Modeling of X-ray excited luminescence intensity dependence on the nanoparticle size

Abstract

The thermalization length distribution of electrons over their kinetic energy in a conduction band is calculated on the basis of the data on the electron effective mass, density of states in conduction band, dielectric permittivity and energy of longitudinal optical phonons. The method of modeling of a recombinational luminescence intensity dependence on the nanoparticle size is proposed on the basis of the assumption that the contribution to a recombinational luminescence gives only those charge carriers which in the result of thermalization did not reach a near-surface layer of nanoparticles. Using such the approach the theoretical dependence of recombinational luminescence intensity on the nanoparticle size for LaPO$_4$ and LuPO$_4$ are calculated. The revealed correlation of experimental and theoretical dependences confirms that the commensurability of electron thermalization length with nanoparticle size is the main reason of the sharp decrease of X-ray excited luminescence intensity when the nanoparticle size decreases