Stress-induced solid flow drives surface nanopatterning of silicon by ion-beam irradiation

M. Castro, R. Gago, L. Vázquez, J. Muñoz-García, and R. Cuerno

Phys. Rev. B 86, 214107 – Published 19 December 2012

Abstract

Ion-beam sputtering (IBS) is known to produce surface nanopatterns over macroscopic areas on a wide range of materials. However, in spite of the technological potential of this route to nanostructuring, the physical process by which these surfaces self-organize remains poorly understood. We have performed detailed experiments of IBS on Si substrates that validate dynamical and morphological predictions from a hydrodynamic description of the phenomenon. We introduce a systematic approach to perform the experiments under conditions that guarantee the applicability of a linear description, helping to clarify the experimental framework in which theories should be tested. Among our results, the pattern wavelength is experimentally seen to depend almost linearly on ion energy, in agreement with existing results for other targets that are amorphous or become so under irradiation. Our work substantiates flow of a nanoscopically thin and highly viscous surface layer, driven by the stress created by the ion beam, as an accurate description of this class of systems.

Received 27 February 2012

DOI:https://doi.org/10.1103/PhysRevB.86.214107

Authors & Affiliations

M. Castro^1,*, R. Gago², L. Vázquez², J. Muñoz-García³, and R. Cuerno³

¹Grupo Interdisciplinar de Sistemas Complejos (GISC) and Grupo de Dinámica No Lineal (DNL), Escuela Técnica Superior de Ingeniería (ICAI), Universidad Pontificia Comillas, E-28015 Madrid, Spain
²Instituto de Ciencia de Materiales de Madrid, Consejo Superior de Investigaciones Científicas, E-28049 Madrid, Spain
³Departamento de Matemáticas and Grupo Interdisciplinar de Sistemas Complejos (GISC), Universidad Carlos III de Madrid, Avenida de la Universidad 30, E-28911 Leganés, Spain

^*Corresponding author: marioc@upcomillas.es

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Vol. 86, Iss. 21 — 1 December 2012

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Images

Figure 1
Schematic view of the IBS process. An incident energetic ion (small red circle) impinges onto the target at an angle $θ$ , inducing a collision cascade that amorphizes a thin region through creation of vacancies and interstitials. At long time scales, the amorphized solid flows as a highly viscous fluid. Here $γ$ is the local slope of the surface profile $h (x, t)$ at time $t$ and point $x$ , $T$ $= T - T^{(ext)}$ with $T$ the fluid stress tensor and $T^{(ext)}$ the stress induced by the irradiation process, $V$ is the fluid velocity, and $σ κ$ is the contribution from surface tension. Different colors are meant to represent the degree of order and kinetic energy.Reuse & Permissions
Figure 2
Experimental morphologies of ion irradiation of Ar $^{+}$ on Si. All the figures are obtained at energy $E = 700$ eV, constant dose of $6 \times 10^{17}$ ions/cm $^{2}$ , and at angles of incidence (a) $θ = 55^{\circ}$ , (b) $θ = 60^{\circ}$ , (c) $θ = 65^{\circ}$ , and (d) $θ = 70^{\circ}$ . For $θ < 50^{\circ} \pm 3^{\circ}$ , no pattern is observed (not shown). Ions arrive from right to left in all cases.Reuse & Permissions
Figure 3
(a) Roughness and (b) wavelength dependence on incidence angle for $E = 700$ eV. Squares were obtained at a constant dose of $6 \times 10^{17}$ ions/cm $^{2}$ ( $J_{0} = 300 μ$ A cm $^{- 2}$ ) and circles correspond to experiments performed in the proper linear regime ( $J_{0} = 30 μ$ A cm $^{- 2}$ ) as estimated by the intrinsic time scale in Eq. (5). Lines in (a) are guides to the eye. The solid line in (b) is a fit to Eq. (2), the dashed lines corresponding to the same fit but assuming a $\pm 3^{\circ}$ uncertainty in $θ$ .Reuse & Permissions
Figure 4
Experimental dynamics for ion irradiation of Ar $^{+}$ on Si. The figures are obtained at fixed energy $E = 500$ eV, flux $J = 30$ $μ A {cm}^{- 2}$ , and constant angle of incidence $θ = 65^{\circ}$ , at increasing irradiation times $t = (a) 3$ min, (b) 15 min, (c) 30 min, and (d) 120 min. Ions arriving from right to left in all cases.Reuse & Permissions
Figure 5
Time evolution of the (a) surface roughness and (b) ripple wavelength for $E = 700$ eV, $J_{0} = 30$ $μ A {cm}^{- 2}$ and $θ = 55^{\circ}$ . The solid line in (a) is an exponential fit in the linear regime, while the dashed line is a power-law fit in the nonlinear regime with exponent $0.32$ . The dashed line in (b) is a guide to the eye. The time regime in which the wavelength grows with time (coarsening) starts at $t ≃ 25$ min, as indicated by the vertical dotted line; this is a signature of the onset of nonlinear effects. At shorter times the wavelength is almost constant. The same crossover time separates exponential from power-law behavior for the roughness.Reuse & Permissions
Figure 6
Ripple wavelength dependence on the ion energy for constant-dose experiments (squares) and intrinsic-time-scale experiments (circles) for an incidence angle of 65 $^{o}$ with $J_{0} = 300$ and $30 μ$ A cm $^{- 2}$ , respectively. The upper line is a power-law fit with exponent $0.5$ , while the lower line is a linear fit validating the theoretical prediction given by Eq. (4).Reuse & Permissions

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