THE KINETIC BOLTZMANN EQUATION IN GENERALIZED MODEL OF ELECTRON TRANSPORT FOR MICRO- AND NANOELECTRONICS

Abstract

In a tutorial article directed to serve researchers, university teachers and students, we study Boltzmann kinetic equation (BKE), which in its application to nanoelectronics serves to solve the same problems as the generalized Landauer-Datta-Lundstrom (LDL) transport model does. For some problems BKE formalism is preferable, for the other – LDL model is. Under correct performance of calculations the two approaches leads to similar results. In this article we answer the following questions: how to compose the equation for distribution function f (r, k, t) as a solution of BKE beyond equilibrium, how to solve this equation for the linear response regime, how to compare the obtained results with those, which can be obtained within LDL model for diffusive transport regime, how to take into consideration the external magnetic field and its effect on electron transport.We formulate BKE in the approximation of relaxation time (RT) and search for its solution in the dynamic equilibrium regime. Than we calculate the transport coefficients. We consider the calculation of the surface concentration of electrons in 2D resistor as an example. The solution for BKE in quasi-equilibrium regime within RT approximation is the expression, well known for LDL model. We also demonstrate that BKE within RT approximation leads to the same expressions for Seebeck coefficient and electron thermo-conductivity, as LDL transport model does. The LDL model advantage is its physical transparency and the fact that it enables to consider quasi-ballistic and ballistic transport regimes as simply, as the diffusive one. On the other hand, BKE formalism should be used for studies of the anisotropic transport.