The GATE Grind

GATE 2025 EC – Question 46

Electronic Devices · Carrier Transport · 2 marks · Multiple choice

The intrinsic carrier concentration of a semiconductor is $2.5\times10^{16}$ /m$^3$ at 300 K.

If the electron and hole mobilities are 0.15 m$^2$/Vs and 0.05 m$^2$/Vs, respectively, then the intrinsic resistivity of the semiconductor (in kΩ.m) at 300 K is ________.

(Charge of an electron $e=1.6\times10^{-19}$ C.)

  1. 1.65
  2. 1.25
  3. 0.85
  4. 1.95

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (B) 1.25

Explanation

$\sigma_i=qn_i(\mu_n+\mu_p)=1.6\times10^{-19}\times2.5\times10^{16}\times0.20=8\times10^{-4}$ S/m. So $\rho_i=1/\sigma_i=1250\ \Omega\text{ m}=1.25\ \text{k}\Omega\text{ m}$.