Antireflection coating of barriers to enhance electron tunnelling: exploring the matter wave analogy of superluminal optical phase velocity

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.