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When two different doped (like a p and n) semiconductors for an intimate contact the energy of the  Fermi level in both semiconductors will be equal. The Fermi level is the level which has a probability of finding the electron there of 0.5 at temperatures `T>0` , of the last...

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When two different doped (like a p and n) semiconductors for an intimate contact the energy of the  Fermi level in both semiconductors will be equal. The Fermi level is the level which has a probability of finding the electron there of 0.5 at temperatures `T>0` , of the last energy level filled with electrons at `T=0` . In a way the equality of Fermi levels in both p and n region is equivalent to say that the filling with electrons is equal in both parts. It is like when you have water at different levels in two cups, and when the separating wall vanishes the water will be at the same level in the two united cups.

Because the Fermi level is pinned to the donor level (in the n semiconductor) and to the acceptor level (in the p semiconductor) the valence and conduction bands will bend around the contact region. Band bending in turn, means a difference in energies, which implies the necessity of existence of an electric field. Electric field builds up because because of electric charges that diffuse in the bending region (electrons from donors tend to cancel the acceptors leaving behind a static positive charge in the n region). Thus a static uncompensated charge (depleted charge) will exist in the band bending region. The static charge build up until the electric field it creates begin to oppose to further diffusion of electrons and holes.

The region where this uncompensated static charge exists is named the depletion layer.

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