Low-voltage power fuses in new applications in dc networks are faced with changing requirements. Fast and reliable switching characteristics are needed, particularly to protect photovoltaic and battery storage systems. Due to the short fusing times in the event of short circuits, fuse elements made of silver are used. A tin solder is applied to the silver fuse element to protect the circuit from overcurrents. In the case of overcurrents in particular, the requirements for fuses in photovoltaic systems have changed compared to conventional semiconductor protection measures. For this reason, the fusing behavior at low overcurrents was investigated for silver fuse elements with tin solder. The diffusion from silver into liquid tin was analyzed during the fusing process. In the case of the latter, the influence of the temperature gradient along the solder was investigated as a design criterion in addition to the absolute temperature. A shorter fusing time with less scatter was found for specially adapted fuse elements with higher temperature gradients along the solder. The respective diffusion process could be analyzed based on microsections of the solder from interrupted fusing tests. For this purpose, energy-dispersive X-ray spectroscopy (EDX) measurements and threshold segmentations of the microsections were carried out. The temperature gradient along the solder initiated convective movements of silver atoms within the solder. More silver was dissolved in the liquid tin on the warmer side of the solder. Silver-rich particles precipitated on the cooler side of the solder and kept the concentration gradient up on the warmer side. The faster fusing process at higher temperature gradients could be correlated with an altered diffusion mechanism. With these investigations, a new and significant design parameter for fuse elements was determined. Silver fuse elements for protection of overcurrents in full-range fuses can now be easily adapted to new and future requirements.