Generalized fractional Wentzel–Kramers–Brillouin approximation for electron tunnelling across rough metal interface

Ramzan, M. W.; Riaz, Kashif; Mehmood, Muhammad Qasim; Zubair, Muhammad; Massoud, Yehia

doi:10.1098/rspa.2022.0600

Cited by 3 publications

References 66 publications

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Concept for a fractional energy barrier tunneling junction

Chen,

Ki,

et al. 2023

Applied Physics Letters

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In general, the tunnel current in field emission tunneling junctions is determined by the barrier height under an applied electric field. Introducing an alternative way to modulate the tunnel current other than tuning the barrier height is important for further improving the related device performance. In this work, we propose a concept of a fractional energy barrier tunneling junction that exploits the field enhancement at the tip structure to modulate the shape of the barrier not just its height to tune the tunnel current. Compared with a classical triangular energy barrier, we find that the fractional energy barrier creates a thinner or thicker barrier width for electrons holes depending on the voltage bias, which allows us to enhance or suppress electron or hole currents by several orders of magnitude. By optimizing the barrier layer thickness for a given barrier height, we were able to make 99% of the total tunnel current to be from electrons only. This can greatly enhance the emission efficiency that is useful for application of tunneling cathode. We note that the concept proposed in this study can be extended to other field-injecting hot carrier devices.

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Concept for a fractional energy barrier tunneling junction

Chen,

Ki,

et al. 2023

Applied Physics Letters

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Characterization of field emission from random nano-structured surface in using fractional field emission models

Kanwal,

Raheem,

Mehmood

et al. 2024

Journal of Applied Physics

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It is known that field emission from random nano-structured surfaces cannot be well characterized with the original field emission model known as the Fowler–Nordheim (FN) law or the Murphy–Good (MG) law. To account for the roughness effects, the traditional approach was to introduce the arbitrary field enhancement factor β in the FN and MG laws. In this paper, by treating the random roughness of field emitters as a fractional dimension object with 0<α<1, fractional models of the FN and MG law, which were formulated recently may serve as alternate characterization tools. At α=1, the models will recover the traditional FN and MG laws valid for a perfect flat planar surface. These generalized fractional FN law (FNα) and the fractional MG law (MGα) will be used to characterize various field emission experiments by finding the best 0<α<1 values to account for the degree of the random roughness. The findings will be compared among the traditional and fractional emission models, where the best-fitting results will be shown for each case. It is found that the fractional field emission models provide more physical and appropriate field emission parameters, i.e., field enhancement factor and field emission area, in comparison with traditional field emission models.

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