Question

If \( E_c \) and \( E_v \) represent the energy of the conduction band and valence band, \( E_D \) represent the donor energy level, and the band gap in a n-type semiconductor, then the true relation among them is:

• A. \( E_c = E_D \)
• B. \( E_D>E_c \)
• C. \( E_D>E_v \)
• D. \( E_c - E_v = 2 E_g \)
• E. \( E_c + E_g = E_v \)

Hint:

In an n-type semiconductor, the donor energy level is just below the conduction band. This allows electrons from the donor level to easily jump into the conduction band, thereby enhancing conductivity.

Answer 1

The Correct Option is C

In a semiconductor, the energy levels can be understood as follows:
- \( E_c \): Energy of the conduction band.
- \( E_v \): Energy of the valence band.
- \( E_D \): Donor energy level in a n-type semiconductor.
- \( E_g \): Band gap of the semiconductor.
For a n-type semiconductor:
- The donor level \( E_D \) is slightly below the conduction band \( E_c \), meaning electrons from the donor energy levels can easily move to the conduction band with minimal energy input.
- The band gap \( E_g \) is the energy difference between the conduction band and the valence band (\( E_c - E_v \)).
In n-type semiconductors, the donor energy level \( E_D \) is closer to the conduction band than to the valence band, so it follows that: \[ E_D>E_v \] Thus, the correct answer is: \[ \boxed{{C) } E_D>E_v} \]