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The gate leakage current present in double-gate fully depleted fin-shaped MOSFETs with metal gate/single oxynitride layer is modeled. It can significantly contribute to the drive current measured in different conditions, according to its dependence on applied voltages to the structure electrodes, as well as, on the Si regions where the gate has control. Direct tunneling of electrons from inverted channel region and trap assisted tunneling at the overlaps in subthreshold regime have been taken into account in order to represent correctly the behavior of gate leakage currents in these kinds of devices. Agreement observed between modeled and experimental gate current characteristics in inversion and depletion operation modes, linear and saturation drain bias, as well as for transistors with different geometry, was excellent.