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Optical nonlinearities in semiconductor microcrystallites are analyzed theoretically. The third-order optical susceptibility is evaluated for different crystallite-size regimes ranging from weak quantum confinement, where only the center-of-mass motion of the electron-hole pairs is modified, all the way down to very small quantum dots, where the individual motion of the electrons and holes is confined and the Coulomb attraction is unimportant. Large optical nonlinearities are computed for sufficiently narrow linewidths of the microcrystallites. It is predicted that the induced two-photon absorption resonance (biexciton resonance) shifts from below to above the exciton resonance when the crystallite radius is reduced from bulk to less than the exciton Bohr radius. The magnitude of the expected optical nonlinearities in the different confinement regimes is analyzed for various semiconductor materials.
Bányai et al. (1988) studied this question.