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Chapter: Basics Of Semiconductor Physics· Applied Physics

The electrical conductivity of intrinsic germanium at room temperature is 2.2 mho/m. Find the intrinsic carrier concentration (electron and hole concentration). Given: mobility of electrons \(=0.39\ \text{m}^2/\text{V s}\), mobility of holes \(=0.19\…

Q.23 The electrical conductivity of intrinsic germanium at room temperature is 2.2 mho/m. Find the intrinsic carrier concentration (electron and hole concentration). Given: mobility of electrons \(=0.39\ \text{m}^2/\text{V s}\), mobility of holes \(=0.19\ \text{m}^2/\text{V s}\).

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Answer: \(n=p=n_i\approx2.37\times10^{19}\ \text{m}^{-3}\).

For an intrinsic semiconductor, \(n=p=n_i\), so the conductivity is

\[\sigma_i=n_ie\mu_e+n_ie\mu_h=n_ie(\mu_e+\mu_h)\]

\[n_i=\frac{\sigma_i}{e(\mu_e+\mu_h)}=\frac{2.2}{1.6\times10^{-19}\times(0.39+0.19)}=\frac{2.2}{9.28\times10^{-20}}\]

\[n_i=2.37\times10^{19}\ \text{m}^{-3}\]

So the electron concentration and the hole concentration are each \(2.37\times10^{19}\) per m³.

Doubtly AI · 27 Oct 2026 AI-verified · Oct 2026 Report
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