Abstract
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 Neumann-to-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.
Highlights
An electron transport in branched semiconductor nanostructures provides many possibilities for creating fundamentally new devices [1,2,3,4,5,6,7,8,9,10,11,12,13,14]
Electrical currents through the network are calculated in the framework of the Landauer– Buttiker formalism [17, 18] based on its transparency
To solve the problems (15), we introduce the concept of the local coordinate frame (LCF) at the boundary of the junction with the branch (Fig. 2)
Summary
An electron transport in branched semiconductor nanostructures provides many possibilities for creating fundamentally new devices [1,2,3,4,5,6,7,8,9,10,11,12,13,14]. As a rule, the boundaries of the junctions are selected so that branches connecting junctions are excluded from consideration This formal technique can simplify calculations, but makes it difficult to study the transport properties of a quantum network depending on the lengths of the branches. The disadvantage of this method is the absence of an explicit formula for the scattering matrix of the entire network in terms of its junctions’ scattering matrices. We will obtain a formula for an extended scattering matrix of a quantum network in terms of extended scattering matrices of its junctions, taking into account the lengths of the branches connecting them. We will demonstrate the effectiveness of the proposed calculation scheme by modeling a nanostructure based on twodimensional electron gas using a model of a quantum network of smooth junctions with one, two and three adjacent branches
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