Modeling and Analysis of an Electrochemical Nanocell

University Of Akron, Akron OH

Investigators

Abstract

Proposal: DMS-0305577 PI: Gerald W. Young [gwyoung@uakron.edu] Institution: University of Akron Title: MODELING AND ANALYSIS OF AN ELECTROCHEMICAL NANOCELL ABSTRACT This project proposes to develop mathematical models for the electrochemical nanocell that forms during scanned probe oxidation. Scanned probe oxidation is a lithographic technique for producing nanoscale patterns on a substrate. These patterns have been employed successfully as an etch mask for wet and dry processes, and as chemical and biological templates. The increased demand for such high quality nanodevices requires better understanding of the growth processes involved in their fabrication. Although data on nanodeposition techniques have been collected over the past decade, investigators are only beginning to develop a qualitative picture of these processes, and are far from a complete quantitative understanding. The proposed research addresses both of these timely needs. Because of the varied and coupled physical phenomena involved (electromagnetic, chemical, thermal, etc.), the development of mathematical models for nanodeposition requires a team of individuals with complementary areas of expertise, and must proceed hand-in-hand with experimental validations. Such a team, consisting of interdisciplinary applied mathematicians, scientists and engineers is already active at The University of Akron and working in the area of nanomechanics and nanostructures. This team proposes to develop models for scanned probe oxidation that will, 1) explain experimental observations that are not well understood, and 2) suggest the range of parameters that is optimal for nanoscale growth. The team intends to develop appropriate solution and analysis procedures for these complex models, and test the validity of the models through comparison with experiments. The models will focus attention on the need to develop efficient solution strategies to solve complicated systems in the presence of noise. Further, the models developed in this work will lead to a significant number of problems in analysis. Questions on well-posedness, the use of similarity solutions, and bounds on solutions for the class of problems represented by the models will arise from the proposed efforts. This project proposes to develop mathematical models for the electrochemical nanocell that forms during scanned probe oxidation. Scanned probe oxidation is a critical technology for writing nanometer-size oxide patterns on the surface of a substrate. These oxide patterns can be used to prototype nanoscale masks, templates and devices. The proposed combination of modeling and experimental efforts will help to address the fundamental unanswered questions concerning the physics and chemistry of nanoscale structure formation and properties. In particular this project will provide the understanding necessary to control the height and width of oxide lines to produce precise nanoscale patterns. In addition to its impact on scientific research, this project will enhance graduate and undergraduate studies in the disciplines of mathematics, physics, chemistry, and engineering. Students participating in the program will, 1) be exposed tointerdisciplinary research involving sophisticated mathematical modeling and experiments, and 2) be trained to work within a multi-disciplinary environment. The educational training at both the graduate and undergraduate level will have a long-term impact on the mathematical sciences, providing students with exposure to a unique interdisciplinary environment and inspiring them to pursue careers in this cutting-edge area of national interest.