pn junction basics: the “barrier potential” (built-in potential) arises from fixed positive and negative ions on either side of the depletion region once diffusion and drift balance. Confirm this description.

Introduction / Context:
The barrier potential is central to understanding diode I-V behavior, rectification, and switching. It is the internal voltage that forms spontaneously when p-type and n-type regions are joined, creating a depletion region and establishing equilibrium.

Given Data / Assumptions:

• Idealized abrupt pn junction in thermal equilibrium (no external bias).
• Ionized donors on the n-side and ionized acceptors on the p-side are immobile.
• Mobile carriers (electrons and holes) diffuse until drift due to the electric field balances diffusion.

Concept / Approach:
At the moment of contact, electrons diffuse from n to p, and holes from p to n, leaving behind charged ions. This uncovered charge region (depletion) creates an electric field and a potential difference called the built-in or barrier potential. This potential opposes further diffusion. The magnitude depends on doping concentrations and temperature and is typically around 0.2–0.9 V for common materials (lower for Ge, higher for Si).

Step-by-Step Solution:

Verification / Alternative check:
Deriving the built-in voltage from semiconductor physics yields V_bi proportional to the logarithm of the product of dopant concentrations divided by intrinsic carrier density squared, consistent with the qualitative description.

Why Other Options Are Wrong:
Incorrect: ignores the well-established depletion region mechanism.

Only at 0 K or only under forward bias: V_bi exists at normal temperatures without external bias; forward bias reduces the effective barrier seen by carriers.

Common Pitfalls:
Confusing the internal barrier with applied forward voltage; assuming ions move (they are fixed in the lattice); overlooking temperature dependence.

Final Answer:
Correct