Conductivity due to holes in a p-type semiconductor In a p-type semiconductor, what is the expression for the contribution of holes to electrical conductivity? (e is the elementary charge, μp is hole mobility, p is hole concentration.)

Introduction / Context:
Electrical conductivity in semiconductors arises from both electrons and holes. In p-type material, holes dominate, and their mobility and concentration determine the majority contribution to conductivity. This formula is foundational for device equations, such as drift currents in diodes and transistors.

Given Data / Assumptions:

• p-type semiconductor with hole concentration p and hole mobility μp.
• Elementary charge magnitude e.
• Drift current under an applied electric field E: J = σ E.

Concept / Approach:

For a carrier species with charge magnitude q, mobility μ, and density N, the drift current density is J = q μ N E. Therefore, the conductivity due to that species is σ = q μ N. For holes in p-type material: σp = e μp p. The total conductivity is σ = σn + σp, but the question asks specifically for hole contribution.

Step-by-Step Solution:

Verification / Alternative check:

Dimension check: e (C) * μp (m^2/V·s) * p (1/m^3) gives C·m^2/(V·s·m^3) = A/(V·m) = S/m, consistent with conductivity units.

Why Other Options Are Wrong:

• Expressions with n or μn concern electrons, not hole contribution.
• Dividing by e μp is dimensionally incorrect.
• Adding μn in a hole-only expression mixes carrier types.

Common Pitfalls:

Forgetting that electrons carry charge −e (magnitude e) and holes carry +e; conductivity uses magnitude since direction is absorbed in current sign convention.

Final Answer:

σp = e μp p