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

Abstract

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 determine the dominant channel of energy transport through a nanoscale Cu layer as a function of its thickness. The energy rapidly transferred across Cu via hot electrons from a photo-excited Pt layer into a buried Ni detection layer translates into a rapid expansion of the Ni layer probed via ultrafast x-ray diffraction. The non-linear dependence of the Ni strain amplitude on the absorbed laser fluence indicates that the transport through Cu becomes more efficient with increasing fluence. This fluence-dependent transport efficiency is reproduced by a diffusive energy transport model and serves as a generally applicable experimental approach to distinguish diffusion from ballistic transport. Following this approach, we identify diffusive electronic energy transport to govern the spatial energy distribution for Cu layer thicknesses larger than twice the electronic inelastic mean free path.

Figures (3)

• Figure 1: Schematic of the UXRD experiment on the Pt-Cu-Ni heterostructures. The metallic heterostructures are excited by $800\,\text{nm}$ femtosecond laser pulses and we monitor the shift of the (111) Bragg peak of the Ni detection layer using hard-x-ray pulses incident under the Bragg angle of Ni ($22.1^\circ$) on a pixelated position-sensitive area detector. Transforming the diffraction pattern on the detector into reciprocal space yields the diffracted intensity along the out-of-plane reciprocal coordinate $q_z$ as function of the pump-probe delay $t$ exemplified for the sample with $22\,\text{nm}$ Cu (a). (b) While for $22\,\text{nm}$ of Cu a significant part of the pump pulse is absorbed by Ni layer (red shaded area), for Cu layers thicker than $70\,\text{nm}$ the direct absorption in Ni is negligible and Ni is only indirectly excited via electronic energy transport (see Fig. S5).
• Figure 2: The fluence-dependent strain response of the Ni layer (symbols) extracted from the transient Bragg peak position for the different samples of Cu thicknesses from 22nm (a), 47nm (b), 136nm (c) and 288nm (d). Solid lines display the modeling in the framework of a diffusive two-temperature model (d2TM) explicitly considering the effect of the initial electron-phonon nonequilibrium on the electronic heat conductivity. All measurements were conducted at 7.5mJ cm (blue) and 25.0mJ cm (red) except for the additional measurements at the PXS on the 22nm sample, which was measured at 3.0mJ cm (darkblue) and 10.0mJ cm (orange). The gray shaded areas mark the delay ranges used to calculate the fluence response parameter $A$ according to Eq. \ref{['eq:nonlinearity']}.
• Figure 3: Nonlinear fluence dependence of the Ni strain in Pt-Cu-Ni heterostructures. (a) The transient Ni strain of the sample with 136nm Cu for the high and low fluence normalized to the respective incident fluence $F$. (b) The fluence response parameter $A$ calculated via Eq. \ref{['eq:nonlinearity']} as a function of Cu layer thickness for the experiment (symbols) and the diffusive (red) and quasi-ballistic (blue) transport models. The measurements are best reproduced by the d2TM with temperature dependent electron conductivity. The errorbars are the standard error calculated from the strain values within the grey shaded areas in Fig. \ref{['fig:fig_2_delayscans']}. The dashed vertical line indicates the inelastic mean free path of electrons in Cu.