*2.1.1 Isothermal surface potential decay experiment*

Experimental conditions always need to be carefully controlled. Isothermal SPD is in the range 298–338 k, while the PI sample is irradiated by low-energy electron beam that has been initially recorded. It has been observed that the conductivity is modified as the irradiation goes on and the trapping state gets filled with electrons. That is why depending on the way it is measured, data might be slightly modified.

Besides, we can consider, to some extent that for PI, the photoconduction is a form of radiation-induced conductivity (RIC) as its conductivity can be increased by several decades when exposed to solar lighting with respect to the conductivity in the dark. It has been reported that thin PI films will not charge in sunlight provided that its back surface is grounded. It is therefore recommended to keep PI sample into the dark while SPD is recorded.

The ISPD curve can be separated into three zones: in the part I (transient process), charge trapping and detrapping are competing, whereas in part III (steady state process), the conduction is predominant. In part II, all phenomena are competing [15]. This region limits are difficult to identify that is why most of the time only the initial transient and final steady-state regions are reported on graphs. As surface resistance of spacecraft dielectrics is higher than volume resistances [16], at least one order higher in the case of PI and because external aggression such as atomic oxygen seems to increase the surface resistance without modifying the bulk resistance [17], it is acceptable to neglect the surface charge transport to estimate the bulk conductivity [15]. It is also acceptable to consider that the relative permittivity of PI remains quite stable with the temperature and the electric field during ISPD. However, it was noticed that the surface potential decay is much faster if the initial surface potential is increased. The steady-state current density obtained for a time t = 3 × 105 s plotted versus the applied voltage show clearly two regime: ohmic (at low voltage below –950 V) and space charge limited current (at high voltage above –950 V). From the slope, the ohmic resistivity was estimated to 1.2 × 1017 Ω.m and the effective charge carrier mobility to 1.9 × 1–19 m2 /V.s and the trap density estimated to 1.3 × 1021m–3. Obviously this type of experiment realized at 298 k needs to be repeated at different temperatures.

Using the 2D ISPD model [18], it is possible to estimate the average surface resistivity, the volume resistivity, and the charge mobility of PI by a genetic algorithm from 298 up to 338 k. In the results reported in **Table 1**, we can observe that the values at 298 k differ a little from the previous estimation by the same authors. This means that these values remain relatively difficult to determine precisely even with the same equipment and the same material. However, the authors managed to calculate the PI surface and volume activation energy and the trap energy which are estimated to 0.3, 0.32, and 0.54 eV, respectively. To get these values, they fitted the surface and volume ohmic resistivity and charge carriers versus the temperature curves using the Arrhenius law.


**Table 1.**

*Surface and volume resistivity estimated from ISPD and simulation with an error of 0.9% [18].*
