Concept:In intrinsic semiconductors, electrical conductivity depends on the thermal generation of electron-hole pairs across the energy bandgap.
Formula:$$\sigma = e n_i (\mu_n + \mu_p), \quad n_i(T) = B T^{3/2} e^{-\frac{E_g}{2 k_B T}}$$
Solution:- At \( 0\text{ K} \), the valence band is completely full and the conduction band is completely empty, so the semiconductor acts as an insulator.
- As temperature rises, thermal energy breaks valence covalent bonds.
- Electrons are excited across the bandgap into the conduction band, leaving equal numbers of holes in the valence band.
- The increased carrier concentration (\( n_i \)) increases electrical conductivity.
Why other options are incorrect:- Option A: Thermal expansion causes minor volumetric changes that do not explain the large exponential increase in conductivity.
- Option B: Intrinsic semiconductors contain no dopant ions, and lattice atoms remain in fixed positions.
- Option D: The energy bandgap (\( E_g \)) typically decreases slightly with increasing temperature rather than increasing.
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