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  4. The electron density of intrinsic semi-conductor at room temperature is 1016 m-3. When doped with a trivalent impurity, the electron density is decreased to 1014 m-3 at the same temperature. The majority carrier density is

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Q. The electron density of intrinsic semi-conductor at room temperature is $10^{16} m^{-3}$. When doped with a trivalent impurity, the electron density is decreased to $10^{14}\,m^{-3}$ at the same temperature. The majority carrier density is

KEAMKEAM 2016Semiconductor Electronics: Materials Devices and Simple Circuits

Solution:

$n_{e} \times n_{h}=n_{i}^{2} $
$n_{i}=10^{16} m ^{-3} $
$n_{e}=10^{14} m ^{-3} $ given
$\Rightarrow n_{h}=\frac{n_{i}^{2}}{n_{e}}=\frac{\left(10^{16}\right)^{2}}{10^{14}}=\frac{10^{32}}{10^{14}}$
$=10^{18} m ^{-3}$
Given semiconductor is doped with a trivalent impurity, therefore majority charge carriers are holes.