Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science (2nd edition)

to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

Manipulating matter at the nanometre scale is important for many electronic, chemical and biological advances, but present solid-state fabrication methods do not reproducibly achieve dimensional control at the nanometre scale. Here we report a means of fashioning matter at these dimensions that uses low-energy ion beams and reveals surprising atomic transport phenomena that occur in a variety of materials and geometries. The method is implemented in a feedback-controlled sputtering system that provides fine control over ion beam exposure and sample temperature. We call the method "ion-beam sculpting", and apply it to the problem of fabricating a molecular-scale hole, or nanopore, in a thin insulating solid-state membrane. Such pores can serve to localize molecular-scale electrical junctions and switches and function as masks to create other small-scale structures. Nanopores also function as membrane channels in all living systems, where they serve as extremely sensitive electro-mechanical devices that regulate electric potential, ionic flow, and molecular transport across cellular membranes. We show that ion-beam sculpting can be used to fashion an analogous solid-state device: a robust electronic detector consisting of a single nanopore in a Si3N4 membrane, capable of registering single DNA molecules in aqueous solution.

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Ion-beam sculpting at nanometre length scales

Publisher Summary A refractive index can be increased by ion implantation by changes in density and structure, by the addition of high-polarizability impurity ions, by a reduction of the plasma effect that increases the index and that is most important in the wavelength region far from the energy gap, and by absorption changing in the index in the region of the gap, that is, via the Kramers–Kronig relation. This chapter discusses the optical properties of implanted semiconductors, electrooptic components formed by ion implantation, general principles that determine most luminescent systems, effects of implantation temperature, luminescence centers in LiF-Mg-Ti radiation dosimeters, and use of line spectra in defect studies. In the LiF system, the luminescence bands are broad, and if alternative versions of the same complex exist, they cannot be resolved from the spectra. The addition, by implantation, of ions with incomplete inner electron shells opens up new possibilities as the lattice distortions of the free-ion energy levels are strongly perturbed by the defects in the neighborhood of the ion.

Optical Effects of Ion Implantation

This updated version of the popular handbook further explains all aspects of physical vapor deposition (PVD) process technology from the characterizing and preparing the substrate material, through deposition processing and film characterization, to post-deposition processing. The emphasis of the new edition remains on the aspects of the process flow that are critical to economical deposition of films that can meet the required performance specifications, with additional information to support the original material. The book covers subjects seldom treated in the literature: substrate characterization, adhesion, cleaning and the processing. The book also covers the widely discussed subjects of vacuum technology and the fundamentals of individual deposition processes. However, the author uniquely relates these topics to the practical issues that arise in PVD processing, such as contamination control and film growth effects, which are also rarely discussed in the literature. In bringing these subjects together in one book, the reader can understand the interrelationship between various aspects of the film deposition processing and the resulting film properties. The author draws upon his long experience with developing PVD processes and troubleshooting the processes in the manufacturing environment, to provide useful hints for not only avoiding problems, but also for solving problems when they arise. He uses actual experiences, called 'war stories', to emphasize certain points. Special formatting of the text allows a reader who is already knowledgeable in the subject to scan through a section and find discussions that are of particular interest. The author has tried to make the subject index as useful as possible so that the reader can rapidly go to sections of particular interest. Extensive references allow the reader to pursue subjects in greater detail if desired. The book is intended to be both an introduction for those who are new to the field and a valuable resource to those already in the field. The discussion of transferring technology between R&D and manufacturing provided in Appendix 1, will be of special interest to the manager or engineer responsible for moving a PVD product and process from R&D into production. Appendix 2 has an extensive listing of periodical publications and professional societies that relate to PVD processing. The extensive Glossary of Terms and Acronyms provided in Appendix 3 will be of particular use to students and to those not fully conversant with the terminology of PVD processing or with the English language. This title is fully revised and updated to include the latest developments in PVD process technology. It includes 'War stories' drawn from the author's extensive experience emphasize important points in development and manufacturing. Appendices include listings of periodicals and professional societies, terms and acronyms, and material on transferring technology between R&D and manufacturing.

Handbook of physical vapor deposition (PVD) processing

Ion bombardment of solids

Experimental studies of 10-40-keV ${\mathrm{Xe}}^{+}$ ion bombardment of Si at polar incidence angles between 0\ifmmode^\circ\else\textdegree\fi{} and 45\ifmmode^\circ\else\textdegree\fi{} to the surface normal at temperatures between 100 and 300 K show little roughening for near normal incidence but ripple production for 45\ifmmode^\circ\else\textdegree\fi{} incidence. It is shown that inclusion of the directed flux of atoms parallel to the surface and generated by ion bombardment in a stochastic differential equation description of the dynamics of surface evolution during sputtering erosion can induce smoothing for near-normal ion incidence. For oblique incidence, roughening and ripple production occurs with a late stage dynamics dictated by the competition between curvature-dependent sputtering processes and surface relaxation (which is also, probably, irradiation motivated), gradient-dependent sputtering, and other higher-order effects.

Roughening and ripple instabilities on ion-bombarded Si.

A theory is developed for the sputtering of amorphous solid by an ion beam and the changes in surface topography to which this sputtering leads. It is shown that surfaces which have pinning regions, such as vertical steps and included impurities, reach an equilibrium in which cones are developed on the surface. The theory is compared with several experimental observations of such conical development.

The equilibrium topography of sputtered amorphous solids

Theories of topographic surface development during ion bombardment fall broadly into two categories, one based upon erosion of intersecting planes [1] and the other on a point by point erosion basis [2–4]. A recent paper by Barber et al [5] has shown how, in semiquantitative fashion, an earlier theory by Frank [6] on chemical dissolution or growth of crystals, can be developed to encompass the ion sputtering case. This theory itself is based upon the kinematic wave equation outlined by Lighthill and Whitham [7, 8] and applies to problems of river flooding [7] and traffic flow [8]. In the present communication, the earlier topographic development theories are shown to fit precisely and analytically into the Frank development of the kinematic wave treatment and it is also shown how the occurrence of sharp angled cones formed on surfaces can be analytically and unequivocally predicted.

The growth of topography during sputtering of amorphous solids

A review is presented of the mathematical treatment of the development of surface topography of amorphous materials bombarded by an energetic beam of particles. In the first section the relevant analytical equations are presented and extended to include surface diffusion. In general the complete analytical approach is shown to be intractable, but in the second section some of the equations are adapted to suit computer programmes which allow calculation of the development of a surface contour provided the original contour and the functional relationship between sputtering coefficient and angle (S(θ)) are specified. Finally, geometrical construction techniques, which allow the topographical development to be predicted, are discussed and a new cursor, which evolves from the appropriate S,θ relationship, is shown to be significantly simpler to use than the erosion slowness curve when making a geometrical construction of the evolving surface.

G. Carter

Papers

Ion bombardment of solids

Roughening and ripple instabilities on ion-bombarded Si.

The equilibrium topography of sputtered amorphous solids

The growth of topography during sputtering of amorphous solids

Analytical modelling of sputter induced surface morphology