Substrate effects on the exciton fine structure of black phosphorus quantum dots

Abstract

We study the size-dependent exciton fine structure in monolayer black phosphorus quantum dots (BPQDs) deposited on different substrates (isolated, Si and SiO${}_2$) using a combination of tight-binding method to calculate the single-particle states, and the configuration interaction formalism to determine the excitonic spectrum. We demonstrate that the substrate plays a dramatic role on the excitonic gaps and excitonic spectrum of the QDs. For reasonably high dielectric constants (${\epsilon }_{sub}\sim {\epsilon }_{Si}=11.7{\epsilon }_0$), the excitonic gap can be described by a single power law $E_X(R)=E_X^{(bulk)}+C/R^{\gamma }$. For low dielectric constants ${\epsilon }_{sub}\le {\epsilon }_{Si{O}_2}=3.9{\epsilon }_0$, the size dependence of the excitonic gaps requires the sum of two power laws $E_X(R)=E_g^{(bulk)}+A/R^n-B/R^m$ to describe both strong and weak quantum confinement regimes, where $A$, $B$, $C$, $\gamma$, $n$, and $m$ are substrate-dependent parameters. We also predict that the exciton lifetimes exhibit a strong temperature dependence, ranging between 2-8 ns (Si substrate) and 3-11 ns (SiO${}_2$ substrate) for QDs up 10 nm in size.