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# Estimate the intrinsic conductivity ($\sigma_i$) and resistivity ($\rho_i$) of silicon atoms and electron-hole pairs at room temperature of $300^{\circ}\;K$.

Note: Concentration of atoms by Avogadro's Law, $n_A = 5 \times 10^{28} \text{atoms}\;m^{-3}$, Intrinsic concentration at room temperature is $1.5 \times 10^{16} \text{electron-hole pairs}\;m^{-3}$, Electron Mobility = $0.135\; m^2/V.s$ and Hole Mobility = $0.048\; m^2/V.s$
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Since in a pure semiconductor, $n = p = n_i$, the intrinsic conductivity is: $\sigma_i = (n\mu_n+p\mu_p) e = (\mu_n+\mu_p) \times e\;n_i$
$\Rightarrow$ Intrinsic Conductivity $\sigma_i = (0.135 + 0.048) \times 1.5 \times 10^{16} \times 1.6 \times 10^{-19} = 4.4 \times 10^{-4} \;S/m$
$\Rightarrow$ Intrinsic Resistivity $\rho_i = \large \frac {1}{\sigma_i}$
$\quad \quad = \large \frac {1}{4.4 \times 10^{-4}}$$= 2280\; \Omega\;m$
answered Jul 13, 2014

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