Interband Transitions and Exciton Effects in Semiconductors

The band structures of Ge, Si, GaAs, GaP, GaSb, InAs, InP, InSb, and AlSb have been studied in reflectivity in the energy region 1.6-5.0 eV at temperatures ranging from 80 to 300 °K. Utilizing a double-beam, single-detector wavelength-modulation system, and ensuing Kramers-Krönig analyses, experimentally unambiguous line shapes have been obtained for the real and imaginary part of the dielectric constants, permitting the identification of the types of critical points involved in an optical transition, and the determination of the existence of hyperbolic exciton interactions. Such an interaction has been verified in all materials, except Si, as an $M_1$ critical point located at $\Lambda$ in the Brillouin zone. The location and energy of the interband transition in these semiconductors correlates with existing band calculations. The interband transitions in Si are dominated by structure from a large region of the Brillouin zone. The high-energy $E_2$ transitions in all materials give evidence of a multiplicity of critical-point structure.