Abstract
Excitons in InGaN quantum wells are investigated numerically, considering random alloy disorder and Coulomb interaction on equal footing in the Schr\"odinger 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 Schr\"odinger equation, with reduced numerical complexity, is introduced.
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