In the framework of Mixed Finite Element Methods, the mathematical analysis of an error indicator, which relies on the residual of a linearized Drift-Diffusion model of the transport equation for electrons in heterojunction semiconductor devices using Fermi-Dirac statistic, is presented. Just now, no numerical experiences have been carried out in order to prove the efficiency of the proposed isotropic estimator. However, from its numerical interpretation, it appears that they are coherent and well indicate the boundary layer and abrupt hetrerojunction problems.