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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.
We analyze here some electron properties and lattice dynamics in semiconductor heterostructures, pointing out the dramatic changes relative to the bulk properties due to the existence of the interfaces in these systems. The first part of the study is devoted to the electron scattering phenomena in noninteracting open systems and to the transport properties described in the Landauer-Büttiker formalism. We develop a resonant theory of transport and apply it first to the conductance through a quantum dot embedded in a quantum wire and second to the capacitance of a two dimensional electron gas formed in a MIS-type semiconductor heterostructure. In the second part of the study we illustrate the four major new features of the optical phonon spectra in a strained semiconductor heterostructure in contrast to an unstrained one. The results are particularized for double heterostructures InP/GaAs/InP grown on the faces (001) and (111) of the substrate.