In a pure silicon crystal electron-hole concentration is 10¹⁶ per m³ at 301 K. Now 10²¹ atoms of phosphorus are added per cubic metre. The new hole concentration in silicon is (in per m³) (a) 10⁵ (b) 10¹¹ (c) 10¹⁹ (d) 10²¹

Answer: (b). Phosphorus is a donor, so ne ≈ 10²¹ m⁻³. nh = (ni²)/(ne) = 10³²10²¹ = 10¹¹ m⁻³ So the answer is (b) 10¹¹.

In a pure silicon crystal electron-hole concentration is 10¹⁶ per m³… | MHT CET 2025 (22 Apr, Shift 1)

Q14MHT CET 2025 · 22 APR · SHIFT 1Easy

Intrinsic & Extrinsic Semiconductors

In a pure silicon crystal electron-hole concentration is $10^{16}$ per $\text{m}^{3}$ at 301 K. Now $10^{21}$ atoms of phosphorus are added per cubic metre. The new hole concentration in silicon is (in per $\text{m}^{3}$ )

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Answer: (b)

Phosphorus is a donor, so $n_e \approx 10^{21}\ \text{m}^{-3}$ .
$n_h = \dfrac{n_i^2}{n_e} = \dfrac{10^{32}}{10^{21}} = 10^{11}\ \text{m}^{-3}$
So the answer is (b) $10^{11}$ .

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