At absolute zero temperature, an intrinsic semiconductor behaves as a

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insulator

Explanation: At absolute zero temperature (0 K), an intrinsic semiconductor behaves as a perfect insulator. This is because there is insufficient thermal energy to excite electrons from the valence band to the conduction band.

Working Principle: In an intrinsic semiconductor, the Fermi level lies exactly in the middle of the forbidden energy gap. At $T = 0$ K, all valence electrons are tightly bound in covalent bonds, and the conduction band is completely empty. Since there are no free charge carriers available for conduction, the electrical conductivity is zero, making the material an ideal insulator.

Key Formulas: $n = p = n_i = A_0 T^{3/2} e^{-\frac{E_g}{2kT}}$ — intrinsic carrier concentration as a function of temperature $T$; $n \approx 0$ at $T = 0$ K — no free carriers available

Key Points: At 0 K, no covalent bonds are broken by thermal agitation.; The electrical conductivity $\sigma$ is directly proportional to carrier concentration.; The Fermi-Dirac distribution function $f(E)$ becomes a step function at $T = 0$ K.; Semiconductors act as insulators at 0 K and conductors at higher temperatures.

Advantages: Useful for creating thermally stable electronic components at cryogenic temperatures.; Fundamental for understanding the temperature dependence of resistivity.

Disadvantages: No current flow possible at this state.; Not useful for practical device switching at 0 K.

Applications: Cryogenic sensors; Superconducting research; Theoretical condensed matter physics

Additional Info: The forbidden energy gap $E_g$ prevents charge carriers from reaching the conduction band without thermal excitation.. Option A is incorrect because conductivity requires free electrons.. Options B and C are incorrect as they refer to extrinsic semiconductor properties which are absent at 0 K.

Answer: D is correct — At absolute zero, all valence electrons are bound in covalent bonds, leaving the conduction band empty and resulting in zero conductivity.

Exam Tip: Remember that conductivity in semiconductors increases with temperature (negative temperature coefficient), which is the exact opposite of metallic conductors.

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