Semiconductor alloys such as silicon-germanium (SiGe) offer attractive environments for engineering quantum-confined structures that are the basis for a host of current and future optoelectronic devices. Although vertical stacking of such structures is routinely achieved via heteroepitaxy, lateral manipulation has proven much more challenging. I describe a new approach that suggests that a patterned elastic stress field generated with an array of nanoscale indenters in an initially compositionally uniform SiGe substrate will drive atomic interdiffusion, leading to compositional patterns in the near-surface region of the substrate. While this approach may offer a potentially efficient and robust pathway to producing laterally ordered arrays of quantum-confined structures, there is a large set of parameters important to the process. Thus, it is difficult to consider this approach using only costly experiments, which necessitates detailed computational analysis. First, I review computational approaches to simulating the long length and time scales required for this process, and I develop and present a mesoscopic model based on coarse-grained lattice kinetic Monte Carlo that quantitatively describes the atomic interdiffusion processes in SiGe alloy film subjected to applied stress. I show that the model provides predictions that are quantitatively consistent with experimental measurements, and I examine the impact of basic indenter geometries on the patterning process. Second, I extend the model to investigate the impact of several process parameters, such as more complicated indenter shapes and pitches. I find that certain indenter configurations produce compositional patterns that are favorable for use as lateral arrays of quantum-confined structures. Finally, I measure a set of important physical parameters, the so-called “activation volumes” that describes the impact of stress on diffusion. The values of these parameters are not well established in the literature. I make quantitative connections to the range of values found in the literature and characterize the effects of different stress states on the overall patterning process. Finally, I conclude with ideas about alternative pathways to quantum confined structure generation and possible extensions of the framework developed.