The GATE Grind

GATE 2025 EC – Question 48

Electronic Devices · Carrier Transport · 2 marks · Multiple choice

The electron mobility $\mu_n$ in a non-degenerate germanium semiconductor at 300 K is 0.38 m$^2$/Vs.

The electron diffusivity $D_n$ at 300 K (in cm$^2$/s, rounded off to the nearest integer) is ________.

(Consider the Boltzmann constant $k_B=1.38\times10^{-23}$ J/K and the charge of an electron $e=1.6\times10^{-19}$ C.)

  1. 26
  2. 98
  3. 38
  4. 10

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Correct answer: (B) 98

Explanation

By the Einstein relation $D_n=\mu_nV_T=\mu_n\dfrac{k_BT}{e}=0.38\times\dfrac{1.38\times10^{-23}\times300}{1.6\times10^{-19}}=0.38\times0.025875=9.83\times10^{-3}$ m$^2$/s $=98.3$ cm$^2$/s, i.e. 98.