  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 8-band Kane model (4
bands with double spin degeneracy), help to explain the significant
disagreements between experiments and theory in the literature to date. 3PA in
the 8-band model exhibits quantum interference between the various possible
pathways that is not observed in previous 2-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 2-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 2-band theories. On the
other hand, our 8-band model shows excellent agreement with the spectral data.
We then use our 8-band theory to predict the 3PA spectra for 15 different
semiconductors in their zincblende form. These results allow prediction and
interpretation of the 3PA coefficients for various narrow to wide bandgap
semiconductors.
