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

点击翻译按钮获取中文摘要

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. ***