We consider the problem of correct measurement of a quantum entanglement in the two-body electron-electron scattering. An expression is derived for a spin correlation tensor of a pure twoelectron state. A geometrical measure of a quantum entanglement as the distance between two forms of this tensor in entangled and separable cases is presented. We prove that this measure satisfies properties of a valid entanglement measure: nonnegativity, discriminance, normalization, non-growth under local operations and classical communication. This measure is calculated for a problem of electron-electron scattering. We prove that it does not depend on the azimuthal rotation angle of the second electron spin relative to the first electron spin before scattering. Finally, we specify how to find a spin correlation tensor and the related measure of a quantum entanglement in an experiment with electron-electron scattering.

Electron transport in branched semiconductor nanostructures provides many possibilities for creating fundamentally new devices. We solve the problem of its calculation using a quantum network model. The proposed scheme consists of three computational parts: S-matrix of the network junction, S-matrix of the network in terms of its junctions' S-matrices, electric currents through the network based on its S-matrix. To calculate the S-matrix of the network junction, we propose scattering boundary conditions in a clear integro-differential form. As an alternative, we also consider the Dirichlet-to-Neumann and Neumannto-Dirichlet map methods. To calculate the S-matrix of the network in terms of its junctions' S-matrices, we obtain a network combining formula. We find electrical currents through the network in the framework of the Landauer-Büttiker formalism. Everywhere for calculations, we use extended scattering matrices, which allows taking into account correctly the contribution of tunnel effects between junctions. We demonstrate the proposed calculation scheme by modeling nanostructure based on two-dimensional electron gas. For this purpose we offer a model of a network formed by smooth junctions with one, two and three adjacent branches. We calculate the electrical properties of such a network (by the example of GaAs), formed by four junctions, depending on the temperature.

Searching of optimal parameters of nanoelectronic devices is a primal problem in their modeling. We solve this problem on example of the electron ballistic switch in quantum network model. For this purpose, we use a computing scheme in which closed channels are taking into account. It allows calculating correctly a scattering matrix of the switch and, consequently, the electric currents flowing through it. Without losing generality, we consider model of two-junction switch at room temperature. Its character is localization of the controlling electric field in the domain before branching. We optimize switch parameters using a genetic algorithm. At the expense of it for InP, GaAs and GaSb switch efficiency reached 77-78%. It is established that, for the considered materials, volt-ampere characteristics of the device are close to the linear ones at bias voltages 0-50 mV. It allowed describing with a good accuracy electron transport in the switch by means of 3 × 3 matrix of approximate conductivity. Finally, based on the performed parameters optimization of two-junction switch we formulate the general scheme of modeling nanoelectronic devices in the framework of quantum network formalism.