A pure Si crystal having 5 × 10²8 atoms m^-3 is dopped with 1 ppm concentration of antimony. If the concentration of holes in the doped crystal is found to be 4.5 × 10^9\ m^-3, the concentration (in m^-3) of intrinsic charge carriers in Si crystal is about (A) 1.2 × 10^15 (B) 1.5 × 10^16 (C) 3.0 × 10^15 (D) 2.0 × 10^16

PhysicsCBSE Class 12 · Board exam 2024, set 55/5/1 · 1 mark · MCQ

CBSE Class 12 Physics 2024: question 12

Set in the CBSE Class 12 board exam of 2024, paper 55/5/1, section A, question 12, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q12 · 1 mark · MCQSemiconductor Electronics: Materials, Devices and Simple Circuits

A pure Si crystal having $5 \times 1 0^{28}$ atoms $m^{- 3}$ is dopped with 1 ppm concentration of antimony. If the concentration of holes in the doped crystal is found to be $4.5 \times 1 0^{9} m^{- 3}$ , the concentration (in $m^{- 3}$ ) of intrinsic charge carriers in Si crystal is about

(A) $1.2 \times 1 0^{15}$
(B) $1.5 \times 1 0^{16}$
(C) $3.0 \times 1 0^{15}$
(D) $2.0 \times 1 0^{16}$

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 55/5/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

1 ppm means one dopant atom per $1 0^{6}$ Si atoms.

Hint 2

Use the mass-action law $n_{e} n_{h} = n_{i}^{2}$ .

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

$n_{e} \approx N_{D} = 5 \times 1 0^{28} \times 1 0^{- 6} = 5 \times 1 0^{22} m^{- 3}$ .
½ mark
$n_{i}^{2} = n_{e} n_{h} = 5 \times 1 0^{22} \times 4.5 \times 1 0^{9} = 2.25 \times 1 0^{32}$ , so $n_{i} = 1.5 \times 1 0^{16} m^{- 3}$ . Option (B).
½ mark

Answer: $1.5 \times 1 0^{16} m^{- 3}$ , option (B)

Where the marks are

Finds $n_{e}$ and uses $n_{i}^{2} = n_{e} n_{h}$ (1 mark)

Revise the chapter

Chapter: Semiconductor Electronics: Materials, Devices and Simple Circuits (notes, formulas, where marks are lost and every past question)

Practise this chapterBoard-style questions from Semiconductor Electronics: Materials, Devices and Simple Circuits, one at a time, marked against the answer key and marking points.Back to the full paper2024 board paper, set 55/5/1: every question, by section.

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CBSE Class 12 Physics 2024: question 12

Hints

Step-by-step solution

Revise the chapter

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