The formulas for describing two-photon absorption in direct-gap crystals, developed by Keldysh, Braunstein, and Basov, are compared. It is shown that the Keldysh formula is closely related to Braunstein's for allowed-allowed transitions, while Basov's proposed formula more closely corresponds to Braunstein's for allowed-forbidden transitions. A number of suggested improvements are introduced in Braunstein's formula and corrections to Basov's are presented. The two-photon absorption coefficients for several direct-gap semiconductors and alkali halides are calculated from these formulas and compared with the available experimental data. The formulas of Keldysh and Braunstein for describing allowed-allowed transitions, where one considers excitonic intermediate states and nonparabolic energy bands, are found to give results in fair agreement with published experimental results. It is noted, in comparison, that Basov's and Braunstein's absorption coefficients for allowed-forbidden transitions are smaller than available experimental data by orders of magnitude.

• Received 10 May 1979

DOI:https://doi.org/10.1103/PhysRevB.21.743