Concept:As temperature rises, the rate of thermal generation increases the intrinsic carrier concentration \(n_i\) exponentially, which reduces the potential barrier across the junction at a rate of approximately \(-2\text{ mV}/^\circ\text{C}\) for both silicon and germanium.
Formula:$$\frac{dV_0}{dT} \approx -2\text{ mV}/^\circ\text{C} = -0.002\text{ V}/\text{K}$$
Solution:- The built-in barrier is given by \(V_0 = \frac{k_B T}{q}\ln\left(\frac{N_A N_D}{n_i^2}\right)\).
- Because \(n_i^2 \propto T^3 e^{-E_g / k_B T}\) grows exponentially with temperature, the logarithmic term decreases faster than \(T\) increases.
- Thus, the barrier potential \(V_0\) decreases as temperature increases.
Why other options are incorrect:- Option A: The barrier potential decreases with rising temperature, it does not increase.
- Option B: Barrier potential is a temperature-sensitive physical property.
- Option D: \(V_0\) depends on temperature and doping, not on external AC frequency.
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