Pressure coefficients for direct optical transitions in MoS2, MoSe2, WS2, and WSe2 crystals and semiconductor to metal transitions

Abstract

The electronic band structure of MoS2, MoSe2, WS2, and WSe2, crystals has been studied at various hydrostatic pressures experimentally by photoreflectance (PR) spectroscopy and theoretically within the density functional theory (DFT). In the PR spectra direct optical transitions (A and B) have been clearly observed and pressure coefficients have been determined for these transitions to be: αA = 2.0 ± 0.1 and αB = 3.6 ± 0.1 meV/kbar for MoS2, αA = 2.3 ± 0.1 and αB = 4.0 ± 0.1 meV/kbar for MoSe2, αA = 2.6 ± 0.1 and αB = 4.1 ± 0.1 meV/kbar for WS2, αA = 3.4 ± 0.1 and αB = 5.0 ± 0.5 meV/kbar for WSe2. It has been found that these coefficients are in an excellent agreement with theoretical predictions. In addition, a comparative study of different computational DFT approaches has been performed and analyzed. For indirect gap the pressure coefficient have been determined theoretically to be −7.9, −5.51, −6.11, and −3.79, meV/kbar for MoS2, MoSe2, WS2, and WSe2, respectively. The negative values of this coefficients imply a narrowing of the fundamental band gap with the increase in hydrostatic pressure and a semiconductor to metal transition for MoS2, MoSe2, WS2, and WSe2, crystals at around 140, 180, 190, and 240 kbar, respectively.

Direct optical transitions at K- and H-point of Brillouin zone in bulk MoS2, MoSe2, WS2, and WSe2

“…25 The van der Waals interactions, very important in geometry optimization of this type of systems, have been included via the DFT-D3 dispersion correction as proposed by Grimme et al 26 used together with generalized gradient approximation (GGA) (PBE) functional. 27 This approach provides an excellent agreement of the geometry optimization with the experimental values (less than 1% of discrepancy), as we have proven in our previous studies 28 where a detailed comparison of different approaches and functionals can be found. To improve the description of the band structure of regular LDA/GGA approach, we have used the modified Becke-Johnson exchange potential with LDA correlation (MBJLDA) 29,30 for all our band structure calculations.…”

“…This approach has been proven by us to be very effective and efficient numerous times over the years in more traditional III-V semiconductors 31,32 as well as in TMDs in Ref. 28 where a detailed reasoning of this choice is presented. A 10 Â 10 Â 6 Monkhorst-Pack mesh was used, as a result of convergence studies.…”

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

“…For direct gap semiconductors the optical transition with the lowest energy is the band gap transition, but for indirect gap semiconductors the direct optical transitions are observed in MR spectra at energies larger than the fundamental band gap. So far MR spectroscopy was applied few times to study van der Waals crystals 12,39–46 but many of them were not studied yet by this technique. In this work we use MR spectroscopy as a complementary method to study the band gap in van der Waals crystals, which allows to determine the character of band gap observed in PA spectra.…”

Оптическая диагностика монослоев WSe-=SUB=-2-=/SUB=-

“…На рис. 3, b показана энергетическая диаграмма экситонных уровней WSe 2 из работы [12]. Согласно этой диаграмме, усиление интенсивности ГВГ при энергии фотона 1.95 eV соответствует 1s(B)-экситону, что согласуется с литера-турными данными [13].…”