Electromagnetic Modeling of Nanowires at Infrared and Optical Wavelengths

Open Access
Author:
Pellen, Michael Emile
Graduate Program:
Electrical Engineering
Degree:
Master of Science
Document Type:
Master Thesis
Date of Defense:
July 16, 2008
Committee Members:
  • Douglas Henry Werner, Thesis Advisor
  • Pingjuan Li Werner, Thesis Advisor
Keywords:
  • particle swarm optimization
  • electromagnetics
  • scattering
  • nanowires
  • nanotechnology
  • method of moments
  • material models
Abstract:
Nanotechnology is a rapidly growing area of research. The ability to manipulate materials at the nanometer scale through lithographic techniques such as electron-beam lithography has made it possible to generate higher density integrated circuits. Nanoscale wires, known as nanowires, have also been created using template-assisted synthesis and vapor-liquid-solid growth techniques. In order to design devices using these nanoscale structures, methods for analyzing these structures need to be developed. The methods developed for device analysis must also incorporate the behavior of materials at the infrared and optical frequencies. This thesis will develop models for analyzing nanowires in the infrared and optical spectrum by examining scattering from semiconducting nanowires and developing surface impedance models for inclusion to the method of moments. The dispersive nature of metals and semiconductors at infrared and optical wavelengths is introduced into our modeling approaches using oscillator models. The oscillator model that was used in this work is the Lorentz-Drude oscillator model. The Lorentz-Drude oscillator model was used to represent the dielectric properties of metals such as gold and silver in the infrared and optical spectrum. Oscillator models do not exist for all materials. Particle swarm optimization was applied to parameter fit a Lorentzian oscillator model for Gallium Phosphide material. The particle swarm optimization approach is general so that other materials may be parameterized to the Lorentzian model and incorporated into time-domain modeling methods such as the finite-difference time-domain (FDTD). Lord Rayleigh first investigated scattering from infinitely long dielectric cylinders in 1918. The analytical solution technique developed by Rayleigh was used to determine the electric fields inside and outside a long nanowire. A numeric code was developed to calculate the electric field magnitude inside and outside the wire for a Gallium Phosphide nanowire excited at normal incidence by a transverse magnetic and transverse electric wave. The intensity integral was introduced for cylindrical geometry and applied to lossless and lossy dielectric nanowires for both transverse magnetic and transverse electric polarizations. It was determined that the transverse magnetic polarization is dominant for diameters below 125 nm. The polarization dependence at normal incidence was also investigated by deriving the internal electric intensity as a function the transverse magnetic and electric polarization intensities and the angle theta. For diameters where the transverse magnetic intensity dominates, it was determined the intensity has a dipole-like pattern. These properties agree with experimental data and discrete-dipole approximation calculations. ewline ewline Surface impedance models are of great utility in electromagnetics because they provide an efficient method for representing the material and geometrical properties of a structure without the need for fine meshing. Surface impedance models for nanoslabs, nanowires and tubular nanowires were studied in this work. A surface impedance for a variable thickness slab surrounded by free-space was derived. It was shown that for slabs of large thickness, the surface impedance agrees with the surface impedance of a half-space. A vanishingly small slab was shown to have the surface impedance of free-space as expected. The surface impedance expression for a nanowire was examined and it was shown that for larger radii nanowires the surface impedance approaches that of a half-space. For the tubular nanowire, the surface impedance was derived using modal analysis and compared to an expression developed by King. It was determined that King's expression yields different results that predict different surface impedance values for small thickness tubular nanowires. Finally, a method of moments formulation for thin-wire dipole antennas was modified to incorporate a surface impedance model. Results comparing a perfectly conducting, gold, and silver nano-dipole show the importance of incorporating material properties at infrared and optical frequencies into the electromagnetic analysis of nanostructures. By developing modeling tools for nanowires, devices may be designed for optical detection and bio-sensing.