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(A) When a $Ge$ specimen is doped with $Al$ (a trivalent impurity),it becomes a $p$-type semiconductor.The concentration of acceptor atoms $(N_A)$ is

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$10^{17} /m^3$

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(A) When a $Ge$ specimen is doped with $Al$ (a trivalent impurity),it becomes a $p$-type semiconductor.The concentration of acceptor atoms $(N_A)$ is approximately equal to the concentration of holes $(p_0)$: $p_0 \approx N_A = 10^{21} /m^3$.According to the law of mass action for semiconductors,the product of the concentration of electrons $(n_0)$ and holes $(p_0)$ is equal to the square of the intrinsic carrier concentration $(n_i)$:$n_i^2 = n_0 	imes p_0$Given:$n_i = 10^{19} /m^3$$p_0 = 10^{21} /m^3$Substituting the values:$(10^{19})^2 = n_0 	imes 10^{21}$$10^{38} = n_0 	imes 10^{21}$$n_0 = \frac{10^{38}}{10^{21}} = 10^{17} /m^3$Thus,the concentration of electrons in the specimen is $10^{17} /m^3$.

$A$ $Ge$ specimen is doped with $Al$. The concentration of acceptor atoms is $\sim 10^{21} \text{ atoms}/m^3$. Given that the intrinsic concentration of electron-hole pairs is $\sim 10^{19} /m^3$,the concentration of electrons in the specimen is:

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