In an intrinsic semiconductor at thermal equilibrium, where is the Fermi energy level ($ E_F $) located relative to th · Electronics MDCAT Past Paper MCQ

Physics Electronics PMDC Conceptual Practice

PMDC Verified Question 424 of 494

In an intrinsic semiconductor at thermal equilibrium, where is the Fermi energy level ($ E_F $) located relative to the energy bands?

Inside the conduction band near its upper energy boundary

Approximately at the geometric midpoint of the forbidden energy bandgap

Inside the valence band near its lower energy boundary

At the top edge of the conduction band

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Official Correct Choice:

Option B: Approximately at the geometric midpoint of the forbidden energy bandgap

Concept:

In an intrinsic semiconductor, electron and hole concentrations are equal ($ n = p = n_i $). Consequently, the Fermi energy level lies near the center of the bandgap.

Formula:

$$E_F = E_i = \frac{E_c + E_v}{2} + \frac{3}{4} k_B T \ln\left(\frac{m_h^*}{m_e^*}\right) \approx \frac{E_c + E_v}{2}$$

Solution:

Because intrinsic generation produces equal numbers of conduction electrons and valence holes, the probability of finding an electron is symmetric relative to the band edges.

Therefore, the intrinsic Fermi level ($ E_F $) sits near the midpoint between the conduction band edge $ E_c $ and valence band edge $ E_v $.

Why other options are incorrect:

Option A: The Fermi level enters the conduction band in degenerate N-type semiconductors.
Option C: The Fermi level enters the valence band in degenerate P-type semiconductors.
Option D: At equilibrium, the intrinsic Fermi level remains within the forbidden bandgap.

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