First-principles study of Ti-doped sapphire. II. Formation and reduction of complex defects

Abstract

Eliminating the effect of residual infrared absorption in titanium sapphire remains a crucial task to fulfill, despite that this kind of laser crystal has been developed for decades. The ${\mathrm{Ti}}^{3+}\text{\ensuremath{-}}{\mathrm{Ti}}^{4+}$ (${\mathrm{Ti}}_{\mathrm{Al}}^{0}\text{\ensuremath{-}}{\mathrm{Ti}}_{\mathrm{Al}}^{1+}$) pair model is the most widely accepted explanation to this residual absorption, but theoretical analyses based on first-principles calculation have not yet depicted a clear picture for the variation of the ${\mathrm{Ti}}_{\mathrm{Al}}^{0}\text{\ensuremath{-}}{\mathrm{Ti}}_{\mathrm{Al}}^{1+}$ pair and a variety of other potentially important defects in titanium sapphire when fabricating conditions change. Here, we extend the work in [W. Jing, M. Liu, J. Wen, L. Ning, M. Yin, and C.-K. Duan, Phys. Rev. B 104, 165103 (2021)] about binding tendencies of ${\mathrm{Ti}}_{\mathrm{Al}}\text{\ensuremath{-}}{\mathrm{Ti}}_{\mathrm{Al}}$ pairs and optical transition properties to providing a comprehensive understanding of the formation and processing condition dependence of various potentially significant defects and complexes besides the (${\mathrm{Ti}}_{\mathrm{Al}}\text{\ensuremath{-}}{\mathrm{Ti}}_{\mathrm{Al}}{)}^{0,1+}$ pairs. Apart from the complexes composed of ${V}_{\mathrm{Al}}^{3\ensuremath{-}}$ and ${\mathrm{Ti}}_{\mathrm{Al}}^{0,1+}$ defects, two new significant negatively charged defects, ${({V}_{\mathrm{Al}}\text{\ensuremath{-}}{\mathrm{Al}}_{i}\text{\ensuremath{-}}{V}_{\mathrm{Al}})}^{3\ensuremath{-}}$ and ${({V}_{\mathrm{Al}}\text{\ensuremath{-}}{\mathrm{Ti}}_{i}\text{\ensuremath{-}}{V}_{\mathrm{Al}})}^{2\ensuremath{-}}$ are revealed. These two complexes are correspondingly an interstitial ${\mathrm{Al}}^{3+}$ and ${\mathrm{Ti}}^{4+}$ surrounded by two neighboring aluminium vacancies ${V}_{\mathrm{Al}}^{3\ensuremath{-}}$. We show that ${V}_{\mathrm{Al}}^{3\ensuremath{-}}$ plays the key role to stabilize ${\mathrm{Ti}}_{\mathrm{Al}}^{0}\text{\ensuremath{-}}{\mathrm{Ti}}_{\mathrm{Al}}^{1+}$ and form various stable complexes with ${\mathrm{Ti}}_{\mathrm{Al}}^{1+}$ and ${\mathrm{Ti}}_{\mathrm{Al}}^{0}\text{\ensuremath{-}}{\mathrm{Ti}}_{\mathrm{Al}}^{1+}$ in weak and moderate reductive atmospheres. Thus, besides annealing at strong reductive atmosphere at elevated temperatures, Al ion injection or annealing in Al vapor is a potential method to eliminate the harmful residual infrared absorption, which is pinpointed at the reduction of the concentration of ${V}_{\mathrm{Al}}^{3\ensuremath{-}}$ and its variant ${({V}_{\mathrm{Al}}\text{\ensuremath{-}}{\mathrm{Al}}_{i}\text{\ensuremath{-}}{V}_{\mathrm{Al}})}^{3\ensuremath{-}}$. While in extremely strong reductive atmosphere, isolated Ti substitution dominates over those complexes containing ${V}_{\mathrm{Al}}^{3\ensuremath{-}}$, but there still remains a tiny amount of ${\mathrm{Ti}}_{\mathrm{Al}}^{0}\text{\ensuremath{-}}{\mathrm{Ti}}_{\mathrm{Al}}^{1+}$ and ${\mathrm{Ti}}_{\mathrm{Al}}^{1+}$, which are charge compensators to balance the charge of trace amount ${\mathrm{Ti}}_{\mathrm{Al}}^{1\ensuremath{-}}$ further reduced from ${\mathrm{Ti}}_{\mathrm{Al}}^{0}$. And this effect can be further eliminated by lower temperature reductive-atmosphere annealing. In addition, we obtain a simple numerical expression to predict the achievable figure of merit when the concentration of ${\mathrm{Ti}}_{\mathrm{Al}}^{1+}$ is given. Formation energies for simple defects and binding energies for complexes obtained in this work may serve as the basis for simulations and design various quenching and annealing processes to further reduce harmful defect species in titanium sapphire.