R. Collins

A first order diffusion approximation to atomic redistribution during ion bombardment of solids, II. finite range approximation

Abstract An improved diffusion approximation, in which diffusion enhancement operates only over a finite depth, to model atomic redistribution resulting from recoil and cascade mixing during ion bombardment of solids is described, it is shown that this model correctly simulates the main results of the more complex linear cascade atomic collision calculations of positive mean depth shifts, negative peak shifts, broadenings and exponential tails in surface concentration of diffusant marker species during sputter erosion. The analytic method of generalisation to any arbitrary and more realistic diffusivity-depth profiles is also outlined.

Preferential sputtering of binary alloys with diffusion: The equilibrium distribution

Abstract The preferential sputtering of a binary alloy is considered using diffusion theory. It is shown that this leads to non-linear-terms in both the bulk diffusion equation and the boundary conditions. The steady-state solution is investigated in detail, and the results indicate that some of the non-linearities are negligible, while others cannot be omitted without appreciable errors. The surface depletion of the more volatile component is much smaller than earlier diffusion studies had suggested.

The influence of preferential enhanced diffusion on composition changes in sputtered binary solids

Abstract The preferential sputter enrichment or depletion of a species in a binary solid is a well established experimental observation. This composition change is usually found to occur over a depth similar to that of the penetration depth of the sputtering projectile. This paper therefore considers a model for preferential sputtering based upon a preferentially enhanced diffusion of one species over a finite depth in the solid which acts as a continuous atomic supply to the surface. Exact solutions are determined for steady state surface and depth distributions of the composition ratio of the two species for the time dependent behaviour of these concentration distributions. The results are compared with models which assume equal diffusion enhancement of both species over both limited and infinite depth and with experimental studies.

The diffusion approximation in atomic mixing

Abstract A brief review is given of the diffusion approximation for atomic mixing by ion beams in the dilute implant case. The case of an initially thin implant is treated, and the shift and broadening of the subsequent sputtering erosion profile are calculated. The results are shown to be in reasonable agreement with those from transport theory. Saturation effects at high implant densities are considered. The concept of a “collective current” is introduced and used to modify the diffusion theory to give a nonlinear equation applicable to saturation conditions. Some qualitative features of this equation are discussed.

The spatial distribution of ions implanted into solids subject to diffusion and surface sputtering

Abstract The depth distributions of ions implanted into solids is evaluated : heoretically for the situation where, following implantation and degradation to rest, each ion can diffuse in the solid whilst simultaneously the surface of the solid is eroded via the sputtering process. Time dependent and equilibrium solutions of the depth distribution or concentration profiles and the total quantities of trapped atoms are determined for cases where (a) the surface is a perfectly transparent boundary for diffusing ions, allowing immediate escape by diffusion only, and (b) the escape of diffusing ions takes place by surface erosion only, the diffusion rate becoming zero at the surface. Two methods of approach for situation (a) are examined-the Laplace transformation technique of the defining partial differential equation and a novel image method. Solutions are compared with earlier work and shown to correspond where appropriate.

Factors determining radiation-induced mixing at interfaces

Abstract A review is given of the principal mechanisms contributing to atomic mixing produced by ion beams at initially well-defined interfaces between solid phases. Their relative importance is discussed in the light of available experimental evidence, and a critical survey is given of current mathematical models. The case of a thin interior implant layer is included. Those aspects of surface sputtering of direct relevance to the construction of the mixing equations are examined. Mixing mechanisms considered are ballistic relocation, diffusion, radiation-induced segregation, and drifts induced by chemical affinities of the elements concerned, together with constraints on all these from packing (Kirkendall) effects. Ballistic terms are subdivided into direct-recoil and cascade contributions. A brief review is given of the established methods of modelling them by using relocation integral cross-sections, and also the limitations and advantages of their approximation by differential equations of Fokker-Plan...

On the “collective current” concept in the theory of atomic mixing

Abstract The concept of a “collective current” of atoms was introduced into atomic mixing theory to treat the bulk relocation of material when extra atoms are injected into a region already full. In the earlier treatment these currents were treated as having a sharp onset when atomic densities reached saturation. This simplication is here critically re-examined, and a revised formalism is proposed which is physically more realistic. A discussion is also given of the use of the collective current concept in the more general transport theory of atomic mixing.

Atomic mixing of silver into a silicon substrate using a 45 keV beam of Ar+ ions

Abstract In separate experiments, Si substrates were coated with Ag layers of thickness ranging from 219 A to 371 A. These were then irradiated with 45 keV Ar+ ions, producing Ag-Si mixing, together with surface erosion by sputtering. The successive internal Ag profiles were measured by RBS techniques, and are presented graphically up to a maximum fluence of 1.85 × 1016 ions cm−2. A corresponding set of profiles has been computed using a diffusion formalism for atomic mixing developed earlier by the authors. A critical comparison between the theoretical and experimental results is given.

Huygens' construction for successive profiles of a surface undergoing sputter erosion

Abstract The steadily eroding profile of an ion-bombarded solid surface has been extensively studied using the method of characteristics in a kinetic-wave formulation. An alternative method is presented here, based on a construction analogous to that of Huygens for an optical wave-front. It is shown to be formally equivalent to the earlier method in the limit of vanishingly small dose increment, but to confer some advantages in stability on the resulting computer program. Results are presented for the erosion of some simple two-dimensional profiles of an isotropic material. An outline is also given of the extension to surfaces in three dimensions, and to anisotropic materials.

Non-linear differential equation for atomic mixing: 2. Numerical results

Abstract A discussion is given of a non-linear Fokker-Planck (diffusion-type) differential equation for atomic mixing, developed in an earlier paper by the authors. Some simplifications of the earlier theory are presented, together with a sign-correction. Numerical results are given, obtained by a recently-developed machine program, for the case of an initial uniform layer of silver on a silicon substrate, irradiated by a 45 keV beam of Ar + ions at normal incidence.