Influence of Vacancies and Pores that Appear during Irradiation in the Surface Metal Layer on Field Emission Current

Authors I.I. Musiienko, R.I. Kholodov

Institute of Applied Physics, National Academy of Sciences of Ukraine, 58, Petropavlivska St., 40000 Sumy, Ukraine

Issue Volume 11, Year 2019, Number 3
Dates Received 24 February 2019; revised manuscript received 10 June 2019; published online 25 June 2019
Citation I.I. Musiienko, R.I. Kholodov, J. Nano- Electron. Phys. 11 No 3, 03015 (2019)
PACS Number(s) 79.70. + q, 03.65.Ge
Keywords Field emission (3) , Potential barrier, Transmission coefficient of the potential barrier, Thickness of the metal surface modification, High-gradient breakdown.

Quantum-mechanical problem on electron motion through the model potential barrier of metal-vacuum system with an additional near-surface dipole layer is considered. An analytical generalization of the Fowler-Nordheim formula was done in the case of this potential barrier. The introduction of such a layer is used as a way of taking into account the effect of vacancies and pores that appear during irradiation in the surface metal layer on the field emission current density. Taking into consideration the continuity conditions of wave functions and their derivatives at the interface between two media, general expressions of the transmission coefficient of potential barrier and the field emission current density are obtained. The influence of effective thickness of an additional near-surface dipole layer on value of field emission current is shown. Thus, the method is used to take into account the influence of vacancies and pores that appear during irradiation of metal surface on field emission current density. It was found that field emission current, considering the influence of vacancies and pores, that emerge during irradiation of copper surface with Cu2+ ions with energy of 300 keV during the processing time of 5·103 s by dose of 1.6·10 21 m − 2, is 1.3 times less than the value of the Fowler-Nordheim current density. The approximations related to the Fowler-Nordheim formula for current density are given in this paper. The considered approach has more visual mathematical proofs than previous theoretical treatments of the phenomenon of field emission. This research can be a useful basis for studying the transmission of electrons through potential barriers for which there is no an exact analytical theory.