Quantum-Based Modelling and Simulation of Materials Used In Small-Scaled Plasmonic Devices - Akinyemi, Lateef Adesola (Department of Electrical Engineering, 2021)
The study of Plasmonics has been evolutionary and fascinating over the last few decades. This area of research has attracted extensive interest predominantly as a result of the possibility to direct and confine light at the nano-scale level using metallic materials as fundamental building blocks. This provides an explanation to the interaction of light and nano-sized metallic devices. The optical properties of nano-structured systems depend on the collective resonance of conducting electrons which are determined by the geometrical features as well the polarization characteristics of the incident light and frequency. For large systems with size in the order of tens of the size of nano-scale materials, the response has been extensively studied and is now well understood. The response of these large systems can be described using classical Maxwell's equations with reasonable accuracy. On the other hand, the application of this classical solution to Plasmonic-based nano-particles is severely limited by quantum phenomena such as tunnelling and non-local screening. These quantum effects can neither be described nor explained by the classical method. There is, therefore, the need to understand how the theory of quantum method can be utilized to describe the properties of nano-materials. This forms the main focus of this thesis. Firstly, the extension of existing classical models to Plasmonic materials is examined. It is ascertained that most of these models are designed for usage only in the highfrequency region. Furthermore, the use of Plasmonic devices including Metal-InsulatorMetal (MIM) and Insulator-Metal-Insulator (IMI) configuration are explored. An algorithm to determine and generate imaginary wave-vector numerically is proposed. The dissipation of electromagnetic fields, dielectric function, electric field, and magnetic field are computed for various values of complex wave-vector. Additionally, a one-dimensional quantum-based frequency-dependent dielectric function for small-scale devices is investigated. A Rigorous analysis and approximation are carried out on a 1-D model and a nano-wire geometry. The effect of transition band and investigation of optical materials of nano-wire for 1-D, 2-D, and 3-D are included in the analysis. The Eigen-pairs of the underlying canonical and associated perturbed quantum systems are computed and utilized for this study. Galerkin's method has been employed to discretize the boundary-value of interest. The introduction of the Sinc function throughout the analysis ensures the robustness and soundness of the computation. The analytical and numerical results demonstrate that the real- and imaginary parts of the dielectric function are even and odd function, respectively, as expected. More so, the cubical, cuboid and spherical geometries of metallic nano-particles are employed to examine the effects on the material. These effects of size-dependent damping constant on the metallic nano-particles and not forgetting the optical properties of the material such as dielectric function, refractive index and absorption coefficient which are considered worthy of investigation in this thesis. Hence, in this thesis, a customized, flexible, and computational software package for efficient assessment of small-scaled Plasmonic devices has been developed in 1-D and 2-D for regular geometry using the Standard Finite Difference Method (SFDM) and Conservative Finite Difference Method (CFDM). This study has been motivated, predominantly, by the tremendous interest in the examination of these geometrical structures. The package enables us to solve the desired homogeneous Dirichlet boundary-value problem. Then, the developed program is applied to solve the time-independent Schr¨odinger equation for the modelling and simulation of the physical properties of metallic nano-particles. Furthermore, the results obtained from SFDM and CFDM are compared. Finally, the concept of density functional theory (DFT) alongside the Kohn-Sham equation boundary-value problem with Dirichlet condition has been employed and demonstrated in this thesis to be a good candidate in solving and computing optical properties such as frequency-dependent dielectric function in small scale metallic nanoparticle of interest. Additionally, neither CFDM nor DFT schemes have been applied to determine optical properties of metallic nanoparticles in the literature, making it the first time such schemes will be used to compute optical properties.