Control of charge state of dopants in insulating crystals: Case study of Ti-doped sapphire

TL;DR

This study uses density functional theory to analyze how to control the charge states and defect concentrations in Ti-doped sapphire crystals, aiming to optimize their laser performance.

Contribution

It introduces a theoretical approach to predict defect concentrations and the effects of codoping, guiding the fabrication of high-quality Ti:sapphire laser crystals.

Findings

The ratio of Ti$^{3+}$ to Ti$^{4+}$ is inversely proportional to Ti$^{4+}$ concentration.

Codoping with nitrogen increases Ti$^{4+}$ concentration and decreases FOM.

Growth or annealing with nitrogen is unfavorable for high-performance Ti:sapphire crystals.

Abstract

We study mechanisms of control of charge state and concentration of different point defects in doped insulating crystals. The approach is based on the density functional theory calculations. We apply it to the problem of obtaining of Ti-doped sapphire crystals with high figure-of-merit (FOM). The FOM of a given sample is defined as the ratio of the coefficient of absorption at the pump frequency to the coefficient of absorption at the working frequency of Ti:sapphire laser. It is believed that FOM is proportional to the ratio of the concentration of isolated Ti$^{3+}$ ions to the concentration of Ti$^{3+}$-Ti$^{4+}$ pairs. We find that generally this ratio is in inverse proportion to the concentration of Ti$^{4+}$ isolated substitutional defects with the coefficient of proportionality that depends on the temperature at which the thermodynamically equilibrium concentration of defects is reached. We argue that in certain cases the inverse proportion between concentrations of Ti$^{3+}$-Ti$^{4+}$ and Ti$^{4+}$ may be violated. We show that codopants that form positively (negatively) charged defects may decrease (increase) the concentration of positively charged defects formed by the main dopants. To evaluate the effect of codoping it is important to take into account not only isolated defects but defect complexes formed by codopants, as well. In particular, we show that codoping of Ti:sapphire with nitrogen results in an essential increase of the concentration of Ti$^{4+}$ and in a decrease of the FOM, and, consequently, growth or annealing in the presence of nitrogen or its compounds is unfavorable for producing Ti:sapphire laser crystals. The approach developed can be used for determining appropriate growth and annealing conditions for obtaining doped crystals with the required characteristics.