**Authors: **Yu.A. Kruglyak, T.V. Kryzhanovskaya

**Year: **2015

**Issue: **19

**Pages: **201-209

**Abstract**

Non-equilibrium Green’s functions method is applied to model transport problems for 1D and 2D uniform conductors using the nearest neighbor orthogonal tight-binding approximation in the frame of the «bottom – up» approach of modern nanoelectronics.

First of all we discuss the construction of the contact matrices of self-energies. The basic idea is that infinitely long conductor described by the Hamiltonian [H] is replaced by a conductor of the finite length described by the matrix [H + Σ1 + Σ2] with the open boundary conditions at the ends meaning “good” contacts, which do not create the reflected streams at its ends. Further we discuss 1D ballistic conductor, a 1D conductor with a single scattering center, then 2D conductor is modeling and explanation is given to the steplike dependence of the transmission coefficients over the energy, and finally there is given the representation of 2D/3D conductor in the form of parallel 1D conductors, which is not only physically correct but also extremely useful in interpreting experimental data.

In summary the physical adequacy of the Huckel approach is stated in the framework of the method of nonequilibrium Green’s functions.

**Tags: **1D conductor; 2D conductor; bottom – up; conductor modeling; molecular electronics; nanoelectronics; nanophysics; NEGF method; quantum transport

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