The isothermal discharge of a polystyrene electret via a distribution of electron trapping states

The distribution in energy of trapping states in a polymer may be studied by populating the traps and observing the current that accompanies the relaxation of the trapped charges. In this relaxation process the carriers from shallow traps are thermally excited, move a short distance, and become retrapped in deeper lying states, and so on through a multiple trapping scheme. The states may be populated by injection from an electron beam. The isothermal discharge that follows the initial charging event takes on a particularly simple form in the non-retrapping limit. The general case of arbitrary distribution of states with retrapping can be analyzed by using a multiple trapping formalism, and this analysis yields the required distribution of trapping states in the dielectric. We use this multiple trapping analysis solution to examine the shortcoming of the non-trapping, approximate solution to the isothermal discharge.