Influence of boundary conditions on transport in a quantum well

The problem of the electrical conductivity of a conducting channel at the boundary of a heterojunction or in a MD transistor is solved, considering the quantum theory of transfer processes. The thickness of the layer can be comparable to and less than the de Broglie wavelength of the charge carriers. The behavior of charge carriers is described by the quantum Liouville equation. The influence of surface scattering of charge carriers is considered through the Soffer boundary conditions. An expression for the electrical conductivity is obtained and its dependence on the strength of the transverse electric field and the roughness parameter of the boundary of the conducting channel with another semiconductor is analyzed. A comparative analysis of theoretical calculations with experimental data is carried out.