GATE 2023 IN Q.38: solution and answer

GATE 2023 · INQ.38 · 2 marks · MCQ

In a p-i-n photodiode, a pulse of light containing $8 \times 1 0^{12}$ incident photons at wavelength $λ_{0} = 1.55 μ m$ gives rise to an average $4 \times 1 0^{12}$ electrons collected at the terminals of the device. The quantum efficiency of the photodiode at this wavelength is ______ %.

(A)
50
(B)
54.2
(C)
62.5
(D)
80

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Answer and solution

ANSWER

The quantum efficiency is 50 %, option (A).

Official answer: ASource: Official answer key, GATE 2023 IN (IIT Kanpur)

Quantum efficiency is the number of collected electron-hole pairs per incident photon: $η = \frac{N _{e}}{N _{p}}$ .
Incident photons: $N_{p} = 8 \times 1 0^{12}$ . Collected electrons: $N_{e} = 4 \times 1 0^{12}$ .
$η = \frac{4 \times 1 0 ^{12}}{8 \times 1 0 ^{12}} = 0.5$
As a percentage, $η = 0.5 \times 100 = 50 %$ .
The wavelength $1.55 μ m$ is not needed here. It would matter only for the responsivity $R = \frac{η q λ}{h c}$ , which the question does not ask for. The answer is option (A).

KEY IDEA

Quantum efficiency is the ratio of collected electrons to incident photons. It is a pure count ratio and does not depend on wavelength.

WATCH OUT FOR

Bringing the wavelength into the calculation, for example by computing responsivity or photon energy. The question gives photon and electron counts directly, so the wavelength is a distractor.

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GATE 2023 IN Q.38: solution and answer

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