Instytut Podstawowych Problemów Techniki

Streszczenie:

Nanotubes and nanorods have been recently established as very good materials to work as electron sources in a field emission (FE) process. These are one-dimensional materials and electron-electron interactions are expected to play a crucial role in their physics. Here we study the influence of electron-electron interactions on the field emission. We study the problem in the low energy regime; thus we need to abandon the antiadiabatic approximation and derive tunneling amplitude for a finite duration of the tunneling process. In this work we identified the parameters when exact analytic expression for tunneling current can be given. We obtained formalism that enables one to capture at the same time the collective effects due to electron-electron interactions and thermionic emission. Our results reveal that different types of nanotubes, and their minigap/compressibility parameters, can be easily distinguished based on FE measurements on these materials.

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Streszczenie:

Herein, the canonical Fowler–Nordheim theory is extended by computing the zero-temperature transmission probability for the more general case of a barrier described by a fractional power law. An exact analytical formula is derived, written in terms of Gauss hypergeometric functions, that fully capture the transmission probability for this generalized problem, including screened interaction with the image potential. First, the quality of approximation against the so far most advanced formulation of Fowler–Nordheim, where the transmission is given in terms of elliptic integrals, is benchmarked. In the following, as the barrier is given by a power law, in detail, the dependence of the transmission probability on the exponent of the power law is analyzed. The formalism is compared with results of numerical calculations and its possible experimental relevance is discussed. Finally, it is discussed how the presented solution can be linked in some specific cases with an exact quantum-mechanical solution of the quantum well problem.

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Streszczenie:

Nanotubes and nanorods have been recently established as very good materials to build electron sources in the cold emission process. These are 1D materials where electron-electron interactions are known to play a crucial role in their physics. The interactions in 1D systems lead to a collective modes’ physics that is usually described using Tomonaga-Luttinger liquid (TLL) formalism. The advantage is that within thismethod all correlation functions are known and can be expressed interms of power laws with non-universal, interaction dependent, ex-ponents. To capture this situation we generalize a canonical Fowler-Northeim theory of field emission to solve the case of a barrier described by any power-law potential. With this generalization, expressed in terms of a confluent hypergeometric function, we are able to compute currents from arrays of carbon nanotubes. We shall present results showing an influence of various interaction terms, as encoded in varying TLL parameters, as well as effects of a finite temperature.

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