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The impact of program/erase (P/E) cycling on the random telegraph noise (RTN) threshold voltage instability of NOR and NAND flash memories is studied in detail. RTN is shown to introduce exponential tails in the distribution of the threshold voltage variation between two subsequent read operations on the cells. Tail height is shown to increase as a function of the stress levels, with a larger relative increase for the NAND case. The slope of the distribution instead remains nearly independent of the number of applied P/E cycles. This reveals that trap generation takes place according to the native trap distribution over the active area and means that the tail slope is a basic RTN parameter, depending on the cell process details for a fixed technology. These results are important for the design of the threshold voltage levels in multilevel nor and NAND technologies.