A Partial Differential Equation (PDE) based model combining surface electromigration and wetting is developed for the analysis of the morphological instability of mono-crystalline metal films in a high temperature environment typical to operational conditions of microelectronic interconnects. The atomic mobility and surface energy of such films are anisotropic, and the model accounts for these material properties. The goal of modeling is to describe and understand the time-evolution of the shape of film surface. I will present the formulation of a nonlinear parabolic PDE problem for the height function h(x,t) of the film in the horizontal electric field, followed by the results of the linear stability analyses and computations of fully nonlinear evolution equation.
","abstract_html":"<p>A Partial Differential Equation (PDE) based model combining surface electromigration and wetting is developed for the analysis of the morphological instability of mono-crystalline metal films in a high temperature environment typical to operational conditions of microelectronic interconnects. The atomic mobility and surface energy of such films are anisotropic, and the model accounts for these material properties. The goal of modeling is to describe and understand the time-evolution of the shape of film surface. I will present the formulation of a nonlinear parabolic PDE problem for the height function <em>h</em>(<em>x</em>,<em>t</em>) of the film in the horizontal electric field, followed by the results of the linear stability analyses and computations of fully nonlinear evolution equation.<em></em></p>","abstract_has_math":false,"creators":["Cinar, Selahittin"],"institution":null,"degree_name":"Master of Science","degree_level":null,"degree_discipline":"Department of Mathematics","degree_department":null,"school":null,"contributors":["Mikhail Khenner (Director), Mark Robinson, Richard Schugart"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-05-01T07:00:00Z","date_published":"2014-05-01T07:00:00Z","updated_at":"2026-07-24T06:08:39Z","subjects":["Differential Equations-Partial","Electrodiffusion","Numerical Analysis","Applied Mathematics","Numerical Analysis and Computation","Partial Differential Equations","Physics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.wku.edu/theses/1368","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Mikhail Khenner (Director), Mark Robinson, Richard Schugart"]},{"key":"dc:creator","label":"Author","values":["Cinar, Selahittin"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Department of Mathematics"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Differential Equations-Partial","Electrodiffusion","Numerical Analysis","Applied Mathematics","Numerical Analysis and Computation","Partial Differential Equations","Physics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.wku.edu/theses/1368"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["A Partial Differential Equation (PDE) based model combining surface electromigration and wetting is developed for the analysis of the morphological instability of mono-crystalline metal films in a high temperature environment typical to operational conditions of microelectronic interconnects. The atomic mobility and surface energy of such films are anisotropic, and the model accounts for these material properties. The goal of modeling is to describe and understand the time-evolution of the shape of film surface. I will present the formulation of a nonlinear parabolic PDE problem for the height function h(x,t) of the film in the horizontal electric field, followed by the results of the linear stability analyses and computations of fully nonlinear evolution equation.
"]},{"key":"dc:title","label":"Title","values":["Analysis of a Partial Differential Equation Model of Surface Electromigration"]}]}],"canonical_facts":{"dc:contributor":["Mikhail Khenner (Director), Mark Robinson, Richard Schugart"],"dc:creator":["Cinar, Selahittin"],"dc:description.abstract":["A Partial Differential Equation (PDE) based model combining surface electromigration and wetting is developed for the analysis of the morphological instability of mono-crystalline metal films in a high temperature environment typical to operational conditions of microelectronic interconnects. The atomic mobility and surface energy of such films are anisotropic, and the model accounts for these material properties. The goal of modeling is to describe and understand the time-evolution of the shape of film surface. I will present the formulation of a nonlinear parabolic PDE problem for the height function h(x,t) of the film in the horizontal electric field, followed by the results of the linear stability analyses and computations of fully nonlinear evolution equation.
"],"dc:identifier":["https://digitalcommons.wku.edu/theses/1368"],"dc:subject":["Differential Equations-Partial","Electrodiffusion","Numerical Analysis","Applied Mathematics","Numerical Analysis and Computation","Partial Differential Equations","Physics"],"dc:title":["Analysis of a Partial Differential Equation Model of Surface Electromigration"],"dc:type":["Thesis"],"thesis:degree_discipline":["Department of Mathematics"],"thesis:degree_name":["Master of Science"]},"updated_at":"2026-07-24T06:08:39Z"}