Pulsed-laser-induced dewetting in nanoscopic metal films : Theory and experiments

Hydrodynamic pattern formation (PF) and dewetting resulting from pulsed-laser-induced melting of nanoscopic metal films have been used to create spatially ordered metal nanoparticle arrays with monomodal size distribution on $\mathrm{Si}{\mathrm{O}}_{2}∕\mathrm{Si}$ substrates. PF was investigated for film thickness $h\ensuremath{\leqslant}7\phantom{\rule{0.3em}{0ex}}\mathrm{nm}l$laser absorption depth $\ensuremath{\sim}11\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$, and different sets of laser parameters, including energy density $E$ and the irradiation time, as measured by the number of pulses $n$. PF was only observed to occur for $E\ensuremath{\geqslant}{E}_{m}$, where ${E}_{m}$ denotes the $h$-dependent threshold energy required to melt the film. Even at such small length scales, theoretical predictions for ${E}_{m}$ obtained from a continuum-level lumped parameter heat transfer model for the film temperature, coupled with the one-dimensional transient heat equation for the substrate phase, were consistent with experimental observations provided that the thickness dependence of the reflectivity of the metal-substrate bilayer was incorporated into the analysis. The model also predicted that perturbations in $h$ would result in intrinsic thermal gradients $\ensuremath{\partial}T∕\ensuremath{\partial}h$ whose magnitude and sign depend on $h$, with $\ensuremath{\partial}T∕\ensuremath{\partial}hg0$ for $hl{h}_{c}$ and $\ensuremath{\partial}T∕\ensuremath{\partial}hl0$ for $hg{h}_{c}\ensuremath{\approx}9\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$. For the thickness range investigated here, the resulting thermocapillary effect was minimal since the thermal diffusion time ${\ensuremath{\tau}}_{H}$ is less than or equal to the pulse time. Consequently, the spacing between the nanoparticles and the particle diameter were found to increase as ${h}^{2}$ and ${h}^{5∕3}$, respectively, which is consistent with the predictions of the thin-film hydrodynamic (TFH) dewetting theory. PF was characterized by the appearance of discrete holes followed by bicontinuous or cellular patterns which finally consolidated into nanoparticles via capillary flow rather than via Rayleigh-like instabilities reported for low-temperature dewetting of viscous liquids. This difference is attributed to the high capillary velocities of the liquid metal arising from its relatively large interfacial tension and low viscosity as well as the smaller length scales of the liquid bridges in the experiments. The predicted liquid-phase lifetime ${\ensuremath{\tau}}_{L}$ was between 2 and $15\phantom{\rule{0.3em}{0ex}}\mathrm{ns}$, which is much smaller than the dewetting time ${\ensuremath{\tau}}_{D}\ensuremath{\geqslant}25\phantom{\rule{0.3em}{0ex}}\mathrm{ns}$ as predicted by the linear TFH theory. Therefore, dewetting required the application of multiple pulses. During the early stages of dewetting, the ripening rate, as measured by the rate of change of characteristic ordering length with respect to $n$, increased linearly with $E$ due to the linear increase in ${\ensuremath{\tau}}_{L}$ with increasing $E$ as predicted by the thermal model. The final nanoparticle spacing was robust, independent of $E$ and $n$, and only dependent on $h$ due to the relatively weak temperature dependence of the thermophysical properties of the metal (Co). These results suggest that fast thermal processing combined with the unique thermophysical parameters of metals can lead to a different pattern formation, including quenching of a wide range of length scales and morphologies.