Trapping kinetics in high trap density silicon nitride insulators

An analytical method has been developed to investigate the trapping kinetics of multiple trap levels in a silicon nitride insulator under very complex conditions. Solutions for the trapped-charge distribution are given for the case of a nonuniform single carrier current in an insulator having very strong charge trapping and various detrapping mechanisms such as Poole-Frenkel emission or photoionization. The trapped-charge distribution is given in terms of a series in the position and time variables, and is given for a single trap level, several trap levels, and an energy distribution of traps. In the more complex models, the series are terminated after a finite number of terms and are used to calculate the trapped-charge centroid as a function of the total trapped charge. The trapped-charge centroid calculations are shown to be useful for studying silicon nitride or other strong trapping insulating materials used for long term charge storage applications.