Electro-optical properties of Cu$_2$O in the regime of Franz-Keldysh oscillations

TL;DR

This paper introduces an analytical method to compute optical properties of Cu$_2$O under electric fields, capturing excitonic effects and FK oscillations, with numerical illustrations for P excitons.

Contribution

An analytical approach that accounts for coherence, excitonic effects, and FK oscillations in the optical functions of semiconductors under electric fields.

Findings

Quantitative description of FK oscillation amplitudes and periodicity.

Influence of Rydberg excitons on FK effects.

Numerical illustrations for Cu$_2$O P excitons.

Abstract

We present the analytical method enables one to compute the optical functions i.e., reflectivity, transmission and absorption including the excitonic effects for a semiconductor crystal exposed to a uniform electric field for energy region above the gap, for external field suitable to appearance of Franz-Keldysh (FK) oscillations. Our approach intrinsically takes into account the coherence between the carriers and the electromagnetic field. We quantitatively describe the amplitudes and periodicity of FK modulations and the influence of Rydberg excitons on FK effect is also taking into account. Our analytical findings are illustrated numerically for $P$ excitons in Cu$_2$O crystal.