The rate equation based optical model for phosphor-converted white light-emitting diodes

An optical model based on the rate equation was developed to calculate the emission spectrum of a phosphor-converted white light-emitting diode (pc-WLED) taking into consideration the phosphor weight percentage, film thickness, and optical properties of phosphor, viz. absorption spectrum, quantum efficiency spectrum and fluorescent emission spectrum. Films containing a mixture of phosphor and silicone elastomer encapsulant were investigated using this model. A linear relationship was found between the peak absorption coefficient and the phosphor weight percentage with slopes of 66.76 ± 0.52 mm^-1 and 29.66 ± 2.05 mm^-1 for a red phosphor CaAlSiN₃:Eu²⁺ and a yellow phosphor Y₃Al₅O₁₂:Ce³⁺, respectively. With these parameters, the model predicted emission spectra which are in good agreement with measurement, thus verifying the validity of the model. The model correctly predicts redshift and spectral width reduction of the emission peak for increasing phosphor weight percentage or film thickness, as expected from the phenomenon of photon reabsorption by the phosphors. This model does not require the use of Monte Carlo simulation and Mie theory.