Semiconductor principles — relationship between depletion region width and barrier (built-in) potential In a P–N junction inside a transistor or diode, when the depletion region becomes wider (for example, due to higher built-in potential or added reverse bias), the electrostatic barrier potential across the junction becomes larger. Evaluate this statement.

Introduction / Context:Understanding how the depletion region and the built-in (barrier) potential of a P–N junction are related is fundamental to semiconductor physics. This determines current flow under forward and reverse bias and explains why diodes, bipolar junction transistors (BJTs), and junction field-effect transistors (JFETs) behave the way they do.

Given Data / Assumptions:

• An abrupt P–N junction at thermal equilibrium unless bias is explicitly mentioned.
• Standard definitions: depletion region is the ionized, carrier-depleted space-charge region; barrier potential (V_bi) is the electrostatic potential opposing majority-carrier diffusion.
• Temperature and doping levels are within normal device ranges.

Concept / Approach:For an abrupt junction, the depletion width W satisfies W ∝ sqrt((V_bi + V_R) * (1/N_A + 1/N_D)), where V_R is applied reverse bias, and N_A, N_D are acceptor and donor concentrations. As V_bi or reverse bias increases, the electric field strengthens and W widens. Thus, larger depletion width accompanies a larger total junction potential (built-in plus any applied reverse bias).

Step-by-Step Solution:

Verification / Alternative check:Device I–V curves under reverse bias show reduced capacitance C_j ≈ εA/W; as W increases, C_j decreases. Measured junction capacitance shrinking with reverse voltage confirms widening depletion tied to increased junction potential.

Why Other Options Are Wrong:

Common Pitfalls:Confusing cause and effect: doping changes can make W smaller even if V_bi is large because W also scales with 1/sqrt(doping). The statement assumes a scenario where an increased potential (built-in or reverse) is what widens W.

Final Answer:Correct