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We have performed two-dimensional (2-D) and three-dimensional (3-D) computer simulations of random dopant fluctuations in 25-nm planar n-channel metal-oxide-semiconductor field effect transistor (MOSFET) with superhalo channel doping. Our study shows that 2-D simulations that neglect lateral percolation of the carriers can overestimate the impact on threshold voltage (VT) fluctuations by as much as a factor of four. Fundamental differences in the way the 2-D and 3-D models describe subthreshold and near-threshold conduction are highlighted in our study. Our models reveal that surface percolation of carriers is an effective agent for reducing VT fluctuations. In addition, the halo only enhances the VT fluctuations by approximately 10%. Though the influence of the superhalo in the device may be overwhelmed by atomistic granularity according to the 2-D model, 3-D simulations show that the halo continues to function coherently for the MOSFET ensemble when charge percolation is accounted.