Diffusivity, solubility and thermodynamic modelling of diffusion growth of Ga³⁺-doped LiTaO₃ thin film for integrated optics

A thermodynamic study was performed on diffusion growth of Ga³⁺-doped LiTaO₃(LT) thin film for integrated optics. Some Ga³⁺-doped LT thin films were grown on LT surface by in-diffusion of homogeneously coated Ga₂O₃ film at the temperature range of (1273 to 1473) K. After growth, the refractive indices at Ga³⁺-doped and un-doped surface parts were measured by prism coupling technique and Li composition there was evaluated from the measured refractive indices. The results show that Ga³⁺ dopant has small effect on the LT index. Li₂O out-diffusion is not measurable. The Ga³⁺ profile in the grown thin film was analysed by secondary ion mass spectrometry. It is found that the grown Ga³⁺ ions follow a complementary error function profile. A thermodynamic model for Ga³⁺ diffusion growth is suggested and verified experimentally. From the measured Ga³⁺ profiles, some thermodynamic parameters were obtained. These include diffusivity, diffusion constant, chemical activation energy, solubility, solubility constant and enthalpy of solution. These parameters are crucial to design and growth of a desired Ga³⁺-doped LT thin film for integrated optics. Comparison shows that Ga³⁺ grows in LT two orders faster than Ti⁴⁺ because of its smaller radius. Ga³⁺ diffusivity/solubility in LT is one order/1.5-fold lower than in LiNbO₃ because Ta has a larger atomic mass and hence a lower mobility than Nb.