Charge trapping and de-trapping properties can affect space charge accumulation and electric field distortion behavior in polymers. Dielectric materials may contain different types of traps with different energy distributions, and it is of interest to investigate the charge trapping/de-trapping dynamic processes in dielectric materials containing multiple discrete trap centers. In the present work, we analyze the charge trapping/de-trapping dynamics in materials with two discrete traps in two cases where charges are injected continuously or only for a very short period. The time dependent trapped charge densities are obtained by the integration of parts in the case of continuous charge injection. In the case of instantaneous charge injection, we simplify the charge trapping/de-trapping equations and obtain the analytical solutions of trapped charge densities, quasi-free charge density, and effective carrier mobility. The analytical solutions are in good agreement with the numerical results. Then, the space charge dynamics in dielectric materials with two discrete trapping centers are studied by the bipolar charge transport (BCT) model, consisting of charge injection, charge migration, charge trapping, de-trapping, and recombination processes. The BCT outputs show the time evolution of spatial distributions of space charge densities. Moreover, we also achieve the charge densities at the same position in the sample as a function of time by the BCT model. It is found that the DC poling duration can affect the energy distribution of accumulated space charges. In addition, it is found that the coupling dynamic processes will establish a dynamic equilibrium rather than a thermodynamic equilibrium in the dielectric materials.
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