Distinguishing physical mechanisms using GISAXS experiments and linear theory: the importance of high wavenumbers

Abstract

In this work we analyze GISAXS measurements of the structure factor of Si surfaces evolving during 1 keV Ar+ ion bombardment. Using newly-developed methods sensitive to the full range of experimentally-available wavenumbers q, we extract the linear amplification rate R(q) governing surface stability over a range of wavenumbers 4–5 times larger than has previously been obtained. Comparing with theoretical models also retaining full wavenumber-dependence, we find an excellent fit of the experimental data over the full range of irradiation angles and wavenumbers. Moreover, the fitted parameter values represent experimental evaluation of the magnitudes of most physical mechanisms currently believed to be important to the pattern-formation process. In all cases, the extracted values agree well with direct observations or atomistic simulations of the same quantities, suggesting that GISAXS analysis may allow more powerful comparison between experiment and theory than had previously been thought.

Ion-induced nanopatterning of silicon: Toward a predictive model

“…The method of Ishii et al, 141 of fitting a "flow defect" model to wafer curvature measurements, seems highly promising in this light (indeed, the values extracted from GISAXS spectra in Ref. 137 exhibit very good agreement with values inferred from Ref. 141).…”

“…A solution, introduced in Ref. 137 and made available to the community through the open-source library PyGLIDRE ("A Python library for GISAXS LInear Dispersion Relation Extraction"), 169 is to fit Eq. (27) to all wavenumber series at once, with a(q) assumed to have a single constant value across all q (i.e., the experimental noise is assumed to be white noise).…”

Stress-driven nonlinear dynamics of ion-induced surface nanopatterns

“…Indeed, nonlinear descriptions of IBS surface nanopatterning are available [26][27][28][29][30], but they assume erosion (sputtering) as the main cause for the surface instability, which implies for instance that pattern formation can occur for any value of the incidence angle including θ = 0 • , contradicting recent experimental observations [25]. The limitations to the predictive power of such nonlinear descriptions are underscored by yet more recent experiments on Si with Ar + ions for very low E at which the sputtering yield is negligible [31], which find a pattern formation process just like the one seen at higher E and erosion rates [24,25,32].…”

“…Our theory reveals nontrivial correlations between dynamic and morphological properties of the patterns which are robust to nonlinear effects and are susceptible of experimental verification. This would further confirm viscous flow driven by ion-induced stress as a crucial contribution to the nonlinear dynamics of IBS surface nanostructuring, not only under negligible sputtering conditions [31] but also at higher energies and erosion rates [24,25,32]. This paper is organized as follows.…”

“…The structural disorder in the irradiated layer makes it more similar to a highly viscous fluid than to an amorphous phase of the same material [23]. In particular, experimental estimates for noble-gas irradiation of Si conclude [32,42] that the viscosity μ of this layer is very high, close to 1 GPa min, while assuming viscoelasticlike constitutive laws between strain and stress, which are more complex than that for a simple Newtonian fluid, does not improve predictive power in our experimental context [32,43]. Thus the effect of the irradiation can be expressed as residual stress (forcing) that is relaxed via Newtonian viscous flow (relaxation) [44][45][46] and which, as experimentally assessed [47], does not depend on the initial structural state (e.g., crystalline or amorphous) of the target.…”