Abstract
The tunnelling of electrons through barriers is important in field emission sources and in interconnects within electronic devices. Here we use the analogy between the electromagnetic wave equation and the Schrodinger equation to find potential barriers that, when added before an existing barrier, increase the transmission probability. A single pre-barrier of negative potential behaves as a dielectric “antireflection coating”, as previously reported. However, we obtain an unexpected and much greater enhancement of transmission when the pre-barrier has a positive potential of height smaller than the energy of the incident electron, an unfamiliar optical case, corresponding to media with superluminal phase velocities as in dilute free electron media and anomalous dispersion at X-ray frequencies. We use a finite difference time domain algorithm to evaluate the transmission through a triangular field emission barrier with a pre-barrier that meets the new condition. We show that the transmission is enhanced for an incident wavepacket, producing a larger field emission current than for an uncoated barrier. Examples are given of available materials to enhance transmission in practical applications. The results are significant for showing how to increase electron transmission in field emission and at interconnects between dissimilar materials in all types of electronic devices.
Highlights
The tunnelling of electrons through barriers is important in field emission sources and in interconnects within electronic devices
We address the problem of antireflection coating of a potential barrier for which (E-V) is negative, that is, when there is no classical transmission
We have outlined the analogies between the propagation of matter waves in a region of given potential and the propagation of electromagnetic waves in a medium of given refractive index and identify cases that are well known and a case that is previously unexplored
Summary
We calculate the transmission probability for two adjacent rectangular barriers, with the aim of achieving antireflection effects for particle probability. In both cases, the interior of the pre-barrier is a site of maximum wave amplitude during the interaction with the incident wavepacket so that the pre-barrier has the effect of confining the probability. In our case confinement is caused by the slowing down of the particle over the pre-barrier as its kinetic energy is diminished; in the latter case, there is a standing wave confined by highly reflecting boundaries
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