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Applet Worksheet

Fermi distribution function, its meaning on the electron occupancy of energy states, and the effect of temperature.
 Answer the following simple questions.

Foot Notes

1 Completely full or completely empty:  Because in this applet there are only 16 energy states at each level, if the probability of occupancy is less than 1/16 or so, none of the states may appear to be occupied at that energy level (completely empty).  Likewise, if the probability of occupancy is greater than 1.0 - 1/16, then all the states may appear to be occupied (completely full).   This discussion is valid only within an accuracy of 6x10-2 for the probability.  It must NOT lead you to conclude that every states will be empty, no matter how many states there are at that energy level, if E - Ef > 4kT, for example.    

A very good example of a very small f(E) value, but a large number of state-occupying electrons comes in the semiconductor energy band.  At 300K (kT = 0.0259 eV), let us consider the conduction band edge, Ec, which is at Ec - Ef = 0.5 eV. Note that Ec - Ef = 19.3kT >> 4kT. Does it mean that ALL states at E = Ec are vacant and no conduction electons ? No !  There are in fact 1.16x1011 electrons per cm3 at energy states at Ec because n = Nc * f(E) or 1.16E11 = 4.13E-9 * 2.8E19. That is, one hundred and sixteen billion electrons per cm3.   This is due to an arithmatic that a zero (or a very small number) times infinity (or a very big number) is not zero.  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.