Biexciton states in semiconductor quantum dots and their nonlinear optical properties

Biexciton states in semiconductor quantum dots (spherical microcrystallites) are investigated variationally, and the biexciton binding energy and the oscillator strength are calculated as a function of the quantum-dot radius, the electron-to-hole mass ratio, and the dielectric constant ratio of the semiconductor to the surrounding medium. The most important mechanisms for enhancing the biexciton binding energy and the oscillator strength are clarified. One is the quantum confinement effect, which increases the spatial overlap between carriers, leading to enhanced Coulomb interaction. Another is the dielectric confinement effect due to the dielectric constant discontinuity at the interface between a semiconductor microcrystallite and the surrounding medium. This effect arises from the penetration of electric force lines through the surrounding medium with a relatively small dielectric constant and leads to an enhancement of the Coulomb interaction. It is found that the frequency dispersion of the third-order nonlinear susceptibility ${\chi }^{\mathrm{}\left(3\right)\mathrm{}}$ shows an out-of-phase behavior at the one- and two-photon resonances, which is characteristic of the exciton and biexciton transitions. For typical materials which are promising for observation of the biexciton state in microcrystallites, the values of the biexciton binding energy, the third-order nonlinear susceptibility ${\chi }^{\mathrm{}\left(3\right)\mathrm{}}$, and the two-photon absorption coefficient $K_2$ of the biexciton state are predicted theoretically.