Concept:According to Poisson's equation (\( \frac{dE}{dx} = \frac{\rho}{\varepsilon} \)), integrating the space-charge distribution shows that electric field intensity peaks at the metallurgical junction.
Formula:$$E_{\text{max}} = -\frac{e N_D x_n}{\varepsilon} = -\frac{e N_A x_p}{\varepsilon} = -\frac{2 V_B}{W} \quad (\text{at } x = 0)$$
Solution:- The electric field rises linearly from zero at the edge of the depletion region in the P-side to a maximum at the interface.
- It then decreases linearly back to zero at the edge of the depletion region in the N-side.
- Therefore, maximum electric field intensity (\( E_{\text{max}} \)) occurs directly at the metallurgical interface (\( x = 0 \)).
Why other options are incorrect:- Options A & B: Outside the depletion boundaries, neutral regions contain zero space charge, so the electric field is zero.
- Option D: The electric field is confined to the depletion region and is non-uniform.
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