Electron-phonon heat transport in arrays of Al islands with submicrometer-sized tunnel junctions

We present experimental evidence of the effect of electrode volume and its shape on thermalization of small metallic islands for single electron tunneling. We have investigated the power law and the magnitude of the thermal transport and found that it obeys the common T-5 law for electron-phonon coupling only for the smallest islands studied, and in other cases considered, with cooling fins attached to the islands, the coupling per unit volume is weaker and it rather follows a law proportional to aT(p), where p<5. We attribute this to local hot electrons adjacent to the tunnel junctions.