Thermodynamics of carrier distribution within localized electronic states with a broad Gaussian energy distribution and its effect on luminescence behavior of localized states

A new carrier distribution function is derived to describe the the thermodynamics of carriers within localized states with a broad energy distribution. With the aid of this function, several luminescence behaviors, i.e., (1) fast redshift of peak positions at low temperatures; (2) decrease of full-width-at-half-maximum (FWHM) of luminescence band at low temperatures; and (3) blueshift of peak positions at high temperatures, frequently observed in above material systems can be explained. Finally, the model is employed to fit the experimental data of cubic InGaN thin film grown on GaAs. A good agreement between the experimental data and the theoretical fitting is obtained.