Both the development of radiation tolerant materials and the modification of materials on the nanoscale by ion beams require thorough understanding and accurate models of the damage evolution processes that occur during ion-solid interactions. Multi-scale computer simulations and experimental techniques have been used to investigate radiation tolerance and the formation of nanoscale structures in ion-irradiated ceramics as functions of ion mass and energy. At lower energies, where nuclear stopping is dominant, atomistic simulations of energetic collision cascades demonstrate the formation of a high density of displaced atoms that can result in the formation of point defects, defect clusters, nanoscale amorphous clusters, or combination of these. The final damage state following a collision cascade depends not only on the damage production process, but also on the pre-existing defect structure and dynamic recovery or relaxation processes that occur simultaneously. Defect and grain boundary engineering can result in “self-healing” processes that minimize ion-beam damage production, while in other materials nanoscale amorphization can occur directly in the collision cascade. Furthermore, point defect accumulation can result in crystalline phase transformations or amorphization. Examples of various damage states predicted by atomistic simulations, along with experimental validation, will be presented for silicon carbide, zircon, zirconia, and pyrochlores. In the high-energy electronic stopping regime of swift-heavy ions, a thermal spike forms in the core of the ion track, and atomistic simulations can describe the local melting, defect production, and phase transitions that occur. In the case of ion tracks, concentric regions of different damage states are observed, both computationally and experimentally, as will be discussed.

The threshold displacement energy of a material Ed is the single most fundamental quantity in determining the primary state of radiation damage in any material. Knowing Ed in silicon is essential not only for the well- known use of the material in the manufacturing of semiconductor devices, but also because of contexts such as particle accelerators, where silicon elements in detectors are exposed to extensive hadron damage. In spite of this vast technological interest in the quantity, and its extensive study during the last few decades, the Ed averaged over all lattice directions remains poorly known in the material. Experimental methods show a widely varying scale of results for the average Ed in the range of 10 - 30 eV, and simulations carried out previously using classical potentials show a similarly wide range of results.We have used Density Functional Theory (DFT) molecular dynamics (MD) simulations to study Ed in bulk Si. We calculated Ed with the DFT code SIESTA over all lattice directions. We found a global minimum of 12.5 +- 1.5SYST eV for the minimum Ed, in excellent agreement with experiment, and a value of 36 +- 2STAT +- 2SYST eV for the average Ed [1].We also showed that a large fraction (~ 65 %) of the produced Frenkel pairs have a tetrahedral interstitial, even though the dumbbell is the ground state configuration for the isolated interstitial. This is because the formation energy of a close Frenkel pair is lower when the interstitial is tetrahedral rather than a dumbbell. Moreover, we found that the other dominating end state is the bond defect complex. If the bond defect is counted in as a stable defect, one obtains a lower threshold displacement energy than without counting it. The average threshold energy for producing either a bond defect or a Frenkel pair was found to be 24 +- 1STAT +- 2SYST eV.We have also examined the threshold displacement energy in Si nanowires using classical MD simulations, to get insight into how the threshold displacement energy in a one-dimensional nanosystem differs from that in the bulk. The results in the nanowire are compared to those in the bulk.

We have studied the strain relaxation mechanism of nano-laminate SiGe in Si/SiGe/Si heterostructure during ion irradiation. During high temperature (300 oC) proton irradiation, vacancies generated in the vicinity of SiGe layer migrate and accumulate within the, which is facilitated by the compressive stress in the SiGe layer. The accumulating vacancies are stabilized by hydrogen, which diffuses from the implanted region simultaneously, thus allowing the nucleation and growth of V-H complex. The formation of V-H complexes is accompanied by the gradual relief of strain in the SiGe layer. Since the diffusion of both vacancies and hydrogen is restricted by the irradiation temperature, strain relaxation of the SiGe layer is not observed during room temperature (20 oC) irradiation. The study supports the idea that the compressive stress in the SiGe layer biases the in-diffusion of vacancies and impurities, and reveals the importance of point defects in the strain relaxation of the nano-laminate SiGe layer. The mechanism proposed may be instructive for the future application of strained semiconductor materials in irradiation environment.

Low-energy ion beam induced erosion is a promising tool for large scale nanostructuring of different materials. Depending on process parameters a multitude of different topographies can evolve on the material surface, usually with mean size below 100 nm. The evolving nanostructures show a very well lateral ordering organized in particular domains. The formation, size and ordering of nanostructures depends on parameters like ion energy, ion incidence angle, ion fluence, secondary ion beam parameters of the ion source etc [1,2].However there is a lack of positional control and large scale ordering of nanostructures. Therefore a new approach is applied, by using pre-patterned substrates, for self-organized processes. This method known as guided self organization has its inspiration in nature and is already successfully applied in heteroepitaxy and in diblock-copolymers. The idea is to use different pre-patterns fabricated with various lithographic techniques as templates for ion beam induced self-organization processes. Due to the periodicity, shape and lateral ordering of pre-patterns an improved ordering, and an exact positional control of nanostructures is achieved. Additionally the method allows for the formation of new type of nanostructures not possible on planar surfaces. Explicitly, the guided self-organization method was applied for the ripple and dot pattern formation on pre-patterned Si surfaces by low energy (ion energy ≤ 2000 eV) ion beam erosion. Some experimental observations are: i) formation of curved ripples on the surface, where the curvature is caused by a continuous change in the local topography within pre-patterned regions; ii) perfectly square ordered dots on exact positions on the surface; iii) enhanced ordering of ripples and the formation of ripples with different orientation due to the local surface orientation. Furthermore the shape and periodicity of pre-patterns on the evolving topography is investigated.In general the main parameters determining the pattern formation with this method are the local incidence of ions, orientation of the local surface with respect to the ion beam direction, and the local surface curvature.In this contribution is demonstrated that by combining “Top-down” (conventional lithographic techniques) and “Bottom-up” (ion beam induced self-organization) techniques a multi-scale patterning is possible with potential applications in micro-and nanooptics.[1] W. L. Chan, and E. Chason, J. Appl. Phys. 101, 121301 (2007)[2] B. Ziberi, M. Cornejo, F. Frost, and B. Rauschenbach, J. Phys.: Condens. Matter submitted.

Focused and unfocused ion beam irradiation of a solid changes the surface morphology by sputter erosion and material relaxation processes. Their interplay can result in completely smooth surfaces; self-organized nanoscale corrugation, dot, or hole patterns; or self-sharpening high-sloped shock fronts that propagate instead of dissipating. Current understanding of these phenomena will be reviewed from an experimental and a theoretical perspective.

We develop a methodology for deriving continuum partial differential equations for the evolution of large scale surface morphology directly from molecular dynamics simulations of the craters formed from individual ion impacts. Our formalism relies on the separation between the length scale of ion impact and the characteristic scale of pattern formation. We demonstrate that the formalism reproduces both the classical Bradley Harper results, as well as ballistic atomic drift, under the appropriate simplifying assumptions. We then apply the formalism directly to a molecular dynamics simulation data set for bombardment of argon onto amorphous silicon, thereby directly predicting the presence and absence of surface morphological instabilities as a function of incident angle. This analysis represents the first work systematically predicting the consequences of molecular dynamics simulations of ion bombardment on partial differential equations yielding topographic pattern-forming instabilities.

The formation of regular nanopatterns during low energy ion sputtering of solid surfaces has become a topic of intense research. This research is mainly motivated by promising applications of nanopatterned surfaces e.g. in thin film growth. On the other hand, these surfaces represent an interesting example of spontaneous pattern formation in non-equilibrium systems exhibiting different features like wavelength coarsening or a transition to spatiotemporal chaos. Different pattern types are observed for different experimental conditions, i.e. wavelike ripple patterns and hexagonally ordered dot arrays under oblique and normal ion incidence, respectively [1]. According to the model of Bradley and Harper (BH) [2], the regular patterns result from the competition between curvature dependent roughening and diffusional smoothing of the surface. Since the local erosion rate is higher in troughs than on crests, the eroded surface is unstable against any periodic perturbances. In the presence of a smoothing mechanism, however, wave vector selection occurs and a periodic pattern with a characteristic spatial frequency is observed. During recent years, several nonlinear extensions of the linear BH model have been proposed with the stochastic Kuramoto-Sivashinsky (KS) equation having played a prominent role [3]. However, although most experimental investigations on ion-induced pattern formation were performed under oblique ion incidence, only few theoretical studies focused on the corresponding anisotropic KS (aKS) equation.In this work, we have investigated the influence of anisotropy on the morphology evolution in numerical integrations of the aKS equation. For a strong nonlinear anisotropy, a rotation by 90° of the initially formed ripple pattern was observed for intermediate and long integration times. Comparison with analytical predictions indicates that the observed rotated ripple pattern arises from anisotropic renormalization properties of the aKS equation. This result may also offer an explanation for the recent observation of transient structures in high-temperature experiments on Si(111) [4].[1]W. L. Chan and E. Chason, J. Appl. Phys. 101, 121301 (2007)[2]R. Bradley and J. Harper, J. Vac. Sci. Technol. A 6, 2390 (1988)[3]R. Cuerno and A.-L. Barabási, Phys. Rev. Lett. 74 4746 (1995) [4]A.-D. Brown, J. Erlebacher, W.-L. Chan, and E. Chason, Phys. Rev. Lett. 95 056101 (2005)

We study the patterns formed on Ar+ ion sputtered Si surfaces at room temperature as a function of the control parameters ion energy and incidence angle. We identify regions in control parameters space where holes, parallel mode ripples and perpendicular mode ripples form, and identify a region where the flat surface is stable. In the vicinity of the boundaries between the stable and pattern forming regions, called bifurcations, we follow the time dependence from exponential amplification to saturation and examine the amplification rate and the wavelength in the exponential amplification regime. The resulting power laws are consistent with the theory of nonequilibrium pattern formation for a Type I (constant-wavelength) bifurcation at low angles and for a Type II (diverging wavelength) bifurcation at high angles. We discuss the failure of all sputter rippling models to adequately describe these aspects of the simplest experimental system studied, consisting of an elemental, isotropic amorphous surface in the simplest evolution regime of linear stabilty.