2.1.

Light Extraction Efficiency

${\eta }_{\mathrm{PKG}}$ is used as an index to verify the LED PKG performance and is defined as

Fig. 2

PKG without mold resin (a) SV PKG, (b) TV PKG with round cavity, and (c) TV PKG with square cavity.

2.2.

Reflection Methods

Mirror (specular), Gaussian, and Lambertian reflections are the reflection methods operating on the surfaces of the PKG resin and L/F silver-plating of each PKG. The Gaussian reflection angle is determined according to the Gaussian function, with the mean being determined by considering the angle of the mirror reflection and the standard deviation $\sigma$, which represents the degree of scattering (mirror reflection corresponds to $\sigma =0\mathrm{deg}$). Lambertian reflection corresponds to complete scattering. Gaussian reflection at $\sigma =0$ to 30 deg in 1-deg increments and Lambertian reflection are the reflection methods considered in this study. The ${\eta }_{\mathrm{PKG}}$ of each PKG is calculated for 1024 combinations of the PKG resin and L/F reflection methods in the simulations.

When rays are reflected from the cavity wall surface and L/F, the relative intensity can be expressed as

In the ray-tracing simulation, actual scattering on the surface of the PKG resin and the L/F silver-plating can be modeled as Gaussian reflection for $\sigma =30\mathrm{deg}$ and over and $\sigma \approx 15\mathrm{deg}$, respectively, according to comparisons between the simulation and actual experimental results. However, the surface conditions are affected by the surface processing methods and materials. For example, the PKG resin reflection method and reflectance are affected by the surface processing conditions of the resin die, its materials (e.g., polyamide is generally used), and its components (e.g., the percentage of titanium oxide). In addition, the silver-plating reflection method is close to mirror reflection and its reflectance is higher than that of general materials; however, these characteristics are significantly affected by the electroplating method. Therefore, the choice of PKG components significantly affects the optical performance of the LED PKG.

3.1.

Simulation Conditions

Figure 3 shows the names and dimensions of the LED PKG components, whereas Tables 1 and 2 show the simulation parameters. The SV PKG models are of three different sizes. In addition, TV PKG models with three different round-cavity bottom diameters and three different square-cavity side bottom lengths are investigated. Both PKG types are already internationally widespread. As noted above, SV PKG is used for LCD backlights in electrical appliances, such as smart phones. Thus, the SV LED has a thin PKG ($<1.0\mathrm{mm}$) and a narrow cavity (Fig. 4). On the other hand, the TV PKG is used for general LEDs with a high output. Both types are still undergoing development and are being enhanced rapidly and intensively. Round- and square-shaped cavities are generally used. In this study, the optimal shape for TV PKG is confirmed.

Fig. 3

Dimensions of SMD LED PKG components.

Table 1

SV PKG dimensions.

Table 2

TV PKG dimensions.

Fig. 4

SV LED packaging.

Table 3 shows the common simulation conditions. The optical properties were obtained from the widely used values for these materials. The LED chip was modeled as a cuboid sapphire with a refractive index of 1.78. The refractive index of sapphire depends on the wavelength of the incident light, and it is $\sim 1.78$ for the wavelength of the blue light emitted from the LED chip. In practice, the structure of the LED chip significantly affects the device ${\eta }_{\mathrm{PKG}}$ because of the absorption in its P-GaN, InGan active, N-GaN, and electrode layers. Moreover, there exist several types of blue LED chips, namely, a horizontal, vertical (thin GaN chip), and flip chip,³⁵ and the emission efficiencies of these LED chips differ from each other. However, in this study, the ray emission is set as a simple Lambertian distribution from the top surface of the LED chip in the upward and downward directions, ignoring the absorption and transmittance of the sapphire. This is done to facilitate easy extraction of the effect of the PKG resin and L/F silver-plating surface conditions only on the ${\eta }_{\mathrm{PKG}}$. In addition, the refractive index of the mold resin is set to 1.43 in the simulation, because silicone may have refractive index values of roughly 1.4 to 1.55; therefore, this value is not very well defined. If the mold resin refractive index is increased, the critical angle is decreased, and the rays are reflected from the light-emitting surface into the PKG cavity as a result of the total reflection on the interface between the mold resin and the air. Hence, ${\eta }_{\mathrm{PKG}}$ is decreased. Generally, the refractive index of silicone is smaller than that of epoxy; therefore, silicone is chosen as the mold resin for LED PKG in which high efficiency is required. (The transmittance of the mold resin is ignored in this study.) Furthermore, the higher the reflectance of the PKG resin and the L/F silver-plating, the higher the ${\eta }_{\mathrm{PKG}}$ (essentially). Thus, the reflectance performance of these materials, which we wish to enhance, is dependent on their surface conditions, which are, in turn, determined by the fabrication processes. Generally, in the case of higher values, the reflectance of polyamide containing titanium oxide and the silver-plating products used for the LED PKG is roughly 90% to 95% and 95% to 97%, respectively; however, these values differ widely among manufacturers in accordance with the various types of technology employed in the fabrication processes.

Table 3

Common simulation parameters.

3.2.

Simulation Results

Figure 5 shows the simulation results. The ${\eta }_{\mathrm{PKG}}$ distributions of all the PKG exhibit mountain-shaped profiles. One peak and neighboring troughs can be observed in the distributions of each PKG (Table 4). It is preferable for the PKG resin reflection to be close to mirror reflection. The TV4 cavity angle can be considered to be of the appropriate degree, because it yields the maximum value and the highest value of all the PKG when the PKG resin reflection is mirror-like. This suggests that the cavity wall functions as a light reflector (Fig. 6). On the other hand, the SV PKG performance is dependent on the PKG size, because of the narrow vertical direction of its PKG. However, when the results for the round-cavity PKG are compared to those of the square-cavity PKG, the ${\eta }_{\mathrm{PKG}}$ of the round cavity is higher than that of the square cavity overall, despite the larger size of the latter. It can be observed that a number of the round-cavity reflections are smaller than those for the square-cavity case in the ray-tracing simulation of Fig. 6. In the square-cavity case, the angle of the plane surface toward the cavity center point is inconsistent, and the rays are reflected between the edges of the adjacent plane surfaces. However, this does not occur in the case of the round cavity. In addition, the extraction efficiencies of all the PKG are at maxima when the standard deviation of the L/F is at $\sigma =30\mathrm{deg}$ and at minima when the standard deviation of the L/F is at $\sigma =0\mathrm{deg}$. Therefore, the reflection on the L/F should correspond to moderate scattering rather than mirror reflection. The total number of reflected rays in the PKG cavity decreases when the L/F surface reflection causes greater scattering, because the scattering tends to prevent total reflection on the PKG light-emitting surface. This can be recognized explicitly by comparing (1) and (2) of each PKG in Fig. 6.

Table 4

Maximum and minimum ηPKG values of each PKG.

Fig. 5

${\eta }_{\mathrm{PKG}}$ distributions for various PKG and L/F combinations (arbitrary unit: a.u.). The vertical and horizontal axes are the $\sigma$ of the PKG resin and L/F silver-plating, respectively: (a) SV1, (b) SV2, (c) SV3, (d) TV4, (e) TV5, (f) TV6, (g) TV7, (h) TV8, and (i) TV9. $\sigma >30\mathrm{deg}$ corresponds to Lambertian reflection.

Fig. 6

Ray-tracing simulation (20 rays): PKG resin and L/F combinations corresponding to maximum and minimum ${\eta }_{\mathrm{PKG}}$ values for each PKG. (a) SV1, (b) SV2, (c) SV3, (d) TV4, (e) TV5, (f) TV6, (g) TV7, (h) TV8, and (i) TV9. (1) and (2) represent maximum and minimum ${\eta }_{\mathrm{PKG}}$ values, respectively.

Figure 7 shows graphs of the ${\eta }_{\mathrm{PKG}}$ and absorption ratios of the PKG resin and L/F for the conditions corresponding to maximum and minimum ${\eta }_{\mathrm{PKG}}$ values, respectively. The ${\eta }_{\mathrm{PKG}}$ is higher if the absorption ratios of the PKG resin and L/F are lower. In addition, greater ray absorption is exhibited by the PKG resin in comparison to the L/F in all the simulation results. This means that the PKG performance is more significantly affected by the PKG resin optical design than that of the L/F.

Fig. 7

${\eta }_{\mathrm{PKG}}$ values and absorption ratios of PKG resin and L/F under conditions corresponding to (a) maximum and (b) minimum ${\eta }_{\mathrm{PKG}}$ values for each PKG.

3.3.

Effect of a Phosphor

In the case of white LEDs, the mold resin contains yellow phosphors to convert blue light emitted from the LED chip to white light. The LED emission efficiency is more significantly affected by the internal quantum efficiencies of the phosphors than the structures and optical properties of the LED PKG components.^30–34 There exists a down-conversion loss known as the “Stokes loss,” which is caused by the difference in the energy between the absorbed and emitted photons in the light wavelength conversion process.³⁶ In addition, it is understood that the scattering caused by the phosphor contained within the mold resin affects the ${\eta }_{\mathrm{PKG}}$. Thus, in this study, we investigate the effect of the phosphors using a Mie scattering simulation performed using LightTools 8.2.0, for a mold resin containing uniformly distributed phosphor particles.^36–38 In the simulation, the absorption, excitation, and emission spectrum distributions of the phosphor are set as default parameters in LightTools 8.2.0. The phosphor particle radius is set to 1000 nm as the default setting. (The phosphor particle size is roughly 1 to $30\mu \mathrm{m}$, in general.) These parameters are close to the properties of yttrium aluminum garnet:cerium (YAG:Ce), which is generally used for white LEDs based on a blue LED chip (Fig. 8). [The excitation (absorption) and emission spectra of YAG:Ce have peak wavelengths at $\sim 460$ and in the range of 550 to 560 nm, respectively.] The spectrum distribution of the blue LED chip is set as a Gaussian distribution (center wavelength: 455 nm, full width at half maximum: 24 nm).³⁸ (A blue LED chip with a peak wavelength of 450 to 470 nm is used for white LEDs.)

Fig. 8

LED chip emission spectrum (blue) and phosphor absorption (red), excitation (green), and emission (yellow) spectra. The emission spectrum is for all wavelengths of the excitation spectrum.

The volume percentage of the phosphor in the mold resin is varied between 1% and 5% in 1% increments, and the ${\eta }_{\mathrm{PKG}}$ of the LED PKG for the PKG resin and L/F silver-plating combinations shown in Table 4 are verified. Table 5 shows the results of the simulation considering the phosphor. Hence, it can be observed that the higher the phosphor percentage by volume, the smaller the difference in the extraction efficiency ${\eta }_{\mathrm{PKG}}$ between the maximum and minimum conditions. In addition, if the phosphor percentage is increased, the absorption ratios of the PKG resin are decreased and those of the L/F are increased (Fig. 9). This is because the rays cannot reach the cavity wall (the PKG resin) as a result of the scattering caused by the phosphors (Fig. 10). Thus, the L/F reflectance becomes more important when the mold resin includes phosphors. In the case of SV PKG, the rays can reach the cavity wall because of the narrow cavity (Fig. 11). The absorption ratios of the SV1, TV4, and TV7 PKG at 1% phosphor by volume are higher than those at 0%, because the number of rays reflected in the cavity are increased by the scattering [Figs. 10(b) and 11(b)].

Table 5

ηPKG of each PKG for combinations corresponding to maximum and minimum ηPKG values in simulation incorporating phosphor.

Fig. 9

Absorption ratios for phosphor-containing mold resin: PKG resin under conditions corresponding to (a) maximum and (b) minimum ${\eta }_{\mathrm{PKG}}$ values. L/F under conditions corresponding to (c) maximum and (d) minimum ${\eta }_{\mathrm{PKG}}$ values.

Fig. 10

Ray-tracing simulation (100 rays) of TV4 for phosphor-containing mold resin: (a) 0%, (b) 1%, (c) 2%, (d) 3%, (e) 4%, and (f) 5% phosphor by volume.

Fig. 11

Ray-tracing simulation (100 rays) of SV1 for phosphor-containing mold resin: (a) 0%, (b) 1%, (c) 2%, (d) 3%, (e) 4%, and (f) 5% phosphor by volume.

3.4.

Discussion

From the simulation results, the following SMD PKG optical design procedure can be proposed:

Designers and engineers must design LED PKG under certain restrictions in order to satisfy specific target product requirements. Thus, the cavity angle should be designed to be as close as possible to mirror reflection in Step 2 above in cases where a cavity angle corresponding exactly to mirror reflection is unrealistic. In addition, it is impossible to obtain complete mirror reflection using the examined components in reality. However, we can choose a combination of the PKG resin and L/F reflection methods that yield results as close as possible to the peak of the ${\eta }_{\mathrm{PKG}}$ distribution, because the distribution exhibits a mountain shape with a single peak (Fig. 5).

From the simulation results, it is preferable that the L/F silver-plating reflection exhibits proper scattering; however, the more the reflection is scattered, the lower the reflectance in actuality. Consequently, an investigation of the relationship between the silver-plating scattering profile and reflectance using physical experiments is required. In the case where the mold resin includes a high phosphor content ratio, the effect of the optical properties of the PKG resin is reduced; however, it is still apparent for a low phosphor ratio (Fig. 9). This is especially true for the SV PKG, which has a narrow cavity. Moreover, the L/F silver-plating reflectance is more important in the presence of phosphor, because the absorption caused by the L/F is increasing.