The density of an electron-hole pair in a pur | vedclass

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(B) Given,the intrinsic carrier density (electron-hole pair density) in pure germanium is $n_i = 3 	imes 10^{16} \ m^{-3}$.After doping with aluminiu

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$2 	imes 10^{10}$

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(B) Given,the intrinsic carrier density (electron-hole pair density) in pure germanium is $n_i = 3 	imes 10^{16} \ m^{-3}$.After doping with aluminium (a trivalent impurity),the semiconductor becomes $p$-type,and the hole density is $n_h = 4.5 	imes 10^{22} \ m^{-3}$.According to the law of mass action for semiconductors,the product of electron density $(n_e)$ and hole density $(n_h)$ is equal to the square of the intrinsic carrier density $(n_i^2)$:$n_e 	imes n_h = n_i^2$Substituting the given values:$n_e = \frac{n_i^2}{n_h} = \frac{(3 	imes 10^{16})^2}{4.5 	imes 10^{22}}$$n_e = \frac{9 	imes 10^{32}}{4.5 	imes 10^{22}}$$n_e = 2 	imes 10^{10} \ m^{-3}$.Therefore,the electron density in the doped germanium is $2 	imes 10^{10} \ m^{-3}$.

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 is:

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