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A new physically based classical model for the potential distribution of an undoped body cylindrical gate-all-around nanowire transistor is proposed. The model is based on the analytical solution of 2-D Poisson's equation in a cylindrical coordinate system and is valid for both (1) weak and strong inversion regimes, (2) long and short-channel transistors, and (3) body surfaces and centers. Using the proposed model, for the first time, it is demonstrated that the body potential versus gate voltage characteristics for the devices having equal channel lengths but different body radii pass through a single common point (termed a ldquocrossover pointrdquo). It is found that, at this crossover point, there is no potential drop (ldquopseudo flatband conditionrdquo) along the radial direction. Using the concept of crossover point, the effect of body radius on the threshold voltage of undoped body multigate transistors is explained. Based on the proposed body potential model, a new compact model for the subthreshold swing is formulated. It is shown that for the devices having very high short-channel effects, the effective subthreshold slope factor is mainly dictated by the potential at the body center rather than that at the surface. All the models are validated against a professional numerical device simulator.