Synergetic effects during sputter-assisted depth profiling: Growth-dominated topography development on InP and a model of the atomic mechanism

Growth-dominated extreme topography development on ionbombarded wafers of InP is reported and is explained in terms of the micro region model presented in summary form. This model postulates the existence of an ion-bombardment-produced ensemble of crystallites and non-crystalline aggregations of atoms (composed of the substrate material, of dopant and of oxygen from the native oxide layer) where the majority of InP micro regions is so small (nanometer dimensions) that most interstitials created in collision events between bombarding ions and atoms of the micro region can reach an interfacial boundary rather than recombine with a vacancy from the same or another collision event. These atoms are then transported via interfacial boundaries and over the surface to screw dislocations where crystal stubs proceed to grow until the damage rate by ion bombardment overtakes the growth rate. Ion-bombardment-induced compressive stresses favour diffusion towards the surface. Temperature transients within micro regions assist both interfacial diffusion and damage repair. The topography is a result of competition between growth and sputtering. Different growth rates cause different topographies. The development of an extreme topography can be suppressed by oxygen flooding of the sputtered surface, by simultaneous electron beam scanning, as well as by Cs⁺ ion bombardment.     

Computation of multiple Lie derivatives by algorithmic differentiation

Lie derivatives are often used in nonlinear control and system theory. In general, these Lie derivatives are computed symbolically using computer algebra software. Although this approach is well-suited for small and medium-size problems, it is difficult to apply this technique to very complicated systems. We suggest an alternative method to compute the values of iterated and mixed Lie derivatives by algorithmic differentiation.     

Bestimmung der orthogonalitätstreuen Permutationen euklidischer Räume

Ohne Zusammenfassung     

Newton’s iterates can converge to non-stationary points

In this note we discuss the convergence of Newton’s method for minimization. We present examples in which the Newton iterates satisfy the Wolfe conditions and the Hessian is positive definite at each step and yet the iterates converge to a non-stationary point. These examples answer a question posed by Fletcher in his 1987 book Practical methods of optimization.