Photoacoustic and modulated reflectance studies of indirect and direct band gap in van der Waals crystals

Photoacoustic (PA) and modulated reflectance (MR) spectroscopy have been applied to study the indirect and direct band gap for van der Waals (vdW) crystals: dichalcogenides (MoS2, MoSe2, MoTe2, HfS2, HfSe2, WS2, WSe2, ReS2, ReSe2, SnS2 and SnSe2) and monochalcogenides (GaS, GaSe, InSe, GeS, and GeSe). It is shown that the indirect band gap can be determined by PA technique while the direct band gap can be probed by MR spectroscopy which is not sensitive to indirect optical transitions. By measuring PA and MR spectra for a given compound and comparing them with each other it is easy to conclude about the band gap character in the investigated compound and the energy difference between indirect and direct band gap. In this work such measurements, comparisons, and analyses have been performed and chemical trends in variation of indirect and direct band gap with the change in atom sizes have been discussed for proper sets of vdW crystals. It is shown that both indirect and direct band gap in vdW crystals follow the well-known chemical trends in semiconductor compounds.