Three-Photon Absorption Spectra and Bandgap Scaling in Direct-Gap Semiconductors

This paper presents three-photon absorption (3PA) measurement results for nine direct-gap semiconductors, including full 3PA spectra for ZnSe, ZnS, and GaAs. These results, along with our theory of 3PA using an eight-band Kane model (four bands with double spin degeneracy), help to explain the significant disagreements between experiments and theory in the literature to date. 3PA in the eight-band model exhibits quantum interference between the various possible pathways that is not observed in previous two-band theories. We present measurements of degenerate 3PA coefficients in InSb, GaAs, CdTe, CdSe, ZnTe, CdS, ZnSe, ZnO, and ZnS. We examine bandgap, Eg, scaling using -band tunneling and perturbation theories that show agreement with the predicted Eg−7 dependence; however, for those semiconductors for which we measured full 3PA spectra, we observe significant discrepancies with both two-band theories. On the other hand, our eight-band model shows excellent agreement with the spectral data. We then use our eight-band theory to predict the 3PA spectra for 15 different semiconductors in their zinc-blende form. These results allow prediction and interpretation of the 3PA coefficients for various narrow to wide bandgap semiconductors.