The stability of elastically strained nanorings and the formation of quantum dot molecules |
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| Institution: | 1. School of Materials Science and Engineering, Tsinghua University, Beijing 100084, PR China;2. Key Laboratory for Advanced Materials Processing Technology, MOE, PR China;1. Eindhoven University of Technology, Mechanics of Materials, Department of Mechanical Engineering, PO Box 513, 5600 MB Eindhoven, The Netherlands;2. Eindhoven University of Technology, Polymer Technology, Department of Mechanical Engineering, PO Box 513, 5600 MB Eindhoven, The Netherlands;1. Olivia Newton John Cancer Research Institute, Melbourne, Victoria, Australia;2. Department of Paediatrics, The University of Melbourne, Melbourne, Victoria, Australia;3. Division of Radiation Oncology and Cancer Imaging, Peter MacCallum Cancer Center, Melbourne, Australia;4. Department of Periodontology and Restorative Dentistry, Faculty of Dentistry, University of Münster OR Muenster, Munster, Germany;1. Department of Mechanical Engineering, University of Houston, Houston, TX 77204, USA;2. Department of Mathematics, Rutgers University, NJ 08854, USA;3. Department of Mechanical Aerospace Engineering, Rutgers University, NJ 08854, USA;4. Department of Physics, University of Houston, Houston, TX 77204, USA;1. Departamento de Física, Universidad de Santiago de Chile and CEDENNA, Avda. Ecuador 3493, Santiago, Chile;2. Department of Physics, University of California, San Diego, La Jolla, CA 92093, United States;3. Departamento de Física, Universidade Federal de Viçosa, Avenida Peter Henry Rolfs s/n, 36570-000 Viçosa, MG, Brazil;1. CNR-Istituto di Scienze e Tecnologie Molecolari, Via C. Golgi 19, Milano, Italy;2. Dipartimento di Scienze e Innovazione Tecnologica, Centro Interdisciplinare NanoSistemi, Università del Piemonte Orientale, Viale T. Michel 11, Alessandria, Italy;3. Dipartimento di Chimica Università degli Studi di Milano, Via C. Golgi 19, Milano, Italy |
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| Abstract: | Self-assembled nanorings have recently been identified in a number of heteroepitaxially strained material systems. Under some circumstances these rings have been observed to break up into ring-shaped quantum dot molecules. A general non-linear model for the elastic strain energy of non-axisymmetric epitaxially strained nanostructures beyond the small slope assumption is developed. This model is then used to investigate the stability of strained nanorings evolving via surface diffusion subject to perturbations around their circumference. An expression for the fastest growing mode is determined and related to experimental observations. The model predicts a region of stability for rings below a critical radius, and also a region for larger rings which have a proportionally small thickness. The predictions of the model are shown to be consistent with the available results. For the heteroepitaxial InP on In0.5Ga0.5P system investigated by Jevasuwan et al. (2013), the nanorings are found to be stable below a certain critical size. This is in good quantitative agreement with the model predictions. At larger sizes, the rings are unstable. The number of dots in the resulting quantum dot molecule is similar to the mode number for the fastest growing mode. Second order terms show that the number of dots is expected to reduce as the height of the ring increases in proportion to its thickness. The strained In0.4Ga0.6As on GaAs nanorings of Hanke et al. (2007) are always stable and this is in accordance with the findings of the analysis. The Au nanorings of Ruffino et al. (2011) are stable as well, even as they expand during annealing. This observation is also shown to be consistent with the proposed model, which is expected to be useful in the design and tailoring of heteroepitaxial systems for the self-organisation of quantum dot molecules. |
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| Keywords: | Variational calculus Semiconductor material Diffusion Surface Elastic material Nanorings |
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