**3. Electrical properties of polyimide**

### **3.1 Dielectric properties**

The complex permittivity of polyimide with thickness of 100 μm was measured at room temperature using a broadband dielectric spectrometer (Concept 80, Novocontrol Technologies, Germany). The applied voltage was 1 Vrms and the *Charging and Discharging Mechanism of Polyimide under Electron Irradiation and High Voltage DOI: http://dx.doi.org/10.5772/intechopen.92251*

frequency was from 10<sup>−</sup><sup>2</sup> –105 Hz. **Figure 2** depicts the real and imaginary parts of the relative complex permittivity, obtained from polyimide sample at room temperature, which is a function of frequency in semi-logarithmic coordinates [29]. **Figure 2** shows that the real part of relative complex permittivity increases slightly as frequency decreases. In the frequency range of 10<sup>−</sup><sup>2</sup> –105 Hz, the imaginary part is lower than 3.6 × 10<sup>−</sup><sup>3</sup> . The small dielectric relaxation strength of the relaxation peak around 30 Hz reveals that the dipolar moment is very low. The dielectric loss, *ε"*/*ε'*, is very low, which indicates that in the dc electrical breakdown experiments at room temperature, the Joule heating generated by the dipole orientation is negligible [29].

### **3.2 Bulk and surface trap properties**

Thermally stimulated depolarization current (TSDC, Concept 90, Novocontrol technologies, Germany) was carried out on a polyimide sample with a thickness of 100 μm to investigate its trap distribution characteristics. **Figure 3** shows the results of TSDC experiments for polyimide [29]. Thermally stimulated relaxation processes can be observed in the temperature range of 10–170°C. One obvious relaxation peak is around 69°C, while another relaxation peak may be located near 135°C. The experimental results were analyzed using the classical TSDC theory to reveal the thermally stimulated processes and their activation energies [30].

The TSDC experimental results were fitted and four relaxation peak components could be obtained. As shown in **Figure 3**, it can be seen that the fitting results are in good agreement with the experiments. We can determine the peak temperature, activation energy and relaxation time for the four relaxation processes listed in **Table 1**. The activation energies of four peaks at 69, 87, 109 and 135.5° are 0.60, 0.65, 0.70 and 0.83 eV, respectively. As the temperature at the relaxation peak increases, the corresponding activation energy increases. The three peaks at 69, 87 and 109°C may correspond to shallow traps that assist carriers hopping process in polyimide, while the peak at 135.5°C may correspond to deep traps that can capture mobile carriers and accumulate space charges. The energy of deep traps is

### **Figure 2.**

*The real and imaginary parts of relative complex permittivity,* ε' *and* ε"*, of polyimide as a function of frequency at room temperature [29].*

### **Figure 3.**

*TSDC experimental results of polyimide after being polarized at an applied voltage of 250 V at 180°C for 30 min. The classical TSDC theory was used to fit the experimental results. Symbols and solid curves represent experimental and fitting results, respectively [29].*


### **Table 1.**

*Parameters for relaxation processes extracted from TSDC experimental results [29].*

consistent with the results obtained from the Arrhenius relation between conductivity and temperature [4].

Surface potential decay was carried out on a polyimide sample under electron radiation to investigate its surface trap distribution characteristics. In this experiment, charging process takes a very short time, about 25 s, as the electron flux density was so high. We set that with a filament emission current of 10 μA and a radiation distance of 300 mm, and the charging process was completed within 30 s. After radiating for 30 s, we turned off the electron gun and then moved the probe over the sample to measure the surface potential. **Figure 4(a)** gives the surface potential decay curves of polyimide under electron radiation of different energy levels (3–11 keV) [31].

It can be seen that the initial surface potential gradually increases with the increase of electron energy. This indicates that the charging process and properties are different under electron radiation of different energy levels. Hence, the dielectric properties during the charging process can be investigated by analyzing the initial surface potential of the dielectric after the charging process.

The surface trap distribution of polyimide can be obtained from surface potential decay model, as shown in **Figure 4(b)** [31]. There are two types of traps, defined as shallow and deep traps, respectively. It can be seen that the trap charge density related to shallow traps is more than that of deep traps under the

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

**Figure 4.**

*Surface potential decay curves (a) and surface trap distributions (b) of polyimide after irradiation by electron beam with different energies [31].*

same electron energy radiation. The charges captured in relatively shallow traps can escape the trap center in a short interval, which is demonstrated by the rapid decay of surface potential. With the time increases, these de-trapped electrons will migrate to the grounded electrode under the effect of the internal electric field. By contrast, deeply trapped charges remain in the trap center for a longer period. The density of deep traps determines the steady surface potential, and the stabilization time depends on the energy level of the deep traps.

The surface trap distribution of polyimide presents different behavior under radiation from electrons of different energy levels. The shallow trap level increases slightly with the increase of electron energy, while the deep trap level remains unchanged about 0.94 eV. Under the radiation of different electron energy, the depth of the electron deposition layer and the range of electrons are different. The higher the electron energy, the deeper the deposition layer. These trapped charges need to overcome a much higher potential barrier to escape the trap center. Therefore, the shallow trap energy level increases with the gradual increase of the electron energy. In addition, the total trap charge density gradually increases with increasing electron energy. Due to the increased electron energy, the distance from the electron deposition layer to the dielectric surface is longer, and much more charges will be captured by the trap centers [31].
