Intrinsic semiconductors at absolute zero (0 K) At 0 K, silicon and germanium have their valence bands completely filled and conduction bands empty. Do they behave like monoatomic crystals in terms of crystal basis and bonding at this temperature?

Introduction / Context:This conceptual question checks your understanding of crystal structure versus electrical behavior at absolute zero. Silicon and germanium are classic covalent semiconductors with a diamond-cubic lattice. The phrase “monoatomic crystal” relates to the basis of the lattice (how many atoms per primitive cell), not to whether carriers exist at 0 K.

Given Data / Assumptions:

• Temperature is 0 K (absolute zero).
• Materials: silicon (Si) and germanium (Ge).
• Consider crystallography (basis) and bonding, not just carrier concentration.

Concept / Approach:

Si and Ge crystallize in the diamond cubic structure, which can be viewed as an fcc Bravais lattice with a two-atom basis. A “monoatomic” crystal has one atom per basis (e.g., simple fcc of a monatomic metal). Electrically, at 0 K, the valence band is full and the conduction band is empty, so they act as perfect insulators; however, that does not convert their lattice into a monoatomic basis. Structure and electronic occupation are distinct ideas.

Step-by-Step Solution:

Verification / Alternative check:

The well-known transition of iron between bcc and fcc shows structure is independent of electronic carrier freeze-out; similarly, Si and Ge remain diamond-structured irrespective of temperature-induced carrier changes.

Why Other Options Are Wrong:

• True: wrongly equates absence of carriers with monoatomic basis.
• “Only silicon/germanium” variants: both share the same diamond-cubic two-atom basis.

Common Pitfalls:

Confusing electronic properties (insulating at 0 K) with crystallographic basis; assuming “no free electrons” implies a monoatomic lattice.

Final Answer:

False