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A threshold voltage model for mesa-isolated fully depleted silicon-on-insulator (FDSOI) MOSFETs, based on the analytical solution of three-dimensional (3-D) Poisson's equation is presented for the first time in this paper. The separation of variables technique is used to solve the 3-D Poisson's equation analytically with appropriate boundary conditions. Simple and accurate analytical expressions for the threshold voltage of the front and the back gate are derived. The model is able to predict short channel as well as narrow width effects in mesa-isolated FDSOI MOSFETs. The model is validated by comparing with the experimental results as well as with the numerical results available in the literature.