(574d) Formation of Ordered Nanostructure Patterns on Surfaces of Biaxially Stressed Thin Films

The development of biaxial stress in epitaxially grown semiconductor thin films due to lattice mismatch with the substrate or in other types of deposited crystalline thin films is a driving force for morphological instability of the films’ surfaces. During heteroepitaxial growth of coherently strained semiconductor thin films, quantum dots (QDs) form on the film surface beyond a critical film thickness as a result of the well-known Stranski-Krastanow growth instability. Experimental studies also have reported that, in addition to formation of such QDs, “QD pairs” or “double QDs” as well as more complex multiple QDs may form on surfaces of epitaxially grown biaxially stressed semiconductor films; ordered patterns of such multiple QDs (also known as QD molecules) have been reported to result from epitaxial growth of coherently strained layers on patterned substrate surfaces. Furthermore, other experimental studies have demonstrated formation of nanorings from QDs upon thermal annealing of biaxially stressed metallic thin films deposited on oxide substrates. Here, we report theoretical results from a systematic analysis of surface morphological evolution of biaxially stressed thin films, which explains the formation of both multiple QD and nanoring patterns that are observed experimentally on such films’ surfaces.

We have developed a surface morphological stability theory that provides a comprehensive interpretation for the formation of experimentally observed multiple QD patterns on coherently strained heteroepitaxial thin films grown on patterned semiconductor substrates. Our analysis is based on a fully nonlinear model of surface morphological evolution that accounts for biaxial stress in the film, a wetting potential contribution to the epitaxial film’s free energy, as well as film surface diffusional anisotropy. Supported by a weakly nonlinear analysis of the epitaxial film’s planar surface morphological stability, self-consistent dynamical simulations based on our model demonstrate formation of multiple QD patterns as a result of the evolution of the epitaxial film surface perturbed from its planar state with perturbations that mimic the substrate pattern. We find that, along with the Stranski-Krastanow instability, long-wavelength perturbations from the planar film surface morphology trigger another nonlinear tip-splitting instability, which is responsible for the transformation of an evolving QD into multiple QDs of smaller sizes. We establish the critical wavelength of the film surface perturbation for the onset of this nonlinear instability and predict the type of multiple QDs or QD molecules formed for given perturbation wavelength. This analysis provides a precise design rule for fabricating QD nanopatterns on coherently strained epitaxial films.

Using the same stressed film surface evolution model, we have also analyzed the formation of self-assembled nanoring (NR) patterns upon thermal annealing of biaxially stressed metallic thin films. Self-consistent numerical simulations based on our model show that the thermal stress induced in the films during their post-deposition thermal annealing can trigger the transformation of quantum dots on the film surface to simple NRs or multiple concentric NRs; the precise NR type formed can be controlled by controlling the thermal stress level in the film, which is, in turn, controlled by setting the annealing temperature. The precise NR type and pattern formed can be predicted accurately by our weakly nonlinear morphological stability theory, which provides a design rule for fabricating NR patterns with precisely controlled features and sizes on metallic thin film surfaces.

Our findings make a strong case for precise engineering of nanoscale surface features with tunable shape and size in strained-layer heteroepitaxy and in post-deposition thermal annealing processes by exploiting film surface nonlinear, pattern forming phenomena. Such processing strategies have potential to revolutionize device fabrication technologies for applications in electronics, optoelectronics, and data storage systems.