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This paper presents a detailed investigation of charge-trap memory programming by means of 3-D TCAD simulations accounting both for the discrete and localized nature of traps and for the statistical process ruling granular electron injection from the substrate into the storage layer. In addition, for a correct evaluation of the threshold-voltage dynamics, cell electrostatics and drain current are calculated in presence of atomistic doping, largely contributing to percolative substrate conduction. Results show that the low average programming efficiency commonly encountered in nanoscaled charge-trap memory devices mainly results from the low impact of locally stored electrons on cell threshold voltage in presence of fringing fields at the cell edges. Programming variability arising from the discreteness of charge and matter will be addressed in Part II of this paper.