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  4. The density of electrons and holes in a pure germanium sample at room temperature are equal and its value is 3× 1016 per m3 . On doping with aluminium, it increases to 4.5× 1022 per m3 . Then, the electron density in doped germanium is nearly,

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Q. The density of electrons and holes in a pure germanium sample at room temperature are equal and its value is $3\times 10^{16}$ per $m^{3}$ . On doping with aluminium, it increases to $4.5\times 10^{22}$ per $m^{3}$ . Then, the electron density in doped germanium is nearly,

NTA AbhyasNTA Abhyas 2022

Solution:

The electron and hole concentration in a semiconductor in thermal equilibrium is given by,
$n_{e}n_{h}=n_{i}^{2}$
$n_{e}=\frac{n_{i}^{2}}{n_{h}}=\frac{\left(3 \times \left(10\right)^{16}\right)^{2}}{4 . 5 \times \left(10\right)^{22}}\approx2\times \left(10\right)^{10}m^{- 3}$ .