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Deep traps are known to play a crucial role in the breakdown performance of polymer [11,12]. Deep traps in polymers mainly originate from crystal interfaces, which can capture a large number of free carriers . Wang et al. found that the enhanced height of barrier, the decrease of mobility of carriers and the formation of homocharges caused by deep traps improved breakdown performance of polymers . Jiang et al. found that the deep traps at the interface had a significant impact on the space charge trapping process and enhance DC breakdown performance of polymers . Moreover, many references have demonstrated that the insulation properties of polymers are affected by the molecular chain displacement [16,17,18]. Min et al. proposed a model combining the charge transport characteristics and molecular motion to characterize the breakdown mechanism of LDPE, and the breakdown phenomenon occurs when the displacement of the molecular chain reaches a certain threshold . Xie et al. found that an increase in temperature will aggravate the movement of molecular chains in the polymer and increase the energy of the carriers, which will eventually lead to a decrease in the breakdown performance of the dielectric .
where Eext represents the external field, and λ represents the mean free path of charges. Φeff represents the potential barrier for trapped electrons to overcome for hopping from localized states. Equation (5) implies that a deeper trap level has a higher potential barrier in hopping polarization behavior. Moreover, increasing the density of deep traps increases the possibility of trapping during carrier migration, enhances trap trapping effects and reduces the mean free path of carriers . Thus, more energy will be required for hopping polarization with the growth of the deep traps density.
As a consequence, the mean free path of electrons (λe) and deep potential barriers (Et) cooperate to affect the dielectric critical breakdown field strength (Ecritical), and the deep trap level represents Et [29,31], which is in the range of 0.92~0.93 eV. The increase of deep traps level can enhance Ecritical, since higher barriers limit the transport and migration of free carriers. All samples in this paper have similar deep trap energy levels as shown in Figure 6, so the electron mean free path is the main factor affecting the breakdown field strength of the sample.
The density of deep traps has a remarkable influence on the free carrier migration , and the increase of deep trap density also enhances the hot electrons trapping possibility and decline the λe, and the trapping possibility of charges can be expressed by [31,32]
Hence, a molecular chain displacement model was established, as shown in Figure 13. It has been widely confirmed that the molecular chains are arranged in parallel and orderly as crystalline regions, while those with loose and irregular aggregation are amorphous regions. The chemical defects on molecular chains can act as deep traps [33,34], electrons can penetrate into the loose amorphous region , and these electrons will have a certain possibility of being captured by the deep traps. Moreover, it is difficult for an electron captured by a deep trap to get enough energy to jump out of the deep trap and become a free carrier , so the charge on the molecular chain will be subjected to a Coulomb force for a sufficient time on account of the long residence time of deep trapped electrons [37,38]. The trap residence time (τtrap) of traps of different energy levels might be several orders of magnitude, which can be expressed as 
Hence, deep traps play a major role in the molecular chain displacement process. This phenomenon of molecular chain displacement process can be further investigated by the following velocity equation .
Hence, a breakdown model combining the molecular chain displacement and carrier trap was established as shown in Figure 14. Electrons injected from the cathode through Schottky barrier can accelerate and accumulate energy in a free volume. The increase in free volume caused by α relaxation enhances the free path of electrons and thus electrons can gain more energy to form hot electrons. The accumulated energy of charges in an electric field is synergistically affected by the molecular chain displacement and electrical field strength, which can be illustrated as [31,45].
To clarify the origin of the deep trap levels in the a-plane GaN layers grown on r-plane sapphire by HVPE, we investigated the DLTS signals as a function of the filling pulse width (tp), as has been described in Fig. 2. It is essential to note that the DLTS signal is independent of the filling pulse width. Indeed, defects can be classified into non-interacting and interacting types. The non-interacting defects such as point defects do not influence each other. On the other hand, the interacting defects such as dislocations and stacking faults affect carrier capture and emission in the surrounding regions. It is well known that trap occupancy in the case of non-interacting defects depends exponentially on tp while that of interacting defects are proportional to ln(tp)13. Because a plot of a DLTS signal as a function of ln(tp) should produce a straight line for linearly arranged interacting defects and a non-linear curve for non-interacting defects, a correlation between the extended defects and deep levels can be identified. From the results of Fig. 2, it is found that A2 can be classified as a point defect because the DLTS signals of A1 and A2 are independent of tp.(See Fig. S1) In addition, considering the size of cross-section of the defects A1 and A2, it can be concluded that both A1 and A2 are point and not dislocation defects.
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