GATE 2021 PH – Question 27
The donor concentration in non-degenerate n-type silicon is increased by a factor of 100. Find the shift in the Fermi level at 300 K, in meV, rounded to the nearest integer. Given $k_BT=25$ meV at 300 K.
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Correct answer: 115 to 116
Explanation
For a non-degenerate semiconductor with ionized donors, $n\simeq N_D=N_Ce^{(E_F-E_C)/(k_BT)}$. At fixed temperature and band edge, taking the ratio before and after doping gives $\Delta E_F=k_BT\ln(N_{D2}/N_{D1})$. Thus $\Delta E_F=25\ln100=115.13$ meV upward, which rounds to 115 meV. The official accepted interval is 115–116 meV.