A semiconductor device has an e-fuse module and a programming current generator. The e-fuse module includes an array of electrically programmable e-fuse elements. The programming current generator has a set of reference transistor elements, a selector for actuating the reference transistor elements to generate a selected reference current, and a current mirror for applying a programming current that is a function of the selected reference current to a selected e-fuse element of the array to program the resistance of the e-fuse element.