Indirect-to-direct bandgap transition in few-layer $\beta$-InSe as probed by photoluminescence spectroscopy

InSe is a promising material for a next-generation of two-dimensional electronic and optical devices, characteristics of which are largely determined by the type of band structure, direct or indirect. In general, different methods can be sensitive to different peculiarities of the electronic structure leading to different results. In this work, we will focus on the luminescent properties of few-layer $\beta$-InSe with a thickness of 6 to 75 monolayers (ML). Low-temperature micro-photoluminescence ($mu$-PL) studies show a sharp increase in PL intensity in the range of thicknesses from 16 to 20 monolayers, where, in addition, there is a singularity in the dependence of the work function on the thickness. Time-resolved photoluminescence spectroscopy (TRPL) reveals three characteristic PL decay times that differ from each other by about an order of magnitude. We associate the processes underlying the two faster decays with the recombination of electrons and holes between the band extrema, either directly or through the interband relaxation of holes. Their contributions to the total PL intensity increase significantly in the same thickness range, 16-20 MLs. On the contrary, the slowest contribution, which we attribute mainly to the defect-assisted recombination, prevails at a smaller number of monolayers and then noticeably decreases. These results indicate the indirect-to-direct bandgap transition near 16-20 MLs, which determines the range of applicability of a few-layer $\beta$-InSe for efficient light emitters.