Origin of Indirect Optical Transitions in Few-Layer\nMoS₂, WS₂, and WSe₂

Abstract

It has been well-established that\nsingle layer MX₂ (M\n= Mo, W and X = S, Se) are direct gap semiconductors with band edges\ncoinciding at the K point in contrast to their indirect gap multilayer\ncounterparts. In few-layer MX₂, there are two valleys along\nthe Γ–K line with similar energy. There is little understanding\non which of the two valleys forms the conduction band minimum (CBM)\nin this thickness regime. We investigate the conduction band valley\nstructure in few-layer MX₂ by examining the temperature-dependent\nshift of indirect exciton photoluminescence peak. Highly anisotropic\nthermal expansion of the lattice and the corresponding evolution of\nthe band structure result in a distinct peak shift for indirect transitions\ninvolving the K and Λ (midpoint along Γ-K) valleys. We\nidentify the origin of the indirect emission and concurrently determine\nthe relative energy of these valleys.