The Fermi level E_F in an intrinsic semiconductor, if effective masses of holes and electrons are same, is: 

Concept:

Fermi Level:

• The Fermi level in an intrinsic semiconductor is nearly midway between the conductive and valence band.
• Fermi level is the highest energy state occupied by electrons in a material at absolute zero temperature.

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• For a p-type semiconductor, there are more holes in the valence band than there are electrons in the conduction band i.e. n < p.
• This implies that the probability of finding an electron near the conduction band edge is smaller than the probability of finding a hole at the valence band edge.
• Therefore, the Fermi level is closer to the valence band in a p-type semiconductor.

Explanation:

• The Fermi level for a p-type lie near the valence band.
• As the temperature increases above zero degrees, the extrinsic carriers in the conduction band and the valence band increases.
• Since the intrinsic concentration also depends on temperature, ni also increases. But for small values of temperature, the extrinsic concentration dominates in comparison to the intrinsic concentration.
• As the temperature continues to increase, the semiconductor starts to lose its extrinsic property and becomes intrinsic, as ni becomes comparable to the extrinsic concentration.

As the temperature increases the p type semiconductor become a simple semiconductor.

Hence, the Fermi level comes back to midway in forbidden energy gap.