At room temperature, an intrinsic (pure) semiconductor contains what relative amounts of free carriers?

Introduction / Context:
Carrier concentrations in semiconductors determine conductivity. Intrinsic semiconductors are undoped crystals (e.g., pure silicon or germanium) in which thermal energy alone generates carriers. Understanding these baseline concentrations is essential before studying doping and device behavior.

Given Data / Assumptions:

• Material is intrinsic (no donors or acceptors).
• Temperature is approximately room temperature.
• Carrier types are electrons (in the conduction band) and holes (in the valence band).

Concept / Approach:
In intrinsic material, electron concentration n equals hole concentration p (n = p = n_i). The value of n_i at room temperature is modest (e.g., for silicon ~10^10 cm^-3), far less than atomic density, hence we describe the amount of carriers as “a few” relative to metals. Both species are present in equal numbers because every thermally excited electron leaves behind a hole.

Step-by-Step Solution:
Recognize intrinsic condition: no dopant imbalance.Apply relation: n = p = n_i.Interpret magnitude: n_i is small compared to metals; thus “a few” of each carrier type are present.

Verification / Alternative check:
Compare to doped semiconductors where n ≠ p; doping raises one carrier type dramatically while reducing the other via mass-action law n * p = n_i^2.

Why Other Options Are Wrong:
Many holes or many electrons: describes heavily doped p-type or n-type, not intrinsic.No holes: impossible at nonzero temperature because thermal generation creates electron-hole pairs.

Common Pitfalls:
Assuming “intrinsic” means zero carriers; forgetting that both electrons and holes exist in equal amounts in pure material.

Final Answer:
a few free electrons and holes