On the way to modelling dopant valence in ionic crystal growth: the Ti:Al2O3 case
Dopant valence and ion distributions during the growth of ionic crystals are investigated with the aim of establishing a physico-chemical model for further numerical simulation of their behavior during the crystal growth process. Ti-doped sapphire growth is studied as an example. It is shown that the relevant physical parameters including diffusion coefficient and reaction rate constant of corresponding point defects and chemical reactions, as well as appropriate boundary conditions, can be obtained from annealing experiments under various atmospheres and temperatures, or from transport mechanism studies. The point defect diffusion–reaction model is then applied to the simulation of Ti ion distributions in Ti:Al2O3 Czochralski growth. The effect of temperature gradient and growth rate is studied. The series of steps needed in order to establish an efficient model is discussed.