Optical absorption by titanium dioxide nanocrystals

Using a variational method within the framework of the effective mass approximation, using a triangular coordinate system of an electron, hole, and exciton moving in a titanium dioxide quantum dot, the exciton energy spectrum was obtained as a function of the radius a of the quantum dot. The variational wave function of the exciton contained factors that took into account the motion of an electron and a hole in a potential well of infinite depth of a quantum dot, as well as the form of a hydrogen-like wave function. It is shown that the occurrence of an exciton in a quantum dot has a threshold character. An exciton, as a bound state of an electron and a hole, is formed starting from a certain critical radius ac, the value of which exceeds the Bohr radius of the exciton in titanium dioxide. The exciton energy levels are located in the band gap of the titanium dioxide quantum dot. In this case, with an increase in the radius a of the quantum dot (so that a≥ac), a band of exciton states appears in the band gap of the titanium dioxide quantum dot. The mechanism for the formation of optical absorption spectra in nanosystems containing titanium dioxide nanocrystals are presented. It is found that the optical absorption of anatase NC, which was observed under the experimental conditions, was due to the appearance of an exciton in the NC. Using the variational calculation of the energy spectrum of an exciton in NC, the position of the absorption peak of NC anatase was determined. This absorption peak differs slightly from the absorption peak, which was obtained in the experimental work.