An analytical method to determine the complex refractive index of an ultra-thin film by ellipsometry

Abstract

We proposed a completely analytical method to determine the complex refractive index of an ultra-thin film on an arbitrary substrate by ellipsometry. The method is based on directly solving the polynomial equation derived from the 2nd-order Taylor expansion of ellipsometric functions without any prior knowledge about electronic transitions of the material. Numerical simulations demonstrate that the proposed method can be applied to deal with ultra-thin films with a wide thickness range from a single atomic layer to 5 nm over an ultra-broad spectral range from deep ultraviolet to infrared regions. With the proposed method, complex refractive indices of typical two-dimensional (2D) materials, including the monolayer graphene and 1–3 layer WSe2, were experimentally investigated over an ultra-wide spectral range (193–1690 nm). The proposed method shows great potential in the accurate determination of complex refractive indices of ultra-thin films especially the emerging 2D materials.