Capacitance theory of open quantum systems with classical contacts

We consider semiconductor devices composed of a small quantum structure as the active device region and two classical environments constituting the source- and the drain contact. The contacts are taken as free electron gases with infinite conductivity defining the chemical potentials in the contacts. The transport through the quantum structure is described in the Landauer–Büttiker formalism using electronic scattering wave functions which determine the electron density in the quantum system. In our Hartree approximation these charges and the induced charges in the contacts are the sources of the self-consistent Coulomb field. As a particular quantum structure we study a GaAs heterostructure device consisting of a two-dimensional electron gas sandwiched between a gate contact and an AlGaAs blocking barrier [see V.T. Dolgopolov et al., Phys. Low-Dim. Struct. 6 (1996) 1]. We demonstrate the quantitative agreement of our theory with the experimental results.