(274e) Semiconductor Nanostructure Pattern Formation in Thin Films Grown Epitaxially on Pit-Patterned Substrates

Numerous applications in electronic and optoelectronic device technologies, as well as data storage systems, are enabled by semiconductor nanostructures such as quantum dots (QDs) and nanorings. The formation of such nanostructures on surfaces of thin films is commonly facilitated by the Stranski-Krastanow (SK) growth instability. These films are deposited epitaxially on thick semiconductor substrates and the induced biaxial stress in the growing film because of its lattice mismatch with the substrate material is the driver of growth instabilities. However, the QDs that are formed as the outcome of SK growth instabilities are randomly arranged on the film surface and are characterized by sizes that are not uniform, while uniform sizing and ordered arrangements of quantum dots are required for device fabrication purposes. Among the numerous strategies that have been developed in recent experimental studies for guiding the growth of orderly arranged and consistently sized QDs, depositing thin films epitaxially on properly engineered pit-patterned substrate surfaces is the most promising and effective approach toward producing ordered nanostructure assemblies.

Here, we report results on the surface morphological response of coherently strained Ge thin films grown epitaxially on pit-patterned Si{100} substrates. Our analysis is based on self-consistent dynamical simulations according to a 3D continuum-scale epitaxial film surface evolution model that has been parameterized based on atomic-scale simulations and validated by comparisons of its predictions with experimental observations on Ge/Si and InAs/GaAs heteroepitaxial systems employing pit-patterned substrates. We discuss the design of patterns of two pit geometries, namely, inverted truncated conical and pyramidal pits, and the effects on the resulting film surface nanopattern of varying the relevant geometrical design parameters, including film thickness, pit-pattern period, pit depth, pit opening dimensions, and pit wall inclination. For conical pits, we find that varying the pit opening diameter and the pit wall slope leads to formation of complex nanostructures inside the pits of a regular pit pattern on the film surface, which include QDs, as well as single nanorings and multiple concentric nanorings that may or may not surround a central QD inside each pit. For pyramidal pits, we show that varying the pit opening length and width and the pit wall inclination can cause the formation of nanostructures inside as well as on the rim of the regularly arranged pits on the film surface that include equi-spaced smaller pits or rectangular arrays of multiple QDs, also known as quantum dot molecules. We also find that using pits with different pit wall inclinations along the two principal pit directions leads to the formation of linear arrays of multiple QDs inside and on the rim of the elongated pits on the deposited film surface, in agreement with experimental studies. The results of our computational analysis are in very good agreement with the predictions of a nonlinear morphological stability theory for the observed nanopattern formation on the film surface as the outcome of a “tip-splitting” instability that determines the qualitative features of the generated nanopatterns, which provides a systematic kinetic interpretation for the findings of the numerical simulations.

Finally, we present a unifying thermodynamic framework that explains the features of the film surface nanostructure pattern as a function of the elastic strain energy of the heteroepitaxial film/substrate system with a film surface morphology characterized by a pit pattern at given film thickness that exactly mimics that of the patterned substrate on which the film is deposited. This periodic pit pattern arrangement, fully defined by a complete set of materials and geometrical parameters, determines the energetics of the pit-patterned heteroepitaxial system, which, in turn, dictates the complex nanostructure patterns that are formed on the surface of the coherently strained epitaxial thin film. Our findings have important implications for designing optimal surface patterns of ordered semiconductor nanostructures in coherently strained epitaxial thin films toward enabling engineering strategies for future nanofabrication technologies by exploiting surface morphological instabilities.