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We use pseudo-2-D analytical models to study the electrostatics of multigate tunneling field-effect transistors (TFETs), providing a portable set of equations to simultaneously describe silicon-on-insulator, double gate, and cylindrical nanowire devices. We validate the model via extensive comparisons with numerical simulations and demonstrate its accuracy and general applicability; 2-D tunneling effects are analytically estimated and found to be small for well-scaled devices within the semiclassical model. We also study the impact of source and drain doping on TFET performance, including a seminal analytical treatment of nonabrupt junctions and degeneracy effects. We present a new simple model to explain the adverse effects of excessive source doping, and show for the first time how degeneracy in low density-of-states materials directly degrades not only the tunneling efficiency, but also the device electrostatics, causing particular problems for III-V p-TFETs.