An Improved Model for Light Transport in the Color Conversion Element of Light-Emitting Diodes

Light transport with fluorescence in a phosphor layer based on radiative transfer theory is an efficient tool for understanding the performance of a phosphor-converted light-emitting diode. In this work, the models based on radiative transfer theory including light conversion of phosphor particles are developed for calculating the light transport in planar remote phosphor layers. The models developed include an ordinary differential approximation and an improved model based on the differential approximation and an integral formulation of the transmission light flux for a phosphor layer with Fresnel boundaries. We calculate the light extraction efficiency (LEE) of a phosphor layer as a function of various parameters, such as the thickness of the layer and the concentration of phosphor. The present models are validated by comparing the results obtained by the present methods, the double spherical harmonics method of order one and a Monte Carlo method. Comparing the results obtained by those methods, one can see that the improvement based on the differential approximation and integral formulation of transmission light flux for calculating the LEE can yield better results for optically thin cases.