Excitons in a disordered medium: A numerical study in InGaN quantum wells

Abstract

Excitons in InGaN quantum wells are investigated numerically, considering random alloy disorder and Coulomb interaction on equal footing in the Schrödinger equation. Their statistical properties are systemically explored as a function of the quantum well thickness and composition, revealing a complex competition between disorder-induced carrier localization, Coulomb attraction, and field-induced wave function separation. This results in a class of semiconductor quasiparticle with hybrid properties in between hydrogenoid excitons and disorder-localized free particles. Exciton screening by free carriers is investigated and shows distinct behavior from the screening of bulk excitons. Finally, a highly accurate approximate solution of the excitonic Schrödinger equation, with reduced numerical complexity, is introduced.