Measuring the Dielectric Properties of Nanostructures using Optical Reflection and Transmission: Bismut Nanowires in Porous Alumina

摘要

This paper develops a method to deduce the dielectric function of nanostructures smaller than the chosen wavelength of light. It modifies the Maxwell - Garnett Effective Medium Theory equations to calculate the dielectric function of a metal embeded inside a dielectric. Specifically, reflection and transmission measurements of an array of bismuth nanowires in an anodized porous alumina template are used to calculate the frequency - dependent dielectric function of the nanowires. The spectra are taken using Fourier transform infrared spectroscopy covering the 500 to 4000 cm~(-1) frequency range. These data are used to determine the real and imaginary parts of the dielectric function of the composite materials. Next, the percentage of the total volume occupied by either Bi or air in the porous alumina (the "filling factor") was found by scanning electron microscopy. The modified Maxwell-Garnett (M-G) equations specify how to use the filling factor and the dielectric function of the composite material to calculate the dielectric function of the alumina. Finally, the modified M-G equations are used a second time to calculate the dielectric function of Bi nanowires using the dielectric function of alumina, the dielectric function of the filled template, and the filling factor. The resulting dielectric function of Bi nanowires is then compared to theoretical predictions.