Spin-orbital effects on the rationalization of quantum-confinement in few quasi-2D metal-dichalcogenides 2H- MX 2 ( M = Mo, W; X = S, Se, Te)

Abstract The quantum-confinement (QC) phenomena in quantum-size quasi-2D solids of transition-metal dichalcogenides (TMDs) are viable to investigate from optoelectronic and photocatalytic perspectives. Here, we have investigated the QC effect using first-principles calculations within density functional theory (DFT) and crystal structure modelling on six hexagonal TMDs, exfoliated from bulk stochiometric 2H- M X 2 ( M = Mo, W and X = S, Se, Te). Local and non-local DFT functional are applied to get geometries of these bulk TMDs and better geometry was obtained from the later one. Pertaining to the inter-layer, intra-layer and spin-orbital coupling (SOC) energies correction on better geometries, our present study rationalizes the QC effect bridging the known experimental evidences of wires (1D) and dots (3D) quantum-size solids. Local and non-local DFT functional is benchmarked with present and previous theoretical data. The cancelation of errors on inter-planer van der Waals spacing ( d v , underestimated) and intra-layer M X 2 thickness ( d t , overestimated) was noticed. SOC bands splitting versus Fermi level ( E F = 0.0 eV), perturbed the nature of optical transitions on-set (direct or indirect) in absolute band gaps ( E g ) opening in bulk versus d t and d v thickness. The layer dependent E g and its deviation ( ∆ E g ) in ultra-thin quantum-size model versus the bulk phase, is also closely associated with SOC effects. S-/Se-based TMDs switch from direct to indirect E g in the monolayer to bi-layers, but the similar multi-layered Te-TMDs are still likely to be direct gap, E g —unfold the possible atomistic role of SOC, inter- and intra-layers interactions on non-forbiden optical transitions. Quantification of QC effect is done based on the estimated slopes ( C ) ≈ 150–300 eV-Å 2 in wells (quasi-2D) and aligned excellent to the known trend for wires and dots, C ≈ 380–400 and 600–620 eV-Å 2 , respectively. Finally, the microscopic origin of the QC effect from k- space resolved bands dispersions allowed to conclude lowest quasi-2D thickness of 3–4 nm for these TMDs.