In semiconductor physics, what is the electrical conductivity of an intrinsic (pure) semiconductor expressed in terms of the intrinsic carrier concentration n_i, electronic mobility μ_n, hole mobility μ_p, and the elementary charge e?

Introduction / Context:Intrinsic semiconductors conduct electricity via thermally generated electrons and holes present in equal numbers. Their macroscopic conductivity depends on how many charge carriers exist per unit volume and how easily each carrier drifts under an applied electric field, captured by mobility parameters. This question tests the fundamental expression for conductivity in a pure (undoped) semiconductor.

Given Data / Assumptions:

• Material is intrinsic: electron concentration n and hole concentration p are equal, n = p = n_i.
• Elementary charge is e (Coulombs).
• Carrier mobilities are μ_n for electrons and μ_p for holes.
• Low-field, ohmic conditions so drift current dominates and mobilities are constant.

Concept / Approach:In semiconductors, the drift current density is J = e (n μ_n + p μ_p) E, where E is the electric field. Conductivity σ is defined by J = σ E. For intrinsic material, substitute n = p = n_i to obtain σ = e n_i (μ_n + μ_p).

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