Determination of critical parameters for design of semiconductor hyperbolic metamaterials

Abstract Hyperbolic metamaterials (HMM) are receiving considerable attention due to their unique properties and are leading to many exciting new application such as modified emission, negative refraction, and enhanced wave guiding. Application and properties of the semiconductor HMMs stem from the fact that a negative dielectric response is achieved for one of the principal components resulting in an “infinite” density of states. Key parameters in designing these stacks are the free electron character of the metallic component and the thickness of the metallic and dielectric regions. Metallic layers are achieved through degenerate doping of a semiconductor layer. In this article, we show that the nominal key parameters are in fact significantly different from the as-grown structure. However when appropriate values are used the effective medium theory accurately represents the optical properties of the composite structure. We show changes occur in both the metal carrier concentration and the thickness of the metallic and semiconductor regions. We argue the change from the nominal structures could result from a combination of simple band bending and depletion effects, which results in an undoped region in the original metallic layer and increased carrier concentration in the remaining metallic region. These effects must be taken into account to accurately predict the properties when designing structures using semiconductor HMMs.