Cr migration associated with interface electric fields during transient LiNbO₃ crystal growth

The role of thermoelectric power and/or charge separation-generated electric fields upon Cr-doped LiNbO₃ crystal growth is treated by investigating both steady-state and initial transient solute redistribution based on the concept of a field-modified partition coefficient and an effective growth velocity. The magnitude of these electric field effects is dominated not only by the strength of the field but also by the solute diffusion coefficient in the phase considered. The high diffusion coefficient of Cr³⁺ in the liquid and the very low diffusion coefficient of Cr³⁺ in the solid combined with the electric field operating in the liquid leads to a strong pulling force on the Cr³⁺ from the solid through the interface into the liquid. This generates a deep solute depletion region in the solid behind the interface. An analytical solution to this depletion phenomena is given for a specific case.