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GATE 2024 PH – Question 27

Solid State Physics · conductivity, electron and hole statistics in intrinsic and extrinsic semiconductors, mobility and effective mass · 1 mark · Multiple choice

The temperature dependence of the electrical conductivity (σ) of three intrinsic semiconductors A, B and C is shown in figure. Let EA, EB and EC be the bandgaps of A, B and C, respectively. Which one of the following relations is correct?

Log conductivity versus inverse temperature for semiconductors A, B, C.
  1. $E_C>E_A>E_B$
  2. $E_B>E_C>E_A$
  3. $E_A>E_B>E_C$
  4. $E_A>E_C>E_B$

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Correct answer: (D) $E_A>E_C>E_B$

Explanation

The slope of $\ln\sigma$ against $1/T$ is $-E_g/(2k_B)$. A has the largest slope magnitude, C the next and B the least.