Affiliation:
1. Department of Theory of Continuous Media and Nanostructures Institute of Fundamental Technological Research Polish Academy of Sciences Adolfa Pawinskiego 5b 02-106 Warsaw Poland
2. School of Mathematics and Physics Queen's University Belfast University Road Belfast NI BT7 1NN UK
Abstract
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.
Funder
H2020 Marie Skłodowska-Curie Actions
Subject
Condensed Matter Physics,Electronic, Optical and Magnetic Materials
Cited by
1 articles.
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