For an intrinsic semiconductor the fermi energy lies in Eg/2 (representing the probability of finding an occupied electron state of 0.5). What I do not understand is why is it in the middle of the forbidden band, where no energy states are allowed, therefore no electrins with that energy will be found. My guess is that, the Fermi function represents the probability, but is the product of the density of states with the fermi function what represents the number of occupied electron states for a particular energy. Hence, if the density of states in the forbidden band is 0 the number is also going to be zero. Am I correct?? I am a little confused, can someone shed some light please :)
Yes, you are correct that the meaningful value is the number of electrons in the particular energy state, which is the multiplication of the distribution function and the density of states. Thus, there is no electrons sitting directly on the Eg, if it is within the band gap. Moreover, the Fermi-energy does not necessarily lies at the Eg/2, since any value within the band gap (at zero temperature) would produce the correct populations of electrons, which are: a filled valence band and an empty conduction band.
you must be aware that in semiconductors we have 2 types of carriers since Egap is not zero. Thus the mathematics of the occupancy of both type of carriers shows that the fermi level is balanced approximately at Egap/2 as if the carriers are excited according to fermi function from the middle Egap. Of course there is no actual occupancy of carriers within the bandgap but the fermi function is not forbidden in the bandgap it is only the density of state g(E) that is zero there..
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