Concept:The built-in potential barrier \( V_0 \) arises from the majority carrier concentration ratio between the neutral regions and the junction interface at thermal equilibrium.
Formula:$$V_0 = V_T \ln\left(\frac{p_{p0}}{p_{n0}}\right) = \frac{k T}{q} \ln\left(\frac{N_A N_D}{n_i^2}\right)$$
Solution:- In the neutral P-region, hole concentration is \( p_{p0} \approx N_A \).
- In the neutral N-region, hole concentration is \( p_{n0} = n_i^2 / N_D \).
- Using the Boltzmann relation: \( V_0 = \frac{k T}{q} \ln\left(\frac{p_{p0}}{p_{n0}}\right) = \frac{k T}{q} \ln\left(\frac{N_A N_D}{n_i^2}\right) \).
Why other options are incorrect:- Option A: Inverting the logarithm argument and ratio gives a negative voltage.
- Option B: The barrier potential depends logarithmically on doping, not linearly.
- Option D: \( n_i^2 / (N_A N_D) \) is dimensionless and lacks thermal voltage scaling.
Quality & Fidelity Assurance:
Every question on BeambePrep is rigorously curated against the official PMDC syllabus with zero filler, zero out-of-syllabus content, and zero typos. When an authentic past paper originally contained a historical mistake or ambiguity from the examining board (such as UHS or NUMS), BeambePrep faithfully reflects the original paper while detailing the nuance and scientific consensus in the autopsy above.