Concept:The knee (threshold or turn-on) voltage is the forward bias voltage required to offset the internal potential barrier so that majority carriers can conduct current.
Formula:$$V_{\text{knee}}(\text{Ge}) \approx 0.2\text{ V} - 0.3\text{ V}, \quad V_{\text{knee}}(\text{Si}) \approx 0.6\text{ V} - 0.7\text{ V}$$
Solution:- Germanium has a smaller energy bandgap (\( 0.67\text{ eV} \)) than silicon (\( 1.1\text{ eV} \)).
- This results in a smaller built-in barrier potential of approximately \( 0.3\text{ V} \).
- Therefore, a forward-biased germanium diode begins conducting significant current when the applied voltage reaches approximately \( 0.3\text{ V} \).
Why other options are incorrect:- Option A: \( 0.7\text{ V} \) is the forward threshold voltage for a silicon (\( \text{Si} \)) diode.
- Option B: \( 1.1\text{ V} \) corresponds to the bandgap of silicon in electron-volts, not the knee voltage of germanium.
- Option C: A real semiconductor diode requires a non-zero forward voltage to overcome its built-in potential barrier.
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