najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2016-7-5-816-834najo-938Research ArticleСтатьиResonance scattering across the superlattice barrier and the dimensional quantizationPavlovB.

Auckland

YafyasovA.

St. Petersburg

yafyasov@gmail.comNew Zealand Institute of Advanced StudiesNew ZealandDept. of Solid State Electronics, St. Petersburg State UniversityRussian Federation20161508202575816834Copyright © Pavlov B., Yafyasov A., 20252025Pavlov B., Yafyasov A.Pavlov B., Yafyasov A.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/938

Carbon nano-cluster cathodes exhibit a low threshold electron emission, which is 2–3 orders lower than on metals and semiconductors. We confirm the effect by direct experiments with graphene structures. We are suggesting a model based on the interference electrons wave function in 3D-space charge region of carbon structure interface with vacuum. The low-threshold emission is explained, in frames of the model, by the resonance properties of the barrier formed on the interface. Also in the following topics: interpretation of recent experimental findings for saturation of the field emission; local spectral analysis of multidimensional periodic lattices: dispersion via DN-map; examples of iso-energetic surfaces associated with solvable models of periodic lattice; Lagrangian version of the operator extension algorithm; solvable models of selected one-body spectral problems; quantum dot attached to the node of a quantum graph; a solvable model of a discrete lattice and spectral structure of a 1D superlattice via analytic perturbation procedure.

periodic interfacecarbon coverWeyl-Titchmarsh functionresonancefield emissionDN-mapThe autors are grateful to V. B. Bogevolnov for providing extremely interesting and inspiring material– the carbon flakes obtained by detonation– which served main object of our experimental and the theoretical study. We are also grateful to Prof. G. Fursey, Prof. P. Konorov, Prof. P. Schwerdtfegger and Dr. Krista Steenbergen for an inspirating discussion of the mathematical analog of the shaky concept of chemical bound with respect to the problem of selection appropriate contact subspaces for fitted solvable models of periodic lattices.ReferencesFursey G.N. Field emission in vacuum microelectronics. Kluwer Academic/Plenum Publishers (now Springer), New York, 2005.Fursey G.N. Field emission in vacuum microelectronics. Kluwer Academic/Plenum Publishers (now Springer), New York, 2005.Fursey G., Konorov P., Pavlov B. and Adil Yafyasov. 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The authors declare that there are no conflicts of interest present.