Physics - Semiconductors Question with Solution | TestHub

Given intrinsic carrier concentration $n_i=10^{16}{\text{ m}}^{-3}$.

Number of donor atoms added $N_D=10^{21}{\text{ m}}^{-3}$.

Since phosphorus is a pentavalent impurity, it donates electrons. The new electron concentration becomes approximately equal to the donor concentration.

$n_e\approx N_D=10^{21}{\text{ m}}^{-3}$

According to the law of mass action for semiconductors:

$n_e{n}_h=n_i^2$

$n_h=\frac{n_i^2}{n_e}$

$n_h=\frac{(10^{16}{)}^2}{10^{21}}$

$n_h=\frac{10^{32}}{10^{21}}=10^{11}{\text{ m}}^{-3}$

Answer: $10^{11}$