Question

For an ideal intrinsic semiconductor, the Fermi energy at 0 K

• A. lies at the top of the valence band
• B. lies at the bottom of the conduction band
• C. lies at the center of the bandgap
• D. lies midway between center of the bandgap and bottom of the conduction band

Answer 1

The Correct Option is C

To solve the question regarding the position of the Fermi energy in an ideal intrinsic semiconductor at 0 K, let's explore the fundamental concepts involved:

Intrinsic Semiconductors: These are pure semiconductors without any significant dopant atoms. The electron concentration in the conduction band is equal to the hole concentration in the valence band.

Fermi Energy Level: The Fermi energy level is defined as the energy level at which the probability of finding an electron is 50%. For intrinsic semiconductors, the Fermi energy level is situated at a position where the number of electrons in the conduction band is equal to the number of holes in the valence band.

Position at 0 K: At absolute zero temperature (0 K), intrinsic semiconductors have no thermal energy to excite electrons from the valence band to the conduction band. Thus, the Fermi level precisely lies in the middle of the bandgap, where:

\(E_F = \frac{E_C + E_V}{2}\)

where \(E_C\) is the energy of the conduction band edge, and \(E_V\) is the energy of the valence band edge.

Explanation: Since the Fermi level at 0 K represents the highest energy electrons can occupy in the valence band without external energy, it naturally aligns at the center of the bandgap. This positioning ensures no electrons are excited to the conduction band, confirming that the Fermi level lies at the center.

Conclusion: The correct option, according to the understanding of intrinsic semiconductors and Fermi energy, is: lies at the center of the bandgap.