Concept:Germanium has a smaller energy bandgap (\( 0.67\text{ eV} \) vs \( 1.1\text{ eV} \)), resulting in a lower barrier potential (\( 0.3\text{ V} \) vs \( 0.7\text{ V} \)) and a lower forward voltage drop for a given current.
Formula:$$V_F(\text{Ge}) \approx 0.3\text{ V} < V_F(\text{Si}) \approx 0.7\text{ V} \quad (\text{at equivalent } I_F)$$
Solution:- Germanium has a higher intrinsic carrier concentration (\( n_i \)) and a smaller bandgap than silicon.
- This gives germanium a lower built-in potential barrier (\( \approx 0.3\text{ V} \) compared to \( \approx 0.7\text{ V} \) for silicon).
- For a given forward operating current, a germanium diode requires less forward bias voltage than a silicon diode.
Why other options are incorrect:- Option A: Germanium has a lower forward voltage drop than silicon.
- Option B: The forward voltage drop depends on the semiconductor bandgap, which differs between Si and Ge.
- Option D: Germanium conducts earlier at lower forward voltages than silicon.
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