Analysis of indirect two-photon interband transitions and of direct three-photon transitions in semiconductors

Abstract

The indirect two-photon interband transition rate has been studied by analysing the absorption coefficient for the photon Ħϖ1 in the presence of a second photon Ħϖ2 as a function of frequency near the band edge at different temperatures. The structure of the curves is similar to that for one-photon indirect absorption and shows discontinuities when Ħϖ1 + Ħϖ2 ±ĦΩ —E g ≈ 0, ĦΩ being the energy of the phonon which makes the transition possible, andE g the indirect energy gap. The results are compared with those for three-photon processes, and it is found that indirect transitions are at least one order of magnitude more probable at the available photon densities. Selection rules for indirect two-photon transitions are discussed for Ge and GaP. It is shown that the process which has highest probability in Ge involves only the L.O. phonon, whereas in GaP all phonons are allowed in the transitions except the L.O. phonon. Numerical calculations of the absorption coefficient are performed for the case of GaP near the indirect energy gap to show the dependence on frequency and temperature. The results indicate that presently available optical laser sources should be of sufficient intensity to produce observable two-photon indirect transitions. Preliminary experimental evidence is discussed.