Nonextensive Fermi statistical theory for the carriers and its applications in complex semiconductor
School of Science, Henan Institute of Technology, 453003, Xinxiang City, China
Accepted: 21 June 2021
Published online: 3 July 2021
In this paper, we develop a generalized Fermi statistical theory in the complex semiconductor, where the ordinary Coulomb interactions between excited carriers are non-negligible. In the grand canonical ensemble, the fundamental distribution formula is the nonextensive grand one where the Coulomb interaction between the carriers is regarded as the origin of the nonextensive effect. And the formula for nonextensive Fermi statistics is derived from the quantum summation of grand canonical partition function, by use of the technique of parameter transformation. Different from the popular power-law one, the statistical formula for nonextensive Fermi system is exponential in form, which is benefit to carry out the exactly quantitative analysis to the statistical research on complex semiconductor. The exponential base a is defined as the self-correlation power of the nonextensive parameter ν, when which tends to unity the base tends to the natural index. It can be found that the densities of the carriers in semiconductor and the saturation current of PN Junction are enhanced in the semiconductors whose forbidden band depth is large enough.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021