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This letter investigates the threshold voltage statistical spread induced by the electron-injection process during programming of barrier-engineered floating-gate NAND Flash memories. The spread is shown to be independent of the tunnel-dielectric stack composition for low amplitudes of the programming staircase, for which the granular electron injection follows the Poisson statistics. Differences in the spread arise instead for large staircase step amplitudes, as in this regime the sub-Poissonian nature of the electron-injection process strictly depends on the steepness of the tunnel-dielectric current-voltage characteristics. This steepness can be modified by changing the electron-injection regime from Fowler-Nordheim (FN) to direct tunneling (DT) to modified FN (MFN): MFN is shown to allow a reduction of the electron-injection spread with respect to FN tunneling, while the DT regime gives rise to a large increase of the spread.