A macroscopic time dependent electrical conduction model for thin phosphosilicate glass films

Starting from the general laws for the macroscopic electric field and charge conservation in a solid material and taking into account the permanent polarization and heat transfer phenomena in chemically vapor deposited phosphosilicate glass thin films, we propose a macroscopic model of the current-time dependence through such layers. This model predicts (i) exponential variations of the current decay and film temperature as a function of time and (ii) the actual time when the steady state current density is reached after the application of a certain dc electric field. Based on the specific chemical states of phosphorus incorporated in the host SiO2 network and the structural changes thus obtained in phosphosilicate glass (permanent polarization, viscous flow, P-related trapping centers), we propose a physical model of transient-time current in terms of permanent dipoles (one dipole associated with one P4O10 incorporation complex) that rotate more easily in the network as the P content or the applied electric field increases. This mathematical model agrees with our experimental results. The model allows the computation of a dipole concentration related constant and of a thermal dissipation coefficient.