GATE 2015 EC – Question 20
A silicon sample is uniformly doped with donor type impurities with a concentration of $10^{16}$ /cm$^3$. The electron and hole mobilities in the sample are 1200 cm$^2$/V-s and 400 cm$^2$/V-s respectively. Assume complete ionization of impurities. The charge of an electron is $1.6 \times 10^{-19}$ C. The resistivity of the sample (in $\Omega$-cm) is ________.
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Correct answer: 0.50 to 0.54
Explanation
The sample is $n$-type, so conduction is almost entirely by electrons, $n \approx 10^{16}$ cm$^{-3}$. The conductivity is $\sigma = q n \mu_n = 1.6 \times 10^{-19} \times 10^{16} \times 1200 = 1.92$ S/cm. The resistivity is $\frac{1}{1.92} = 0.52\ \Omega$-cm.