Mathematical Sciences: Mathematical Modeling of Island Formation in Strained Semiconductor Films

数学科学：应变半导体薄膜中岛形成的数学模型

• 批准号: 9622930
• 负责人: Brian Spencer
• 金额: $ 7.84万
• 依托单位: SUNY at Buffalo
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-06-01 至 2000-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9622930&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Modeling; Island; Formation

9622930 Spencer The objective of this research is to develop mathematical models to predict and control morphology development in strained solid films, which are of great technological importance in semiconductor device applications. The research project focuses on the consequences of the stress-driven morphological instability which occurs during film growth. In particular, the formation of the "island" morphology will be explained in terms of mathematical models for the morphological instability. The research program consists of two projects, one focusing on single-component films, the second focusing on alloy films. In the first project, a "state of the art" model for the formation of three-dimensional islands will be developed. This model will include a crucial treatment of the wetting layer between the film and its underlying substrate. In the second project, a basic model will be developed for the more complicated problem of morphology development in alloy films, where composition variations and stress variations are coupled. In both projects the mathematical models are nonlinear free boundary problems for the shape of the film. These problems will be analyzed using applied mathematical techniques which include analytical, asymptotic, and numerical methods. In particular, an asymptotic description for the island shape will be derived which takes advantage of the fact that islands generally have a much smaller height than width. The results of the work will be compared to observations of islands in strained film systems from both collaborative research projects and published experimental results. The models will be evaluated to determine the extent to which they can be used to predict and control morphologies, as well as to determine future directions for improving mathematical models of strained film growth as part of a long-term research program. %%% The objective of this research is to develop mathematical models to predict and control mo rphology development in strained solid films. Strained solid films are of great technological importance in semiconductor device applications. The strained films are grown from a vapor through the deposition of the solid film onto an underlying substrate of a different material. Because of the bonding of the film to the substrate, the film is grown in a state of stress. During the growth of these films, the stresses in the film can lead to the formation of bumps, or "islands." The presence of these islands has a crucial effect on the electronic properties of the thin film device, so a knowledge of what controls island formation enables a better control over the electronic properties of the strained film device. The objective of this research is to describe island formation from physically-derived mathematical models of the film growth process. This mathematical model represents a complementary alternative to traditional experiment-based research on strained films. The primary benefit of developing such a model is that it allows one to quickly and easily determine how the growth of the film is affected by the different material parameters and process parameters. Thus, the model has three main applications in the development and production of strained solid films. Firstly, by changing the parameters in the model, the model can be used as a low-cost way to "experiment" with different materials and growth configurations. Secondly, the mathematical model can be used to help engineer materials by determining the necessary process inputs required to achieve a strained solid film with specified physical and electronic properties. Finally, the mathematical model can assist in the determination of optimum and/or acceptable processing conditions for the manufacture of strained films in industry. ***

9622930 Spencer 这项研究的目的是开发数学模型来预测和控制应变固体薄膜的形态发展，这在半导体器件应用中具有重要的技术重要性。 该研究项目的重点是薄膜生长过程中发生的应力驱动的形态不稳定的后果。 特别是，“岛”形态的形成将用形态不稳定性的数学模型来解释。 该研究计划由两个项目组成，一个重点关注单组分薄膜，第二个重点关注合金薄膜。 在第一个项目中，将开发用于形成三维岛屿的“最先进”模型。 该模型将包括对薄膜与其底层基材之间的润湿层进行关键处理。 在第二个项目中，将为合金膜中更复杂的形态发展问题开发一个基本模型，其中成分变化和应力变化是耦合的。 在这两个项目中，数学模型都是薄膜形状的非线性自由边界问题。 这些问题将使用应用数学技术进行分析，包括解析法、渐近法和数值方法。 特别是，将导出岛形状的渐近描述，该描述利用岛通常具有比宽度小得多的事实。 这项工作的结果将与合作研究项目和已发表的实验结果对应变薄膜系统中岛屿的观察结果进行比较。 将评估这些模型，以确定它们可在多大程度上用于预测和控制形态，并确定作为长期研究计划的一部分改进应变薄膜生长数学模型的未来方向。 %%% 这项研究的目的是开发数学模型来预测和控制应变固体薄膜的形态发展。 应变固体薄膜在半导体器件应用中具有重要的技术重要性。 通过将固体膜沉积到不同材料的底层基板上，应变膜从蒸气中生长出来。 由于薄膜与衬底的结合，薄膜在应力状态下生长。 在这些薄膜的生长过程中，薄膜中的应力可能导致形成凸块或“岛”。 这些岛的存在对薄膜器件的电子特性具有至关重要的影响，因此了解控制岛形成的因素可以更好地控制应变薄膜器件的电子特性。 这项研究的目的是根据薄膜生长过程的物理推导数学模型来描述岛的形成。 该数学模型代表了传统基于实验的应变薄膜研究的补充替代方案。 开发这种模型的主要好处是，它允许人们快速、轻松地确定不同材料参数和工艺参数如何影响薄膜的生长。 因此，该模型在应变固体薄膜的开发和生产中具有三个主要应用。 首先，通过改变模型中的参数，该模型可以作为一种低成本的方式来“实验”不同的材料和生长配置。 其次，数学模型可用于通过确定获得具有指定物理和电子特性的应变固体薄膜所需的必要工艺输入来帮助设计材料。 最后，数学模型可以帮助确定工业中应变薄膜制造的最佳和/或可接受的加工条件。 ***