Calculations of Step -Edge Currents on Crystal Surfaces
Pflueger, Randall John
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https://hdl.handle.net/2142/82790
Description
Title
Calculations of Step -Edge Currents on Crystal Surfaces
Author(s)
Pflueger, Randall John
Issue Date
2006
Doctoral Committee Chair(s)
Greene, Joseph E.
Department of Study
Materials Science and Engineering
Discipline
Materials Science and Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mineralogy
Language
eng
Abstract
In this thesis, I present the results of research on methods for calculating adatom currents in the vicinity of steps on crystal surfaces. I first focus on adatom interactions with an isolated ledge (no adatoms hopping past kinks to adjacent ledges) along a single-atomic-height step, and develop an exact, compact, closed form representation of the probability density function (PDF) for an adatom undergoing a random walk along such a ledge. The representation allows for an arbitrary energy barrier structure between adjacent binding sites and accounts for the possibility of desorption from the ledge to adjacent terraces. This and related PDFs are used to construct kinetic reactive-convective boundary conditions for terrace adatom continuity equations. Solutions of these continuity equations and boundary conditions are given for one- and two-domain surfaces, and the nature of short- and long-range adatom currents on these vicinal surfaces is explained. Next, I obtain an exact representation for the PDF describing long-range adatom migration along a step comprised of identical unipolar ledges. Based upon this long-range PDF, I develop a procedure for calculating the diffusion coefficient of adatoms migrating along the step-edge, a modification of the limiting process used in computing the Einstein diffusion coefficient, in which the transit time of adatoms across a homogeneous region of the step-edge is evaluated iteratively while compensating for the effects of adatom desorption to the terraces.
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