Modern semiconductor devices often require the use of multi-material systems in order to operate. This inevitably requires the formation of an interface where the two dissimilar materials are joined. Two such examples are quantum dots (QDs) which incorporate 3D geometries with non-planar interfaces and 2D materials which comprise single atom thick geometries. These promise to revolutionize nanoelectronics with increases in device performance and efficiency spanning applications such as photovoltaics, quantum computing, memory storage, and transistors. However, a limiting factor in the realization of such devices is the often undesirable defect formation that arises from the combination of lattice mismatched materials which motivates the study of compatible material selections and improved fabrication techniques. One way in which these discoveries can be realized is through computational modeling which can provide a thorough understanding of the energetics of accompanying defect structures and, therefore, the accompanying conditions in which they might be expected. Continuum based methods offer one solution for predicting their defect or dislocation onset. However, this implementation does not easily allow for the fine, atomistic detail needed for predicting the important core structures involved. Atomistic modeling offers a more detailed solution but the defect structure must often be assumed in order to compute the accompanying configurational energy. When the exact defect structure is unknown, methods such as molecular dynamics (MD), Monte Carlo (MC) techniques, or other ad-hoc implementations are used to find the atomistic structure with the lowest energy among all the possibilities available. Although these approaches include the detail needed to describe core structures and other complex processes, they can often fail to find minimum energy structures due to long time-scales or sampling limitations that make them computationally expensive. Also, many of these studies either neglect or inefficiently implement the relative energy contributions associated with a Grand Canonical (GC) ensemble where a much more favorable defect structure can be obtained with more or fewer atoms than the initialized system. A complete mapping of this high dimensional energy landscape can present valuable insight when predicting low energy structures associated with a specific material combination as most 2D and 3D materials have competing defect structures across a variable number of atoms. In this work, a new GC potential energy surface (GC-PES) exploration technique is presented known as the Grand-Canonical Minima Hopping (GCMH) method, which provides an efficient and adaptive energy landscape exploration for predicting the lowest energy configuration or defect structures present in a given system.Leading to the details of this new procedure, three studies are first discussed in order to highlight the role of dislocations for strain relief and the coupling that these defects have to material properties. These works include a continuum analysis of strain and band alignment in 3D GaAs/GaSb QDs, a critical thickness study in 2D h-BN/graphene heterostructures, and an investigation of moir\'e patterns in 2D materials. Following a description of the underlying Minima Hopping method (MH), the procedure behind the GCMH method is presented along with a case study on fullerene structures. Next, the importance of the atomistic representation for a PES exploration is shown and a parallelization scheme based on distributed softening is discussed. The GCMH is applied to a dislocated graphene system and the structural manifestation of several types of defects is compared to experiments.
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Dislocation structures in materials using grand-canonical minima hopping energy minimization
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