Knowledge-based modelling of charge transport in insulating polymers: From experiments to model optimization

More than fifty years after the publication of the early work on electrical transport in disordered insulating solids, we are still unable to describe quantitatively the electrical response of these materials. During this period of time, concepts derived from semiconductor physics have been transposed to the case of insulating solids, and among them, to polymers. In spite of this, there is still no agreement on how to describe charge transport and there is still some controversy as regards the applicability of semiconductors physics to the case of disordered insulating materials and in particular to polymers used in electrical engineering applications. Our starting point is to accept the semi-conductor like description for polymeric materials as a basis to develop models. Up-to-date measurement techniques are used to produce data set pertaining to different kinds of measurements with the objective to reduce the number of solutions for the set of adjustable parameters associated with the model. In a first part of the paper, we give the basis of the bipolar charge transport model developed for low density polyethylene under dc stress: it features trapping, detrapping and recombination of positive and negative charge carriers, each of them being generated by a Schottky injection at the metal-dielectric interface. In a second part, we introduce measurements used to evaluate the model: space charge distribution through the sample, external current and electroluminescence measurements, all being time dependent, at different fields. In a third part, we introduce the optimization method used to estimate parameter values that best fit the all set of experimental data. The algorithm is a combination of the Gauss-Newton algorithm and the method of gradient descent. Like other numerical minimization algorithms, the Levenberg-Marquardt algorithm is an iterative procedure used especially for nonlinear problems. In our case, this algorithm is used to minimize the sum of the squares of the deviations between experimental data and simulation data. We show that the optimization tool developed as an interface between the numerical model and the experimental data can readily produce a set of values of physical parameters for the model.