GATE 2019 EC – Question 58
A Germanium sample of dimensions 1 cm $\times$ 1 cm is illuminated with a 20 mW, 600 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 dioxide-Germanium 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 nm is $3\times10^4\ \text{cm}^{-1}$ and the bandgap is 0.66 eV, the thickness of the Germanium layer, rounded off to 3 decimal places, is ________ $\mu$m.
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Correct answer: 0.22 to 0.24
Explanation
After the oxide, $20\times\frac34=15$ mW remains; $5$ mW is reflected at the interface and $10$ mW enters the germanium. Of this, $5$ mW is absorbed and $5$ mW is transmitted, so the transmitted fraction is $e^{-\alpha T}=0.5$. Hence $T=\frac{\ln2}{3\times10^4\ \text{cm}^{-1}}=2.31\times10^{-5}$ cm $=0.231\ \mu$m.