# Estimate the conductivity ($\sigma_i$) and resistivity ($\rho_i$) of silicon atoms and electron-hole pairs at room temperature of $300^{\circ}\;K$ if every 10-millionth silicon atom is replaced by an atom of Indium.

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 = $0.048\; m^2/V.s$

In a pure semiconductor, $n = p = n_i$, the intrinsic conductivity is: $\sigma_i = (n\mu_n+p\mu_p) e = (\mu_n+\mu_p) \times e\;n_i$. However, in the case of a doped semiconductor, the concentration of mobile charges is dependent solely on the concentration of doping atoms. In this case, $\sigma_p \approx N_a \mu_p e$
Since there are $5 \times 10^{28} \text{silicon atoms}\; m^{-3}$, the necessary concentration of acceptor atoms $N_a = 5 \times 10^{28} \times 10^{-7} = 5 \times 10^{21}$
$\Rightarrow \sigma_p = 5 \times 10^{21} \times 0.048 \times 1.6 \times 10^{-19} = 38.4 \; S/m$
$\Rightarrow$ Resistivity $\rho_p= \large \frac {1}{\sigma_p}$
$\quad \quad = \large \frac {1}{38.4}$$= 2300\; \Omega \;m$
edited Jul 13, 2014