The extended Beer–Lambert theory for ray tracing modeling of LED chip-scaled packaging application with multiple luminescence materials

•The Beer–Lambert law is expended to multiple luminescence materials mixed system.•The equivalent spectrum is used, and self-absorption in phosphors system has been considered.•The modeling results fit the experiment result, in terms of color temperature and efficacy.•This paper enables engineers to reduce trial-n’-error, by applying virtual prototype technique.

Optical ray tracing modeling applied Beer–Lambert method in the single luminescence material system to model the white light pattern from blue LED light source. This paper extends such algorithm to a mixed multiple luminescence material system by introducing the equivalent excitation and emission spectrum of individual luminescence materials. The quantum efficiency numbers of individual material and self-absorption of the multiple luminescence material system are considered as well. By this combination, researchers are able to model the luminescence characteristics of LED chip-scaled packaging (CSP), which provides simple process steps and the freedom of the luminescence material geometrical dimension. The method will be first validated by the experimental results. Afterward, a further parametric investigation has been then conducted.