Study on phosphor sedimentation effect in white light-emitting diode packages by modeling multi-layer phosphors with the modified Kubelka-Munk theory

In this study, we studied the phosphor sedimentation effect in white phosphor-converted light-emitting diode packages by modeling the multi-layer phosphors with gradient concentrations. The essence of phosphor sedimentation can attribute to the variation of phosphor concentrations. By modifying the Kubelka-Munk theory, we built a multi-layer phosphor model with considering the light scattering, light absorption, and light conversion process simultaneously. With a brief review of Kubelka-Munk theory, multi-layer phosphors were modeled on the basis of single-layer phosphor model. The phosphor sedimentation effect was characterized by modeling multi-layer phosphors with gradient concentrations, whereas keeping the total amount of phosphors at the same level. It is found from the five calculation cases that phosphor sedimentation will cause the drop of light extraction efficiency (LEE) by 13.04%. Furthermore, the phosphor layer with inverse-gradient concentrations will enhance the LEE 16.56%. To figure out the reasons, the light losses were calculated, and it is proved that the light loss is enhanced when phosphor sedimentation happens.