Abstract
A direct current through a metal-insulator-metal tunneling junction emits light when surface-plasmon polaritons (SPPs) are excited. Two distinct processes are believed to coexist in this light emission mediated by surface plasmons: inelastic tunneling, where electrons excite SPPs in the insulator gap, and hot-electron radiative decay, which occurs in the electrodes after elastic tunneling. Previous theoretical approaches to study light emission by inelastic tunneling have relied on Bardeen’s approximation where the electronic wave functions are considered only in the barrier of the junction. In this work, we introduce an extension to models of inelastic tunneling by incorporating the full quantum device solution of the Schrödinger equation, which can also account for processes in the metallic electrodes. The extension unveils the existence of long-range correlations of the current density across the barrier and enables us to establish the equivalence between two models widely used in the past: (i) a calculation of the inelastic transition rate between two states across the barrier based on Fermi’s golden rule and (ii) a calculation of the power transferred to plasmons by current fluctuations. Importantly, the new model accounts for processes that take place in the metallic electrodes and that could not be described within Bardeen’s approximation. Hence, it is no longer necessary to invoke a hot-electron mechanism to obtain a dependence on the geometry of metallic electrodes. The new framework enables to discuss the role of surface plasmons localized in different metal-insulator interfaces and to include possible nonlocal effects at the interfaces.
- Received 1 October 2023
- Revised 24 January 2024
- Accepted 27 March 2024
DOI:https://doi.org/10.1103/PhysRevX.14.021017
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
When applying a voltage across two bits of metal separated a few nanometers by an insulating film, there is an electrical current through the gap due to quantum tunneling. Remarkably, visible light can be emitted. This effect, called “light emission by inelastic tunneling,” could have important applications, but its development has been hampered for almost 50 years by the lack of a fully quantitative theory. In this Letter, we use an alternative description of electrical transport that enables us to show that light is emitted both in the gap and in the metal.
So far, two different mechanisms have been invoked to explain different aspects of the experiments. One considered that light is emitted in the gap, whereas the second assumed an emission process in the metal. None of the two mechanisms could account for all experiments. By abandoning traditional approximations in the theory of the tunnel effect, we establish a unified theory that accounts naturally for emission processes taking place both in the metal and in the gap. We also unveil correlations of the current across the junction, which corresponds to the intuitive picture of an electron and a hole moving on both sides of the junction and recombining in the gap.
The extended theory should enable researchers to improve the design of light sources based on inelastic tunneling, with possible applications for optical interconnects. It could also be used to understand electroluminescence in quantum cascade structures, a topic that has remained elusive.
