Modeling and Analysis of an Electrochemical Nanocell

提案：DMS-0305577PI：Gerald W. Young [gwyoung@uakron.edu]机构：阿克伦大学标题：电化学纳米电池的建模和分析摘要该项目建议开发扫描探针氧化过程中形成的电化学纳米电池的数学模型。 扫描探针氧化是一种在基板上产生纳米级图案的光刻技术。 这些图案已成功用作湿法和干法工艺的蚀刻掩模以及化学和生物模板。 对这种高质量纳米器件的需求不断增加，需要更好地了解其制造过程中涉及的生长过程。 尽管过去十年已经收集了有关纳米沉积技术的数据，但研究人员才刚刚开始对这些过程进行定性描述，距离完整的定量理解还很远。 拟议的研究解决了这两个及时的需求。 由于所涉及的物理现象多种多样（电磁、化学、热等），纳米沉积数学模型的开发需要一个由具有互补专业领域的人员组成的团队，并且必须与实验验证齐头并进。这样一个由跨学科应用数学家、科学家和工程师组成的团队已经活跃在阿克伦大学，致力于纳米力学和纳米结构领域的工作。 该团队建议开发扫描探针氧化模型，该模型将：1）解释尚未充分理解的实验观察结果，2）提出最适合纳米级生长的参数范围。 团队打算针对这些复杂模型开发合适的解决方案和分析程序，并通过与实验的比较来检验模型的有效性。 这些模型将重点关注开发有效的解决策略以解决存在噪声的复杂系统的需求。 此外，这项工作中开发的模型将导致大量的分析问题。 关于适定性、相似性解决方案的使用以及模型所代表的一类问题的解决方案的界限的问题将在拟议的工作中出现。该项目建议为扫描探针氧化过程中形成的电化学纳米电池开发数学模型。 扫描探针氧化是在基材表面写入纳米尺寸氧化物图案的关键技术。 这些氧化物图案可用于制作纳米级掩模、模板和器件的原型。 所提出的建模和实验工作的结合将有助于解决有关纳米级结构形成和性质的物理和化学的基本未解答问题。 特别是，该项目将提供控制氧化物线的高度和宽度以产生精确的纳米级图案所需的理解。 除了对科学研究的影响外，该项目还将加强数学、物理、化学和工程学科的研究生和本科生的研究。 参与该计划的学生将：1）接触涉及复杂数学建模和实验的跨学科研究，2）接受在多学科环境中工作的培训。 研究生和本科生的教育培训将对数学科学产生长期影响，为学生提供独特的跨学科环境，并激励他们在这个国家利益的前沿领域追求职业生涯。

Proposal: DMS-0305577PI: Gerald W. Young [gwyoung@uakron.edu]Institution: University of AkronTitle: MODELING AND ANALYSIS OF AN ELECTROCHEMICAL NANOCELLABSTRACTThis 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.