Ion beam-generated surface ripples: new insight in the underlying mechanism
© Kumar et al.; licensee Springer. 2013
Received: 25 June 2013
Accepted: 18 July 2013
Published: 26 July 2013
A new hydrodynamic mechanism is proposed for the ion beam-induced surface patterning on solid surfaces. Unlike the standard mechanisms based on the ion beam impact-generated erosion and mass redistribution at the free surface (proposed by Bradley-Harper and its extended theories), the new mechanism proposes that the incompressible solid flow in amorphous layer leads to the formation of ripple patterns at the amorphous-crystalline (a/c) interface and hence at the free surface. Ion beam-stimulated solid flow inside the amorphous layer probably controls the wavelength, whereas the amount of material transported and re-deposited at a/c interface control the amplitude of ripples.
KeywordsIon beam Ripples TEM AFM PACS 81.16.Rf 68.35.Ct 68.49.Sf 79.20.Rf
Fabrication of self-organized nano-structures over solid surfaces using energetic ion beam irradiation has received a remarkable attention in the last couple of decades. It is an elegant and cost-effective single-step approach over lithographic methods for device fabrication. In general, a uniform ion irradiation of solid surfaces for intermediate energies (102 to 104 eV) causes a self-organized topographic pattern of ripples, holes, or dots [1–4]. On the other hand, irradiation with higher energies (106 to 108eV) causes the phase transformations . In 1988, the first analytical approach to study the surface patterning was given by Bradley and Harper (BH)  on the basis of two competing processes: the destabilizing effect of curvature dependent roughening and the stabilizing effect of surface diffusion. Further theoretical refinements of BH's model have been proposed to underline the secondary effect of local curvature-dependent sputtering, ion beam-induced smoothing, and hydro-dynamical contribution [7, 8]. BH's linear and its extended models explain many experimental observations but suffered many limitations also [9–11]. Investigations by Madi et al.  and Norris et al.  showed that the ion impact-induced mass redistribution is the prominent cause of surface patterning and smoothening for high and low angles, respectively. Castro et al. [13, 14] proposed the generalized framework of hydrodynamic approach, which considers ion impact-induced stress causing a solid flow inside the amorphous layer. They pointed out that the surface evolution with ion beam is an intrinsic property of the dynamics of the amorphous surface layer . All above experimental findings and their theoretical justification raise questions on lack of a single physical mechanism on the origin and evolution of ripples on solid surface.
In this work, we propose a new approach for explaining all ambiguity related to the origin of ripple formation. We argue that amorphous-crystalline interface (a/c) plays a crucial role in the evolution of ripples. We have shown that the ion beam-induced incompressible solid flow in amorphous layer starts the mass rearrangement at a/c interface which is responsible for ripple formation on the free surface rather than earlier mentioned models of curvature-dependent erosion and mass redistribution at free surface.
Presentation of the hypothesis
Testing the hypothesis
Implication of the hypothesis
To physically understand the underlying mechanism, we considered a radical assumption that the formation of ripples is initiated at a/c interface due to the erosion and re-deposition of Si atoms under the effect of solid flow. Due to incompressible nature of this solid mass flow inside amorphous layer, structures formed at the a/c interface reciprocate at the top surface. Similar process of ripple formation on sand (ripples caused by air flow on sand dunes, etc.) has been well observed and studied [17, 18]. Here, we assume that the rearrangement of Si atoms is taking place at the a/c interface due to solid flow inside damaged layer, which controls the process of ripple formation. In the case of set A samples, the rearrangement of Si atoms at the a/c interface starts instantaneously with second stage irradiation as the ion range is equal to depth of a/c interface. However, for set B samples, second stage irradiation results in surface erosion before the ion beam effect reach at a/c interface. Thus, the process of mass rearrangement at a/c interface lags behind in set B samples as compared to set A samples. This fact was confirmed by the formation of ripples with appreciable average amplitude (23 nm) and wavelength (780 nm) observed at still higher fluence of 1.5 × 1018 ions per square centimeter. Therefore, amplitude is less in magnitude in set B samples as compared to set A samples at corresponding fluences. Since the ion beam parameters are identical in the second stage of irradiation, so the solid flow would be identical in both set of samples. This solid flow is probably responsible for the similar wavelength of ripples for both set of samples. Castro et al. [13, 14] and Kumar et al.  have also discussed role of solid flow for surface rippling. As already discussed, our AFM and XTEM results could not be explained by existing models of BH and its extended theories, where they consider it only surface effect. The role of a/c interface has not been considered in the formation of ripples on solid surfaces by earlier groups [6, 12, 13]. By considering ripple formation as an a/c interface-dependent process, all phenomena like ripple coarsening, propagation, etc., can be correlated.
In conclusion, by designed experiments and theoretical modeling, a new approach for explaining the origin of ripple formation on solid surface has been proposed. Formation of ripples at top surface is a consequence of mass rearrangement at the a/c interface induced by incompressible solid flow inside the amorphous layer. The control parameter for ripple wavelength is solid flow velocity, while that for the amplitude is amount of silicon to be transported at the interface.
One of the authors (Tanuj Kumar) is thankful to Council of Scientific and Industrial Research (CSIR), India, for financial support through senior research fellowship. The help received from S. A. Khan, Parvin Kumar, and U. K. Rao during the experiment is gratefully acknowledged here.
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