As the best performing light emitting diodes (LEDs) are approaching the conventional limit of unity efficiency, a unique heat-pump operating mode of the devices has been proposed to address this problem, in which case lattice heat is pumped from the phonon field of the device into the incoherent photon field of emission at the expense of consuming zero-entropy electrical power. To better understand the potential of visible LEDs for further efficiency improvement in this mode, we present a thermodynamic framework that allows us to estimate the Carnot limit for their wall-plug efficiency (WPE) at different operating conditions. We find that the theoretical efficiency limit drops at higher light intensities but can still be well above 100% even at 10 W/cm^2. Ideally, realizing such high efficiency at useful output powers requires the device to possess an external quantum efficiency (EQE) close to unity. Here we are able to introduce dissipation into the thermodynamic model and thus determine a minimum EQE required for an LED to achieve unity WPE. In addition, the thermodynamic study for visible LEDs yields one surprising result. The first observation of above-unity WPE was on a heated mid-infrared (2.2 um) LED, and the subsequent demonstration at room temperature necessarily required a longer-wavelength 3.4 um device in order to realize sufficient carrier injection for measurable optical output. On the contrary, this thermodynamic analysis indicates that at useful optical powers – and hence useful cooling powers – visible LEDs of shorter wavelength are expected to show higher cooling at a lower current density.
It is known that the wall-plug efficiency (WPE) of a light-emitting diode (LED) can exceed unity and that electroluminescence cooling (ELC) happens in this scenario. However, it is difficult to observe the associated temperature drop due to the relatively small cooling power and the overwhelming heat flux from the ambient. In this work, we design a photonic crystal (PhC) enhanced LED which has smaller surface area as well as thermal mass compared with an encapsulated LED. We also present thermal models to evaluate the temperature drop of the LED in air and vacuum.