#### The resistivity of pure silicon is $\mathrm{2300 \Omega-m}$ and the mobilities of electrons and holes in it are 0.135 and $\mathrm{0.048 \mathrm{~m}^{2} / \mathrm{V}}$-s respectively. The resistivity of a specimen of silicon doped with $\mathrm{10^{19}}$ atoms of phosphorus per meter is:  Option: 1 Option: 2 Option: 3 Option: 4

The resistivity of pure silicon is $2300\, \Omega\: \mathrm{m}$

$\text{and}\: \mu_{\mathrm{e}}=0.135 \mathrm{~m}^{2} / \mathrm{V}-\mathrm{s}, \mu_{\mathrm{h}}=0.048 \mathrm{~m}^{2} / \mathrm{N}-s.$

$\text{Using,}\: \sigma=1 / \rho=\left(n_{1} \mu_{e}+n_{\mid} \mu_{h}\right) e$

$(2300)^{-1}=n_{\perp}(0.135+0.048) \times 1.6 \times 10^{-19}$
$\mathrm{n_{I}=1.5 \times 10^{16} / \mathrm{m}^{3}}$

Is the intrinsic electron & hole concentration. The resistivity of a specimen doped with $\mathrm{10^{19} \mathrm{P}}$- atoms/mcan be found from :

$\mathrm{\sigma \text { (conductivity) } =\mathrm{n}_{\mathrm{e}} \text { e. } \mu_{\mathrm{e}} \quad\left(\because \mathrm{n}_{\mathrm{e}}=10^{19} / \mathrm{m}^{3}>>\mathrm{n}_{\mathrm{l}}\right) }$
$=10^{19} \times 1.6 \times 10^{-19} \times 0.135$
$=0.216\, \mathrm{mho} / \mathrm{m}$.
$\rho =\frac{1}{\sigma}=4.6 \Omega-\mathrm{m}$