**5. Deep charging and discharging mechanism of polyimide**

### **5.1 Deep charging model of polyimide radiated by electrons**

Energetic electrons are difficult to conduct when they are deposited inside polyimide due to its low conductivity, resulting in deep charging of insulation. Under the condition of typical electron radiation environment in geosynchronous orbit (GEO), deep charging of polyimide normally does not cause discharge risk. However, during the energetic electron storm, the electron flux will increase by 2–3 orders of magnitude within a few days and last for 10 days or so. At this point, the incident electron flux will exceed the threshold of 0.1 pA/cm2 , resulting in a great risk of ESD [5, 36].

FLUMIC model, proposed by Rodgers et al., based on spacecraft data of GOES/ SEM and STRV-1b/REM was utilized in this paper to manifest the electron radiation *Charging and Discharging Mechanism of Polyimide under Electron Irradiation and High Voltage DOI: http://dx.doi.org/10.5772/intechopen.92251*

environment in GEO [37, 38]. It is commonly agreed that FLUMIC model is suitable for charging risk assessment and spacecraft design due to its complete demonstration of seasonal and annual variations in energetic electron flux. **Figure 12(a)** depicts FLUMIC spectrum under typical and extreme space environment [36].

The penetration depth of energetic electrons in polyimide can be obtained from the Weber semi-empirical equation. The charge conduction process consists of inherent charge conductivity and radiation-induced conductivity. Charge transport process satisfies the current conduction equation, the charge continuity equation and Poisson's equation [36].

Assume that electrons irradiate a plate polyimide from the upper side. HV is applied to one side of the sample, and the other side is suspended or grounded. Four cases of the sample are considered altogether, that is, (A) suspended-HV; (B) HV-suspended; (C) grounded-HV; and (D) HV-grounded, as shown in **Figure 12(b)** [36]. The condition before the hyphen indicates condition on the upper surface, and the latter indicates condition on the lower surface.

Here, the first case will be discussed: HV is 0 V, that is, and the electrode is grounded. Case A becomes suspended-grounded, case B becomes groundedsuspended, and cases C and D are merged into grounded-grounded. We take the condition with enhancement of 100 and radiation time of 5 days for an example.

### **5.2 Simulation results and discussion**

In case A, the maximum electric field strength reached 5.00 × 107 V/m, appearing near the lower electrode. Most of the charge deposited near the radiated surface, though part of the charge mitigated toward the lower electrode driven by the electric field, as shown in **Figure 13(a1)**–**(a3)** [36]. In case B, the maximum electric field strength reached 4.39 × 107 V/m, appearing near the upper electrode. Vast charges are accumulated at the region near the radiated surface. As **Figure 13(b1)**–**(b3)** shows, compared with case A, the electric field in case B tends to move downward, inhibiting the migration of electrons from the field to the bulk of sample, which leads to deposition of the charges near the surface and formulate a local high-space charge area [36]. When both electrodes are grounded, it is clear that, similar to the results in case B, the electric field near the upper electrode is at a lower position vertically, restricting the transformation of the electrons to the bulk of the sample and electrons accumulated at the region near upper electrode. In addition, as **Figure 13(c1)**–**(c3)** shows, the electric field close to the downward electrode tends to move up vertically, fostering the electron migration downward [36].

Furthermore, the impact of electron flux promotion on the charging of polyimide is addressed. Here, with four cases considered, we take the HV of 500 V and radiation time of 10 days for an example. It is shown in **Figure 14(a)** and **(b)** that

**Figure 12.** *(a) The FLUMIC model value at GEO environment. (b) Four cases of the sample [36].*

### **Figure 13.**

*Distribution of charge density, electric field and potential. (a) Suspended-grounded, (b) grounded-suspended, (c) grounded-grounded [36].*

### **Figure 14.**

*(a) Influence of electron flux enhancement on total space charge density. (b) Influence of electron flux enhancement on maximum electric field. (c) Influence of operating voltage on total space charge density. (d) Influence of operating voltage on maximum electric field [36].*

case A has the highest total space charge density and maximum electric field, which are significantly higher than those in other three cases at the same enhancement [36]. With flux enhancement increases, total space charge density reaches the valley *Charging and Discharging Mechanism of Polyimide under Electron Irradiation and High Voltage DOI: http://dx.doi.org/10.5772/intechopen.92251*

value under case D when enhancement is 1, while when enhancement increases to 100 and 1000, lowest charge density is seen in case B. Additionally, though charge density in cases B and D is varied, lines representing maximum electric field almost overlap. In case A, considering the voltage is applied to the lower electrode and electric field moves upward, accumulated electrons are attracted to the lower electrode; therefore, more electrons may be injected into the sample. On the contrary, in case B, the voltage is applied to upper electrode and electric field moves down; hence, vast charges are accumulated at the region near upper electrode, inhibiting further electron injection. In cases C and D, the electric field moves down and up at the region near upper and downward electrode, respectively. Based on the previous analysis, it can be determined that with an increase in flux enhancement, its impact on case A is more obvious than that in other cases.

At last, the influence of operating voltage on the charging of polyimide is discussed. Take the enhancement of 1 and the radiation time of 10 days as an example; we discuss the influence of operating voltage on the charging of polyimide in the four cases. As can be seen from **Figure 14(c)** and **(d)**, the increase of operating voltage has a small influence on cases A and B, since the virtual electrode is at infinity in both cases A and B [36].
