Modeling of titanium diffusion into LiNbO3 using a depth-dependent diffusion coefficient

A theoretical description of the diffusion of a thin film of titanium (Ti) into a lithium niobate (LiNbO3) crystal is reported. A variable depth diffusion coefficient is used to explain the prominent lateral surface diffusion generally observed in the fabrication of Ti-diffused optical waveguides on non-Z-cut LiNbO3. A finite integral transform technique is used to solve the diffusion equation described by Fick’s law. Since the enhanced lateral diffusion is usually ascribed to anisotropic diffusion, we compare our calculations with those obtained using different diffusion coefficients for each diffusion direction. The approach with a variable depth diffusion coefficient can explain the enhancement of lateral diffusion and the peak of Ti concentration close to the surface observed experimentally.