Polarization field gradient effects in inhomogeneous metal-ferroelectric bilayers: Optical response and band gap tunability

Optical constants, reflectivity response and direct band gap energy (Egd) were calculated and simulated by developing an electrodynamic-based model for a three medium system, namely vacuum/ferroelectric film/metallic substrate. Depolarization effects due to the contact between the metallic substrate and the FE film, as well as the spatially dependent profile of the dielectric susceptibility ε(z) enter into the formalism by adapting the phenomenological Landau-Ginzburg-Devonshire theory (LGD). Absorption coefficient is obtained from the Lambert-Beer-Bouguer (LBB) approximation and the direct band gap energy as a function of the characteristic length is calculated by using the general Tauc power law. Numerical simulations lead to range of values for tunable Egd from 2.6 to 2.8 eV for characteristic lengths up to 30% the thickness of the film, in concordance with recent reports.