Concept:The built-in barrier potential is determined by the semiconductor bandgap, doping concentrations, and temperature. For silicon at room temperature (\(300\text{ K}\)), it is approximately \(0.7\text{ V}\), whereas for germanium it is approximately \(0.3\text{ V}\).
Formula:$$V_0 = \frac{k_B T}{q} \ln\left(\frac{N_A N_D}{n_i^2}\right)$$
Solution:- For Silicon (\(\text{Si}\)): Built-in barrier potential \(V_0 \approx 0.7\text{ V}\).
- For Germanium (\(\text{Ge}\)): Built-in barrier potential \(V_0 \approx 0.3\text{ V}\).
Why other options are incorrect:- Option A: \(0.3\text{ V}\) is the barrier potential for Germanium (\(\text{Ge}\)).
- Option B: \(1.1\text{ V}\) (specifically \(1.12\text{ eV}\)) represents the forbidden energy bandgap \(E_g\) of silicon, not its junction potential barrier.
- Option D: \(0.025\text{ V}\) (\(25\text{ mV}\)) is the thermal voltage \(V_T = k_B T / q\) at room temperature.
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