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A First Principles Approach to Understand Plasmonic Phenomena

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A First Principles Approach to Understand Plasmonic Phenomena ABSTRACT A First Principles Approach to Understand Plasmonic Properties in Physical Systems by Runmin Zhang Plasmonic resonances in multiple systems are theoretically investigated with a first principles approach. The plasmonic behaviors of doped semiconductor nanocrystals are explored with a quantum TDLDA approach and a classical hybridization theory. The origins and properties of plasmonic resonances from a wide variety of physical systems are explored using rigorous quantum mechanical computations. A universal metrics, the generalized plasmonicity index, is proposed to classify plasmonic resonances from other optical resonances. Using the generalized plasmonicity index, the plasmonicity of optical resonances in multiple systems are quantified, including jellium spheres, atomic-scale metallic clusters, nanostructured graphene, and polycyclic aromatic hydrocarbons. The generalized plasmonicity index provides a rigorous way to quantify the plasmonic behaviors in ultra-small systems. It also offers a quantitative foundation for the design of devices based on molecular plasmonics. iii Acknowledgments I would like to express my deepest gratitude and great appreciations to my advisor, Prof. Peter Nordlander, for his tremendous guidance and unbelievable help during my PhD study. His remarkable insights and visions always spark fantastic ideas and discoveries. His extensive understandings of physics have always been an incredible source. I admire his enthusiasm for science and curiosity for life. The wonderful experience in Nordlander’s group during the past five years will be a lifelong precious treasure for me. I would like to thank my committee members Prof. Naomi J. Halas and Prof. Stephan Link, for their precious suggestions and valuable time in attending my defense. I would like to express my special thanks to Dr. Hui Zhang, who mentored and helped me when I joined the group. I thank all my past and present group members: Dr. Chizuko Matsubara Dutta, Dr. Manvir Singh Kushwaha, Dr. Lifei Liu, Dr. Yang Cao, Dr. Vikram Kulkarni, Dr. Alejandro Manjavacas, Mr. Thawda Aung, Dr. Jun Liu, Dr. Yao Cui, Dr. Yue Zhang, Dr. Xiao Yang, Dr. Hangqi Zhao, Dr. Alesandro Alabastri, Dr. Luca Bursi, Dr. Arash Ahmadivand, Mr. Jian Yang, Mr. Ming Zhang, Mr. Minhan Lou, Mr. Yage Zhao, Mr. Burak Gerislioglu for their valuable conversations and discussions. Also, I would like to thank my collaborators from Prof. Naomi J. Halas and Prof. Stephan Link’s group for their wonderful creative works. I would like to thank all the funding agencies. Finally, I would like to thank my father, my mother, my sister, and Ms. Yuchen Peng for their unconditional love, support and help. It has been a long journey, and it will a long journey. Contents Acknowledgments ..................................................................................................... iii Contents ................................................................................................................... iv List of Figures ............................................................................................................ vi List of Equations ......................................................................................................... x Nomenclature ........................................................................................................... xi Introduction ............................................................................................................... 1 Plasmons in Doped Silicon Nanocrystals ..................................................................... 5 2.1. Introduction .............................................................................................................. 5 2.2. Theoretical Background ........................................................................................... 7 2.3. Optical Properties of Doped Silicon nanocrystals .................................................. 14 2.4. Classical Hybridization Model for a Two-Component System ............................... 19 2.5. Conclusion .............................................................................................................. 24 Identification of Plasmonic Resonance from Other Optical Resonances ..................... 25 3.1. Introduction ............................................................................................................ 25 3.2. Theoretical Analysis ................................................................................................ 26 3.2.1. Plasmons and Single-Particle Excitations ........................................................ 26 3.2.2. Identification of Plasmons within the Random-Phase Approximation ........... 30 3.2.3. Plasmonicity Index and Generalized Plasmonicity Index ................................ 32 3.2.4. GPI and ab Initio Excitation Energies ............................................................... 35 3.3. Implementation of the GPI ..................................................................................... 38 3.3.1. Plasmons in Jellium Nanospheres ................................................................... 38 3.3.2. Probing Classical Mie Modes with the GPI ...................................................... 43 3.3.3. Quantifying Plasmon Modes with GPI ............................................................. 46 3.3.4. GPI for Metal and Semiconductor Clusters from TDDFT ................................. 49 3.3.5. Emergence of Plasmonic Behaviors in a Jellium Sphere ................................. 53 3.3.6. Plasmons in Polycyclic Aromatic Hydrocarbons and Nanostructured Graphene ................................................................................................................................... 56 3.4. Conclusion .............................................................................................................. 61 v Conclusion ............................................................................................................... 62 References ............................................................................................................... 64 List of Figures Figure 1: (a) Illustration of the experimental setup for nanoparticle synthesis. (b) Schematic of our model: two branchesof carriers coexist in an 8 nm- diameter Si nanosphere. The charge distribution of anti-bonding mode is plotted as an example. (c, d) Carrier distribution for surface boron- (c) and bulk P-doping (d) with doping densities as �. �, �, ��, �� × ������ − � respectively. (e, f) The calculated absorption spectra with a damping parameter � = �. ���. ........................................................................................................... 14 Figure 2: Measured (left) and calculated (right) absorption spectra. (a) Oxidized B-doped Si nanocrystals (�� = ��%) for as-produced, 2, 18, and 98h oxidizaton. The corresponding fitted doping concentration are 1.5, 1.9, 2.0, 2.3× ������ − �. (b) Oxidized P-doped Si nanocrystals (�� = ��%). The fitted doping concentrations are �. �, �. �, �. �, �. � × ������ − �. (c) Annealed B-doped Si Nanocrystals (�� = ��%). The fitted doping concentrations are �. �, �. �, �. �, �. � × ������ − �. (d) As-produced P-doped Si Nanocrystals with different doping concentration. (�� = ��, ��, ��, ��, ��%). The fitted doping concentrations are �. �, �. �, �. �, �. �, �. � × ������ − �. The damping parameter used is � = �. ���� (a,c) and 0.04eV (b,d). .............................................. 17 Figure 3: (a) Illustration of the plasmon hybridization theory of a two component system. (b) Eigenenergies of � + and � − as a function of the screening parameter � with doping concentration as �� = ��= �. � × ������ − �. (c) The evolution of absorption spectra when increasing the screen parameter �. (d) Total absorption spectra and the contributed absorption spectra from each component with different doping concentraions. The concentration we used in each panel from top to bottom: �� = �� = �. � × ������ − �; �� = �. � × ������ − �, �� = �. � × ������ − �; �� = �. � × ������ − �, �� = �. � × ������ − �. The background permittivity is chosen as �∞ = ��. ��, a suitable value for silicon. ............................. 21 Figure 4: (a) Absorption spectra of different doping concentrations in boron- doped Si Nanocrystals. The corresponding number of electrons inside Nanocrystals, from bottome to top, are 67, 93, 107, 120, and 147. The diameter of all Nanocrystals are 8nm. (b) The absorption spectra with different radius of Nanocrystals. The doping concentration is �. � × ������ − �, and the total number of electrons are 45, 71, 107, 152 respectively. ............ 23 Figure 5: Illustration of the differences between a dipolar plasmon (left) and a pure e-h pair excitation (right). The plasmon involves the coherent excitations vii of conduction electrons in the nanoparticle, which can be modeled as incompressible deformation of electron gas. Strong surface charges will be induced at the interface along with a significant field Eind (the depolarization field) inside the nanoparticle. Therefore, plasmonic excitations continue as damped oscillations after the driving external field is turned off (vertical dashed line in the lower panels). On the other hand, an e-h pair has no significant induced field beyond the screened internal Coulomb interaction between the hole and the electron: Rabi oscillations induce a time-dependent dipolar field as the external field persists, while after decay the
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