Concept:In an indirect bandgap semiconductor, the conduction band minimum and valence band maximum occur at different crystal momentum values (\( k \)). Recombination requires an interaction with a lattice vibration (phonon), which dissipates the transition energy as heat rather than emitting a photon.
Formula:$$e^- + h^+ \longrightarrow \text{Phonon (Heat)} \quad [\text{Radiative Probability } \ll 0.1\%]$$
Solution:- In direct bandgap semiconductors (e.g., GaAs, GaN), electrons can transition straight down to recombine with holes, efficiently emitting photons.
- In Silicon, the mismatch in momentum requires a three-body interaction (electron, hole, and phonon), making radiative recombination very inefficient and dissipating nearly all energy as heat.
Why other options are incorrect:- Option B: Silicon's band gap of \( 1.1\text{ eV} \) corresponds to infrared light, but its low efficiency is due to band structure rather than gap size alone.
- Option C: Doped silicon is a good conductor in forward bias and is the basis of modern electronics.
- Option D: Silicon has a high melting point (\( 1414^\circ\text{C} \)) and operates stably under normal forward currents.
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