Study on temperature and electric field dependence of conductivity in polyimide

Abstract

The deep dielectric charging (DDC) imposes a potential threat on spacecrafts. On the one hand, this kind of polymer insulator dielectric, represented by polyimide, is significantly dependent on temperature; on the other hand, during the charging process the high electric field (at the level of 107 V/m) will enhance the conductivity of the dielectric. Therefore, in order to make a precise assessment of DDC by computer simulation, the conductivity model should take into account the temperature and electric field dependences. In this field, two conductivity models are usually adopted for DDC simulation. One of them is proposed by Adamec. It puts emphasis on the enhanced conductivity due to high electric field, while its temperature dependence is based on the famous Arrhenius formula. Adamec model can make good performance versus electric field, but it is inappropriate in low temperatures. Another model combines the thermally assistant hopping conductivity and the variable-range hopping conductivity together, so it shows advantage in the temperature dependence, which is named as TAH VRH model. Although this model also can include the influence from electric fields, the effectiveness is not so good as that of Adamec model. In order to combine the advantages of these two models, i.e. the Adamec model and TAH VRH model, a new conductivity model is proposed with fewer parameters than those in TAH VRH. It is derived by replacing the Arrhenius formula in Adamec model with a simplified temperature model referred to as TAH VRH model. This formulation enables the new model to deal with a wider temperature range and keep the good performance versus high electric fields. The proposed model is verified partly by the measured data of a kind of polyimide. Satisfactory agreement is obtained in data fitting by using the new model, where the temperature dependence is better than that of Adamec model. In addition, to overcome the unreasonable increase in conductivity in low temperature and high electric field, a useful technique is proposed. By temperature mapping in the electric field correlated factors namely the carrier concentration and mobility enhancement factor, this technique can extend the feasible temperature range to a lower limit. This is done according to the assumption that the carrier concentration is small at low temperatures, and consequently the electric field influence should not be large. At high temperatures or in low electric fields, the temperature mapping is of little effect. Finally, analysis of the model's sensitivity versus several parameters is provided, demonstrating the advantage of applicability of the new model with fewer parameters.