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  • A piece of silicon at room temperature (300 K) has an electrical resistivity of <img alt="6.4 \times 10^{-3} \Omega m" src="https://entrancecorner.oncodecogs.com/gif.latex?6.4%20%5Ctimes%2010%

A piece of silicon at room temperature (300 K) has an electrical resistivity of 6.4 \times 10^{-3} \Omega m . If the doping concentration of the silicon is 1.2 \times 10^{16} \mathrm{~cm}^{-3} What is the mobility of electrons in silicon?

 

Option: 1

1.35 \times 10^{-4} \mathrm{~m}^2 / \mathrm{Vs}


Option: 2

8.33 \times 10^{-4} \mathrm{~m}^2 / \mathrm{Vs}


Option: 3

2.50 \times 10^{-3} \mathrm{~m}^2 / \mathrm{Vs}


Option: 4

4.17 \times 10^{-3} \mathrm{~m}^2 / \mathrm{Vs}


Answers (1)

best_answer

The electrical resistivity of a material is related to the electron concentration 

\rho=\frac{1}{n_e e \mu}

Substituting the given values, we get:


\begin{aligned} \mu & =\frac{1}{n_e e \rho} \\ \mu & =\frac{1}{\left(1.2 \times 10^{16} \mathrm{~cm}^{-3}\right) \times\left(1.6 \times 10^{-19} \mathrm{C}\right) \times\left(6.4 \times 10^{-3} \Omega \mathrm{m}\right)} \\ \mu & =1.35 \times 10^{-4} \mathrm{~m}^2 / \mathrm{Vs} \end{aligned}

Therefore, the mobility of electrons in silicon is  1.35 \times 10^{-4} \mathrm{~m}^2 / \mathrm{Vs} 

 The correct answer is option a).

 

Posted by

manish

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