 70 results may arise due to the mixing with the dark states which causes an asymmetry in polarization memory. To further the effects of the spatial separation of the hole states in the spin fine structure doublet, barrier dependent polarization-resolved measurements were performed. The observed degree of circular polarization memory results for the 2 nm, 4 nm, and 6 nm, barriers between the top and the bottom dots of the CQD structure is depicted in Figure As the barrier separation is increased the hole in the top dot becomes more spatially separated from the bottom dot electron and hole, and this tends to reduce its overall effect to the electron-hole exchange interaction. This creates a more intra-dot neutral exciton-like configuration that depicts relatively higher electron-hole exchange interaction energy at low relative electric fields for the spin fine structure doublet. This is indeed a singly charged positive trion with two holes in separate dots. Moreover, with relatively low applied electric fields, the degree of circular polarization percentage is reduced for the higher barrier CQD structures as evident from Figure When the top dot hole becomes more atomic-like it has reduced effects on the bottom dot electron-hole pair due to reduced tunneling effects between the two dots. Therefore, both barrier separation and applied electric field can be tuned to effectively control the overall spin interactions in the spin fine structure of the singly charged positive trion state.

71 71 Figure 4.12: Barrier dependence of the degree of circular polarization on X LD as a function of relative electric field (After K. C. Wijesundara, et al., IEEE Nanotechnology 11, 887 (2011) [42]). 4.6 Control of the Electron-Hole Exchange Interaction Through polarization dependent photoluminescence spectra, spin dependent interactions in CQDs were investigated along with the identification of excitonic and biexcitonic states as discussed in section 4.4. Especially in biexciton-exciton cascade paths, exchange splitting results are distinguishable through which-path information [55] due to the anisotropic exchange interaction that mixes the spin states and splits the resulting states into a linearly polarized doublet. By spatially separating the electron and the hole we can eliminate the exchange splitting as manifested from the results presented in section 4.4. However, as we further tune the excitonic emission from intra-dot to interdot, the electron-hole wave function overlap reduces due to the largely eliminated exchange interaction that causes an increase in the circular polarization memory up to 42 kv/cm [43] (top panel of Figure 4.13).

72 72 As the exciton energy separation was increased with an applied field, a clear reduction in the polarization percentage of the indirect exciton was observed ~ 37 kv/cm, which again increased beyond the singly charged positive trion state, according to the top panel in Figure Polarization-resolved PL measurements were extended for other CQDs with different barrier separations between the top and the bottom dot. Observed results further revealed the anomalous behavior in polarization memory that is consistent with any CQD system. This observed polarization memory dip was coincident with the onset of the positively charged exciton state. Figure 4.13: Polarization dependent photoluminescence spectra as a function of applied electric field that tunes inter-dot and intra-dot excitons by ~ 14 mev (as shown in the bottom panel) along with a dip in the circular polarization memory of the indirect exciton (depicted in the top plot) (After K. C. Wijesundara, et al., Control of the exchange interaction in indirect exciton states, Unpublished Manuscript (2012) [43]).

73 73 Intriguingly, the degree of circular polarization memory minimum appeared to be correlated with the single hole molecular resonance [Figure 4.14(a), (b)]. In each of the CQDs studied, the minimum of the dip occurred at an electric field where the single hole anti-crossing appeared. This is identified in the spectra by a pair of anti-crossings in the singly charged positive trion that is highlighted with a dashed circle [Figure 4.14(b)]. A possible mechanism for the circular polarization memory dip is schematically illustrated in Figure 4.14(c), (d). Figure 4.14: (a) Polarization memory dip coincident with ground state hole molecule. (b) Possible mechanism through mixing of hole states that enhances relaxation channels as illustrated in (c, d) (After K. C. Wijesundara, et al., Control of the exchange interaction in indirect exciton states, Unpublished Manuscript (2012) [43]). When a hole relaxes into the molecule at a specific applied electric field, it will initially be in a molecular state as shown in Figure 4.14(c). Then when an electron is added the energy levels are no longer in resonance, and do change corresponding to the coulomb interaction, which ultimately shifts the hole levels out of resonance [Figure

74 (d)]. Initially, having the hole in a molecular state, certain spin mixing relaxation channels may be enhanced, which results in a loss of circular polarization memory in coincidence with the ground state hole molecular level. Next, we observed the intra-dot spectral line at an electric field corresponding to the ground state hole molecular level as depicted in Figure 4.15 with linearly polarized excitation, and tested for both horizontal and vertical component PL. Figure 4.15: Linearly polarized doublet with splitting energy analogous to the anisotropic exchange energy (After K. C. Wijesundara, et al., Control of the exchange interaction in indirect exciton states, Unpublished Manuscript (2012) [43]). The splitting of the indirect exciton PL lines for horizontal and linear components were measured with the highest spectral resolution in the setup in order to eliminate any virtual line shifting artifacts. Due to the consequence of the anisotropic exchange interaction, which mixes pure states and results in a linearly polarized doublet, the energy splitting corresponds to the exchange energy was observed [Figure 4.15]. These results further confirm the regain of the anisotropic exchange energy at ground states hole

75 75 molecular level even though the electron and hole are spatially separated in the indirect states. As discussed earlier, being in this particular ground state hole molecular level may enhance relaxation through a polarization mixing excited state. If this is the case, it may be that as we change the relaxation dynamics by exciting resonantly, we might change the mixing. Polarization memory results of the inter-dot exciton at electric fields corresponding to the onset of the singly charge state were plotted as shown in Figure Figure 4.16: Variation of the minimum at the polarization dip as a function of laser excitation energy (After K. C. Wijesundara, et al., Control of the exchange interaction in indirect exciton states, Unpublished Manuscript (2012) [43]). To determine the outcome of the degree of circular polarization percentage, we conducted tests via different laser excitation energies from the quasi-continuum of the wetting layer and below. From the above figure it is evident that as the laser excitation becomes resonant, the minimum of the polarization dip can be eliminated. Furthermore, with polarization excitation energy of an optical phonon above the inter-dot exciton, the

76 polarization dip can be completely wiped out due to efficient relaxation channel that avoids relaxation via mixing of spin states Chapter Summary The primary focus of this chapter was to identify and control the electron hole exchange interaction in CQD systems through multiple techniques including applied electric field, barrier width control between the top and bottom dots, and resonant laser excitation energy. The spin dependent interactions in CQDs were investigated through polarization-resolved photoluminescence spectra, as it directly couples to the spin states of the carriers while conserving the angular momentum. The degree of circular polarization was used to measure the anisotropic exchange interaction which causes pure states to be mixed and causes a shift in degeneracy. Besides widely discussed spin elimination to identify exchange interactions, a novel technique was introduced to control the exchange energy by simply varying the applied electric field. In indirect neutral exciton states the electron and hole were spatially separated via an applied field, which resulted in a reduction in electron and hole wave function overlap. Because of this the exchange splitting energy was eliminated to a size comparable with the homogeneous linewidths of the optical spectra. An optically resolved spectral doublet was identified on the singly charged positive trion state due to the isotropic part of the exchange interaction. Observed results on the trion doublet were illustrated with the associated spin states. Interestingly, the spectator hole in the top dot of the singly charged state could be spatially separated with

77 77 the applied field and then attained exchange energy control. Barrier dependent polarization-resolved spectra further confirmed the control of the wave function overlap in the singly charged trion doublet. Extending the spatial separation of the electron and hole in the inter-dot exciton, it is viable to erase the lifted spin degeneracy. However, in resonance with the ground state hole molecular level of the positive trion, regain of the anisotropic exchange energy was observed via a dip in circular polarization memory. These observations were confirmed through linear polarized spectral splitting and were hypothesized to arise due to development during a mixing of excited states. With resonant laser excitation below the quasi-continuum energy, the polarization minimum was eliminated in agreement with the above assumption. The main results presented in this chapter are the author s primary work on electric field controlled anisotropic exchange interaction and spin effects on singly charged states through isotropic exchange energy, which resulted in two publications [41,42]. A third publication on controlling the anisotropic energy of inter-dot exciton associated with the ground level hole molecular states [43], is in preparation for submission, along with a book chapter on spin control in CQDs to be published in Nanoelectronic Device Applications [56] by the summer of 2012.

78 78 Chapter 5 Tunable Exciton Relaxations and Time-Resolved Spectroscopy Based on spin [57] and charge [58] effects on coupled quantum dot systems there have been many quantum information implementation schemes proposed and discussed in the literature. The interest in solid-state implementation of quantum information processing [59] is mainly justified in these devices by the expected long coherence time scales that are necessary for the manipulation of quantum states [60,61]. However, various interaction mechanisms present in electrons and holes, along with strong coupling to the environment [62], restrict the physical implementation of such schemes. Therefore, better understanding and controllability of the relaxation dynamics is preferred in CQD systems. Efforts have been taken recently to identify exciton dynamics at more molecular-like levels of ~ < 4 mev energy separations [63] between the direct and indirect neutral exciton. In this chapter we present novel experimental results and theoretical insight into the leading causes of exciton relaxation channels as well as electrical controllability in CQDs that extends from molecular to atomic-like levels; these results can be useful in quantum information processing, photonics, and optoelectronics applications.

79 Exciton Relaxation in Quantum Dots In bulk semiconductors, relaxation processes take place between the continuum of states. Due to the discrete nature of energy levels in low-dimensional systems, the relaxation processes are restricted [64]. However, as compared to real atoms, quantum dots have faster relaxation rates at cryogenic temperatures due to the strong coupling of excitons with the crystal lattice [65,66,67]. With PL spectroscopy, phonon interactions have also been determined via temperature dependence of the homogeneous linewidths as discussed in the literature [68,69,70]. Additionally, for cryogenic temperatures ( k T B L0 ) the linewidths are only directly related to acoustic phonon scattering because the optical phonon populations are inadequate to provide a significant thermal influence. In vertically coupled quantum dots with exciton energy separation of ~ < 32 mevs, the dominant scattering mechanism that limits the associated lifetimes is mainly due to acoustic phonons [71]. In addition to spatially-resolved techniques, time-domain measurements have proven to be useful in understanding characteristic transitions that take place in low-dimensional structures [72,73,74]. In the indirect exciton states of CQDs, carrier wave functions are spatially delocalized which reduces the wave function overlap and results in modified phonon interactions as a function of both the electric field and inter-dot separation. In addition to the phonon-mediated relaxation channels, indirect excitons also contribute to carrier tunneling to create other charge exciton states. Therefore, through tailored structural design, along with external electric field control, exciton relaxation channels in CQDs can be modified. This can be utilized to

80 achieve tunable lifetimes in specific excitonic states, a potentially useful feature for the applications of CQD systems Luminescence Intensity InAs quantum dots on a GaAs substrate that were epitaxially grown by the Stransky-Krastanov growth technique were used for the present study; the CQDs were attained by stacking two layers of such InAs QDs. As the CQDs were embedded in an n+ Schottky diode structure, electric field controllability was achieved through an applied field along the growth direction (z direction) as discussed in section 2.2. In our n-doped CQD system, by varying the electric field we attained hole levels in resonance at low enough forward biases, as the device itself has a relatively larger bottom dot compared to the top dot size. The tunnel coupling of hole states results in the formation of molecular states and we observe anti-crossing signatures as shown schematically in Figure 5.1. The overlap between the electron wave function and the symmetric hole wave function gives rise to the direct exciton (X D ), while the overlap of the electron wave function with the asymmetric hole wave function results in the formation of the indirect exciton transition (X I ). A detailed identification of direct and indirect excitons in terms of wave function overlap mechanism is explained in section 4.4. By varying the applied electric field we can then shift from a more molecular-like state to a more atomic-like state. This enables us to tune the coupled state energy splitting and in turn helps us to control the mixing between the direct and indirect excitons.

81 81 From the photoluminescence spectra that has been obtained through non-resonant CW laser excitation one can clearly identify both spatially direct exciton and indirect exciton states, along with the anti-crossing region due to tunnel coupling of hole states as depicted in the inset of Figure 5.1(b). Figure 5.1: Exciton states and intensity profiles. (a) Schematic representation of the exciton states. Rectangles represent the CQD strcuture with top (T) and bottom (B) quantum dots. The electron (e) tends to localize in the bottom dot while the holes (h) form molecular states (D and I), which results in both direct (X D ) and indirect (X I ) excitons. (b) Inset depicts the actual PL spectra associated with the anti-crossing region and the direct (X D ) and indirect (X I ) excitons, which are analogous to the schematic in (a). The main plot illustrates the intensity profile of the two excitons. With an applied electric field relative to the anti-crossing region, a decrease in indirect exciton intensity is prominent as opposed to the direct exciton intensity.

82 82 Furthermore, as the overlap between the envelop wave functions increases, the probability density of the associated recombination becomes larger. This development results in an increased number of photons emerging from a particular recombination process, which gives rise to the intensity profile associated with specific exciton states and will be explored first in this chapter. With a low applied electric field across the Schottky diode (or an increased field relative to the exciton anti-crossing) band edge becomes oriented in the forward bias direction. This allows the energy levels of the top dot to move out of resonance from tunnel coupled hole states. Hence the wave function overlap between the electron wave function and the anti-symmetric hole wave function tends to decrease with the presence of an applied electric field as opposed to the symmetric hole wave function schematically represented by the rectangles in Figure 5.1(a). With a decrease in wave function overlap we would anticipate a reduction in the photon emission from indirect excitons; the intensity will decrease as we increase the energy splitting between the direct and indirect exciton states. The individual intensity variations of indirect and direct excitons from the neutral exciton anti-crossing region up to relative electric field of ~ 1.1 kv/cm is illustrated in the main plot of Figure 5.1(b). From this figure we can clearly observe that the two excitonic branches, namely indirect and direct excitons, have equal relative intensities. The energy with which this happens is coincident with the minimum of the splitting energy between the two excitonic states according to the PL spectra depicted in the inset of Figure 5.1(b). This further exhibits that the radiative rates and populations are similar for both excitonic

83 83 states at the hole level resonance. Furthermore the excitonic decay times associated with the two excitonic states at this minimum splitting energy are almost identical as has been discussed in the literature [63]. With an applied electric field, a decrease in the indirect exciton intensity is anticipated in this region, as the overlap between the electron wave function and the asymmetric hole wave function reduces with forward applied bias. This can be clearly observed from the PL spectra corresponding to the indirect exciton as illustrated in the inset of Figure 5.1(b). From the latter effect we can deduce that the indirect excitonic lifetime should increase with the presence of an applied electric field. According to the wave function overlap model, photons emerging from the direct exciton recombination process should give rise to an almost constant intensity profile. However, as the applied electric field is reduced (more forward bias), fewer excitons are ionized creating an overall increase in the observed photoluminescence Intensity Modulations The intensity variations near the molecular states were consistent with reported results [63]. However, to gain insight into both molecular-like and atomic-like states the intensity profile of the neutral exciton states were measured and analyzed for the entire visible bias range. Such PL spectra are depicted in Figure 5.2.

84 84 Figure 5.2: Photoluminescence spectra of the exciton states as a function of energy separation between indirect and direct excitons, relative to the neutral exciton anticrossing. To compare between different quantum dot molecules and for consistency, plot axes are denoted as a function of energy separation (between the indirect and direct excitons relative to the neutral exciton anti-crossing) as opposed to the relative electric field. At higher energy separations, along with the neutral excitons, singly charged excitons (positive trions X + ) do appear in the spectra as illustrated in section 4.5. Furthermore, a clear increase in the overall intensity at higher energy separations is evident as discussed in the previous section. According to Figure 5.2, both indirect and direct exciton intensities are comparable at the anti-crossing region. With increased energy separation, the indirect exciton intensity is minimized around 6-8 mev as anticipated by the wave function overlap model. However, as we increase the neutral exciton energy separation, the indirect exciton intensity gradually increases to a maximum level of ~12 mev. This is quite the opposite of what one would expect from the wave function overlap model.

85 85 However, there is a possibility that the increased intensity of the indirect exciton can be a result of the overall enhancement of the PL emission at lower applied field, again due to reduced exciton ionization. In order to overcome such ambiguity indirect exciton intensity was normalized to the total intensity as depicted by the analysis in Figure 5.3(a). Figure 5.3: Indirect exciton intensity modulations. (a) Measured normalized indirect exciton intensity to compensate for the overall increase in the PL intensity. (b) Indirect to direct exciton intensity ratio derived from the decay rates associated with non-resonant excitation. (c) PL spectra plotted as a function of exciton energy separation to clearly identify processes related with intensity modulations.

86 86 According to the normalized indirect exciton spectra, at exciton energy separation of up to ~ 6-8 mev, the intensity profile is in agreement with the wave function overlap representation. Since the normalized indirect exciton should compensate for the overall increase in the intensity, with larger energy separation between the direct and indirect exciton we would expect less overlap between electron and the asymmetric hole wave functions that results in a reduced normalized X I intensity in the forward bias. However, from the analysis in Figure 5.3(a) it is evident that there is a local maximum of X I intensity near the energy separation of ~ 12 mev that corresponds to a singly charged exciton generation (X + ) as illustrated in Figure 5.3(c). This indicates that there are other processes within the CQD system that need to be examined, which affects the exciton population and the recombination rates. These processes will be examined next Decay Rate Model As discussed in the previous section, wave function overlap representation alone is insufficient to explain the intensity profile of the indirect exciton. One such major process that has been widely discussed in the literature but needs to be examined and applied to this particular exciton intensity modulation is the phonon assisted relaxations. The reported results indicate that the coupling of acoustic phonons and QDs tends to be dominant for specific exitonic energy separations in CQDs [75]. Due to the nature of our asymmetric CQD system we should consider the carrier-phonon coupling mechanism. For simplicity we ignore both multi-phonon and phonon absorption processes in

87 considering the level diagram in Figure 5.4. From which we derived the rate equations and corresponding discussion related to the indirect exciton intensity modulation. 87 Figure 5.4: Possible mechanisms associated with the exciton decay process including phonon scattering and carrier tunneling to other exciton states. Indirect (I) and direct (D) exciton states decay radiatively with rates of R I and R D and the other charge states with R +. Phonon assisted non-radiative process is denoted by γ along with the tunneling to other exciton states through ν. According to the level diagram presented in Figure 5.4, at a specific bias, carrier recombination can take place from I state to the ground state either by emitting a photon, or through a second channel after relaxing non radiatively ( ) down to a lower state D, and then later recombine by emitting a photon with a different energy. At a lower applied field there is also the possibility of carrier tunneling, which creates other charge states ( X ) with rates of. In order to quantify the recombination process of the indirect exciton from I state to the ground state we consider rate equations where the exciton decay rate is proportional to both electric field dependent radiative recombination rate ( R I ) and phonon assisted relaxation rates ( ) along with possible tunneling

88 processes. For the indirect neutral exciton we denote the rate using Equation 5.1 with population N I corresponding to the latter processes. 88 dn dt I R N I I N N I I G (5.1) Here the generation rate of the indirect exciton state is denoted by G along with to describe the tunneling processes to other exciton states due to non-resonant laser excitation. In a similar way, we can represent the decay rate for the direct exciton with population N D from Equation 5.2. Where RD is the rate at which D is either lost to radiative recombination or via tunneling processes to the contacts. dn dt D R D N D N I N D G (5.2) Considering single phonon scattering processes and solving Equations 5.1 and 5.2 at a steady state, along with CW non-resonant laser excitation, we obtained the PL intensity ratio for indirect to direct excitons ( I I I D ) as depicted in Equation 5.3. (5.3) I I I D 1 / RD 1 ( 2 ) / R I The indirect to direct exciton intensity ratio that has been determined from the above equation is plotted in Figure 5.3(b) where a clear identification of the intensity modulation can be observed. The exciton intensity ratio also illustrates the intensity minimum around energy separation of 6-8 mev as expected by the wave function overlap model. Furthermore, the PL intensity ratio plot [Figure 5.3(b)] demonstrates a clear agreement with the measured normalized intensities of the indirect exciton as depicted in

89 89 Figure 5.3(a). Hence, the hypothesis built upon the combined model can be applied to describe the observed modulations of the indirect exciton intensities. One of the challenges in obtaining the intensity profile of the indirect exciton is the extensively reduced emission. To overcome this issue one can increase the spectral collection at desired biases with much longer integrations. However, due to thermal fluctuations there can be artificial intensity variations within the PL spectra associated with the exciton emissions that can be prominent with longer time durations. Furthermore, there can also be bias fluctuations, to which indirect exciton intensity is especially susceptible due to its large electric field dependence, which the direct exciton state lacks. On the other hand exciton lifetime measurements are independent of any spatial fluctuations of the sample. This is because in photon counting experiments the emitted photons are measured at a specific energy that does not depend on spatial fluctuations. Furthermore, exciton lifetimes are correlated with recombination processes and hence it is desirable to perform time-domain measurements to further our knowledge and to quantify tunable exciton relaxation processes associated with the indirect excitons. 5.3 Time - Correlated Single Photon Counting Photoluminescence (PL) measurements were used to investigate the electric field, energy, and intensity dependence of the radiative recombination processes associated with charge carriers in the CQD system. However, in order to gain insight into the carrier dynamics of both the radiative recombination and non-radiative relaxation processes,

90 90 time-domain experiments are essential. Therefore, in this chapter, we use the timecorrelated single photon counting (TSCPC) technique to better understand and quantify exciton relaxation processes in our CQD system. Using the TCSPC techniques, CQDs were excited with a mode-locked Ti:Sapphire laser operating at 80 MHz, along with a pulse width of 1.5 ps, which created a population of carriers within the system. Initially using a 0.75 m spectrograph, a PL signal was dispersed onto a CCD to identify the exciton state of interest. Once identified, photons were detected through a Perkin-Elmer SPCM-AQRH-13 avalanche photodiode (APD) system that had ~300 dark counts per second along with a timing resolution of ~500 ps. Carrier lifetimes were then acquired through standard time-resolved photon counting electronics; namely, a SR 400 single photon counter, Ortec 467 time to amplitude converter (TAC) with 0-50 ns full-scale resolution, and Canberra 8076 multi channel analyzer (MCA) with custom electronics for time binning. In the single photon counting measurement, we specifically used the electrical pulse that was generated from the APD as the start signal along with synchronized laser diode pulse as the stop signal for the process of counting the time interval as depicted in Figure 5.5. From the associated electronics, a voltage histogram corresponding to the measured time interval was generated. Such histograms from multiple channels are then used to create the specific time decay curve associated with the carrier dynamics. Via our experiments, we measured counts with an S/N ratio of more than 100:1, as such, long integration times were encountered for weak PL emissions.

91 91 Figure 5.5: Schematic representation of the time-correlated single photon counting (TCSPC) experimental setup. Excitation was provided by a mode-locked Ti:Sapphire laser (pulse width of ~ 1.5 ps operating at 80 MHz) attached to a high powered diode pumped solid state laser (CW-DPSS). From the avalanche photodiode (APD) and allied electronics [SYNC Synchronized laser diode pulse, TAC Time to amplitude converter, and MCA Multi channel analyzer] acquired lifetimes are illustrated in the bottom right plot. A photograph of the actual experimental setup is depicted in the top left corner. 5.4 Exciton Lifetimes Time-domain measurement is a powerful tool that relies on a single photon counting technique, which is highly pertinent in determining associated processes such as

92 92 relaxation and recombination of different exciton states. For the initial experiments, a time-resolved experimental setup was used (section 5.3). The excitation was provided through a mode-locked Ti:Sapphire laser source while exciting to the quasi-continuum of the InAs wetting layer energy. As the energy separation between the indirect and direct exciton was increased relatively to the anti-crossing energy, we observed a strong non-monotonic modulation of the indirect exciton lifetimes as shown in Figure 5.6(a). For direct comparison, previously discussed normalized intensity of the indirect exciton (section 5.2.1), along with the associated CQD PL spectra, is also plotted in Figure 5.6(b) and (c) respectively. The direct and indirect exciton intensities and lifetimes are comparable near the anti-crossing energy. As the energy separation became larger the observed lifetimes increased first to a maximum at ~ 3-4 mev. Further increase in the exciton energy resulted in a minimum indirect exciton lifetime at a separation of ~ 6-8 mev, which is in agreement with the observed intensity minimum. Using a vertical colored band, we have highlighted the coincidence of the measured lifetime and intensity minima across Figure 5.6(a) and (b). An additional increase in energy separation resulted in another maximum in the exciton lifetime at ~ 14 mev before it began to decrease. The time-domain experiment was extended to a few different CQDs and the strong indirect exciton lifetime modulation [76] was clearly observed. A comparison for these two different CQDs is presented in Figure 5.6. It is evident from Figure 5.6(a) and (d) that the lifetime maximum/minimum beyond the anti-crossing happens at almost similar energy separations in each CQD.

93 Conversely, the subsequent maximum of the indirect exciton lifetime tends to vary with different CQDs. 93 Figure 5.6: Indirect exciton lifetime and intensity modulation for two different CQDs. (a) Indirect exciton lifetime behavior as a function of exciton energy separation. (b) Normalized intensity modulation associated with the indirect exciton. (c) PL spectra as a function of exciton energy separation between indirect (X I ) and direct (X D ) excitons relative to the anti-crossing energy. The blue stripe [(a), (b), (d), and (e)] highlights both intensity and lifetime minima that correspond to an exciton energy separation of ~ 6-8 mev. Dotted vertical lines represent the X-pattern signature and the onset of the singly charged exciton (X + ) along with its dominant effects shown by the gray shading in the top four plots. (f) PL spectra for a different CQD along with the lifetime and intensity profile are depicted in (d) and (e) respectively. (After K.C.Wijesundara, et al., Phys. Rev. B 84, (R) (2011) [76]).

94 94 However, this lifetime maximum always tends to overlap with the onset of the singly charged exciton state (exciton molecular anti-crossing signature [54]) as shown by the dotted vertical line across Figure 5.6. If we consider only the exciton recombination process and exclude relaxation channels, the PL intensity of excitons should be inversely proportional to their lifetimes. This is not always the case, and from the lifetime plots in Figure 5.6 it is clearly evident that there has to be exciton relaxation processes that account for the observed lifetime modulations. One such major process would be relaxation to other charge states. From CQD to CQD the position of the peak indirect exciton lifetime as a function of exciton energy separation tends to vary. However, it is always coincident with the onset of the singly charged exciton state or the positive trion state. Extending the schematic representation of excitonic states as a function of energy separation (Figure 5.1) we can visualize the region where possible indirect exciton relaxation to trion states can occur (Figure 5.7). Figure 5.7: Schematic representation of the exciton states via spread of the electron and hole wave functions as a variable of energy separation. The prominent region for indirect exciton relaxation to trion states is shown in the shaded area of the plot.

95 95 Such a singly charged state formation mechanism is illustrated in Figure 5.8. Figure 5.8: Indirect exciton relaxation to positively charged exciton (positive trion) state. (a) Indirect exciton state. (b) At high enough forward bias voltages, the electron can tunnel out to the substrate. Consequently, with reduced Coulomb energy, the top (T) dot hole tunnels into the bottom (B) dot. (c) Subsequent excitation results in creating an e-h pair in the B dot and generating the positively charged exciton state. One of the large loss mechanisms of the indirect exciton can be attributed to the formation of singly charged positive trions. Starting from the indirect exciton [Figure 5.8(a)], at a high enough forward bias, localized electrons can tunnel out from the bottom dot to the n-doped substrate as depicted in Figure 5.8(b). Then the top dot hole can tunnel in and relaxes down to the ground state of the bottom dot due to reduced Coulomb energy. Subsequent non-resonant excitation can create an electron-hole pair at the bottom dot, which results in the formation of the singly charged exciton states as schematically shown in Figure 5.8(c). The normalized intensity profile of the singly charged exciton state (positive trion) also illustrates a clear agreement with the indirect exciton loss mechanism discussed in the previous paragraph. According to the normalized intensity profile as

96 96 shown in Figure 5.9, the trion formation starts at the charged exciton molecular anticrossing signature, and continues to be more prominent at higher forward bias voltages. Consequently the indirect exciton states completely die out as apparent by the intensity profile and also from measured indirect lifetime signatures previously discussed in beginning of this section. Figure 5.9: Normalized relative intensity of the indirect exciton and singly charged exciton (positive trion) states. "X" symbolizes the positive trion molecular anti-crossing signature that appears in the PL spectra as a function of exciton energy separation. Green doted vertical line represents the energy separation corresponding to both intensity and lifetime minimum that can be associated with other relaxation processes within the CQD system. If we can eliminate the possibility of charge tunneling we should see an increased indirect exciton lifetime as predicted in the literature [76]. Furthermore, this can lead to the isolation of relaxation channels due to phonons, which may increase interest in these CQD systems.

97 Resonant Excitation The strong non-monotonic trend in the indirect exciton lifetimes clearly suggests the existence of non-radiative relaxation channels other than the charged exciton generation as discussed in the previous section. In order to experimentally quantify and separate out the contribution from the non-radiative relaxation channels, (such as phononmediated relaxations) we performed resonant excitation experiments. Using the same mode-locked laser excitation source as discussed in section 5.3 we resonantly excited the laser to the indirect exciton state (X I ) at different neutral exciton energy separations and measured the corresponding direct exciton (X D ) lifetimes. Theoretically, with resonant excitation into a specific indirect exciton energy, a different charge state formation is prohibited due to the Coulomb correction of the extra charge. With this technique we can eliminate the carrier tunneling process in other charged exciton states. Observed bi-exponential behavior of the direct exciton lifetimes with resonant excitation is shown in Figure 5.10 for selected exciton energy separations. From the semi-log plot we can clearly identify the two associated lifetimes. In the resonant excitation process, the direct exciton exhibits its expected lifetime behavior from the first exponent (larger slope). The recombination process of the direct exciton has no dependence on the wave function overlap model or on any subsequent tunneling processes to the first order, despite the change to the exciton energy separation. As a result the direct exciton has a lower lifetime compared to the indirect exciton states. Additionally, it does not vary with higher exciton energy separations that can be clearly observed from Figure From the same figure it is evident that the second

98 exponent (lower slope) varies with the exciton energy separation and therefore can be attributed to the indirect exciton lifetimes. 98 Figure 5.10: Bi-exponential behavior of the direct exciton lifetimes due to resonant laser excitation into the indirect exciton state as a function of exciton energy separation. The semi-log plot visualizes the time decays of the two exponents that correspond to both indirect exciton (lower slope) and direct exciton states (higher slope). Next, considering the decay rate model as discussed in section 5.2.2, we can obtain exciton relaxation channel contributions to the indirect exciton lifetime. With the resonant excitation we can also simplify the rate equations (Equations 5.1 and 5.2) presented in section Hence, the indirect exciton population decay rate is only proportional to the rate at which X I is lost to the recombination and tunneling to the

99 contacts ( R ), the non- radiative phonon relaxation ( ), and the generation rate of the X I I (G ) as illustrated in Equation dn dt I R N N I I I G (5.4) Similarly, a simplified expression can be presented for the direct exciton population decay rate as given in Equation 5.5. dn dt D R D N D N I (5.5) Where the rate at which the X D is lost to radiative recombination is given by R D. With resonant excitation the generation rate of the direct exciton is neglected as opposed to the non-resonant excitation. Additionally, we can eliminate the creation of other charge states, which has simplified the above two equations in the resonant excitation process. Solving the above two equations we can determine the phonon contribution even though the pure radiative rates cannot be extracted. From Equations 5.4 and 5.5, we can obtain the time dependencies of the indirect and direct exciton normalized populations as given in Equations 5.6 and 5.7 respectively. N I exp ( t / ) I (5.6) N I ( D I 1 ) exp ( t / ) exp ( t / ) (5.7) Where R 1/, R /, and ( R R ). I I D 1 D I D

100 The time dependences I and D 100 from the above two equations (5.6 and 5.7) are analogous to the lifetimes extracted from the bi-exponential fits, which have been obtained from the resonant excitation process into the indirect exciton state as depicted in Figure 5.11(a). It is evident from Figure 5.11 that the indirect exciton lifetimes ( I ) are identical for both non-resonant and resonant excitations up to where the singly charged exciton appears in the PL spectra. Beyond the onset of the trion generation energy (~14 mev), indirect exciton lifetimes diverge up to 4 ns from the resonant case. Figure 5.11: (a) Extracted lifetimes I, D corresponding to indirect and direct excitons with resonant laser excitation. For comparison, indirect exciton lifetimes with nonresonant excitation are shown as a dotted line. In the resonant case, indirect exciton lifetimes tend to diverge up to 4 ns beyond the generation of the trion state denoted by X and can be mapped from the PL plot (b) (After K.C.Wijesundara, et al., Phys. Rev. B 84, (R) (2011) [76]).

101 101 Colored arrows in the top plot indicate several exemplary points of resonant excitation into the indirect exciton state that resulted in bi-exponential lifetime behavior as was illustrated in Figure This variation in the indirect exciton lifetimes clearly reveals the formation of the positive trion state with the non-resonant excitation as we have theoretically discussed and schematically illustrated in Figure 5.8. We can also modify the simplified processes related to the indirect exciton as discussed earlier by inserting a formation rate of for the singly charged exciton state. From this, we obtained additional terms of the indirect excition time dependence as given in Equation 5.8. ' 1 / R I I (5.8) Finally, from the processes and associated expressions [Equations ] discussed in this section along with the measured data, we directly extorted different contributions that resulted in the strong modulation of the indirect exciton lifetimes. Such contributions from the singly charged state formation ( ), phonon-mediated relaxations ( ), and data extracted for both direct and indirect exciton recombination rates ( R, R ) were plotted as illustrated in Figure 5.12(a). To identify features coupled with the extracted rates as a function of exciton energy separation, PL spectra [Figure 5.12(b)] is shown for comparison. This plot illustrates that the indirect exciton relaxation rate decreases monotonically, as expected, from the reduced oscillator strengths associated with increased exciton energy separation. We also observed a rapid rate increase in the parameter as expected with the formation of the singly charged state beyond the exciton D I

102 energy separation of 14 mev. Other than the above expected results we observed a rather interesting profile for the extracted phonon-mediated relaxation rates ( ). 102 Figure 5.12: (a) Recombination rates for the direct and indirect excitons and nonradiative contributions to the exciton lifetimes via phonon-mediated relaxation channels and trion formation rates extracted from the bi-exponential data. (b) PL spectra corresponding to the neutral exciton and positive trion states as a function of exciton energy separation. To better understand the physics behind these observed results, especially the strong indirect exciton lifetime modulations and oscillatory phonon-mediated relaxation process, a theoretical model was necessary to generalize the results for wider applications in nanostructures.

103 Theoretical Model Carrier relaxation processes within strained InAs/GaAs QDs have been widely discussed in the literature [77,78]. The observed experimental results associated with the indirect exciton lifetime modulations can be attributed predominantly to charging effects beyond 14 mev and phonon-mediated relaxations below 14 mev, with exciton energy separations. Therefore, scattering associated with the longitudinal optical (LO) phonons is neglected and instead the interactions associated with longitudinal acoustic (LA) phonon modes were considered for our CQD system. Consequently, a model for the phonon-mediated relaxation in the asymmetric CQDs was constructed by our collaborators, Prof. S. E. Ulloa and J. E. Rolon, and is summarized [also see Figure 5.13(a)] and compared with the experimental results in this section. Exciton states were determined by the direct products of the ground state wave functions confined in three dimensions. The energy eigenvalues were obtained through diagonalizing the single particle Hamiltonian for hole states from which the field dependent energy separation between indirect and direct excitons was obtained as given in Equation 5.9 [76,79], E ID 2 2 ( eed ) 4t (5.9) with hole tunneling amplitude as t, applied field E, and inter-dot distance d (7 nm for our CQD system [79]) respectively. For zero applied electric field relative to the hole anti-crossing, the equation yields ID E 0.8 mev consistent with the experimental results. Additionally, for the carrier-phonon scattering, the interaction Hamiltonian

104 104 involves scattering matrix elements M, which include phonon polarizations [longitudinal acoustic (LA) and transverse acoustic (TA)], piezoelectric effects (PZ), and deformation potential (DP). This results in an expression for the phonon assisted relaxation rate that can be determined by the Fermi golden rule given in Equation 5.10 [76,79], 2 2 ik. M( k ) D e r k where sound velocity is given by I 2 E ID v k v and the structure factor by k k i. D e k r I 2. (5.10) Thus, from Equation 5.10 it is evident that an efficient phonon-mediated relaxation only occurs when the energies and k are equivalent. Furthermore, EID v k structure factor calculations indicated maximum values (0 and odd multiples of ) for the modulations as illustrated by contour plots in the inset of Figure 5.13 (a). When the field dependent phonon wave vector dispersion line [ k d E ) ] coincides with the maximum z ( ID structure factor [inset of Figure 5.13(a)], it results in efficient phonon relaxations that can be observed as peaks in the oscillatory phonon relaxation rate ( ) as illustrated in the main plot of Figure 5.13(a). Moreover, scattering matrix element calculations revealed different contributions to the total relaxation rate ( ) by DP and PZ effects (, TAPZ LADP, and PZ ) as shown in the main plot. An additional theoretical model detailing LA the structure factor calculations and scattering matrix elements with associated polarization effects can be found elsewhere [79]. To better compare the theoretical outcome with the experimental observations, we have plotted the extracted exciton relaxation rates from the bi-exponential data discussed

105 in section in the same energy scale as depicted in Figure 5.13(b). Where the 105 theoretical total phonon-mediated relaxation rate (green solid line - theory ) illustrates a clear agreement with experimentally extracted phonon relaxation rates ( ) both of which occur as a function of exciton energy separation. Figure 5.13: Comparison between theoretical and experimentally extracted phonon relaxation rates. (a) Total phonon relaxation rate derived from the deformation potential (DP), piezoelectric effects (PZ), and phonon polarizations. Structure factor contour plots as a function of the exciton energy separation are illustrated, along with phonon wave vector dispersion in the inset. (b) Experimentally extracted phonon-mediated relaxation rates and exciton recombination rates. Accordingly, a clear agreement between theory and can be established (After K.C.Wijesundara, et al., Phys. Rev. B 84, (R) (2011) [76] and J. E. Rolon, et al., JOSA B 29, A146 (2012) [79]).

106 106 Experimental relaxation rates demonstrate apparent peaks for energy separations of ~ 6.2 mev (corresponding to a phonon axial wave vector value of 3and subsequent energies. However, the experimental phonon rate tends to suppress near the first peak as opposed to the theoretical result. This can be attributed to the thermal effects that are prominent near energy separations of ~ 1 2 mev (k B T ), which can account for both absorption and emission of the phonons. Furthermore, it manifests from Figure 5.13 that the oscillatory phonon-mediated relaxation rate, as well as the overall trend, is consistent with the theoretical model calculations. 5.5 Photon Correlation Measurements The resonant excitation experiment discussed in section was the basis for the results on tunable exciton relaxation channels in CQDs that were derived using extracted bi-exponential data for the direct exciton. To further justify that the direct exciton indeed can be generated through a relaxation channel originating from the indirect exciton, we performed a Hanbury Brown-Twiss (HBT) interferometer type photon correlation measurement [80] as depicted in Figure The HBT system was utilized by extending the TCSPC experimental setup that was illustrated in Figure 5.5, where the photons in the detection path are now directed to a 50:50 beam splitter. Next, photons are focused to each APD via the two stages of the spectrometer and the signals are fed to two channels (CH-1 and CH-2) of the photon counting module along with the allied electronics so that we can measure the coincidence counts as a function of delay time of the photon detection by the two APDs. From this setup one can measure both auto-correlation (same

107 emission energy) and cross-correlation (two emission energies) measurements, which have been widely discussed for different types of quantum emitters [81,82] and represent the probability of detecting a second photon after detecting the initial photon at time t Figure 5.14: Schematic representation of the Hanbury Brown-Twiss (HBT) interferometer type setup which can be used for both photon auto-correlation and crosscorrelation experiments. By aligning the indirect and direct excitons to the APDs and appropriate channels, a characteristic anti-bunching signature was observed as illustrated in Figure 5.15(a), which indicates that both exciton states exist within the same CQD system. Furthermore, as there are no other higher energy exciton states in most of the CQDs that can be excited from the laser pulse, we can deduce that the direct exciton is indeed generated through the relaxation of the indirect exciton state.

108 108 Both the lifetime and intensity modulations that have been discussed earlier were consistent with many CQD apertures. However, in one of the apertures, the PL spectra seem to have higher energy lines above and closer to the indirect exciton for exciton energy separations of 19 mev and above. To identify the origin of the higher energy exciton lines and their effect on the measurements, we performed cross-correlation experiments between the direct exciton and these higher energy exciton states; the results are depicted in Figure 5.15(b). Figure 5.15: Photon correlation measurements illustrated through coincidences as a function of delay time. (a) Anti-bunching signature observed from cross-correlation between indirect and direct excitons. (b) Coincidence as a function of delay time for the neutral exciton and unknown higher energy state that was observed in one CQD aperture. Completely random cross-correlation elucidates exciton states arising from two different CQD apertures and validates the consistency of the reported tunable exciton relation rate measurements. From the coincidence between the neutral exciton and unknown higher energy states as a function of delay time, it is apparent that there is no cross-correlation as the

109 109 events are completely random in time intervals and hence equally likely as described by Poisson statistics. This further exemplifies that the unknown higher energy states and direct exciton indeed resulted from different CQD apertures. Therefore, through photon correlation experiments, (HBT type), it is further substantiated that the exciton intensity and lifetime modulations, along with oscillatory phonon relaxations, are consistent with any CQD system. 5.6 Chapter Summary Interest in solid state implementation of quantum information processing is characterized by long coherence time scales [83]. However, associated thermalization, relaxation, and recombination processes within solid state structures limit such desired time scales; zero dimensional systems, especially, exhibit strong coupling with the lattice as reported in the literature [84]. Therefore, to better understand phonon-mediated relaxations in tunnel coupled neutral exciton states, we implemented time-resolved spectroscopy and PL intensity measurements, while the energy separation between the direct and indirect exciton was continuously tuned using an applied electric field. As we controlled the mixing between the spatially direct and indirect states by varying the coupled state energy splitting from mev, lifetime modulations between ns along with intensity variations of 8% were observed. Closer to molecular-like levels of the two excitonic states, both intensity and lifetime oscillations are consistent with the overlap integral of the envelop wave functions. To understand the behavior of intensities and lifetimes at energy splitting of up

110 110 to 18 mev from the resonance, wave function overlap, phonon-mediated exciton relaxation channels, and charge tunneling effects were taken into consideration. Furthermore, through resonant excitation experiments, the singly charged formation was eliminated due to the Coulomb correction of additional charges and the phonon-mediated relaxation rates were extracted from the bi-exponential lifetime data. Moreover, photon correlation HBT type experiments revealed that the direct exciton is indeed generated from the indirect exciton relaxation channel and is consistent with any CQD structure. Additionally, a theoretical model was also developed to validate our results. Both experimentally observed and theoretically proved oscillatory phonon relaxation rates have features that are strongly dependent on the hole wave function confinement along the lateral and vertical directions. These in turn are determined by the entire CQD structural parameters such as the inter-dot distance, dot heights, and lateral size. As the hole wave functions are tuned from molecular-like to atomic-like, the required energy and momentum that matches an available acoustic phonon mode necessary for relaxation is found to modulate. Thus, when the required energy and momentum are matched, relaxation happens efficiently through the available phonon modes. Additionally, for highly strained QDMs with small inter-dot barriers, piezoelectric field (PZ) mediated phonon scattering can have a non-negligible contribution to the total scattering rate, especially for low transition energies at small applied electric fields, near the anti-crossing region, where phonon assisted transitions would require only small phonon momenta. However, all of the observed features occurred at moderate electric field values, which can be considered far from the anti-

111 111 crossing region, and where DP contributions were larger than the PZ effects. We also found that the oscillatory structure is, not surprisingly, most sensitive to structural parameters such as dot heights, diameters, and separations. Our main results presented in this chapter were contributed by the Wijesundara et.al., and were published in PRB Rapid Comm., [76] followed by supplemental detailed theoretical analysis by Rolon et al., [79]. Following the initial work on tunable exciton relaxation rates in CQDs, rigorous theoretical investigation on the role of sub band mixing of hole states has been taken into consideration by other groups [85], which have demonstrated both consistency and validity of our experimental findings.

112 112 Chapter 6 Conclusion Semiconductor quantum dots, being single photon sources, have the distinctive ability to integrate with optoelectronic devices. Characteristics in these structures, including molecular behavior, arise due to their tunability in exciton levels. Especially unique to CQDs are their largely field dependent, inter-dot transitions due to their coupled nature. Insight into the underling physical phenomenon in these III-V confined semiconductor structures was sought with opto-electrical and time-resolved techniques. Observed novel effects on these semiconductor nanostructures are presented in this dissertation, which has also resulted in numerous journal publications. Unique effects associated with CQD devices for fast, non-contact, electric field modulations were initially researched using the gated photon counting method. With the two color quasi-pump probe technique and excitation below and above the wetting layer, the temporal response of the generated optical field was monitored by means of highly field sensitive indirect transitions. Due to charge carrier trapping at impurity sites and material boundaries, decay time of the optical field was measured to be ( ) 10 2 μs. Moreover, the optical field was not influenced by carrier density as evidenced by power dependent measurements. As reported, unexpectedly fast MHz frequency response in the onset of the optical field was a novelty that can be monitored via inter-dot excitons and will be widely applicable in opto-electronics.

113 113 Next, innovative investigations on electron and hole exchange interaction that arise due to structural anisotropy of the CQDs were executed through optical orientation techniques. Robust experiments involving the electric field, control of barrier width, and resonant laser excitation were employed to erase the lifted spin degeneracy within both neutral and singly charged inter-dot exciton states. First, the electron and hole wave function overlap was varied by spatially separating the charge carriers in the indirect exciton, which resulted in novel control of the anisotropic exchange that was measured via the degree of circular polarization memory. Next, the spin fine structure of the indirect spectral doublet that arises due to the isotropic exchange splitting was examined via polarization-resolved spectra. Both electric field and barrier dependent polarized spectra exemplified the exchange control via the top dot spectator hole in the singly charged state. Finally, the regaining of anisotropic exchange was observed through a minimum in circular polarization memory, along with a linearly polarized doublet in coincidence with the ground state hole molecular level. Control in these exchange energy effects was obtained through resonant laser excitation as it eradicated polarization mixing. In all, electron hole exchange interaction in CQD systems was managed experimentally; this provides a promising procedure for spin control. The final, yet most exciting, original results on relaxation channels within CQDs were obtained through fast time-resolved PL and luminescence intensity measures while tuning the energy separation between the intra-dot and inter-dot excitons with the applied field. Oscillatory lifetime modulations from ns and luminescence intensity variations of 8% were observed while controlling the energy separation from

114 114 mev, between spatially indirect and direct exciton states. Insight into these results was achieved by considering wave function overlap, phonon-mediated relaxation channels, and charge tunneling effects. At low energy separations near the anti-crossing region, observed intensity and lifetime modulations in the indirect exciton were readily identified from the electron-hole wave function overlap. The charge tunneling phenomenon was present beyond the singly charged state as it could be eradicated through the resonant excitation that resulted in Coulomb correction of additional charges. Thus, the remaining phonon-mediated relaxation effects were isolated and extorted via bi-exponential lifetime results. The observed modulations in phonon relaxation rates are dependent on structural parameters of the CQD and efficient relaxations arise via a required match between energy and momentum. Thus, the phonon-mediated relaxations are consistent with any such system and could be tuned to provide the desired exciton lifetimes.

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123 123 Appendix: Publications and Conference Presentations A Publications 1. Kushal C. Wijesundara, Allan S. Bracker, Daniel Gammon, and Eric A. Stinaff, Control of the exchange interaction in indirect exciton states, Unpublished Manuscript (2012). 2. Juan E. Rolon, Kushal C. Wijesundara, Sergio E. Ulloa, Allan S. Bracker, Daniel Gammon, and Eric A. Stinaff, "Oscillatory acoustic phonon relaxation of excitons in quantum dot molecules" JOSA B 29, A146 (2012). 3. Kushal C. Wijesundara, Juan E. Rolon, Sergio E. Ulloa, Allan S. Bracker, Daniel Gammon, and Eric A. Stinaff, Tunable exciton relaxation in vertically coupled semiconductor quantum dots, Physical Review. B 84, (R) (2011). 4. Kushal C. Wijesundara, Allan S. Bracker, Daniel Gammon, and Eric A. Stinaff, Spin effects of charged exciton states in electric field tunable quantum dot molecules, Proceeding of the 11th IEEE Conference on Nanotechnology (IEEE- NANO 2011) pages , (2011). 5. Mauricio Garrido, Kushal C. Wijesundara, Swati Ramanathan, A. S. Bracker, D. Gammon, and E. A. Stinaff, Electric field control of a quantum dot molecule through optical excitation, Applied Physics Letters. 96, (2010). 6. Kushal C. Wijesundara, Mauricio Garrido, Swati Ramanathan, E. A. Stinaff, A. S. Bracker, and D. Gammon, Temporal response of the optically generated electric field in InAs/GaAs coupled quantum dots, Materials Research Society Proceedings. 1208E, 1208-O05-02 (2010). 7. Kushal C. Wijesundara, Mauricio Garrido, Swati Ramanathan, E. A. Stinaff, M. Scheibner, A. S. Bracker, and D. Gammon, Electric field tunable exchange interaction in InAs/GaAs coupled quantum dots, Materials Research Society Proceedings. 1117E, 1117-J04-08.R1 (2009). 8. Mauricio Garrido, Kushal C. Wijesundara, Swati Ramanathan, A. S. Bracker, D. Gammon, and E. A. Stinaff, Characterization of the shell structure in coupled quantum dots through resonant optical probing, Materials Research Society Proceedings. 1117E, 1117-J05-03.R1 (2009).

124 Jihoon H. Lee, Zhiming M. Wang, Morgan. E. Ware, Kushal C. Wijesundara, Mauricio Garrido, Eric A. Stinaff, and Gregory J. Salamo, Super low density InGaAs semiconductor ring-shaped nanostructures, Crystal Growth & Design, 8, 1945 (2008). 10. E. A. Stinaff, Swati Ramanathan, Kushal C. Wijesundara, Mauricio Garrido, M. Scheibner, A. S. Bracker, and D. Gammon, Polarization dependent photoluminescence of charged quantum dot molecules, Physica Status Solidi (c), 5, 2464 (2008). B Book Chapters 1. Kushal. C. Wijesundara, Allan. S. Bracker, Daniel Gammon, and Eric. A. Stinaff, Unpublished Book Chapter edited by K. Iniewski and J. Morris. Nanoelectronic Device Applications (2012). C Conference Presentations (Oral) 1. Kushal C. Wijesundara, Allan Bracker, Daniel Gammon, and Eric A. Stinaff, Nanoelectronic Devices: novel materials and devices; Spin effects of charged exciton states in electric field tunable quantum dot molecules, 11 th IEEE International Conference on Nanotechnology (IEEE-NANO 2011) Portland, OR, Aug (2011). 2. Kushal C. Wijesundara, Juan E. Rolon, Sergio E. Ulloa, Eric A. Stinaff, Allan Bracker, and Daniel Gammon, Control of exciton relaxation channels in quantum dot molecules, American Physical Society (APS) March Meeting, Dallas, TX (2011). 3. Eric A. Stinaff, Kushal C. Wijesundara, Allan Bracker, and Daniel Gammon, Exchange-controlled spin dynamics in coupled quantum dots, American Physical Society (APS) March Meeting, Dallas, TX (2011). 4. Kushal C. Wijesundara, Optical properties and temporal response of InAs/GaAs coupled quantum dots Nanoscale and Quantum Phenomena Institute (NQPI) NanoForum Seminar at Ohio University, USA, May 18 (2010).

125 Kushal C. Wijesundara, Mauricio Garrido, Swati Ramanathan, Eric Stinaff, Allan Bracker, and Daniel Gammon, Direct and indirect exciton lifetimes in InAs/GaAs coupled quantum dots, American Physical Society (APS) March Meeting, Portland, OR (2010). 6. Kushal C. Wijesundara, Mauricio Garrido, Swati Ramanathan, Eric Stinaff, Allan Bracker, and Dan Gammon, Exchange interaction and structural information of quantum dot molecules, Biomimetic Nanoscience and NanoTechnology (BNNT) Conference, Ohio University, USA, May 9 (2009). 7. Kushal C. Wijesundara, Mauricio Garrido, Swati Ramanathan, Eric Stinaff, Allan Bracker, and Daniel Gammon, Direct Exchange interactions in coupled quantum dots observed through polarized photoluminescence, American Physical Society (APS) March Meeting, Pittsburgh, PA (2009). 8. Kushal C. Wijesundara, Mauricio Garrido, Swati Ramanathan, Michael Scheibner, Allan Bracker, Daniel Gammon, and Eric Stinaff Material Science for Quantum Information Processing Technologies: Electric field tunable exchange interaction in InAs/GaAs coupled quantum dots, Materials Research Society (MRS) Fall Meeting, Boston, MA, Dec. 1-3 (2008). 9. Kushal C. Wijesundara, Mauricio Garrido, Swati Ramanathan, Eric Stinaff, Michael Scheibner, Allan Bracker, and Daniel Gammon, Spin interactions in a coupled InAs/GaAs quantum dot studied by polarization dependent photoluminescence, American Physical Society (APS) March Meeting, New Orleans, LA (2008).

126 Thesis and Dissertation Services