Refractive index and dielectric constant transition of ultra-thin gold from cluster to Film

Xuefeng Wang,Ming Zhao,Kuo-Ping Chen,David D Nolte

doi:10.1364/oe.18.024859

Abstract

Using high-speed picometrology, the complete cluster-to-film dielectric trajectories of ultra-thin gold films on silica are measured at 488 nm and 532 nm wavelengths for increasing mass-equivalent thickness from 0.2 nm to 10 nm. The trajectories are parametric curves on the complex dielectric plane that consist of three distinct regimes with two turning points. The thinnest regime (0.2 nm-0.6 nm) exhibits increasing dipole density up to the turning point for the real part of the dielectric function at which the clusters begin to acquire metallic character. The mid-thickness regime (0.6 nm~2 nm) shows a linear trajectory approaching the turning point for the imaginary part of the dielectric function. The third regime, from 2 nm to 10 nm, clearly displays the Drude circle, with no observable feature at the geometric percolation transition.

Highlights

The noble metals lie at the interface between optical and electronic physics [1]
The trajectories are parametric curves on the complex dielectric plane that consist of three distinct regimes with two turning points
We extracted g of gold films with arbitrary thickness in the range of 0.2 nm to 10 nm, and demonstrated that the g trajectory traces out the Drude circle for massequivalent thicknesses greater than 2 nm

Summary

Introduction

The noble metals lie at the interface between optical and electronic physics [1]. As the scale of metal nanophotonic and plasmonic elements shrink, metallic behavior becomes size dependent, and thin layers fragment into clusters that have different optical properties than the bulk [2,3]. Traditional methods select two or more photonic states of the probe light, such as wavelength, polarization or incidence angle [4] to execute multiple-parameter measurements. Ellipsometry measures n by monitoring reflectances at two different polarization states of oblique-incident light [8,9]. Changing the photonic state of the probe light potentially limits the measurement of n because of optical dispersion or anisotropy which occurs for sub-nanometer metal films. These consequences limit the validity of traditional methods in the ultra-thin regime. Ellipsometric measurements become erratic when the gold film thickness is below 6 nm [7,10]

Methods

Discussion

Conclusion