# Space Charge Accumulation and Decay in Dielectric Materials with Dual Discrete Traps  
Zhaoliang Xing  
1 State Key Laboratory of Advanced Power Transmission Technology, Global Energy Interconnection Research Institute Co. Ltd., Beijing 102209, China; [EMAIL_ADDRESS] (Z.X. ); zhangc\(\_\)[EMAIL_ADDRESS] (C.Z.) Chong Zhang  
1 State Key Laboratory of Advanced Power Transmission Technology, Global Energy Interconnection Research Institute Co. Ltd., Beijing 102209, China; [EMAIL_ADDRESS] (Z.X. ); zhangc\(\_\)[EMAIL_ADDRESS] (C.Z.) [PERSON]  
2 State Key Laboratory of Electrical Insulation and Power Equipment, Xi'an Jiaotong University, Xi'an 710049, China; [EMAIL_ADDRESS] (H.C.); [EMAIL_ADDRESS] (Y.H.) [PERSON]  
2 State Key Laboratory of Electrical Insulation and Power Equipment, Xi'an Jiaotong University, Xi'an 710049, China; [EMAIL_ADDRESS] (H.C.); [EMAIL_ADDRESS] (Y.H.) [PERSON]  
Charge trapping/de-trapping dynamics should be influenced by the trap energy of dielectric materials. Trapping centers in polymer dielectric materials can be produced by physical and chemical defects [1]. It is usually assumed that the charges in localized states produced mainly by physical defects (or shallow traps) of polymer dielectric materials are in thermodynamic equilibrium in the time window of experiments such as space charge distribution measurements and transient space charge limited current (SCLC) measurements [1]. In other words, the maximum time constant of charge trapping/de-trapping dynamics in shallow traps is much smaller than the response time of experimental equipment. We can just consider the charge migration in the shallow traps and can neglect their charge trapping/de-trapping dynamics. Nevertheless, chemical impurities can form deep traps in polymers [1]. It will take a very long time for charge trapping/de-trapping dynamics in deep traps to reach an equilibrium state, which is often confirmed by space charge measurements [11; 12]. Therefore, the charge trapping/de-trapping dynamics of deep traps should be considered during the analysis of transient electrical properties of dielectric materials, such as transient SCLC, space charge accumulation and dissipation, and transient electroluminescence. The charge trapping/de-trapping dynamics can be affected by the energy distribution of deep traps in dielectric materials. For single discrete traps, the charge trapping/de-trapping dynamic responses can be obtained analytically by solving the first order charge trapping/de-trapping equation. The space charge responses and external currents or surface potentials have been widely studied theoretically and experimentally in various conditions, such as high electric field [13], electron beam irradiation [14], and corona charging [15]. In the case of multiple discrete traps, [PERSON] et al. developed a charge trapping/de-trapping theory based on two discrete traps [16]. The theory has been used to fit experimental results on space charge build-up and decay in additive-free low-density polyethylene (LDPE) [16; 17]. From the fitting of space charge decay curves, the de-trapping probability and trapped charge densities were evaluated. Then, the trap energies and trap densities can be obtained. The trap energies are consistent with those obtained by other experimental techniques such as thermally stimulated current (TSC) [18] and surface potential decay (SPD) [19; 20; 15], whereas the trap densities are several orders smaller than those calculated by other methods [15; 18; 21]. One possible reason is that the charge trapping/de-trapping kinetics of two discrete trapping centers cannot be analyzed separately. Moreover, an exponential function was adopted to approximate the energy distribution of traps calculated by the density-functional theory [22]. Then, they assumed that the trap centers are filled with free charges from the bottom to the top. However, the simulation result shows that the trapped charge densities do not increase with time, which is different from the space charge experimental results.