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GATE 2022 EC – Question 17

Electronic Devices · Energy Bands and Carrier Concentration · 1 mark · Multiple choice

In a non-degenerate bulk semiconductor with electron density $n=10^{16}\ \text{cm}^{-3}$, the value of $E_C-E_{Fn}=200$ meV, where $E_C$ and $E_{Fn}$ denote the bottom of the conduction band energy and electron Fermi level, respectively. Assume the thermal voltage as 26 meV and the intrinsic carrier concentration is $10^{10}\ \text{cm}^{-3}$. For $n=0.5\times10^{16}\ \text{cm}^{-3}$, the closest approximation of the value of $(E_C-E_{Fn})$, among the given options, is ________.

  1. 226 meV
  2. 174 meV
  3. 218 meV
  4. 182 meV

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Correct answer: (C) 218 meV

Explanation

For a non-degenerate semiconductor $n=N_Ce^{-(E_C-E_{Fn})/kT}$. Halving $n$ raises $E_C-E_{Fn}$ by $kT\ln2=26\times0.693\approx18$ meV, so the new value is $200+18=218$ meV.