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This paper presents a comprehensive investigation of statistical effects in deeply scaled nitride memory cells, considering both atomistic substrate doping and the discrete and localized nature of stored charge in the nitride layer. By means of 3-D TCAD simulations, the statistical dispersion of the threshold voltage shift induced by a single localized electron in the nitride is evaluated in presence of non-uniform substrate conduction. The role of 3-D electrostatics and atomistic doping on the results is highlighted, showing the latter as the major spread source. The threshold voltage shift induced by more than one electron in the nitride is then analyzed, showing that for increasing numbers of stored electrons a correlation among single-electron shifts clearly appears. The scaling trend and the practical impact of these statistical effects on cell operation are discussed in Part II of this paper.