The GATE Grind

GATE 2020 EC – Question 16

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

A single crystal intrinsic semiconductor is at a temperature of 300 K with effective density of states for holes twice that of electrons. The thermal voltage is 26 mV.

The intrinsic Fermi level is shifted from mid-bandgap energy level by

  1. 18.02 meV.
  2. 9.01 meV.
  3. 13.45 meV.
  4. 26.90 meV.

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Correct answer: (B) 9.01 meV.

Explanation

For an intrinsic semiconductor $n=p$, which gives $E_i=\frac{E_C+E_V}{2}+\frac{kT}{2}\ln\frac{N_V}{N_C}$. With $N_V/N_C=2$ the shift is $\frac{26}{2}\ln2=9.01$ meV.