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  4. The density of an electron-hole pair in a pure germanium is 3 × 1016 m-3 at room temperature. On doping with aluminium, the hole density increases to 4.5 × 1022 m-3. Now the electron density (in m-3) in doped germanium will be

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Q. The density of an electron-hole pair in a pure germanium is $3 \times 10^{16} \, m^{-3}$ at room temperature. On doping with aluminium, the hole density increases to $4.5 \times 10^{22} \, m^{-3}$. Now the electron density (in $m^{-3}$) in doped germanium will be

KCETKCET 2018Semiconductor Electronics: Materials Devices and Simple Circuits

Solution:

$n^2_1 = n_hn_e$
$ \Rightarrow n_e = \frac{(3\times 10^{16})^2}{4.5 \times 10^{22}}= \frac{9 \times 10^{32}}{4.5\times 10^{22}} $
$= 2 \times 10^{10} \,m ^{-3}$