In this thesis a model involving two coupled nonlinear PDEs is developed to study instability of a two-component metal film due to horizontal electric field and in a high-temperature environment similar to operational conditions of integrated circuits. The proposed model assumes the anisotropies of the diffusional mobilities for two atomic species, and negligible stresses in the film. The purpose of the modeling is to describe and understand the time-evolution of the shape of the film surface. Toward this end, the linear stability analysis (LSA) of the initially planar film surface with respect to small shape perturbations is performed. Such characteristics of the instability as the perturbation growth rate omega and the cut-off wave number are studied as functions of key physical parameters.
","abstract_html":"<p>In this thesis a model involving two coupled nonlinear PDEs is developed to study instability of a two-component metal film due to horizontal electric field and in a high-temperature environment similar to operational conditions of integrated circuits. The proposed model assumes the anisotropies of the diffusional mobilities for two atomic species, and negligible stresses in the film. The purpose of the modeling is to describe and understand the time-evolution of the shape of the film surface. Toward this end, the linear stability analysis (LSA) of the initially planar film surface with respect to small shape perturbations is performed. Such characteristics of the instability as the perturbation growth rate omega and the cut-off wave number are studied as functions of key physical parameters.</p>","abstract_has_math":false,"creators":["Bandegi, Mahdi"],"institution":null,"degree_name":"Master of Science","degree_level":null,"degree_discipline":"Department of Mathematics","degree_department":null,"school":null,"contributors":["Mikhail Khenner (Director), Nezam Iraniparast, Lan Nguyen"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-08-01T07:00:00Z","date_published":"2014-08-01T07:00:00Z","updated_at":"2026-07-24T06:08:39Z","subjects":["Surface Diffusion","Linear Stability Analysis","Perturbation","Dispersion Relation","Wavenumber","Applied Mathematics","Dynamic Systems"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.wku.edu/theses/1386","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Mikhail Khenner (Director), Nezam Iraniparast, Lan Nguyen"]},{"key":"dc:creator","label":"Author","values":["Bandegi, Mahdi"]}]},{"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":["Surface Diffusion","Linear Stability Analysis","Perturbation","Dispersion Relation","Wavenumber","Applied Mathematics","Dynamic Systems"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.wku.edu/theses/1386"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this thesis a model involving two coupled nonlinear PDEs is developed to study instability of a two-component metal film due to horizontal electric field and in a high-temperature environment similar to operational conditions of integrated circuits. The proposed model assumes the anisotropies of the diffusional mobilities for two atomic species, and negligible stresses in the film. The purpose of the modeling is to describe and understand the time-evolution of the shape of the film surface. Toward this end, the linear stability analysis (LSA) of the initially planar film surface with respect to small shape perturbations is performed. Such characteristics of the instability as the perturbation growth rate omega and the cut-off wave number are studied as functions of key physical parameters.
"]},{"key":"dc:title","label":"Title","values":["A Coupled PDE Model for the Morphological Instability of a Multi-Component Thin Film During Surface Electromigration"]}]}],"canonical_facts":{"dc:contributor":["Mikhail Khenner (Director), Nezam Iraniparast, Lan Nguyen"],"dc:creator":["Bandegi, Mahdi"],"dc:description.abstract":["In this thesis a model involving two coupled nonlinear PDEs is developed to study instability of a two-component metal film due to horizontal electric field and in a high-temperature environment similar to operational conditions of integrated circuits. The proposed model assumes the anisotropies of the diffusional mobilities for two atomic species, and negligible stresses in the film. The purpose of the modeling is to describe and understand the time-evolution of the shape of the film surface. Toward this end, the linear stability analysis (LSA) of the initially planar film surface with respect to small shape perturbations is performed. Such characteristics of the instability as the perturbation growth rate omega and the cut-off wave number are studied as functions of key physical parameters.
"],"dc:identifier":["https://digitalcommons.wku.edu/theses/1386"],"dc:subject":["Surface Diffusion","Linear Stability Analysis","Perturbation","Dispersion Relation","Wavenumber","Applied Mathematics","Dynamic Systems"],"dc:title":["A Coupled PDE Model for the Morphological Instability of a Multi-Component Thin Film During Surface Electromigration"],"dc:type":["Thesis"],"thesis:degree_discipline":["Department of Mathematics"],"thesis:degree_name":["Master of Science"]},"updated_at":"2026-07-24T06:08:39Z"}