At absolute zero temperature a semiconductor behaves like:
A. an insulator
B. a superconductor
C. a good conductor
D. a variable resistor

Hint:In order to answer this question, you must be aware about the concept of valence band theory.Semiconductors are the materials which have a conductivity between conductors (generally metals) and non-conductors or insulators (such as ceramics).Semiconductors can be compounds such as gallium arsenide or pure elements, such as germanium or silicon.

Complete answer:
Any material is said to be an insulator when it has no free electrons for the conduction of current. Free electrons in the semiconductor are the ones that leave the valence band to enter the conduction band. The forbidden band between conduction band and valence band is very small, which is only 1eV.

The process of transference of electrons from the valence band to the conduction band requires energy; but at absolute zero temperature i.e. at 0 Kelvin, the semiconductors do not have enough thermal energy to overcome the forbidden energy gap.Therefore, molecular movement ceases which means that all electrons are tied to valence band and there are no free electrons in the conduction band and the conduction band is empty.Hence, it acts as an insulator.

Therefore, option A is correct.

Note: In semiconductors, electron vibration occurs only at room temperature. At low temperatures, electrons cannot get energy and so it cannot vibrate. Therefore at absolute zero temperature, the conduction band becomes empty and the valence band becomes completely filled.