Question Analysis: Assertion-Reasoning type question.

Step 1 (Governing Principle): [0.25 Mark]
The depletion layer in a $p-n$ junction diode is formed due to the diffusion of charge carriers. Its thickness ($d$) is governed by the potential barrier ($V_B$) and the applied external bias voltage ($V$). The relationship is defined by the electric field ($E$) across the junction: $$E = \frac{V_B \pm V}{d}$$

Step 2 (Step-by-Step Logical Deduction): [0.50 Mark]

• Forward Bias: When a positive terminal is connected to the $p$-side, the external voltage opposes the barrier potential. The effective barrier becomes $(V_B - V)$, which reduces the depletion layer thickness ($d \propto \sqrt{V_B - V}$).
• Reverse Bias: When a negative terminal is connected to the $p$-side, the external voltage supports the barrier potential. The effective barrier becomes $(V_B + V)$, which increases the depletion layer thickness ($d \propto \sqrt{V_B + V}$).
• Since the thickness changes based on the applied bias, the Assertion (A) is correct.
• The Reason (R) correctly identifies that the thickness depends on the biasing of the semiconductor, which is the physical cause for the variation mentioned in (A).

Step 3 (Final Concluded Answer): [0.25 Mark]
Correct Option: Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

💡 EL10 Concept Insight: Think of the depletion layer like a "no-man's land" between two countries; if you push the soldiers (voltage) forward, the no-man's land shrinks, but if you pull them back, the no-man's land grows wider!