The kinetics of photoinitiated polymerization for active packaging of light-emitting diodes (LEDs) is presented. The LED chip in our model was considered to consist of an upper emission surface and a lateral emission surface. Light emission from the LED chip triggers the photoinitiated polymerization reaction, leading to the formation of a mushroom-shaped encapsulant lens on the LED chip. With our proposed simulation process, the concentrations of both the photoinitiator and monomer, and the photolysis as time evolves can be calculated by the finite-difference method. The time evolution of the lens profile during polymerization can be analyzed as the monomer concentration varies. The proposed technique can depict the shape and precise size of the mushroom-shaped lens for any specific parameters in the polymerization reaction, e.g., LED power, polymerization time, absorptivity of the epoxy, and photolysis. LED encapsulation experiments with different LED power and polymerization time were made to support our simulation results, and the simulation results agree well with the experiment results. Finally, the radiation patterns of the LEDs with the encapsulant lenses are measured to prove the light focusing characteristics of the mushroom-shaped lenses.
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