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

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 one of standard specifications of commercial Ti:sapphire laser crystals. 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. The role of codoping in the control of the charge state of dopants is analyzed. 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.

Luminescence Properties of Al2O3:Ti in the Blue and Red Regions: A Combined Theoretical and Experimental Study

“…It is at this point that theoretical calculations must play a pivotal role. Nevertheless, despite the intense development of new theoretical calculation techniques, one could not fully assess the Ti-related luminescence properties in Al 2 O 3 so far, even though some electronic transitions (through defect formation enthalpy computations) and defect formation energies are known. − The luminescence properties are still challenging to model, and up to now, nobody succeeded in simulating simultaneously the red and the blue luminescence signatures with a good accuracy. In this paper, we draw upon recent computational techniques that we have developed with the aim of simulating luminescence.…”