Concept:Semiconductors have a negative temperature coefficient of resistance (\( \alpha < 0 \)); increasing temperature excites valence electrons across the bandgap into the conduction band.
Formula:$$\sigma = q (n \mu_n + p \mu_p) \quad \text{where } n_i^2 \propto T^3 e^{-\frac{E_g}{k T}}$$
Solution:- At higher temperatures, covalent bonds break thermally, generating electron-hole pairs.
- The exponential increase in carrier concentration (\( n \) and \( p \)) outweighs the slight reduction in carrier mobility, increasing total conductivity.
Why other options are incorrect:- Option B: Lattice vibrations increase with temperature, which reduces carrier mobility.
- Option C: The bandgap \( E_g \) slightly decreases (narrows) with temperature, it does not widen.
- Option D: Recombination does not eliminate all carriers; thermal generation maintains a higher equilibrium carrier density.
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