It is known that if we want to calculate some electronic thermodynamic property, like electronic heat capacity Cel at finite temperature, we have to account for temperature dependence of the Fermi-Dirac function. If the electronic density of states function has peculiarities in the vicinity of the Fermi energy, the temperature dependence of Cel can be considerable. However, the derivative of the Fermi-Dirac function is a narrow peak near the Fermi energy and therefore integration problems appear (especially at low temperatures). There is a small number of papers, where this issue is addressed by expanding the Fermi integral in a series, like
http://iopscience.iop.org/0034-4885/44/4/001
http://iopscience.iop.org/0953-8984/8/18/008
or newer but where calculating of the Fermi integrals is considered for another class of problems (like http://arxiv.org/abs/astro-ph/0102329v1).
I am wondering, are there any studies, where the issue is considered from a solely numerical approach, e.g. by constructing a temperature-dependent integration mesh? Thank you in advance.
Dear Anton,
yes , the numerical Fermi integral tables exist and we have used these (you can find them on internet/Wikipedia) in our work on electrical response in materials. It is my collaborator who has used them in our general numerical simulations of the electrical response and if you will have problems "googling them up" , let me know and I will ask him for the reference.
With best regards
Petr
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