  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.
