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Using the Glasgow ldquoatomisticrdquo simulator, we have performed 3D statistical simulations of random-dopant-induced threshold voltage variation in state-of-the-art 35- and 13-nm bulk MOSFETs consisting of statistical samples of 105 or more microscopically different transistors. Simulation on such an unprecedented scale has been enabled by grid technology, which allows the distribution and the monitoring of very large ensembles on heterogeneous computational grids, as well as the automated handling of large amounts of output data. The results of these simulations show a pronounced asymmetry in the distribution of the MOSFET threshold voltages, which increases with transistor scaling. A comprehensive statistical analysis enabled by the large sample size reveals the origin of this observed asymmetry, provides a detailed insight into the underlying physical processes, and enables the statistical enhancement of simulations of random-dopant-induced threshold voltage variation.