Resonance scattering across the superlattice barrier and the dimensional quantization

B. Pavlov – New Zealand Institute of Advanced Studies, Auckland, New Zealand
A. Yafyasov – Dept. of Solid State Electronics, St. Petersburg State University, St. Petersburg, Russia; yafyasov@gmail.com

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.

Keywords: periodic interface, carbon cover, Weyl-Titchmarsh function, resonance, field emission, DN-map.

DOI 10.17586/2220-8054-2016-7-5-816-834


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