Modelling of potential decay experiments. How to interpret the experimental results?

Potential decay experiments are considered as an efficient method for studying the transport properties of insulators. The interpretation of their results is nevertheless still delicate. In most cases, the decay is controlled by the transient conduction of the injected charges through the sample. The interpretation in terms of microscopic properties of the material then requires a good knowledge of the connections between the carriers transport process and the macroscopic observable. These connections can be attained by describing theoretically the relaxation of a charged sheet under its own field. We propose such a modelling and give a practical method for the data interpretation. The study is carried out for physical examples of field-dependent mobilities (small polaron hopping transport and Poole-Frenkel effective mobility) and accounts for the trapping-detrapping processes undergone by the mobile carriers (multiple trapping). The influence of traps is tackled through a discrete and an exponentially decaying density of trapping states. It is shown how these various transport processes generate specific features that can be identified on experimental plots. In each case, the quantitative analysis of the measurements can be achieved from the derived observable expressions which are explicit functions of the relevant microscopic parameters.