The most peculiar feature exhibited by $I(V)$ characteristics of amorphous chalcogenides materials is undoubtly its S-shape given by a negative differential-resistance behavior. In order to pursue a theoretical control of such a behavior so important for technological exploitation, in this paper we give a microscopic particle description of the charge transport across a simple device of amorphous $mathrm{Ge_2Sb_2Te_5}$ sandwiched between two planar metallic contacts. Specifically, a transport scheme based on the generalization of the variable range hopping has been implemented in a current-driven Monte Carlo simulation that allows one to investigate the aspects of the microscopic picture responsible for the electrical properties...