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explain why the two fermi levels move toward the middle of the gap at high temperature; one up and one down.

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Answer:

In a semiconductor material, there exists a valence band and a conduction band, with an energy gap between them. At absolute zero temperature, all the electrons in the valence band are completely filled and there are no free electrons in the conduction band. Under these conditions, the Fermi level lies in the valence band.

As temperature is increased, some of the valence band electrons acquire enough thermal energy to be excited across the energy gap into the conduction band, leaving behind holes in the valence band. With increased thermal energy, the number of electrons and holes available for conduction increases. Electrons and holes are both charge carriers that are involved in conduction through a semiconductor material.

The Fermi level is the energy level at which there is a 50% probability of finding an electron with that energy level. At high temperatures, as more and more electrons are excited across the energy gap into the conduction band, the concentration of electrons in the conduction band increases. This causes the Fermi level to move upward in the conduction band, as more electrons are present in energy states closer to its energy level.

At the same time, the number of holes in the valence band also increases due to the excitation of electrons into the conduction band. As a result, the concentration of holes in the valence band decreases. This causes the Fermi level to move downward toward
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