We present a theoretical model that allows us to describe the polariton dynamics in a semiconductor microcavity at large densities, for the case of non-resonant excitation. Exciton-polariton scattering from a thermalized exciton reservoir is identified as the main mechanism for relaxation into the lower polariton states. A maximum in the polariton distribution that shifts towards lower energies with increasing pump-power or temperature is shown, in agreement with recent experiments. Above a critical pump-power, macroscopic occupancies (5 times 10^4) can be achieved in the lowest energy polariton state. Our model predicts the possibility of Bose-Einstein Condensation of polaritons, driven by exciton-polariton interaction, at densities well below the saturation density for CdTe microcavities.
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