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GATE Electronics and Communications (EC) 2019 Solved Paper

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Question : 40 of 65

Marks: +1, -0

A germanium sample of dimensions

1\ \text{cm} \times 1\ \text{cm}

is illuminated with a

20\ \text{mW}, 600\ \text{nm}

laser light source as shown in the figure. The illuminated sample surface has a 100 nm of loss-less Silicon dioxide layer that reflects one-fourth of the incident light. From the remaining light, one-third of the power is reflected from the Silicon dixodieGermanium interface, one-third is absorbed in the Germanium layer, and one-third is transmitted through the other side of the sample. If the absorption coefficient of Germanium at

600\ \text{nm}

3 \times

10^{4}\ \text{cm}^{-1}

and the bandgap is

0.66\ \text{eV}

, the thickness of the Germanium layer, rounded off to 3 decimal places, is ____________

\mu\ \text{m}

Your Answer:

Solution:

1-e^{-\alpha x}=0.5

e^{-\alpha x}=0.5

now

\propto = 3 \times 10^{4}\ \text{cm}^{-1}

\therefore x = \frac{-\ln(0.5)}{3 \times 10^{4}}

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