Band Filling Diagram

As you can see, this diagram determines the place of Fermi level in different types of matter. I don't understand the later part which is related to semiconductors and insulators? Why do we set Fermi level right in the middle of insulators, while in 3 different positions in semiconductor?


Undoped (intrinsic) semiconductors and insulators are identical in this picture. They only differ by the value of their electronic bandgap. Elevated temperature leads to intrinsic carriers in the semiconductor and therefore makes it conduct at T > 0 K. The bandgap of an insulator is so large that this effect can be neglected for common temperatures. The material would probably decompose before reasonable conductivity is reached.

The two missing cases are n- and p-type semiconductors. Again, you start from the undoped case and start adding impurities. The Fermi level is always defined as the point, where the Fermi-Dirac function reaches an occupation probability of 0.5. Impurities either contribute with additional electrons and therefore shift the Fermi level close to or into the conduction band or they create vacancies (holes) and thus shift the Fermi level towards the valence band.

  • $\begingroup$ So if I understand your answer correctly the fermi level is in the middle of the band gap for intrinsic semiconductors and insulators because that is where, theoretically the occupancy would be 0.5. (Theoretically because there are no levels for the electrons to occupy in the middle of the band gap) $\endgroup$ – tom Jan 12 '15 at 9:57
  • $\begingroup$ Technically the existence of allowed states is not coupled to the position of the Fermi level. See the above case for a semi-metal. For a pure semiconductor material, free of impurities and defects, the thermally created population of electrons and holes (or the lack of at T = 0 K) is symmetric around the middle of the bandgap. $\endgroup$ – engineer Jan 12 '15 at 10:00

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