Question

The intrinsic semiconductor behaves as an insulator at
(A) $0\,^\circ C$
(B) $100\,^\circ C$
(C) $100\,K$
(D) $0\,K$

Answer 1

Hint
At the absolute zero temperature, the electrons don’t have enough energy to jump from the valence band to the conduction band. So there are no electrons present in the conduction band in order to conduct electricity.

Complete step by step answer
The intrinsic semiconductor is a type of semiconductor, which does not have any impurities present in it. So the conducting electrons for an intrinsic semiconductor are the electrons that leave the valence shell leaving behind a hole.
The gap between the conduction band and the valence band, that is, the forbidden gap for an intrinsic semiconductor will be approximately equal to the value of 1 eV.
At the temperature, $T = 300\,K$ or $T = 27\,^\circ C$, the room temperature, the electrons from the valence band jump into the conduction band after gaining some amount of energy leaving behind holes in the valence band.
At the temperature, $T = 0\,K$, the electrons of the valence band will remain in this band only, because they don’t get enough energy to jump to the upper forbidden band. As the electrons cannot jump to the conduction band at this temperature, thus, the electricity will not be conducted. Hence the semiconductor becomes insulator in nature.
$\therefore $ The intrinsic semiconductor behaves as an insulator at $T = 0\,K$.
Thus, option (D) is correct.

Additional Information
Conductors are the materials that allow current to pass through them. Insulators are the materials that do not allow current to pass through them. Semiconductors are the materials that have the conductivity between that of the conductors and insulators.
The main difference between the conductor, semiconductor and insulator is in its conduction state. The extrinsic semiconductor is a type of semiconductor, in which the number of electrons will be more than the number of holes.

Note
The intrinsic semiconductors are those which have no impurities added in them. So unlike extrinsic there are no completely free electrons in the case of intrinsic semiconductors. The electrons in the valence band gain energy from the atmosphere, and jump from the valence to conduction band.