Concept:Reverse saturation current depends directly on the square of the intrinsic carrier concentration (\( I_0 \propto n_i^2 \)). Because Silicon has a wider bandgap than Germanium, its intrinsic carrier concentration at room temperature is roughly \( 10^3 \) times lower, making \( I_0 \) roughly \( 10^6 \) times smaller.
Formula:$$I_{0,\text{Si}} \approx 10^{-9}\text{ A} \ (\text{nA}) \quad \text{vs} \quad I_{0,\text{Ge}} \approx 10^{-6}\text{ A} \ (\mu\text{A})$$
Solution:- At \( 300\text{ K} \), \( n_i(\text{Si}) \approx 1.5 \times 10^{10}\text{ cm}^{-3} \) and \( n_i(\text{Ge}) \approx 2.5 \times 10^{13}\text{ cm}^{-3} \).
- Because \( I_0 \propto n_i^2 \), the thermally generated minority leakage current in Silicon is on the order of nanoamperes (\( \text{nA} \)) or picoamperes (\( \text{pA} \)).
Why other options are incorrect:- Option A: Amperes represents massive forward current, not reverse leakage.
- Option B: Milliamperes is typical for forward conduction current.
- Option D: Kiloamperes occurs only in industrial power distribution faults.
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