Measuring the Dielectric Properties of Nanostructures using Optical Reflection and Transmission: Bismuth Nanowires in Po
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ABSTRACT 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 embedded 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.
INTRODUCTION AND METHODOLOGY A material's dielectric function offers considerable insight into its electronic structure. It sheds light on the bandgap, the free carrier concentration, and the phonon frequencies. Many groups are interested in studying nanostructures using wavelengths of light larger than their sample's feature size. Unfortunately, obtaining the dielectric function at such large wavelengths requires extracting the relevant information from measurements on composite samples that include both the nanostructure of interest and the host material. Many prior studies have developed an effective medium theory (EMT) for such a situation [1-4]. When a sample is composed of more than one constituent material with the size of the constituent smaller than the wavelength (A) of the optical fields, EMT models this inhomogeneous material as a single material with a single dielectric function. In this study we utilize Maxwell-Garnett (M-G) EMT which is valid for metal nanoparticles smaller than A inside a dielectric material. M-G EMT relates the dielectric function of the composite to that of the metal and host material by : fcomposite -
fcomposite
+ K
Chost
* 6host
f
metal -
6metal
Ecomposite
+ K
* Ehost
623 Mat. Res. Soc. Symp. Proc. Vol. 581 © 2000 Materials Research Society
(1)
where K is the screening parameter and f is the volume fraction of the metal in the composite. For infinitesimally small nanowires, K = 1. EMT has been used by several groups to determine the dielectric function of a composite material when the dielectric functions of the separate materials were known [5-14]. In this study, we use M-G EMT to deduce the die
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