Experimental evidence of dominant ultrafast diffusive energy transport by hot electrons in Cu

When the dimensions of structures shrink to the order of the inelastic mean free path of the energy-carrying quasi-particles, the character of energy transport changes from diffusive to ballistic. However, the point of transition remains a matter of debate. Here, we leverage the fluence-dependent transport efficiency to distinguish ballistic and diffusive electron transport in an approach not relying on the transport velocity. We follow the energy that is rapidly transferred across Cu layers of different thicknesses via hot electrons from a photo-excited Pt layer into a buried Ni detection layer. In the Ni layer, the transported energy linearly relates to a rapid lattice expansion, which we probe via ultrafast x-ray diffraction. A nonlinear dependence of the Ni strain amplitude on the absorbed laser fluence indicates that the transport through Cu becomes more efficient with increasing fluence, which is inconsistent with a ballistic scenario but reproduced by a diffusive energy transport model. We already identify that for a Cu thickness of about 50 nm, i.e., about twice the electronic inelastic mean free path, diffusive electronic energy transport dominates the spatial energy distribution. Our experimental approach is generally applicable to distinguish diffusion from ballistic energy transport.