Concept:The reverse saturation current \(I_s\) is governed by the rate of thermal generation of minority charge carriers in the depletion layer and neutral regions. Thermally activated carrier generation increases exponentially, approximately doubling for every \(10^\circ\text{C}\) increase in temperature.
Formula:$$I_s(T_2) = I_s(T_1) \times 2^{\frac{T_2 - T_1}{10}}$$
Solution:- When \(\Delta T = T_2 - T_1 = 10^\circ\text{C}\):
- $$I_s(T_2) = I_s(T_1) \times 2^{\frac{10}{10}} = 2 \times I_s(T_1)$$
- Thus, the reverse leakage current doubles with every \(10^\circ\text{C}\) increase in temperature.
Why other options are incorrect:- Option A: Reverse current is highly sensitive to temperature and does not remain constant.
- Option B: Thermal carrier generation increases with temperature, never decreases.
- Option D: A ten-fold increase would require a temperature rise of more than \(30^\circ\text{C}\) (\(2^{3.32} \approx 10\)).
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