Optical refraction index and polarization profile of ferroelectric thin films

Abstract Analytical calculations of polarization and optical refraction index in ferroelectric thin films are performed in the framework of thermodynamic theory. The solution of Euler-Lagrange equation with different extrapolation lengths δ1 and δ2 on different surfaces enables to obtain the thickness dependence of inhomogeneous polarization. The maximal polarization decreases with the decrease of film thickness. The dimensionless critical thickness l 1c of thickness induced ferroelectric phase transition was expressed via extrapolation lengths and was shown to decrease from l 1c= π (δ1 = δ2 = 0) to l c = 0 (δ1, δ2 → ∞). The thickness dependence of the optical refraction index was found to be proportional to squared polarization. Refraction index and pyroelectric coefficient profiles were measured respectively by ellipsometry and LIMM methods in PbZr0,235Ti0,765O3 (PZT) thin films deposited onto Si/SiO2/ adhesion layer/(111) Pt substrate by RF sputtering. The comparison of the theory with observed refract...