Small particles of Indium Arsenide show the slow process of the decay of photoluminescence (PL). Using the electron-phonon interaction we present an explanation of this effect. We assume that at the beginning of the PL process, just after the exciting laser pulse, the electron occupies the conduction band minima which are outside of the center of the Brillouin zone. The inter-valley multiple electron-phonon scattering promotes the electrons to the higher-energy Γ valley. We show numerically that the scattering leads to the power-law time dependence of the decay of PL intensity. We also suggest that the mechanism under consideration could be the origin of the photoluminescence of small particles of materials with indirect band gap.

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