Combined experimental-numerical identification of radiative transfer coefficients in white LED phosphor layers

An inverse analysis of the phosphor layer of a commercially available, conformally coated, white LED is done based on tomographic and spectrometric measurements. The aim is to determine the radiative transfer coefficients of the phosphor layer from the measurements of the finished device, with minimal assumptions regarding the composition of the phosphor layer. These results can be used for subsequent opto-thermal modelling and optimization of the device. For this purpose, multiple integrating sphere and gonioradiometric measurements are done to obtain statistical bounds on spectral radiometric values and angular color distributions for ten LEDs belonging to the same color bin of the product series. Tomographic measurements of the LED package are used to generate a tetrahedral grid of the 3D LED geometry. A radiative transfer model using Monte Carlo Ray Tracing in the tetrahedral grid is developed. Using a two-wavelength model consisting of a blue emission wavelength and a yellow, Stokes-shifted re-emission wavelength, the angular color distribution of the LED is simulated over wide ranges of the absorption and scattering coefficients of the phosphor layer, for the blue and yellow wavelengths. Using a two-step, iterative space search, combinations of the radiative transfer coefficients are obtained for which the simulations are consistent with the integrating sphere and gonioradiometric measurements. The results show an inverse relationship between the scattering and absorption coefficients of the phosphor layer for blue light. Scattering of yellow light acts as a distribution and loss mechanism for yellow light and affects the shape of the angular color distribution significantly, especially at larger viewing angles. The spread of feasible coefficients indicates that measured optical behavior of the LEDs may be reproduced using a range of combinations of radiative coefficients. Given that coefficients predicted by the Mie theory usually must be corrected in order to reproduce experimental results, these results indicate that a more complete model of radiative transfer in phosphor layers is required.