Thickness-dependent band gap of α-In₂Se₃: from electron energy loss spectroscopy to density functional theory calculations

α-In₂Se₃ has attracted increasing attention in recent years due to its excellent electrical and optical properties. Especially, attention has been paid to its peculiar ferroelectric and piezoelectric properties which most other two-dimensional (2D) materials do not possess. This paper presents the first measurement of the thickness-dependent band gaps of few-layer α-In₂Se₃ by electron energy loss spectroscopy (EELS). The band gap increases with decreasing film thickness which varies from 1.44 eV in a 48 nm thick area to 1.64 eV in an 8 nm thick area of the samples. Further, by combining the improved exchange-correlation potential and proper screening of the internal electric field in an advanced 2D electronic structure technique, we have been able to obtain the structural dependence of the band gap within density functional theory up to hundreds of atoms. This is also the first calculation of a similar type for 2D ferroelectric materials. Both experiment and theory suggest that the variation of the band gap of α-In₂Se₃ fits well with the quantum confinement model for 2D materials. (paper)