MHT CET · Physics · Semiconductors
A pure Si crystal has \(4 \times 10^{28}\) atoms per \(\mathrm{m}^3\). It is doped by \(1 \mathrm{ppm}\) concentration of antimony. The number of free electrons available will be
- A \(4 \times 10^{34} \mathrm{~m}^{-3}\)
- B \(4 \times 10^{28} \mathrm{~m}^{-3}\)
- C \(4 \times 10^{22} \mathrm{~m}^{-3}\)
- D \(4 \times 10^{20} \mathrm{~m}^{-3}\).
Answer & Solution
Correct Answer
(C) \(4 \times 10^{22} \mathrm{~m}^{-3}\)
Step-by-step Solution
Detailed explanation
Given: Density of Si atoms \(=4 \times 10^{28}\) atoms \(/ \mathrm{m}^3\) After doping with \(1 \mathrm{ppm}\) of Sb,
\(\begin{aligned}
\text { No. of Sb atoms } & =\frac{4 \times 10^{28}}{10^6} \\
& =4 \times 10^{22}
\end{aligned}\)
The above number of \(\mathrm{Sb}\) atoms donates 1 electron each.
\(\therefore \quad\) The total number of free electrons will be \(4 \times 10^{22} \mathrm{~m}^{-3}\)
\(\begin{aligned}
\text { No. of Sb atoms } & =\frac{4 \times 10^{28}}{10^6} \\
& =4 \times 10^{22}
\end{aligned}\)
The above number of \(\mathrm{Sb}\) atoms donates 1 electron each.
\(\therefore \quad\) The total number of free electrons will be \(4 \times 10^{22} \mathrm{~m}^{-3}\)
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