PHYSICS · Subjective · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Semiconductor physics and devices · Dielectric and optical properties of solids
Solid State Physics, Ch Tight binding and the band structures of real materials
Problem
Someone argues: "Silicon has an indirect gap of 1.12eV, and a certain hypothetical semiconductor has a direct gap of the same 1.12eV. Since the photon needed to cross the gap carries the same energy in both materials, and the optical transition rate depends only on the density of states available at that energy, silicon should emit light from electron-hole recombination just as readily as the direct-gap material." Find the error in this reasoning, and state which physical quantity, left out of the argument, actually controls the difference in recombination rate.