| Ion bombardment is a widely used technique to modify the properties of materials for technological applications. In recent years, surface evolution during ion bombardment has also attracted considerable fundamental interest because of the desire to better understand the physical processes occurring at the surface and the frequent instability of surfaces to the spontaneous formation of nanostructures during bombardment.; In this research, the surface morphology evolution of Silicon(100) and Gallium Antimonide(100) during low energy Argon ion bombardment was studied using real-time grazing-incidence small angle X-ray scattering and ex-situ atomic force microscopy.; The surface morphology evolution of Si during ion bombardment as a function of substrate temperature was examined. Although, the surface was amorphized during bombardment at room temperature, above approximately 400°C a transition from amorphous to crystalline structure occurred. Above 500°C, the surface remained crystalline and the growing corrugations exhibited dynamic scaling with power law growth in amplitude and characteristic length scale.; The ripple formation by off normal incidence low energy ion bombardment and ripple smoothening by normal incidence ion bombardment at room temperature were studied. Using real-time X-ray scattering, an exponential growth of the intensities during ripple formation was observed confirming that the early time kinetics obeyed the Bradley-Harper model. However, at later times the growth slowed and deviated from the predictions of the linear model. Ripple smoothening experiments, on the other hand, showed that the ripple structures eroded during normal incidence ion bombardment, possibly due to an additional lateral atomic smoothening mechanism active at these incidence angles. The real-time measurements showed that the small length scales decayed faster than the large length scales as predicted by the linear model, however the decay mechanisms were more complex than expected from existing linear theory.; It was observed that, although Si surfaces remained smooth during bombardment at room temperature when a small amount of Molybdenum atoms was supplied to the surface during ion bombardment, correlated structures with two different characteristic length scales developed. The shorter length scale features ("dots") coarsened with time until they reached a constant spatial wavelength. The longer length scale corrugations associated with kinetic roughening, however, continued to grow in amplitude during bombardment. The evolution of this kinetic roughening could be described by the Family-Vicsek scaling hypothesis. A new noise term associated with inhomogeneities in local relaxation was proposed to quantitatively explain the early time kinetics. In addition, in-situ wafer curvature measurements were performed during ion bombardment to study the real-time stress state of the surface. The measurements showed that initially a compressive stress developed during bombardment, likely due to amorphization of the surface. However, seeding caused a larger tensile stress to develop with further bombardment, possibly due to the formation of higher density regions around the Mo seed atoms on the surface. The effects of this large tensile stress on the surface instability and the formation of the nanodots were also examined.; Simulations of existing continuum equations of surface morphology evolution during normal incidence ion bombardment at room temperature were performed to study the effects of individual terms on the surface morphology, as well as their relations with each other. It was observed that the noisy Kuramoto-Sivashinsky model could only qualitatively predict the surface evolution, but could not reproduce all of the experimental results.; Finally, the morphology evolution of GaSb(100) surfaces during ion bombardment at different energies was also studied. Formation of correlated nanodots with a length scale of approximately 30... |