(271g) Formation of Semiconductor Nanostructure Patterns in Coherently Strained Thin Films Grown Epitaxially on Pit-Patterned Substrates

Semiconductor nanostructures, such as quantum dots (QDs) and nanorings, play a crucial role in enabling electronic, optoelectronic, and data storage device fabrication technologies. These nanostructures typically form on surfaces of coherently strained thin films through the Stranski-Krastanow (SK) growth instability, induced by the lattice mismatch between the film and thick semiconductor substrate materials. However, the QDs that are formed as the outcome of SK growth instabilities are randomly arranged on the film surface and have non-uniform sizes, while uniform sizing and ordered arrangements of quantum dots are required for device fabrication purposes. In recent experimental studies, numerous strategies have been developed for guiding the growth of periodically arranged and consistently sized QDs. Among such strategies, depositing thin films epitaxially on precisely 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 thin films grown epitaxially on pit-patterned semiconductor substrates, placing emphasis on the Ge/Si{100} heteroepitaxial system. We have developed 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; our analysis is based on self-consistent simulations according to this model. We focus on patterns of two pit geometries, namely, inverted truncated conical and pyramidal (or prismatic) pits, and explore the effects on the resulting film surface nanopattern of varying the relevant geometrical design parameters: these include film thickness, pit-pattern period, pit depth, pit opening dimensions, and pit wall inclination. For conical pits, our analysis reveals 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, including 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 find 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; such nanostructures 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 strongly supported by 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; this instability is responsible for the appearance of the detailed features of the generated nanopatterns, and the morphological stability theory provides a systematic kinetic interpretation for the findings of the numerical simulations.

Finally, we present a comprehensive thermodynamic explanation of the features of the film surface nanostructure pattern as a function of the surface chemical potential 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 is fully defined by a complete set of materials and geometrical parameters and determines the energetics of the pit-patterned heteroepitaxial system. This energetics, 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 enabling future nanofabrication technologies by exploiting morphological instabilities on surfaces of coherently strained epitaxial thin films.