In an intrinsic semiconductor at room temperature, the number of electrons and holes are equal. If the temperature increases, how does the Fermi level shift?

C. It remains exactly in the middle of the band gap — For an intrinsic semiconductor, the Fermi level is located at the center of the band gap. As temperature increases, the effective masses of electrons and holes change slightly, but the Fermi level remains essentially at the center of the forbidden energy gap.

A. It shifts towards the conduction band

B. It shifts towards the valence band

D. It moves into the conduction band

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$In an intrinsic semiconductor at room temperature, the number of electrons $n_e$ and holes $n_h$ are equal. If the temperature $T$ increases, how does the Fermi level $E_f$ shift?$

A.It shifts towards the conduction band
B.It shifts towards the valence band
C.It remains exactly in the middle of the band gap
D.It moves into the conduction band

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Correct answer: C — It remains exactly in the middle of the band gap

Solution

The Fermi level for an intrinsic semiconductor is given by

E_{f} = \frac{E _{c} + E _{v}}{2} + \frac{3}{4} k_{B} T ln (\frac{m _{v}^{*}}{m _{c}^{*}})

. Since the ratio of effective masses is close to unity, the Fermi level remains at the center of the band gap.

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In an intrinsic semiconductor at room temperature, the number of electrons $n_e$ and holes $n_h$ are equal. If the temperature $T$ increases, how does the Fermi level $E_f$ shift?

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$In an intrinsic semiconductor at room temperature, the number of electrons $n_e$ and holes $n_h$ are equal. If the temperature $T$ increases, how does the Fermi level $E_f$ shift?$