Fermi Level, Fermi Function and
Electron Occupancy of Localized Energy States

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  • Fermi distribution function, and its meaning on the electron occupancy of energy states:  This applet shows the Fermi function at a given temperature T.   Answer the following questions.

  • Foot Notes

    1 Completely full or completely empty:  Because there are 16 energy states at each level, if the probability of occupancy is less than 1/16 or so, none of the states may be occupied at that level (completely empty).  Likewise, if the probability of occupancy is greater than 1.0 - 1/16, then all the states may be occupied (completely full).   This discussion is only valid within an accuracy of 6x10-2 of the probability.  It must not lead you to conclude that EVERY states will be empty, no matter how many states there are, whenever the E - Ef > 4kT.    A very clear example of a very small f(E) value, but a large number of state-occupying electrons comes in the semiconductor band.  For example, at 300K (kT = 0.0259 eV), let us consider Ec - Ef = 0.5 eV. You note that Ec - Ef = 19.3kT >> 4kT. Does it mean that ALL states at or above E = Ec (the conduction band edge) are empty and thus there are no conduction electons ? No !  There are in fact 1.16x1011 electrons per cm3 at energy states at or above Ec !   That is, one hundred and sixteen billion electrons per cm3 !   This is due to the simple arithmatic that (a very small number) times (a very big number) is not necessarily very small !  Here, f(E) = f(Ec - Ef) = f(0.5 eV) = 4.13 x 10-9, meaning that just about 4 states will be occupied for every one billion states !  But in the conduction band of Si, you have about 2.8x1019 states per cm3 (Nc = 2.8x1019 cm-3), a number so large that I can not even spell it out in English.  Out of 2.8x1019 states, a mere one hundred and sixteen billion states are occupied by electrons ( n = Nc * f(E) or 1.16E11 = 4.13E-9 * 2.8E19) !

  • Copyright (c) C.R.Wie, SUNY-Buffalo, 1996-1997