Anisotropic energy funneling effect in wrinkled monolayer GeSe

Two-dimensional materials with tunable wrinkled structures opening up new avenue to modulate their electronic and optoelectronic properties. However, the formation mechanisms of wrinkles and their influences on the band structures and associated properties remains unclear. Here, we investigate the strain distributions, bandgap, and anisotropic energy funneling of wrinkled monolayer GeSe and their evolution with the wrinkle wavelength based on the atomic-bond-relaxation approach and continuum medium mechanics. We find that the top and valley regions of wrinkled monolayer GeSe exhibit tensile and compressive strains, respectively, and the strain increases with decreasing wrinkle wavelength. Moreover, the periodic undulation strain in the wrinkles can lead to continuously adjustable bandgaps and band edges in wrinkled monolayer GeSe. For zigzag wrinkled monolayer GeSe, when the wrinkle wavelength is large, the conduction band minimum (valence band maximum) continuously decreases (increases) from the top to the valley, forming an energy funneling. As a result, the excitons accumulate in the valley of wrinkles, and their accumulation ability increases with decreasing wrinkle wavelength. However, as the wavelength further decreases, the energy funneling will disappear, resulting in the excitons to part accumulate at the top of wrinkles and another part to accumulate at the valley of wrinkles. The critical wavelength for disappearance of energy funneling of zigzag wrinkled GeSe is 106nm. The physical origin is that when the top strain exceeds 4%, the bandgap will decrease. Due to the monotonic variation of bandgap with strain, the energy funneling effect of armchair wrinkled monolayer GeSe is still retained when the wavelength is reduced to 80 nm, and the accumulation of excitons is further enhanced. Our results demonstrate that the energy funneling effect induced by nonuniform can realize excitons accumulation in one material without the need for p-n junctions, which is of great benefit to collection of photogenerated excitons. Therefore, the proposed theory not only clarifies the physical mechanism regarding the anisotropic energy funneling effect of wrinkled monolayer GeSe, but also provides a new avenue to design next-generation optoelectronic devices.