Morphological Development in Strained Alloy Films

Suny At Buffalo, Amherst NY

Investigators

Abstract

Strained solid films are an important component of newly-developed electronic devices such as the quantum-well semiconductor and the bipolar heterojunction transistor. The strain in the film is essential to these devices because it modifies the electronic band gap in the device to generate the desired electronic properties. The strain in the film, however, is also responsible for the generation of instabilities during growth, resulting in nonplanar films with inhomogeneous microstructure, such as "quantum dots" and "quantum wires". Because of the strain localization associated with the inhomogeneous microstructure, the resulting electronic properties can be enhanced due to quantum electronic effects. Thus, there has been intense interest in natural "self-assembly" of quantum dot and quantum wire morphologies during the growth process. The research of the PI will focus on the analysis of mathematical models for the development of such inhomogeneous microstructures in strained alloy films. The theoretical description of morphological development in strained films is difficult because of the major role that elastic strain plays in the development of the morphology; the generic case is that of a free boundary or moving boundary elasticity problem. While there has been a significant amount of progress made on the mathematical modeling of the growth of single-component strained films, models for the growth of alloy strained films are still in their infancy. The proposed research will examine the microstructure generated from the new alloy film models as nonlinear solutions to the moving boundary elasticity problem using a combination of both analytical and numerical techniques. The research will focus on three areas relating to the formation of microstructure in strained alloy films. First, the possibility of generating a new type of microstructure based on self-assembled compositional modulations in thick films will be investigated by a bifurcation analysis of the nonlinear free boundary problem. Second the growth of inhomogeneous alloy quantum dots will be described using a hybrid asymptotic and numerical approach, and the theoretical predictions will be compared to experiments carried out in parallel by a collaborator. Finally the appropriate mathematical modeling of facet corners in strained alloy crystals will be examined through a model which incorporates atomic-scale behavior in a macroscopic model for film growth. The overall goal of the research is to develop mathematical approaches that enable a comprehensive theoretical description of nanostructure formation in strained alloy films. In nanoscale electronic devices, strained solid layers play an important role because of the improved electronic properties of the strained material. While flat, planar strained films have been used successfully, they can be susceptible to instabilities during the growth process and develop nanoscale bumps ("dots"). These nanoscale "quantum dots" have been found to give superior electronic behavior because of quantum-physics electronic effects. There is thus interest in growing quantum dots with a controlled size and spacing to give a material with specified or optimum electronic properties. The research supported by this grant focuses on the development of mathematical models for describing the formation of quantum dots and other nanostructures from detailed modeling of the physics of the growth process. In particular, the work will focus on the growth of alloy films, for which theoretical understanding not well developed. The goal of the theoretical work will be to evaluate the effect of different growth parameters to guide the development of "optimum" quantum dot structures. To solve the mathematical problem, advanced mathematical techniques will be developed and applied to determine the characteristics of the solutions and how they depend on the material properties and growth conditions. In addition, the research will also address the difficult question of how to incorporate atomic-level behavior into a large scale model for strained film growth. The theoretical predictions will be compared to experiments conducted in parallel by a collaborator here at the University at Buffalo. The results of the work will be twofold. The understanding of how to treat the mathematical issues of strained alloy film growth well will be improved. Also, a useful "parameter map" describing the important physical processes that influence the development of nanostructures will be developed. This parameter map can be used as a guide to the design of strained alloy nanostructures with specified or optimum properties.