Abstract
We study the transmission coefficient of onedimensional barriers that are relevant to fieldemission problems. We compare, in particular, the results provided by the simple JeffreysWentzelKramersBrillouin(JWKB) approximation, the continuedfraction technique and the transfermatrix methodology for the electronic transmission through square, triangular and SchottkyNordheim barriers (the SchottkyNordheim barrier is often used in models of field emission from flat metals). For conditions that are typical of field emission (Fermi energy of 10eV, work function of 4.5eV and field strength of 5Vnm ), it is shown that the simple JWKB approximation must be completed by an effective prefactor P in order to match the exact quantummechanical result. This prefactor takes typical values around 3.4 for square barriers, 1.8 for triangular barriers and 0.84 for the SchottkyNordheim barrier. For fields F between 1 and 10Vnm and for work functions between 1 and 5eV, the prefactor P to consider in the case of the SchottkyNordheim barrier actually ranges between 0.28 and 0.98. This study hence demonstrates that the FowlerNordheim equation (in its standard form that accounts for the image interaction and that actually relies on the simple JWKB approximation) overestimates the current emitted from a flat metal by a factor that may be of the order of 23 for the conditions considered in this work. The study thus confirms Forbes's opinion that this prefactor should be reintegrated in fieldemission theories.
Original language  English 

Journal  Journal of Physics: Condensed Matter 
Volume  22 
Issue number  17 
DOIs  
Publication status  Published  1 Jan 2010 
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