Precise model of phosphor geometry formed in dispensing process of LED packaging

Phosphor geometry is one of key factors which affect the optical performance for white light emitting diode (LED). In the optical simulation of LED packaging, the phosphor geometry was usually assumed as a sphere cap, but in fact, it is not a sphere cap. Therefore, the simulation results based on such an assumption may not be accurate. In this paper, a precise model of phosphor geometry for a common LED packaging type was built. With consideration of the comprehensive effect of surface tension and gravity, a second-order differential equation is established for describing the axisymmetric phosphor geometry. This equation was solved by the numerical algorithm based on the four-order Runge-Kutta method. Through the solution of this model, the curve of contact angle versus the volume of dispensing phosphor slurry can be achieved.