Thanks to its low noise level, the LSBB environment provides particular environment to carry out high quality electrical characterizations. In this paper, we propose a complete modeling approach of the experimental results from our experimental microelectronic setup. The tested device is a Metal Oxide Semiconductor (MOS) floating gate capacitor which can be found in electrostatic non volatile memories such as Flash. The main idea is to characterize and model the leakage current through the tunnel oxide. We proposed, in a previous work, a model for charge loss considering a fractional Poisson process, involving only two parameters, expressed as a Mittag-Leffler (ML) function. Here, we also propose a combo of Fowler-Nordheim (FN) and Poole-Frenkel (PF) models for leakage currents, based on tunnel effect transport through the oxide. It gives the leakage current on a medium-to-long scale of time while the ML model can possibly take into account a shorter time step. The perspective is to find a relationship between these different models, used in various fields, to propose a generic model of phenomena involving leakage in complex and porous materials at different scales of time and space.