Dynamics of the processes of electron-hole recombination and capture of charge carriers in anatase doped with boron, carbon, or nitrogen

The first-principles investigation of the processes of nonradiative recombination of electron-hole pairs and binding of excited charge carriers with impurity atoms in anatase doped with boron, carbon, or nitrogen has been carried out using the perturbation theory method. The perturbation is provided by a dynamically screened electron-electron interaction potential calculated in the random phase approximation. It has been shown that the most probable processes occurring upon doping with boron and carbon are exchange processes in which electrons are bound with the impurity atom, whereas the most probable processes observed upon doping with nitrogen are exchange processes in which holes are bound with the impurity atom. These processes occur within a time interval of shorter than 2 fs. The next in probability are the processes of energy losses by unbound electrons and holes due to the generation of phonons. For the case of nitrogen doping, the time of this process is estimated at approximately 300 fs. For excitons formed in this case, the luminescence photon energy and the binding energy of electrons or holes with the impurity atom are estimated. The agreement between the calculated data and the results of experiments on the photocatalysis proceeding on the surface of $N$-doped anatase is discussed.