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Tytuł pozycji:

Generalized Boltzmann relations in semiconductors including band tails.

Tytuł:
Generalized Boltzmann relations in semiconductors including band tails.
Autorzy:
Beckers, Arnout
Beckers, Dominique
Jazaeri, Farzan
Parvais, Bertrand
Enz, Christian
Temat:
CONDUCTION bands
SEMICONDUCTORS
QUANTUM computing
HYPERGEOMETRIC series
VALENCE bands
Źródło:
Journal of Applied Physics; 1/28/2021, Vol. 129 Issue 4, p1-10, 10p
Czasopismo naukowe
Boltzmann relations are widely used in semiconductor physics to express the charge-carrier densities as a function of the Fermi level and temperature. However, these simple exponential relations only apply to sharp band edges of the conduction and valence bands. In this article, we present a generalization of the Boltzmann relations accounting for exponential band tails. To this end, the required Fermi–Dirac integral is first recast as a Gauss hypergeometric function followed by a suitable transformation of that special function and a zeroth-order series expansion using the hypergeometric series. This results in simple relations for the electron and hole densities that each involve two exponentials. One exponential depends on the temperature and the other one on the band-tail parameter. The proposed relations tend to the Boltzmann relations if the band-tail parameters tend to zero. This work is timely for the modeling of semiconductor devices at cryogenic temperatures for large-scale quantum computing. [ABSTRACT FROM AUTHOR]
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