A Reaction Diffusion Model Of Pattern Formation In Clustering Of Adatoms On Silicon Surfaces

We study a reaction diffusion model which describes the formation of patterns on surfaces having defects. Through this model, the primary goal is to study the growth process of Ge on Si surface. We consider a two species reaction diffusion process where the reacting species are assumed to diffuse on the two dimensional surface with first order interconversion reaction occuring at various defect sites which we call reaction centers. Two models of defects, namely a ring defect and a point defect are considered separately. As reaction centers are assumed to be strongly localized in space, the proposed reaction-diffusion model is found to be exactly solvable. We use Green's function method to study the dynamics of reaction diffusion processes. Further we explore this model through Monte Carlo (MC) simulations to study the growth processes in the presence of a large number of defects. The first passage time statistics has been studied numerically. Copyright 2012 Author(s). This article is distributed under a Creative Commons Attribution 3.0 Unported License. [http://dx.doi.org/10.1063/1.4757592]Microelectronics Research Cente

Extended point defects in crystalline materials: Ge and Si

B diffusion measurements are used to probe the basic nature of self-interstitial 'point' defects in Ge. We find two distinct self-interstitial forms - a simple one with low entropy and a complex one with entropy ~30 k at the migration saddle point. The latter dominates diffusion at high temperature. We propose that its structure is similar to that of an amorphous pocket - we name it a 'morph'. Computational modelling suggests that morphs exist in both self-interstitial and vacancy-like forms, and are crucial for diffusion and defect dynamics in Ge, Si and probably many other crystalline solids

Point Defect Dynamics in Two-Dimensional Colloidal Crystals

We study the topological configurations and dynamics of individual point defect vacancies and interstitials in a two-dimensional colloidal crystal. Our Brownian dynamics simulations show that the diffusion mechanism for vacancy defects occurs in two phases. The defect can glide along the crystal lattice directions, and it can rotate during an excited topological transition configuration to assume a different direction for the next period of gliding. The results for the vacancy defects are in good agreement with recent experiments. For the interstitial point defects, which were not studied in the experiments, we find several of the same modes of motion as in the vacancy defect case along with two additional diffusion pathways. The interstitial defects are more mobile than the vacancy defects due to the more two-dimensional nature of the diffusion of the interstitial defects.Comment: 8 pages, 9 postscript figures. Version to appear in Phys. Rev.

Space-charge mechanism of aging in ferroelectrics: an exactly solvable two-dimensional model

A mechanism of point defect migration triggered by local depolarization fields is shown to explain some still inexplicable features of aging in acceptor doped ferroelectrics. A drift-diffusion model of the coupled charged defect transport and electrostatic field relaxation within a two-dimensional domain configuration is treated numerically and analytically. Numerical results are given for the emerging internal bias field of about 1 kV/mm which levels off at dopant concentrations well below 1 mol%; the fact, long ago known experimentally but still not explained. For higher defect concentrations a closed solution of the model equations in the drift approximation as well as an explicit formula for the internal bias field is derived revealing the plausible time, temperature and concentration dependencies of aging. The results are compared to those due to the mechanism of orientational reordering of defect dipoles.Comment: 8 pages, 4 figures. accepted to Physical Review

Ab initio studies of defect concentrations and diffusion in metal oxides

This work presents a methodology for determining the concentrations and diffusion coefficients of point defects in metal oxides using ab initio calculations of defect formation energies and diffusion barriers, and the binding energies of defect-impurity clusters. The methodology is applied to analyse the long-standing mysteries surrounding the mechanism of self-diffusion in α-Al2O3. Al2O3 is a prototypical large band gap ceramic with extensive applications, many of which depend on its defect chemistry. In particular, point defect concentrations, that vary with temperature and impurity doping, govern diffusion properties such as creep, sintering, or the oxidation rate of Al-containing alloys. Experimental measurements of the self-diffusion coefficients in bulk alumina reveal three important truths that theory cannot reconcile, collectively termed the ’corundum conundrum’. First, large experimental activation energies for oxygen and aluminum diffusion and low theoretical formation energies imply unreasonably high diffusion barriers of ∼ 5eV. Second, aluminum diffusion is orders of magnitude faster than oxygen diffusion. Third, the oxygen diffusion coefficient is relatively insensitive to aliovalent doping, increasing by a factor of 100 on heavy Mg2+-doping, and decreasing by a similar amount on Ti4+-doping. We attempt to resolve this conundrum by calculating the formation energies and binding energies of a raft of native point defects and defect-impurity clusters as functions of temperature T and oxygen partial pressure pO2 , and the diffusion barriers of the native defects, using density functional theory. We then use a thermodynamic mass action approach to determine the concentrations of the defects and clusters, and the diffusion coefficients of the defects, as functions of T, pO2 , and the concentrations of aliovalent dopants, [Mg2+] and [Ti4+]. In the process, we discover new ground-state defect structures for the aluminum vacancy and oxygen interstitial, and demonstrate that diffusion of aluminum vacancies and interstitials occurs by extended vacancy and interstitialcy mechanisms, and oxygen interstitials by a dumbbell interstitialcy mechanism, all of which yield much lower migration barriers than previous theory. Unfortunately, the results do not demonstrate the experimentally-found insensitivity of the oxygen diffusivity to aliovalent doping. This could be an artefact of approximations within density functional theory and our methodology, and we show that modest changes in the calculated binding energies lead to significant defect clustering. This defect clustering could result in a buffering mechanism that can explain the insensitivity of the diffusivity to aliovalent doping, and may occur in other ionic materials. More accurate calculations, employing hybrid functionals or quantum Monte Carlo methods, may be necessary to elucidate this effect, but are currently computationally intractable for our purposes