GATE 2023 EC – Question 56
In an extrinsic semiconductor, the hole concentration is given to be $1.5n_i$, where $n_i$ is the intrinsic carrier concentration of $1\times10^{10}$ cm$^{-3}$. The ratio of electron to hole mobility for equal hole and electron drift current is given as ________ (rounded off to two decimal places).
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Correct answer: 2.24 to 2.26
Explanation
$np=n_i^2$, so $n=\dfrac{n_i^2}{1.5n_i}=\dfrac{n_i}{1.5}$. Equal drift currents need $qn\mu_nE=qp\mu_pE$, so $\dfrac{\mu_n}{\mu_p}=\dfrac pn=\dfrac{1.5n_i}{n_i/1.5}=1.5^2=2.25$.