Thermodynamic framework for nanostructure pattern formation in thin epitaxial films grown on pit-patterned semiconductor substrates

We present a comprehensive study of nanostructure pattern formation on coherently strained epitaxial thin films grown on crystalline semiconductor substrates patterned with periodic arrays of inverted truncated pyramidal and conical pits. Using an experimentally validated three-dimensional kinetic model for surface morphological evolution, we investigate how pit geometry and surface free energy anisotropy govern the formation and spatial organization of self-assembled nanostructures such as quantum dots and nanorings. We analyze in detail the influence of the film’s anisotropic surface free energy per unit area on the morphological features of the resulting nanostructures on the epitaxial film surface. We find that while surface free energy anisotropy alters the detailed morphological features, creating faceted morphologies rather than rounded ones in the grown nanostructures, the overall pattern and number of the formed nanostructures remain unaffected. Furthermore, we propose a thermodynamic framework based on the average surface chemical potential of the initial film/substrate heteroepitaxial configuration, which enables predictive control over nanostructure patterns through rational design of pit geometry. Simulations across a broad range of pit design parameters for both inverted truncated pyramidal and inverted truncated conical pits reveal that the surface chemical potential serves as a reliable descriptor for predicting nanostructure pattern formation. Our findings provide new insights that offer a foundational basis for engineering semiconductor surface topographies that can guide next-generation nanofabrication strategies.