GATE 2025 MT – Question 57
An intrinsic semiconductor has conductivity 100 Ω$^{-1}$ m$^{-1}$ at 300 K and 300 Ω$^{-1}$ m$^{-1}$ at 500 K. Its band gap is ______ eV (rounded to two decimal places). Given: $k_B=8.6\times10^{-5}\ \mathrm{eV\,K^{-1}}$.
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Correct answer: 0.13 to 0.15
Explanation
Using the constant-prefactor approximation $\sigma=\sigma_0\exp[-E_g/(2k_BT)]$, take the conductivity ratio to eliminate $\sigma_0$.
$\ln3=E_g(1/300-1/500)/(2k_B)$. Hence $E_g=2(8.6\times10^{-5})\ln3/(1/300-1/500)=0.1417\ldots$ eV.
The answer under this approximation is **0.14 eV**.