The discovery that a gate electrode suppresses the supercurrent in purely metallic systems is missing a complete physical understanding of the mechanisms at play. We here study the origin of this reduction in a Superconductor-Normal metal-Superconductor Josephson junction by performing, on the same device, a detailed investigation of the gate-dependent switching probability together with the local tunnelling spectroscopy of the normal metal. We demonstrate that high energy electrons leaking from the gate trigger the reduction of the critical current which is accompanied by an important broadening of the switching histograms. The switching rates are well described by an activation formula including an additional term accounting for the injection of rare high energy electrons from the gate. The rate of electrons obtained from the fit remarkably coincides with the independently measured leakage current. Concomitantly, a negligible elevation of the local temperature is found by tunnelling spectroscopy which excludes overheating scenarios.
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