Anisotropic energy funneling effect in wrinkled monolayer GeSe

Two-dimensional materials with tunable wrinkled structures open up a new way to modulate their electronic and optoelectronic properties. However, the mechanisms of forming wrinkles and their influences on the band structures and associated properties are still unclear. Here, we investigate the strain distribution, bandgap, and anisotropic energy funneling effect 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 region and valley region of wrinkled monolayer GeSe exhibit tensile and compressive strains, respectively, and the strain increases with wrinkle wavelength decreasing. 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 long, the conduction band minimum value (valence band maximum value) continuously decreases (increases) from the top to the valley, forming an energy funnel. As a result, the excitons accumulate in the valleys of wrinkles, and their accumulation capability increases with wrinkle wavelength decreasing. However, as the wavelength further decreases, the energy funnel will disappear, causing some excitons to t accumulate at the top of wrinkles, while the remaining excitons will accumulate in the valleys of wrinkles. The critical wavelength for the energy funnel of zigzag wrinkled GeSe to disappear is 106nm. The physical origin is that when the top strain exceeds 4%, the bandgap will decrease. Owing to the monotonic variation of bandgap with strain, the energy funneling effect of armchair wrinkled monolayer GeSe is still retained when the wavelength decreases 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 of p-n junctions, which is of great benefit to the 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 for designing the next-generation optoelectronic devices.