Calculate electron and hole concentration in intrinsic silicon at room temperature if its electric conductivity is 4x10-4 mho/m. Given that mobility of electron is 0.14 m2/V-Sec mobility of holes is 0.04 m2/V-Sec.

Given: \(\sigma_i=4\times10^{-4}\) mho/m, \(\mu_e=0.14\) m²/V s, \(\mu_h=0.04\) m²/V s.

Formula: For an intrinsic semiconductor, \(n=p=n_i\) and \(\sigma_i=n_ie(\mu_e+\mu_h)\).

\[ n_i=\frac{\sigma_i}{e(\mu_e+\mu_h)}=\frac{4\times10^{-4}}{1.6\times10^{-19}\times(0.14+0.04)}=\frac{4\times10^{-4}}{2.88\times10^{-20}}=1.39\times10^{16}\ \text{m}^{-3} \]

Electron concentration = hole concentration = \(n_i\approx1.39\times10^{16}\) m\(^{-3}\)

Check: \(1.389\times10^{16}\times1.6\times10^{-19}\times0.18=4.0\times10^{-4}\) mho/m. The answer checks out.