Ion beam sputtering of silicon: Energy distributions of sputtered and scattered ions

The properties of sputtered and scattered ions are studied for ion beam sputtering of Si by bombardment with noble gas ions. The energy distributions in dependence on ion beam parameters (ion energy: 0.5-1 keV; ion species: Ne, Ar, Xe) and geometrical parameters (ion incidence angle, polar emission angle, and scattering angle) are measured by means of energy-selective mass spectrometry. The presence of anisotropic effects due to direct sputtering and scattering is discussed and correlated with process parameters. The experimental results are compared to calculations based on a simple elastic binary collision model and to simulations using the Monte-Carlo code sdtrimsp. The influence of the contribution of implanted primary ions on energy distributions of sputtered and scattered particles is studied in simulations. It is found that a 10% variation of the target composition leads to detectable but small differences in the energy distributions of scattered ions. Comparison with previously reported data for other ion/target configurations confirms the presence of similar trends and anisotropic effects: The number of high-energy sputtered ions increases with increasing energy of incident ions and decreasing scattering angle. The effect of the ion/target mass ratio is additionally investigated. Small differences are observed with the change of the primary ion species: The closer the mass ratio to unity, the higher the average energy of sputtered ions. The presence of peaks, assigned to different mechanisms of direct scattering, strongly depends on the ion/target mass ratio

Stability problem for the torque-free gyrostat by using algebraic methods

We apply an algebraic method for studying the stability with respect to a set of conserved quantities for the problem of torque-free gyrostat. If the conditions of this algebraic method are not fulfilled then the Lyapunov stability cannot be decided using the specified set of conserved quantities

Visual Causality: Investigating Graph Layouts for Understanding Causal Processes

Causal diagrams provide a graphical formalism indicating how statistical models can be used to study causal processes. Despite the extensive research on the efficacy of aesthetic graphic layouts, the causal inference domain has not benefited from the results of this research. In this paper, we investigate the performance of graph visualisations for supporting users’ understanding of causal graphs. Two studies were conducted to compare graph visualisations for understanding causation and identifying confounding variables in a causal graph. The first study results suggest that while adjacency matrix layouts are better for understanding direct causation, node-link diagrams are better for understanding mediated causation along causal paths. The second study revealed that node-link layouts, and in particular layouts created by a radial algorithm, are more effective for identifying confounder and collider variables

Energy spectrum of a 2D Dirac electron in the presence of a constant magnetic field

In this paper we obtain exact solutions of a 2D relativistic Dirac oscillator in the presence of a constant magnetic field. We compute the energy spectrum and discuss its dependence on the spin and magnetic field strength.Comment: 7 page