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The random telegraph signal in nanoscale devices is critically dependent on the spatial distribution and number of trapped charges in the gate oxide. Also, the drain-current fluctuation ΔID therein is known to be made up of the fluctuations in carrier number and mobility. In this paper, the local potential variation (LPV) arising from the single charge is incorporated into well-known mobility model and the effect of discrete trapped charges in the oxide layer is statistically investigated, using the in-house 3-D drift-diffusion and density-gradient device simulators. The LPV model covers the conventional distributed trapped charge mobility model but it can also accurately account for the observed fluctuations in ID in terms of carrier number and mobility fluctuations.