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

Abstract

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 (MoS 2 , MoSe 2 , MoTe 2 , HfS 2 , HfSe 2 , WS 2 , WSe 2 , ReS 2 , ReSe 2 , SnS 2 and SnSe 2 ) 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.Van der Waals (vdW) crystals are known for a long time 1-14 but in recent years some of them have gained significant interest because of unique mechanical and optical properties of samples obtained by exfoliation of bulk material to atomically thin layers [15][16][17][18][19][20][21][22][23][24][25] . Since pioneering reports on optical properties of MoS 2 layers 15,16 , it is well established that the electronic band structure of MoS 2 strongly varies with the number of layers and exhibits indirect-to-direct band gap transition with the size reduction to a single layer. Similar studies of optical properties and the electronic band structure have been performed on other van der Waals crystals such as MoSe 2 , MoTe 2 , WS 2 , and WSe 2 22-25 . Some of them were investigated quite recently as bulk materials 13,14 but interest in these materials was low due to no potential applications in semiconductor devices. At this moment the situation is different. VdW crystals are exciting because of interesting physics of two-dimensional (2D) layers and their potential applications in novel semiconductor devices [26][27][28] . Because of this even bulk van der Waals crystals are interesting to study since many of them are not explored experimentally. One method which has never been applied to study most of van der Waals crystals is photoacoustic (PA) spectroscopy. We show that this technique is an excellent tool to study the band gap in van der Waals crystals since it is sensitive to indirect gap transitions which cannot be observed in photoluminescence. In combination with modulated reflectance (MR), which is known as a state of the art absorption-like technique to study direct optical transitions 29 , it is possible to conclude about the band gap character in van der Waals crystals and the spectral separation between the indirect and direct gap. In this work we applied PA and MR to study indirect and direct gap in many van der Waals crystals ...

Non equilibrium anisotropic excitons in atomically thin ReS 2

“…43 The latter is in agreement with our DFT calculations presented in Supplementary Information and absorption measurements for the bulk crystals. [18][19][20][21]45 However, none of these prediction is fully supported by the PL behavior as we show in the next paragraphs.…”

“…4,5,38,[42][43][44] Studies regarding the absorption edge indicate that both materials have an indirect band gap in the bulk form. [18][19][20][21]45 This assignment is supported by recent angle-resolved photoemission spectroscopy (ARPES) 44 and photoemission electron microscopy (PEEM) 43 for the few-and monolayer crystals. However, the observed PL 3,5,46 might suggest a direct nature of the band gap in this semiconductor.…”

Hidden spin-polarized bands in semiconducting 2H-MoTe2

“…Molybdenum ditelluride (2H-MoTe 2 ) is a semiconductor that belongs to the family of transition metal dichalcogenides (TMDCs), which are layered crystals of the form MX 2 (M being a transition metal and X a chalcogenide). Amongst all semiconducting TMDCs, MoTe 2 is unique because it exhibits the smallest indirect (direct) band gap, around 0.85 eV (1.15 eV) [1]. Hence, the small gap of MoTe 2 allows to extend the optoelectronic applications of TMDCs into the near-infrared range, close to the band gap of silicon.…”

“…So far TMDCs have been investigated both at high and ambient pressure by several modulation spectroscopies including photoreflectance (PR). Measurements at ambient pressure resolved many excitonic transitions (including A and B) and assigned most of them to direct transitions in the band structure [1,12,18]. High-pressure PR measurements allowed to establish the pressure coefficients for the A and B transitions and infer the semiconductor to metal transition pressure of MoS 2 , MoSe 2 , WS 2 and WSe 2 [19].…”

Electronic Band Structure of Rhenium Dichalcogenides

“…The recent photoacoustic spectroscopy study gives an indirect gap of 1.18 eV and direct gap of 1.31 eV [30]. However, both computational studies only report band dispersions along specific paths in the BZ and it would be interesting in future to apply these more sophisticated models to the whole BZ.…”