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We consider semiconductor devices at very low temperatures, composed of a mesoscopic quantum structure (QS) constituting the active region contacted by ideal probes with infinite conductivity. The coherent transport through the QS is described in the Landauer-Büttiker formalism. We perform self-consistent calculations for the electron density in the QS. We present a capacitance model that takes into account the openness of the QS and the existence of finite contacts embedding the system. For single-barrier tunnelling structures, we present the implicit connection between the capacitance and the conductance. For a field induced two-dimensional electron gas in a special GaAs/AlxGa1-xAs heterostructure we present a detailed analysis of the coupling to the contact reservoir. Excellent quantitative agreement in the C-V characteristic is obtained. It is also analized the conductivity of systems with confinement in more dimensions.