Assertion–Reason on majority carriers in p-type semiconductors Assertion (A): Holes are the majority carriers in a p-type semiconductor. Reason (R): In a p-type semiconductor, electrons produced by thermal agitation recombine with holes.

Introduction / Context:
Understanding majority and minority carriers is central to semiconductor device physics. P-type material is formed by acceptor doping, which creates an abundance of holes relative to electrons. This item evaluates whether a common statement about recombination properly explains majority carrier status.

Given Data / Assumptions:

• P-type semiconductor (acceptor concentration Na ≫ Nd and Na ≫ ni).
• Thermal generation and recombination occur.
• Equilibrium at a given temperature.

Concept / Approach:

The assertion is correct: p-type doping yields holes as majority carriers. The reason statement is also true—thermally generated electrons can recombine with holes. However, this is not the reason holes are majority carriers. Majority status arises from the higher equilibrium concentration set by doping, not from recombination events, which affect both carrier types and help establish steady-state concentrations consistent with mass-action law.

Step-by-Step Reasoning:

Verification / Alternative check:

Charge neutrality: p ≈ Na (if full ionization and Nd negligible). Minority electron density n = ni^2 / p, confirming holes dominate.

Why Other Options Are Wrong:

• “R explains A”: incorrect causality; recombination does not determine which carrier is majority.
• “A false” or “R false”: both statements individually are true.

Common Pitfalls:

Confusing physical mechanisms (doping versus recombination) and mixing cause with effect; recombination influences lifetimes but not the doping-defined majority/minority designation.

Final Answer:

Both A and R are true but R is not the correct explanation of A