Low-temperature behavior — what happens to a semiconductor as T → very low? At very low temperatures (carrier freeze-out regime), a semiconductor most closely behaves as:

Introduction / Context:
Carrier concentration in semiconductors is strongly temperature dependent. As temperature decreases, thermal energy becomes insufficient to ionize dopants (in doped material) or excite intrinsic electron–hole pairs, leading to the freeze-out of carriers and a transition toward insulating behavior.

Given Data / Assumptions:

• “Very low temperature” means well below room temperature, approaching cryogenic conditions.
• No strong optical or impact ionization; equilibrium conditions only.
• Standard semiconductors (Si, Ge, GaAs) without special impurity band conduction at the temperature considered.

Concept / Approach:
Carrier density n (and p) depends on temperature through dopant ionization and intrinsic excitation over the band gap. As T decreases, donors and acceptors fail to ionize (freeze-out), and intrinsic excitation is negligible. Conductivity σ = q (n μ_n + p μ_p) therefore drops dramatically, approaching insulating levels.

Step-by-Step Solution:
Lower T → fewer ionized dopants → n and/or p decrease sharply.Intrinsic n_i also falls exponentially with decreasing T.Hence σ falls; limiting behavior is insulating for most semiconductors.

Verification / Alternative check:
Conductivity vs. temperature curves show three regions: freeze-out (low T), extrinsic (moderate T), and intrinsic (high T). In the first region, conductivity is smallest, consistent with insulating behavior.

Why Other Options Are Wrong:
(a) reverses the trend; metals increase resistance slightly with T but remain conductive. (c) is not random; physics dictates freeze-out. (d) ignores the strong temperature dependence. (e) superconductivity is a separate phenomenon not typical for semiconductors.

Common Pitfalls:

• Confusing semiconductor behavior with metallic behavior.
• Overlooking dopant ionization energy effects at low T.

Final Answer:
An insulator (carriers frozen out)