The Lattice Lends the Momentum
The Lattice Lends the Momentum
Light carries energy in abundance but almost no momentum, not at the scale a crystal lattice measures things. That mismatch would be irrelevant if a semiconductor's conduction band minimum sat directly above its valence band maximum in momentum space — a direct gap, where a photon can simply pay the energy toll and cross. Silicon offers no such convenience. Its conduction band minimum is displaced sideways from the valence band maximum, so an electron struck by a photon of exactly the right energy still cannot make the jump alone. It is short on momentum, and light has none to spare.
What completes the transaction is the lattice itself. The crystal is never truly still; it vibrates, and those vibrations are quantized into phonons, each one carrying a definite parcel of momentum and only a little energy. An electron crossing an indirect gap must catch or throw a phonon in the same instant it absorbs the photon — a three-body negotiation, photon and electron and trembling lattice, settled all at once or not at all. The photon pays the energy bill. The lattice pays the momentum bill. Only together do they clear the gap.
This is why silicon is a mediocre light emitter but a superb light absorber. Emission asks the same three-body coincidence to run in reverse — an electron falling back across the gap must simultaneously shed both the right energy and the right momentum, radiating a photon and emitting or absorbing a phonon in the same breath, an event so improbable that silicon LEDs barely exist. Absorption has no such timing problem; sunlight arrives in such abundance that even a rare phonon-assisted event happens often enough to run a solar panel.
The gap in the band structure was never the whole story. What silicon needed, to let a photon in, was a lattice willing to lend the electron the one thing light itself could never carry.
Seed: Semiconductor band structure — direct vs. indirect band gap, phonon-assisted absorption.