A model was proposed for describing the 2-dimensional diffusion of Ti into an initially congruent LiNbO3 crystal under a Li-enriched atmosphere created by a mixed 2-phase (Li3NbO4 + LiNbO3) powder at high temperatures. The influence of this vapor transport equilibration treatment upon Ti diffusivity was included in the model. In order to solve the model, 4 key input parameters including Li-concentration dependent Li and Ti diffusivities and 2 switching times were determined. Prior to solving the Ti-diffusion model, a 1-dimensional vapor transport equilibration model was first solved in order to obtain the dynamic Li2O-concentration depth profile. The Li-diffusion and Ti-diffusion models were solved by using finite difference methods. Based upon secondary-ion mass spectrometry analyses, the validity of the vapor transport equilibration and Ti-diffusion models, as well as of the numerical method used, were confirmed. Diffusion at 1100C of an 8µm-wide, 100-nm-thick Ti strip defined on the surface of a Z-cut or an X-cut substrate was then simulated for vapor transport equilibration durations of up to 130h. Based upon the numerical results, the Ti- and Li-diffusion characteristics were considered with regard to the relationship of the depth and width profile functions of the Ti concentration to the vapor transport equilibration duration, and to the substrate-cut effect upon both the Ti and Li diffusion. Also considered were the relationship of the 1/e Ti-concentration depth and half-width to the vapor transport equilibration duration, and the vapor transport equilibration duration dependence of the mean [Li]/[Nb] ratio within the Ti-diffused layer.

Simulation of Ti Diffusion into LiNbO3 in Li-Rich Atmosphere. D.L.Zhang, Y.R.Zhuang, P.R.Hua, E.Y.B.Pun: Journal of Applied Physics, 2007, 101[1], 013101 (11pp)