Abstract In order to consider quantum transport under the influence of an electron--electron (e--e) interaction in a mesoscopic conductor, the Boltzmann equation and Poisson equation are investigated jointly. The analytical expressions of the distribution function for the Boltzmann equation and the self-consistent average potential concerned with e--e interaction are obtained, and the dielectric function appearing in the self-consistent average potential is naturally generalized beyond the Thomas--Fermi approximation. Then we apply these results to the tunneling junctions of a metal--insulator--semiconductor (MIS) in which the electrons are accumulated near the interface of the semiconductor, and we find that the e--e interaction plays an important role in the transport procedure of this system. The electronic density, electric current as well as screening Coulombic potential in this case are studied, and we reveal the time and position dependence of these physical quantities explicitly affected by the e--e interaction.
Received: 17 October 2008
Revised: 18 February 2009
Accepted manuscript online:
Fund: Project supported by the National
Natural Science Foundation of China
(Grant No 10404037).
Cite this article:
Zhang Li-Zhi(张礼智) and Wang Zheng-Chuan(王正川) Analytical solution of the Boltzmann--Poisson equation and its application to MIS tunneling junctions 2009 Chin. Phys. B 18 2975
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