Energy fluctuations in optical transitions in CuHal crystals

This paper reports on a comprehensive study of fundamental-absorption spectra of CuCl and CuBr nanocrystals measured in the temperature range extending from 80 K up to the melting point. The temperature dependences of the energy E, oscillator strength f, and temperature-broadening coefficient σ of optical-transition spectral to excitonic states were determined. A new approach to the calculation of the shape and temperature-broadening of absorption spectra, based on quantum statistics, was employed. The crystal is treated as a quantum statistical ensemble. The set of atoms involved in the electronic transition initiated by a photon absorption is taken as an element of the ensemble. Energy fluctuations of electronic states occurring in the elements of the ensemble give rise to temperature broadening of the optical-transition spectra. The temperature dependence of the χ coefficient of thermodynamic fluctuations of the Z _{1, 2} and Z ₃ exciton states was found. A theoretical substantiation of the Urbach rule was obtained in terms of the model proposed.