Temperature dependence of electrical conductivity How does electrical conductivity change with increasing temperature in (i) metals and (ii) intrinsic semiconductors?

Introduction / Context:
Materials respond differently to temperature because their charge transport mechanisms differ. Metals conduct via abundant free electrons in partially filled bands, whereas intrinsic semiconductors conduct via thermally generated electrons and holes. Recognizing the opposite temperature trends is crucial in device selection and thermal design.

Given Data / Assumptions:

• Metal: conduction dominated by electron scattering (phonons, impurities).
• Intrinsic semiconductor: pure material with negligible doping.
• Moderate temperature ranges where phase or structural changes do not occur.
• Conductivity σ = n q μ for carriers of density n and mobility μ.

Concept / Approach:

In metals, carrier density n is essentially constant; increasing temperature enhances lattice vibrations (phonons), which scatter electrons more strongly and reduce mobility μ, so σ decreases. In intrinsic semiconductors, the carrier density n rises exponentially with temperature due to band-to-band excitation, which overwhelms the mobility reduction; hence σ increases rapidly with temperature.

Step-by-Step Solution:

Verification / Alternative check:

Resistivity–temperature curves: metals show positive temperature coefficient of resistivity; intrinsic semiconductors show negative coefficient (conductivity increases). This is observed in silicon and germanium near intrinsic regimes at high temperature.

Why Other Options Are Wrong:

(a), (b), and (d) contradict one or both material behaviors; (e) is not supported by standard transport theory.

Common Pitfalls:

Confusing intrinsic with extrinsic semiconductors (doped materials can show different trends at low T); assuming mobility changes dominate in semiconductors—carrier generation is the key factor for intrinsic cases.

Final Answer:

Decreases in metals but increases in intrinsic semiconductors