Concept:Because reverse saturation current arises from minority carrier generation throughout the depletion region, total current scales directly with cross-sectional junction area \( A \).
Formula:$$I_0 = J_0 \cdot A = q A \left( \frac{D_n n_{p0}}{L_n} + \frac{D_p p_{n0}}{L_p} \right) \propto A$$
Solution:- The reverse saturation current density \( J_0 \) (in \( \text{A/cm}^2 \)) depends on material properties.
- Multiplying current density \( J_0 \) by junction area \( A \) gives the total reverse saturation current: \( I_0 = J_0 \cdot A \).
- Larger junction areas collect more thermally generated minority carriers, increasing \( I_0 \) proportionally.
Why other options are incorrect:- Option A: Larger junction areas increase total current rather than decreasing it.
- Option B: Total current scales with device area, even though current density \( J_0 \) remains constant.
- Option C: The relationship with junction area is linear, not quadratic.
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