The width of forbidden gap in silicon crystal is 1.1eV. When the crystal is converted into n-type semiconductor, then the distance of fermi energy level from conduction band is

Options

A. equal to 0.55eV
B. equal to 1.leV
C. less than 0.55eV
D. greater than 0.55eV

Answer

To find the distance of the Fermi energy level from the conduction band in an n-type semiconductor made from silicon, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Energy Band Structure**:
- In a semiconductor, the energy band structure consists of the valence band, conduction band, and the forbidden energy gap (band gap).
- For silicon, the width of the forbidden gap (Eg) is given as 1.1 eV.

2. **Identify Fermi Energy Levels**:
- For intrinsic silicon, the Fermi energy level (Ei) lies approximately in the middle of the band gap.
- When silicon is doped to become an n-type semiconductor, the Fermi energy level (Ef) shifts closer to the conduction band.

3. **Calculate the Fermi Level Position**:
- The distance from the conduction band (Ec) to the Fermi level (Ef) can be expressed as:
\[ Ec - Ef = \frac{Eg}{2} - (Ef - Ei) \]
- Since for intrinsic silicon, \(Ef \approx Ei\), we can simplify our calculations.

4. **Substitute the Known Values**:
- Given that \(Eg = 1.1 \, \text{eV}\), we can substitute this value into the equation:
\[ Ec - Ef = \frac{1.1}{2} - (Ef - Ei) \]
- This simplifies to:
\[ Ec - Ef = 0.55 - (Ef - Ei) \]

5. **Determine the Shift in Fermi Level**:
- In n-type semiconductors, the Fermi level is closer to the conduction band, so \(Ef\) will be greater than \(Ei\).
- Therefore, we can conclude that:
\[ Ec - Ef < 0.55 \, \text{eV} \]

6. **Final Conclusion**:
- The distance of the Fermi energy level from the conduction band in an n-type silicon semiconductor is less than 0.55 eV. Thus, the correct answer is:
- **Option A: Less than 0.55 eV**.