Bond relaxation mechanisms of bandgap in two-dimensional materials: Layer number, composition, and electric field effects

Based on the bond-order-length-strength correlation, local bond average approach, and core–shell structural model, the layer number-, composition-, and electric field-dependent bandgaps for transition metal dichalcogenide and group-IV monochalcogenide semiconductors and their alloy materials are probed. The findings verify that the layer number effect of the bandgap is due to the surface local bond contraction and energy pinning posed by the coordination number deficiency. Using the small atom to dope the large one increases the compression lattice strain, shortens the bond length, enhances the bond energy, and raises the bandgap, whereas using the large atom to dope the small one increases the tensile lattice strain, stretches the bond length, weakens the bond energy, and decreases the bandgap. The bandgap for the monolayer system shows slight electric field dependence due to the only contribution from the weakly softened intralayer covalent bond, whereas the bandgap for the multilayer systems strongly depends on the electric field on account of the contribution from both the weakly softened intralayer covalent bond and the significantly softened interlayer van der Waals bond. This formulation goes beyond the scope of available approaches, which not only reveals quantitative information from the measurements but also offers a deeper penetration into the physical essence of the impacts of layer number, composition, and electric field on bandgap.