Coefficient-of-Performance Analyses for Light-Emitting-Diode Cycles Resembling Carnot Heat Pumps

Abstract

Designing the light-emitting diodes (LEDs) that yield maximal coefficients of performance (<inline-formula> <tex-math notation= LaTeX >${\\boldsymbol {\\xi }}_{\\boldsymbol {max}}$ </tex-math></inline-formula>) subject to prescribed electrical powers constitutes a desirable and challenging task. In this paper, via an analogy between the reverse Carnot cycle and the LED cycle, we have identified two distinctive situations. Under normal operations, the electrical power is supplied to allow LED electrons to overcome the p/n junction barrier and is converted to thermal energy rate, which is dissipated to the surroundings. Meanwhile, the LED absorbs the very small amount of thermal energy rate (approximately zero and much smaller than the electrical power) from surroundings as a result of the Peltier effect. Therefore, the maximal light power emitted by the LED must not exceed electrical power (<inline-formula> <tex-math notation= LaTeX >$\\boldsymbol {P}_{\\boldsymbol {ele}}$ </tex-math></inline-formula>) minus the barrier-overcoming power (<inline-formula> <tex-math notation= LaTeX >$\\boldsymbol {I}\\boldsymbol {V}_{\\boldsymbol {net}}$ </tex-math></inline-formula>). Subsequently, <inline-formula> <tex-math notation= LaTeX >${\\boldsymbol {\\xi }}_{\\boldsymbol {max}}$ </tex-math></inline-formula> is obtained as <inline-formula> <tex-math notation= LaTeX >$(\\boldsymbol {P}_{\\boldsymbol {ele}}-\\boldsymbol {I}\\boldsymbol {V}_{\\boldsymbol {net}})/\\boldsymbol {P}_{\\boldsymbol {ele}}$ </tex-math></inline-formula>. Under relatively unusual situations when LEDs are capable of absorbing sufficient thermal energy rates from surrounding reservoirs (the same order of magnitude as the electrical power), <inline-formula> <tex-math notation= LaTeX >${\\boldsymbol {\\xi }}_{\\boldsymbol {max}}$ </tex-math></inline-formula> can possibly exceed the unity, and its expression is theoretically derived in the text. Fundamentally, this paper may contribute to areas of energy saving and light-power illumination.