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A model including the presence and effect of discrete quantum energy levels and trap states in nanocrystals is proposed in order to describe the anomalous peaks observed in current-voltage characteristics of emerging Si quantum dot based floating gate flash memory cells. The model is employed to investigate the effect of energy levels in quantum dots with a size distribution in the range of 0 to 12 nm in explaining the charging dynamics and current versus time characteristics. The simulated results are in close agreement with the experimental results. It is speculated that the additional peaks observed in the experimental current versus voltage characteristics above threshold voltage are because of the filling up of nanocrystals with more than one electron into quantum levels, shifted to higher energy levels due to the increase in charging energy determined by self capacitance.