Photoluminescence efficiency of MBE-grown MoSe$_2$ monolayers featuring sharp excitonic lines and diverse grain structures

Recent studies have demonstrated that using h-BN as a substrate for the growth of transition metal dichalcogenides can significantly reduce excitonic linewidths. However, many other optical parameters still require optimization. In this work, we present a detailed study of the low-temperature photoluminescence efficiency of MBE-grown MoSe$_2$ monolayers on h-BN substrates, comparing them to state-of-the-art exfoliated monolayers encapsulated in h-BN. We demonstrate that a quantitative comparison between samples requires accounting for interference effects and Purcell enhancement or suppression of the emission. By accounting for these effects in both photoluminescence and Raman signals, we show that the overall intrinsic luminescence efficiency is proportional to the sample coverage. Consequently, we find that exciton diffusion and edge effects are negligible in spectroscopy of MBE-grown samples, even for nanometer-sized crystals.