# Fabrication Process and Performance Analysis of CSP LED Filaments with a Stacked Package Design
## 3 Results and Discussion
With the law of conservation of energy, when a short wavelength light excites a phosphor, part of the energy is converted to long wavelength light and the other part is dissipated in the form of heat. As shown in Equation (F1), the input power from \begin{table}
\begin{tabular}{c c c} \hline  & **Traditional Dispensing Method** & **Stacked Packaging Method** \\ \hline CCT at 30 mA (K) & 2499 & 2506 \\ CRI at 30 mA (Ra) & 89.7 & 87.6 \\ CIE at 30 mA & (0.4797, 0.4180) & (0.4797, 0.4180) \\ Luminous efficiency at 30 mA (Lm/W) & 68.62 & 73.88 \\ Luminous efficiency at 210 mA (Lm/W) & 44.95 & 53.48 \\ The variations in luminous efficiency & 23.67 & 20.4 \\ The rate of variations in luminous efficiency & 34.94\% & 27.61\% \\ \hline \end{tabular}
\end{table} 
Table 1: Electroluminescence data of traditional dispensing packaged filament and stacked-type packaged filament. Figure 7: EL spectra of traditional dispensing packaged filament and stacked-type packaged filament. the blue LED chip (\(\mathbf{E_{input}}\)) can be transferred to the blue photon energy that transmits out of silicone (\(\mathbf{E_{transmitted}}\)), the absorbed energy by phosphors that is used for the light conversion (\(\mathbf{E_{converted}}\)) and the heat generated from both Stokes shift (\(\mathbf{E_{ss}}\)) and non-radiation (\(\mathbf{E_{nonRad}}\)). \[\mathbf{E_{input}}=\mathbf{E_{transmitted}}+\mathbf{E_{converted}}+\mathbf{E_{ss}}+\mathbf{E_{nonRad}} \tag{1}\]  
Within the optical tracing process, the light scattering, absorption and conversion are normally considered as dominant effects in most YAG based yellow phosphor models [27]. As shown in Figure 9, light 1 is the blue light emitted by the chip, which is directly emitted through the package. When the blue light emitted by the chip propagates to the green phosphor, it is absorbed and transformed into green light like light 3, and the propagation direction is isotropic. Light 3 shows that the green light is not absorbed, but directly scattered through the green phosphor when the light fired by one green powder again propagates to another green phosphor. There are very few blue lights absorbed by the green phosphor that can propagate to the red phosphor, as light 4, that can then reabsorb the photon and turn into red light. The transmission direction of the emitting light of the red phosphor follows the same isotropy. When a blue light emitted by the chip reaches the red phosphor in the film, it is converted into red light like light 5, and then directly ejected. Some light, like light 6, does not reach any red phosphor and goes straight through the film. This kind of blue light is only absorbed by the green phosphor and emitted into green light. Light 7 indicates that the emitting light of the red phosphor will not be absorbed when the emitting light of the red phosphor is transmitted to the green phosphor, but instead the scattering phenomenon occurs. Light 8 indicates that blue light is absorbed by the red phosphor and no spectral transformation occurs. This is because the quantum efficiency of the red phosphor is much lower than that of the green phosphor, and the probability of non-radiative recombination is larger. Figure 8: CIE-1931 chromaticity coordinates of traditional dispensing packaged filament and stacked-type packaged filament. From the schematic diagram, Figure 9, we can clearly see that all light propagates in this special package structure. The excellent luminescence performance of the filament is mainly due to the absorption and transformation of some blue light directly by the green phosphor, which makes up for the defect that the red phosphor in the film blocks the light path, which leads to a reduction in luminous efficiency. We also found that this special packaging structure can save a large amount of phosphor cost, using a simple calculation.