Band-Gap Engineering in two-dimensional periodic photonic crystals

TL;DR

This paper theoretically analyzes the dispersion of plasmons in two-dimensional periodic semiconductor-dielectric systems, revealing large band gaps that could impact semiconductor device design in solid state plasmas.

Contribution

It introduces a comprehensive plane-wave method analysis of plasmon band structures in 2D periodic systems, highlighting the existence of significant low-frequency band gaps.

Findings

Large full band gaps with a gap to midgap ratio of about 2.

The lowest band gap extends from a threshold frequency down to zero.

Greater dielectric mismatch results in larger lowest band gaps.

Abstract

A theoretical investigation is made of the dispersion characteristics of plasmons in a two-dimensional periodic system of semiconductor (dielectric) cylinders embedded in a dielectric (semiconductor) background. We consider both square and hexagonal arrangements and calculate extensive band structures for plasmons using a plane-wave method within the framework of a local theory. It is found that such a system of semiconductor-dielectric composite can give rise to huge full band gaps (with a gap to midgap ratio $\approx 2$) within which plasmon propagation is forbidden. The most interesting aspect of this investigation is the huge lowest gap occurring below a threshold frequency and extending up to zero. The maximum magnitude of this gap is defined by the plasmon frequency of the inclusions or the background as the case may be. In general we find that greater the dielectric (and plasmon frequency) mismatch, the larger this lowest band-gap. Whether or not some higher energy gaps appear, the lowest gap is always seen to exist over the whole range of filling fraction in both geometries. Just like photonic and phononic band-gap crystals, semiconducting band-gap crystals should have important consequences for designing useful semiconductor devices in solid state plasmas.