In a P type silicon conductor $n_{i} =$ charge carrier concentration of $4.4 \times 10^{19} m^{- 3}$ . The density of dopant is $3.8 \times 10^{24} A t o m / m^{3}$ . The electron and hole mobility are 0.5 and 0.4 $m^{2} V^{- 1} s^{- 1}$ respectively. What is the conductivity before and after addition of dopant respectively

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$6.336 Ω^{- 1} m^{- 1}, 2.432 \times 10^{5} Ω^{- 1} m^{- 1}$

$5.1 \times 10^{- 19} Ω^{- 1} m^{- 1}, 1.95 \times 10^{6} Ω^{- 1} m^{- 1}$

$5.0 \times 10^{- 20} Ω^{- 1} m^{- 1}, 2.0 \times 10^{6} Ω^{- 1} m^{- 1}$

$6.0 \times 10^{- 20} Ω^{- 1} m^{- 1}, 1.99 \times 10^{8} Ω^{- 1} m^{- 1}$

answer is D.

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Detailed Solution

$C o n d u c t i v i t y b e f o r e d o p i n g σ = n_{i} e (μ_{e} + μ_{h})$

$\Rightarrow σ = 4.4 \times 10^{19} \times 1.6 \times 10^{- 19} [0.4 + 0.5] \Rightarrow σ = 6.336 Ω^{- 1} m^{- 1}$

$C o n d u c t i v i t y a f t e r d o p i n g, σ = n_{h} e μ_{h} = 3.8 \times 10^{24} \times 1.6 \times 10^{19} \times 0.4 = 2.432 \times 10^{5} Ω^{- 1} m^{- 1}$

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