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(f18)
This function is plotted in the figure below.
fermi.xls - fermi.gif
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| bet | 5/57 | | Sana | 09.05.2021 | | Hajmi | 0,62 Mb. | | #14427 |
(f18)
This function is plotted in the figure below.
fermi.xls - fermi.gif
Fig. 2.4.4 Fermi function at an ambient temperature of 150 K (red curve), 300 K (blue curve) and 600 K (black curve).
The Fermi function has a value of one for energies, which are more than a few times kT below the Fermi energy. It equals 1/2 if the energy equals the Fermi energy and decreases exponentially for energies which are a few times kT larger than the Fermi energy. While at T =0 K the Fermi function equals a step function, the transition is more gradual at finite temperatures and more so at higher temperatures.
Impurity distribution functions
The distribution function of impurities differs from the Fermi-Dirac distribution function although the particles involved are Fermions. The difference is due to the fact that a filled donor energy level contains only one electron which can have either spin (spin up or spin down) , while having two electrons with opposite spin occupy this one level is not allowed since this would leave a negatively charge atom which would have a different energy as the donor energy. This yields a modified distribution function for donors as given by:
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