Concept:The reverse saturation current \( I_0 \) is caused by thermally generated minority carriers and is proportional to the square of the intrinsic carrier concentration: \( I_0 \propto n_i^2 \propto T^3 e^{-E_g / (kT)} \).
Formula:$$I_0 = q A \left( \frac{D_n n_{p0}}{L_n} + \frac{D_p p_{n0}}{L_p} \right) \propto n_i^2 = B \cdot T^3 \exp\left(-\frac{E_g}{k T}\right)$$
Solution:- Minority carrier densities \( n_{p0} \) and \( p_{n0} \) are proportional to \( n_i^2 \).
- Because \( n_i^2 = N_c N_v e^{-E_g / (kT)} \propto T^3 e^{-E_g / (kT)} \), the reverse saturation current \( I_0 \) increases exponentially with temperature.
Why other options are incorrect:- Option A: Reverse saturation current is strongly temperature-dependent, roughly doubling every \( 10^\circ\text{C} \).
- Option C: The temperature dependence is exponential, not inversely proportional.
- Option D: \( I_0 \) depends on \( e^{-E_g/kT} \); a positive exponent would incorrectly imply that wider-bandgap materials have higher leakage.
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