Analytical calculation of the extraction efficiency of microcavity light-emitting diodes for display and fiber coupling applications

This paper presents a simple analytical expression of the extraction efficiency for planar dielectric microcavity light-emitting diodes (MCLEDs) based on two distributed Bragg reflectors (DBRs). The calculations take into account the optical properties of the resonator (reflectivities and index contrast of the DBRs, cavity length, refractive index of the outside medium), as well as the spectral properties of the active material. The analytical results are compared to exact numerical calculations based on the plane wave expansion method and show good agreement. Simple design rules for optimizing the extraction efficiency of MCLEDs are proposed and discussed for display and fiber coupling applications. The limits of MCLEDs are finally investigated and compared to those of conventional light-emitting diodes.