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The improvement of our model concerning a single nanocrystal that belongs to a nanocrystal floating gate of a flash memory is presented. In order to extend the gate voltage range applicability of the model, the 3D continuum of states of either metallic or semiconducting electrodes is discretized into 2D subbands. Such an approach gives precise information about the mechanisms behind the charging or release processes of the nanocrystal. Then, the self-energy and screening effects of an electron within the nanocrystal are evaluated and introduced in the model. This enables a better determination of the operating point of the nanocrystal memory. The impact of those improvements on the charging or release time of the nanocrystal is discussed.