Concept:Semiconductors have a negative temperature coefficient of resistance (\(\alpha < 0\)). Lowering the temperature reduces thermal energy, leading to the recombination of free carriers and a drastic reduction in mobile carrier concentration, which increases resistance.
Formula:$$R = R_0 e^{\frac{E_g}{2 k_B T}}$$
Solution:- At lower temperatures, fewer covalent bonds are thermally broken.
- The density of mobile charge carriers (electrons and holes) decreases exponentially.
- Consequently, electrical resistivity and resistance increase (at \(0\text{ K}\), an intrinsic semiconductor behaves as a perfect insulator).
Why other options are incorrect:- Option B: Resistance decreases with temperature in metals (conductors), not semiconductors.
- Option C: Semiconductor resistance is strongly sensitive to thermal changes.
- Option D: Resistance dropping to zero describes superconductivity, not intrinsic semiconductor behavior.
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