Formation of Ge nanocrystals embedded in HfAlO high-k dielectric by co-sputtering of HfO2, Al2O3, and Ge, followed by rapid thermal annealing was demonstrated. Analysis by transmission electron microscopy and x-ray photoelectron spectroscopy confirmed the formation of nonoxidized Ge nanocrystals with a minimum size of about 5nm embedded in HfAlO dielectric. We also demonstrated the application of such nanocrystals in nonvolatile memory devices, achieving a 2.2V memory window as obtained from the C–V characterization of the memory device.

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We prove that a connected vertex-transitive graph G with degree k > 2 and girth g > 4 is super restricted edge-connected, that is, if F is a set of 2k − 2 edges of G such that G − F is disconnected and every component of G − F has at least two vertices, then F is the set of edges adjacent to a certain edge in G. We also show that neither the condition k > 2 nor g > 4 can be weakened.

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