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Excitonic Effects in the Interband Absorption of Semiconductors
Author(s) -
Velický B.,
Sak J.
Publication year - 1966
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.19660160113
Subject(s) - coulomb , exciton , singularity , gravitational singularity , physics , limiting , electron , condensed matter physics , absorption (acoustics) , semiconductor , absorption edge , quantum mechanics , sum rule in quantum mechanics , mathematics , mathematical analysis , optics , band gap , quantum chromodynamics , mechanical engineering , engineering
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.