Fluidity and morphological stability of an amorphous thin film with radiation-induced defect kinetics

TL;DR

This work addresses how radiation-induced defect kinetics modify the fluidity of an irradiated amorphous thin film and its surface relaxation. It develops a coupled continuum model where Frenkel-pair defect concentrations $C_V$ and $C_I$ set a spatially varying fluidity via $\eta^{-1}$, and energy deposition from off-normal irradiation drives defect production through a Gaussian energy density $P(x,z;\theta)$ with Kinchin-Pease yields. Linear stability analysis shows that, in the long-wavelength limit, the model recovers the Orchard-style surface relaxation form while defect kinetics adjust growth rates and the effective fluidity; moreover, mean fluidity scales with flux, angle, and energy as $\langle\eta^{-1}\rangle \sim \sqrt{f\cos\theta}\, E^{1/4}/h_0(\theta)$ under controlled temperature, with heating capable of reducing fluidity. These findings imply that defect kinetics cannot be ignored in ion-induced pattern formation on silicon and related semiconductors, and they highlight the need for accurate estimates of defect diffusion and recombination parameters to predict surface morphologies under irradiation.

Abstract

It is common to model ion-irradiated amorphous thin films as if they were highly viscous fluids. In such models, one is frequently concerned with the ion-enhanced fluidity, a measure of the ability of the free interface to relax surface energy. Motivated by usual fluid dynamics problems, the ion-enhanced fluidity is near-universally treated as a constant throughout the amorphous layer. However, for an irradiated thin film, the fluidity is ultimately caused by radiation-induced defect kinetics within the film, leading to regions with greater or lesser fluidity, and sensitive dependence on ion energy, species, flux, irradiation angle, temperature, and other experimental parameters. Here, we develop and analyze a model of radiation-induced defect kinetics coupled to the continuum equations of a viscous thin film. Using realistic parameter values, we show that defect kinetics can meaningfully alter theoretical predictions of surface relaxation and ion-enhanced fluidity. Implications for aligning theoretical and experimental work, especially for surface nano-patterning of silicon induced by low-energy argon irradiation, are discussed.

Figures (3)

• Figure 1: Comparison of $\Sigma_{PM}$ and $\Sigma_{Orchard}$ for selected energies, wavenumbers, and irradiation angle. There is broad agreement between the two, which worsens somewhat at higher wavenumbers and lower fluxes. An intuitive explanation for this is discussed in the main text.
• Figure 2: Comparison of $\Sigma_{PM}$ and $\Sigma_{Orchard}$, as in Figure \ref{['fig:resultsfig1']}, while using $D_{A0}$ and $D_{B0}$ two orders of magnitude lower. The curves are indistinguishable up to a scaling factor of $10^{-1}$.
• Figure 3: Left: angle-dependence of $\eta^{-1}$ for selected energies and fluxes. For comparison, $\cos(\theta)$ and $\sqrt{\cos(\theta)}$ are plotted. The data is evidently consistent with a $\sqrt{\cos(\theta)}$ dependence at these energies and fluxes. Center: flux dependence under selected thermal conditions. When temperature is controlled, and especially near room temperature, $\eta^{-1}$ scales approximately as $\sqrt{f}$. Right: energy dependence of $\eta^{-1}$. When temperature is controlled, and especially near room temperature, $\eta^{-1}$ scales with $E^{1/4}$.