Excitonic Effects in the Interband Absorption of Semiconductors

Abstract Elliott's work on exciton effects at the direct absorption edge is extended to include other van Hove singularities and deviations from the effective mass approximation. The sum rule which replaces the f ‐sum rule in this case is derived. The Koster‐Slater and Coulomb interactions are treated as limiting cases. Due to the electron‐hole interaction, the M 0 and M 1 branch‐points of ϵ 2 are enhanced and sharpened, whilst the M 2 and M 3 branch‐points are weakened and smoothed out. Only the M 0 points generate (quasi) discrete levels; no evidence for these is found near the M 1 points. For a very prolate M 1 singularity, certain branch‐points appear asymptotically below the critical energy.