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Real-time observation of nanoscale topological transitions in epitaxial PbTe/CdTe heterostructures
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39.A seemingly related material system consists of the semimetallic monopnictide ErAs (rs) and the semiconductor InxGa1−xAs (zb). Still, this material system is only partly comparable to our system, because the heats of formation of the involved materials differ strongly. As a consequence, ErAs on In1−xGaxAs grows forthright three-dimensionally, and therefore cannot be brought into the layered initial structure, which we exploited in the PbTe/CdTe system to set well-defined initial conditions for the annealing experiments.
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The almost completely immiscible PbTe/CdTe heterostructure has recently become a prototype system for self-organized quantum dot formation based on solid-state phase separation. Here, we study by real-time transmission electron microscopy the topological transformations of two-dimensional PbTe-epilayers into, first, a quasi-one-dimensional percolation network and subsequently into zero-dimensional quantum dots. Finally, the dot size distribution coarsens by Ostwald ripening. The whole transformation sequence occurs during all stages in the fully coherent solid state by bulk diffusion. A model based on the numerical solution of the Cahn-Hilliard equation reproduces all relevant morphological and dynamic aspects of the experiments, demonstrating that this standard continuum approach applies to coherent solids down to nanometer dimensions. As the Cahn-Hilliard equation does not depend on atomistic details, the observed morphological transformations are general features of the model. To confirm the topological nature of the observed shape transitions, we developed a parameter-free geometric model. This, together with the Cahn-Hilliard approach, is in qualitative agreement with the experiments.
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