Space charge characterization in nano-dielectrics by the Thermal Step Method

This paper reports, for the first time, a new calculation approach for the application of the Thermal Step Method (TSM) in nano-scale dielectrics. It is based on the Ballistic-diffuse transport of heat phonons and their interaction with the trapped space charges. The temperature distributions are obtained by applying the numerical finite element and the Newmark method. The local space charge density and the electric field are calculated from the integral equation of the electrical image charges using the mean value theorem and the composite Simpson approximation. Results of temperature distributions are validated with those obtained by Boltzmann´s and Chen models. Then, we have compared our approach with the TSM previous works using the Fourier´s model for space charge characterizations in the nano-polyethylene. Results show an overvalued of the electrical image charge when applying the Fourier´s model that lead to overestimated space charge densities. This problem is mainly caused by the infinite speed of the thermal excitation front in the Fourier´s approach. Besides, we show that our approach is a good alternative for space charge characterization from macro to nano-scales.