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  4. In a semiconductor, the number density of intrinsic charge carriers at 27° C is 1.5 × 1016 / m 3. If the semiconductor is doped with impurity atom, the hole density increases to 4.5 × 1022 / m 3. The electron density in the doped semiconductor is × 109 / m 3

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Q. In a semiconductor, the number density of intrinsic charge carriers at $27^{\circ} C$ is $1.5 \times 10^{16} / m ^{3}$. If the semiconductor is doped with impurity atom, the hole density increases to $4.5 \times 10^{22} / m ^{3}$. The electron density in the doped semiconductor is______ $\times 10^{9} / m ^{3}$

JEE MainJEE Main 2021Semiconductor Electronics: Materials Devices and Simple Circuits

Solution:

$n_{e} n_{h}=n_{i}^{2}$
$n_{e}=\frac{n_{i}^{2}}{n_{h}}=\frac{\left(1.5 \times 10^{16}\right)^{2}}{4.5 \times 10^{22}}$
$=\frac{1.5 \times 1.5 \times 10^{32}}{4.5 \times 10^{22}}$
$5 \times 10^{9} / m^{3}$