Band theory and conduction: for electron current in a crystalline solid, are the mobile charge carriers counted for conduction those electrons promoted to the conduction band (rather than electrons remaining in the valence band)?

Introduction / Context:
Band theory explains why some electrons contribute to conduction while others remain bound. Understanding which electrons carry current clarifies the roles of electrons and holes in semiconductors and the behavior of metals and insulators.

Given Data / Assumptions:

• Crystalline solid with valence and conduction bands separated by a bandgap (zero for ideal metals, finite for semiconductors/insulators).
• Focus is on electrons as carriers; holes are a separate contribution in semiconductors.
• Steady fields and small-signal conditions.

Concept / Approach:
Electrons in a fully filled valence band cannot change net momentum under an applied field because states are symmetrically occupied; the band contributes little to conduction unless there are available empty states. Conduction requires partially filled bands where electrons can accelerate into nearby unoccupied states. In semiconductors, thermal or optical energy promotes electrons across the bandgap into the conduction band, leaving holes in the valence band. Electron current is then due to these conduction-band electrons, while hole current occurs in the valence band via motion of vacancies.

Step-by-Step Solution:

Verification / Alternative check:
Temperature increases raise intrinsic carrier concentration in semiconductors, increasing conduction by creating more conduction-band electrons and valence-band holes, matching the described mechanisms.

Why Other Options Are Wrong:
Incorrect: contradicts band theory.

Only for metals or only at cryogenic temperatures: the principle is general; in metals, the conduction band (or overlapping band) is partially filled; in semiconductors, excitation creates conduction-band electrons.

Common Pitfalls:
Equating “electron current” with all electrons in the material; ignoring that in semiconductors holes also carry current, but they are counted separately from electron current.

Final Answer:
Correct