The quantum efficiency and responsivity (R) at wavelength \lambda (in \mu {m} ) in a p-i-n photodetector are related by

Correct Answer is : R=η×λ1.24

{R}=\frac{1.24 \times \lambda}{\eta}

R=\frac{\eta \times \lambda}{1.24}

R=\frac{1.24}{\eta \times \lambda}

{R}=\frac{\lambda}{\eta \times 1.24}

GATE Electronics and Communications (EC) 2019 Solved Paper

Question : 45 of 65

Marks: +1, -0

The quantum efficiency and responsivity (R) at wavelength

λ

(in

µ {m}

) in a p-i-n photodetector are related by

Solution:

Quantum Efficiency

η=\;{ {R}_{ {e}}}/{ {R}_{ {p}}}

{Re}=

Corresponding Electron Rate (electrons\/sec)

{Rp}=

Incident Photon Rate (Photons\/sec)

{R}_{ {e}}=\;{ {I}_{ {p}}}/{ {q}}, {R}_{ {p}}=\;{ {P}_{ {in}}}/{ {hv}}, {R}=\;{ {l}_{ {p}}}/{ {P}_{ {in}}}

η=\;{ {l}_{ {P} {/} {q}}}/{ {P}_{ {in} {/} {hv}}}

η=\;{ {I}_{ {P} {/} {q}}}/{ {P}_{ {in} {/} {hv}}}=\;{ {lph} {v}}/{ {qP}_{ {in}}}=\;{ {hvR}}/{ {q}}

⇒ {R}=\;{ {qη}}/{ {hv}}=\;{ {qη} λ}/{ {hc}}=η ×(\;{ {q}}/{ {hc}})

q=1.6 × 10^{-19} {c}, {h}=6.63 × 10^{-34} {Js}, {C}=3 × 10^{8} {m} {/} {s}

{R}=\;{η λ}/{1.24}

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