Concept:The reverse saturation current \( I_0 \) depends on the thermally generated minority carrier concentration, which is proportional to \( n_i^2 \propto e^{-E_g / kT} \).
Formula:$$I_0 \propto n_i^2 \propto T^3 \exp\left(-\frac{E_g}{k T}\right)$$
Solution:- Germanium has a smaller bandgap (\( E_g \approx 0.7\text{ eV} \)) compared to silicon (\( E_g \approx 1.1\text{ eV} \)).
- At room temperature, this smaller bandgap yields a much higher intrinsic carrier concentration in Ge (\( \approx 10^{13}\text{ cm}^{-3} \)) than in Si (\( \approx 10^{10}\text{ cm}^{-3} \)).
- Consequently, the reverse leakage current in Ge is on the order of microamperes (\( \mu\text{A} \)), whereas in Si it is on the order of nanoamperes (\( \text{nA} \)).
Why other options are incorrect:- Option B: Silicon has a higher melting point (\( 1414^\circ\text{C} \)) than Germanium (\( 938^\circ\text{C} \)).
- Option C: Both Silicon and Germanium are Group IV elements with exactly four valence electrons.
- Option D: Both materials form covalent diamond cubic crystal lattices.
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