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We investigate the behavior of a electric potential profile inside amesoscopic region attached to a pair of superconducting leads. It turns outthat ${\rm I}-V$ characteristic curves are strongly modified by this profile.In addition, the electronic population in the mesoscopic region is affected bythe profile behavior. We discuss the single particle current and the mesoscopicelectronic population within the non-equilibrium Keldysh Green functionstechnique. The Keldysh technique results are further converted in a selfconsistent field (SFC) problem by introducing potential profile modificationsas proposed by Datta. Evaluation of ${\rm I}-V$ characteristics are presentedfor several values of the model parameters and comparison with currentexperimental results are discussed.

Self consistent charge-current in a mesoscopic region attached to superconductor leads