**4.1 Surface charging process and model of polyimide radiated by low-energy electrons**

The synergistic effect of surface electron movement and charge transport in dielectric surface layer should be taken into account when studying the charging process under low-energy electron radiation (1–50 keV). A schematic diagram of charge transport on polyimide surface and in its surface layer under low-energy electron radiation is shown in **Figure 8**. 'Surface layer' refers to the area inside the material that is about a few micrometers from the surface of the dielectric material.

The intrinsic conductivity of polyimide with high resistivity is very low, but its total conductivity will increase due to the radiation-induced conductivity (RIC). The incident electrons are mainly deposited in a dielectric surface layer of about a few microns [16], and they will migrate to the interior of polyimide. However, the charge in the surface layer will continue to be accumulated, because the charge conduction velocity is far lower than that of deposition [5].

The surface potential is very low in the initial stage of electron radiation, whose reverse effect on the incident electron energy is very weak. Rather than being released by the secondary electrons, the incident electrons will be deposited on the surface. On the one hand, the change of the distribution of the deposited electrons in the surface layer and the change of the charge transfer characteristics occur due to the change of the incident electron energy and density on the dielectric surface, and it will further affect the negative potential and the induced reverse electric field on the surface in turn. On the other hand, these deposited electrons will generate an internal electric field, whose intensity will gradually increase with the radiation duration. A reverse-acting force will be produced by this field on the moving electrons reaching the dielectric surface [16]. As a result, the incident trajectory and the kinetic energy of the incident electron can be changed by the reverse electric field, by which the secondary electron yield characteristics of dielectric surface will be greatly affected.

The charging process will be stable, if the incident electron current is equal to the sum of the conduction current in the surface layer and the secondary electron generation current on the surface. Therefore, the key to the study of the charging

*Charging and Discharging Mechanism of Polyimide under Electron Irradiation and High Voltage DOI: http://dx.doi.org/10.5772/intechopen.92251*

### **Figure 8.**

*Schematic diagram of charge transport on polyimide surface and in the surface layer under low-energy electron radiation [31].*

process is a thorough understanding of the charge transfer properties in the dielectric surface layers and kinetic electrons in the surface [31].

### *4.1.1 Surface kinetic electron properties*

A reverse electric field will be formed in the process of electron radiation by the electrons accumulated in the polyimide surface layer, by which the trajectory of the incident electrons will be changed, and thus there will be a dynamic impact on the density and energy of the electrons reaching the polyimide surface. The characteristics of the subsequent incident electrons are different from those of the initial electrons. They will change with time, thus affecting the yield attributes of the surface secondary electrons. **Figure 9(a)** gives the energy and density of electrons reaching the polyimide surface over radiation time. **Figure 9(b)** shows the current density of secondary electrons emitted from polyimide surface and the surface conduction current against time [31].

Due to the repelling effect from the electric field forming in the surface layer, with the radiation time increasing, the energy and density of electrons reaching the polyimide surface gradually decrease, as shown in **Figure 9(a)** [31]. It can also be observed that, with radiation time increasing, the energy and density of electrons reaching the polyimide surface become a whole range of values from single values, resulting in a great impact on the dynamic processes of secondary electron movement and electron deposition, transport and accumulation behavior in the dielectric surface layer. Secondary electron yield coefficient gradually increases with the drop of the energy of kinetic electrons reaching the polyimide surface, and correspondingly the secondary electron yield current gradually increases, as shown by the red curve in **Figure 9(b)** [31]. In addition, the phenomenon that some of the incident electrons deposit in the surface layer after penetrating the dielectric surface will occur, especially at the initial stage. With different radiation time and material position, the distributions of deposited electrons are different. The change of charge conduction current density on the polyimide surface is shown by the blue curve in **Figure 9(b)** [31]. In the initial radiation stage, the charge conduction process can be overcome by most of the incident electrons under the radiationinduced conductivity, after they penetrate the dielectric surface. On the contrary,

**Figure 9.**

*Surface kinetic electron properties. (a) The energy and density of electrons reaching the polyimide surface over the radiation time and (b) secondary electron emission and charge conduction on polyimide surface over the radiation time [31].*

the production process of secondary electron is very weak. The secondary electron yield current increases with the energy of the kinetic electron to the surface of polyimide decreasing over radiation time. With the radiation time increasing, the conduction current density on the polyimide surface will gradually decrease, resulting in most of the incident electrons on the polyimide surface being released by the secondary electrons, and only a few electrons penetrating the surface. In the case of low-energy electron radiation, the influence of secondary electron generation process is more obvious than that of deposition electron transport process. The dynamic process of charge transport in the dielectric surface layer plays a leading role in the initial stage of radiation, so it cannot be ignored [31].

### *4.1.2 Charge transport properties in the surface layer of polyimide*

A non-uniform distribution of potential and electric field is caused by the different spatial distribution of charge in polyimide surface layer under low-energy electron radiation. By solving charge balance equation, current conduction equation and Poisson equation, the distribution of electric potential and electric field can be obtained. **Figure 10(a)** and **(b)** depicts the spatial and temporal distributions of the internal potential and electric field of polyimide under electron radiation. The electron energy is 10 keV and the flux density is 5 × 10<sup>−</sup><sup>4</sup> A/m2 .

**Figure 10(a)** shows that with the radiation time increasing, the surface potential increases gradually, and the maximum potential appears at about 25–30 s. Meanwhile, with the material depth increasing, the potential decreases. It can be seen in **Figure 10(b)** that the electric field intensity increases with the radiation time increasing, which is due to the electrons accumulating in the polyimide surface layer. The electric field tends to be stable when the radiation time is more than 25 s. It can be obtained that the electric field decreases gradually from the maximum electron range to the dielectric surface, on which the electric field is equal to zero, according to Poisson's equation. The distribution of the maximum potential and the maximum electric field over the radiation time is depicted in **Figure 10(c)**. It can also be seen from **Figure 10(c)** that the maximum surface potential increases with the radiation time increasing and tends to stabilize at 25–30 s. When the radiation time is 30 s, the stable potential reaches −8778 V. The corresponding experimental result that was measured by the non-contact surface potentiometer was −8424 V, which is slightly lower than the simulated value. Correspondingly, the maximum electric field is 1.78 × 108 V/m, which is very high, but does not cause damage to the material. Once electron radiation stops, the electric field value will drop sharply.

*Charging and Discharging Mechanism of Polyimide under Electron Irradiation and High Voltage DOI: http://dx.doi.org/10.5772/intechopen.92251*

**Figure 10.**

*Charge transport properties in polyimide surface layer. Distributions of internal potential (a) and internal electric field (b) at various material positions and radiation times. Maximum potential and maximum electric field (c) and surface potential (d) as a function of radiation time [31].*

**Figure 10(d)** shows the distribution of surface potential with over the radiation time under different incident electron energy levels [31].

### **4.2 DC surface flashover mechanism of polyimide irradiated by electrons**

Li et al. measured the DC surface flashover voltage of insulating material in vacuum under electrons irradiation by controlling the energy, emission flux and incident angle of the electron beam [16, 35]. Combining the common effects of deposited electrons and kinetic incident electrons, they proposed a physical model of surface flashover under electrons irradiation.

**Figure 11(a)**–**(c)** depicts the effect of electron energy, incident angle and electron flux on DC surface flashover voltage of polyimide during electron irradiation. The surface flashover voltage of polyimide irradiated by electron beam is determined not only by the deposited electrons in the surface layer of the dielectric but also by the kinetic incident electrons striking the dielectric surface [35].

During low-energy electron irradiation, for one thing, deposited electrons will reduce the electric field in the vicinity of CTJ; thus, the field-emission effect is suppressed, hindering the initiation of SEEA. For another, the surface potential established by deposited electrons is proportional to the electron energy. The secondary electrons will be repelled away from the polyimide surface, hindering the development process of SEEA. Both of these two effects will promote the surface flashover voltage.

However, during high-energy electron irradiation, the kinetic incident electrons will strike the polyimide surface to generate secondary electrons, which promotes the development of SEEA. If the impact points of kinetic incident electrons are close to the CTJ, they will be an alternative to field-emission electrons as the seed of SEEA. Thus, a high voltage to generate field-emission electrons and initiate the SEEA is no longer needed. A lower applied voltage can provide energy for secondary

**Figure 11.**

*DC surface flashover properties of polyimide under electron irradiation. Effects of electron energy (a), incident angle (b), and electron flux (c) on surface flashover voltage. (d) The surface flashover model for dielectric materials under electron irradiation [35].*

electron multiplication. In other words, the applied voltage for electron multiplication is much lower than that for the field-emission–initiated SEEA. For another, the electron beam bombardment will release the adsorbed gases on the irradiated area of polyimide surface. Considering the shielding effect of the cathode, when the applied voltage is the same value, the irradiated area of the case during high-energy electron beam irradiation is larger than that of the case during low-energy electron beam irradiation. When enough adsorbed gases are released, ionization may be caused by electron beam bombardment as well as secondary electrons that gain enough energy from the applied electric field. If the electron beam can approach the polyimide surface, the effects of deposited electrons will be suppressed by those kinetic incident electrons. The model of surface flashover under electrons irradiation is shown in **Figure 11(d)** [35].
