Question

The donor concentration in a sample of n-type silicon is increased by a factor of 100. Assuming the sample to be non-degenerate, the shift in the Fermi level (in meV) at 300 K (rounded off to the nearest integer) is \(\underline{\hspace{2cm}}\).
\text{(Given: } k_B T = 25 \, \text{meV at 300 K).}

Hint:

To calculate the shift in Fermi level, use the relation \( \Delta E_F = k_B T \ln \left( \frac{N_d}{N_{d0}} \right) \).

Answer 1

Correct Answer: 115

The donor concentration in a non-degenerate semiconductor is related to the shift in the Fermi level by: \[ \Delta E_F = k_B T \ln \left( \frac{N_d}{N_{d0}} \right), \] where:
- \( N_d \) is the final donor concentration,
- \( N_{d0} \) is the initial donor concentration.
Given that the donor concentration is increased by a factor of 100, we have: \[ \frac{N_d}{N_{d0}} = 100. \] Substitute \( k_B T = 25 \, \text{meV} \): \[ \Delta E_F = 25 \, \text{meV} \times \ln(100) \approx 25 \, \text{meV} \times 4.605 = 115 \, \text{meV}. \] Thus, the shift in the Fermi level is approximately 115 meV.