Semiconductor light emitting diodes (LEDs) have been around for decades and they're used in a wide variety of high-tech applications. When an electrical potential is applied across an LED, work is done to each electron in the system, in an amount equal to the product of the electron's charge and the potential difference.  This work excites electrons and creates holes, and some of these electron-hole pairs recombine producing a photon that ultimately escapes the device and can be observed. This fraction of leaving photons relative to input energy is an amount referred to as the external quantum efficiency. 

LEDs have a second efficiency, called the wall-plug efficiency, that's a measure of the ratio of energy that is emitted as photons to the electrical energy that gets put in. If one wishes to write an equation for this, it would be the energy of the emitted photon(s) times the external quantum efficiency (the fraction of hole-electron pairs that combine into photons), divided by the product of the electron charge and the applied voltage.  

Recently, researchers made the news because they managed to create an LED with a wall-plug efficiency that's greater than one—it emitted more energy as photons than the researchers put into it as electricity. Unfortunately, many of the reports were short on details. Have no fear:  the gods of thermodynamics have their say, this isn't violating any laws of the Universe. We've taken a look at the Physical Review Letter that those reports were based on.

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