*2.1.2 Charge transport model based on deep and shallow traps*

In order to model the charge transport in PI, complementary experiment such as thermally stimulated current (TSC) is often performed [19] to investigate the relaxation polarization properties that cannot be easily obtained by dielectric spectroscopy. The charge transport is controlled by high field mechanism as soon as the charging potentials exceed the transition voltage of the ohmic regime. It was reported that the time-dependent permittivity εr(t) in PI obeys to Cole-Cole equation rather than Debye ones. Besides, the trap depth could be estimated to be near 1.35 eV [20]. Once released from the surface traps, the charges migrate through the shallow trap to the rear electrode. At 298 k, the carrier residence time was estimated between 7.92 × 10–12 and 1.34 × 104 s in trap depth of 0.1 and 1 eV, respectively [21]. The carriers can easily hop in the shallow traps but will stay in deep traps much longer. Therefore, shallow traps assist conduction processes, whereas deep traps will control the space charge dynamics [22].

It is considered that the shallow traps will control the temperature-dependent hopping at low temperature; then at high temperature, deep traps can also assist the conduction processes as the residence time carriers drops (at 400 k, the residence time carriers in 1 eV trap depth is reduced to 0.648 s). At room temperature, it is reasonable to develop a unipolar charge transport model with a single deep trap level in a first stage (**Figure 3(a)**). It was notice that the surface electrons are easily released from traps surface center whereas they can remain into the bulk for a very long time when they are stored into deep traps. The steady state was reached after 94.8 h; at that time, 39.72% of electrons deposited close to the surface creating a surface potential of –2056 V [21] were released. The resistivity of PI was estimated in the range 8.08 × 1016–9.40 × 1016 Ω.m. However, in order to improve the model, it would be better to refine the trap distribution characteristics (**Figure 3(b)**) and consider the density of localized state [23, 24].
