Simulation of Ti diffusion into LiNb O₃ in Li-rich atmosphere

A model is proposed for describing two-dimensional diffusion of Ti into an initially congruent LiNb O3 crystal under a Li-enriched atmosphere created by a mixed two-phase (Li3 Nb O4 and LiNb O3) powder at elevated temperature [vapor transport equilibration (VTE)]. The influence of VTE treatment on Ti diffusivity is considered in the model. To solve the model, four key input parameters including Li-concentration-dependent Li and Ti diffusivities and two switching times t1 and t2 were determined. Prior to solve the Ti-diffusion model, a one-dimensional VTE model is solved at first to obtain the dynamic Li2 O concentration depth profile. Both the Li-diffusion and Ti-diffusion models were solved by using finite difference method. Based on secondary-ion-mass spectrometry analysis, the validity of the VTE and Ti-diffusion models as well as the numerical method employed are confirmed. After that, diffusion at 1100 °C of an 8-μm -wide, 100-nm -thick Ti strip defined on the surface of a Z -cut or an X -cut substrate was simulated for the VTE duration up to 130 h. Based on the numerical results, the Ti-(Li-)diffusion characteristics are discussed in the aspects of (1) the relation of depth and width profile function of Ti concentration to the VTE duration, (2) the substrate cut effect on both the Ti and Li diffusions, (3) the relation of the 1e Ti-concentration depth and half-width to the VTE duration, and (4) the VTE duration dependence of the mean [Li] [Nb] ratio within the Ti-diffused layer.