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The Fermi level starts to change location when temperature reaches 300K as a room temperature and Fermi level will getting close to conduction band or valence band depending on energy band gap determines.

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Q: Effect of temperature on fermi level?
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What is the probability of an electron state being filled if it is at the fermi level?

1/2 independent from temperature


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What is fermi level?

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Why fermi level is found in the energy gap region since this region is forbidden for electrons and how does its probability is half?

The Fermi level is also known as the electron chemical potential (μ), and is a constant appearing in the Fermi-Dirac distribution formula: F() = 1 / [1 + exp((-μ)/kT)] Even though the gap may not contain any electronic states, there may be some thermally excited holes in the valence band and electrons in the conduction band, with the occupancy given by the Fermi-Dirac (FD) function. By inspecting the FD function, it becomes clear that if a state existed at the Fermi level, it would have an occupancy of 1/[1 + exp(0)] = 1/[1+1] = 1/2. Lastly, do not confuse Fermi level with Fermi energy. One is the chemical potential of electrons, the other is the energy of the highest occupied state in a filled fermionic system. In semiconductor physics, the Fermi energy would coincide with the valence band maximum.


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How does elevation above sea level effect temperature?

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What are the conditions for the fermi level to be exactly in the middle of the energy band gap of a semiconductor material?

For intrinsic semiconductors like silicon and germanium, the Fermi level is essentially halfway between the valence and conduction bands. You don't have to do anything; just keep the semiconductor intrinsic!