Sputtering by ion bombardment theoretical concepts

We derive a stochastic nonlinear continuum equation to describe the morphological evolution of amorphous surfaces eroded by ion bombardment. Starting from Sigmunds theory of sputter erosion, we calculate the coefficients appearing in the continuum equation in terms of the physical parameters characterizing the sputtering process. We analyze the morphological features predicted by the continuum theory, comparing them with the experimentally reported morphologies. We show that for short time scales, where the effect of nonlinear terms is negligible, the continuum theory predicts ripple formation. We demonstrate that in addition to relaxation by thermal surface diffusion, the sputtering process can also contribute to the smoothing mechanisms shaping the surface morphology. We explicitly calculate an effective surface diffusion constant characterizing this smoothing effect and show that it is responsible for the low temperature ripple formation observed in various experiments. At long time scales the nonlinear terms dominate the evolution of the surface morphology. The nonlinear terms lead to the stabilization of the ripple wavelength and we show that, depending on the experimental parameters, such as angle of incidence and ion energy, different morphologies can be observed: asymptotically, sputter eroded surfaces could undergo kinetic roughening, or can display novel ordered structures with rotated ripples. Finally, we discuss in detail the existing experimental support for the proposed theory and uncover novel features of the surface morphology and evolution, that could be directly tested experimentally. � 2002 Published by Elsevier Science B.V.

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Morphology of ion-sputtered surfaces

Calculation of projected ranges — analytical solutions and a simple general algorithm

The computer code, Stopping and Range of Ions in Matter (SRIM), is widely used to describe energetic processes of ion-solid interactions; its predictive power relies on the accuracy of energy loss/transfer and collision processes being considered. While the SRIM code is commonly applied in radiation effects research to predict damage production and in the semiconductor industry to estimate ion range and dopant concentration profiles, two challenges exist that affect its use: (1) inconsistency in estimations of atomic displacements between full-cascade and quick (modified Kinchin–Pease) options and (2) overestimation of electronic stopping power for slow heavy ions in light targets (e.g., Be and Si) or in compound targets containing light elements (e.g., C, N and O in carbides, nitrides and oxides). Based on a literature review and our experimental investigations, we discuss the underlying reasons for the discrepancies, clarify the physical limitations of the SRIM predictions, and, more importantly, provide recommendations to address the two challenges.

Predicting damage production in monoatomic and multi-elemental targets using stopping and range of ions in matter code: Challenges and recommendations

This paper presents a zero order approximation of ion collection during sputtering. Neglecting diffusion, range shortening and knock-on effects and assuming a constant sputtering yield general analytical results are developed which allow a comparison with experimental data. The accumulation of implantation profiles and the build-up of surface concentrations and collected quantities are described in detail for Gaussian range distributions. A thorough discussion of available experimental results indicates that the model is suitable for a variety of projectile-target combinations, in particular for medium mass noble gas atoms collected in high melting point targets. Application to sputtering experiments presents further evidence of a strong fluence dependence of the silicon sputtering yield. Some comments are devoted to recently reported analytical and numerical treatments of ion collection during sputtering.

Model calculation of ion collection in the presence of sputtering

Detailed distributions of the ranges of heavy ions in amorphous targets and of the associated radiation damage have been obtained for low (keV) incident-ion energies, neglecting electronic stopping. Moments of the distributions (mean depth, straggling, and so on) and some distributions have also been computed with electronic stopping taken into account for dimensionless energies ∊ up to ∼10-100. These calculations are exact within the LSS theory; in particular, nuclear and electronic stopping are separated, the target is amorphous and infinite, collisions are binary, and electronicstopping is included as a continuous retardation, proportional to the velocity of the moving ion. Results have been obtained for various ratios of projectile and target mass, and for some compound targets. Interpretation of the results is discussed, and possible experimental verifications suggested.

Heavy-ion range profiles and associated damage distributions.

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Heavy-ion range profiles and associated damage distributions.