Concept:When a \( \text{P-N} \) junction forms, majority electrons and holes diffuse across the interface and recombine, exposing immobile ionized impurity atoms that establish a built-in electric field.
Formula:$$V_B = \frac{k_B T}{e} \ln\left(\frac{N_A N_D}{n_i^2}\right)$$
Solution:- Electrons diffusing from the N-region leave behind positively charged donor ions (\( N_D^+ \)).
- Holes diffusing from the P-region leave behind negatively charged acceptor ions (\( N_A^- \)).
- These fixed, uncompensated ions form a space-charge region that creates a built-in potential barrier (\( V_B \)) opposing further majority carrier diffusion.
Why other options are incorrect:- Option B: The depletion region is depleted of mobile carriers; it contains fixed, uncompensated ions.
- Option C: Minority carrier drift constitutes the reverse saturation current, not the formation of the equilibrium potential barrier.
- Option D: Atmospheric pressure does not drive the formation of the potential barrier.
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