NANOSYSTEMS: PHYSICS, CHEMISTRY, MATHEMATICS, 2017, 8 (2), P. 247–259
Kolmogorov equation for Bloch electrons and electrical resistivity models for nanowires
S. B. Leble – Immanuel Kant Baltic Federal University, ul. Aleksandra Nevskogo, 14, Kaliningrad, 236016, Russia; email@example.com
The problem of a nanowires conductivity is studied from a kinetic point of view for quasiclassical Bloch electrons in an electric field. Few statements of problems with cylindrical symmetry for the integro-differential Kolmogorov equation are formulated: the dynamic Cauchy problem and two stationary boundary regime ones. The first is for an empty cylinder with scattering of the conduction electrons on walls, the second takes into account scattering on defects inside the wire. The integro-differential equations are transformed to integral ones and solved iteratively. There are two types of expansions with the leading terms in the right and left sides. The iteration series is constructed and its convergence studied.
Keywords: Kolmogorov kinetic equation, N-fold series, Bloch electrons, electrical resistivity, nanowires.
PACS 02.30.Mv, 02.60.Nm, 05.20.Dd, 73.23.b