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

We study the size-dependent exciton fine structure in monolayer black phosphorus quantum dots (BPQDs) deposited on different substrates (isolated, Si, and SiO2) using a combination of the tight-binding method to calculate single-particle states and the configuration interaction formalism to determine the excitonic spectrum. We demonstrate that the substrate plays a dramatic role in the excitonic gaps and excitonic spectrum of the QDs. For reasonably high dielectric constants (sub∼ Si=11.70), the excitonic gap can be described by a single power law EX(R)=EX(bulk)+C/Rγ. For low dielectric constants sub≤ SiO2=3.90, the size dependence of the excitonic gaps requires the sum of two power laws EX(R)=Eg(bulk)+A/Rn-B/Rm to describe both strong and weak quantum confinement regimes, where A, B, C, γ, 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 (SiO2 substrate) for QDs up 10 nm in size.