Concept:In an intrinsic semiconductor, thermal energy breaks covalent bonds in the crystal lattice. Each broken bond generates exactly one free conduction electron and leaves behind exactly one vacancy (hole).
Formula:$$n_i = p_i = A T^{3/2} e^{-\frac{E_g}{2 k_B T}}$$
Solution:- Thermal generation creates electron-hole pairs in equal numbers.
- As temperature increases, more covalent bonds break, increasing the concentrations of both electrons (\(n\)) and holes (\(p\)) identically: \(\Delta n = \Delta p\).
- This explains why semiconductors have a negative temperature coefficient of resistance.
Why other options are incorrect:- Option A: Electrons and holes are created in pairs; one carrier cannot increase while the other decreases upon heating.
- Option B: Violates the conservation of charge and pair-generation physics in intrinsic semiconductors.
- Option D: Carrier concentrations are strongly temperature-dependent, not constant.
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