The manufacturing process flow of flexible LED filament with a length of 100 mm is shown in Fig. 1. An average of 100 flip-chips was distributed on the copper substrate, the size of which was 200 μm × 510 μm × 250 μm. SY-6021 silicone A (Shenzhen Shenghuayang Electronic Material Co. Ltd), SY-6021 silicone B (Shenzhen Shenghuayang Electronic Material Co. Ltd), Lu₃Al₅O₁₂: Ce phosphor (particle size 13 μm, emission band 530 nm, Yinghe in China), (Sr, Ca)AlSiN₃: Eu phosphor (emission band 640 nm, Yinghe in China), and (Sr, Ca)AlSiN₃: Eu phosphor (emission band 628 nm, Yinghe in China) were used in this study. The insulation was located in the middle of the paste to prevent short circuits of the electrode. When these procedures were finished, a flexible filament could be obtained. In Table 1, the component dimensions of the multiple chip modules and the thermal properties of the encapsulated materials are shown.

Fig. 1.

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	Fig. 1. (color online) Graphic of the process flow of flexible LED filament.

Flexible filaments without and with injection currents are shown in Figs. 2(a) and 2(b), respectively. A single chip was extracted to the model according to the symmetry of the package structure, and the temperature field and heat transfer process were calculated when the flexible filament is working. We assume that 80% of the rated power of the filament input is converted into heat energy.^[4–7]

Fig. 2.

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	Fig. 2. (color online) Flexible filaments (a) without and (b) with injection currents.

Table 1.

Table 1.

Table 1. Filament module component size and thermal property parameters of packaging materials. . Component Material Thermal conductivity/W · m−1 · K−1 Size Chip sapphire 35 200 μm×510 μm×250 μm Solder SnAgCu 58 180 μm×150 μm×200 μm Phosphor layer silica glue 0.15 R 2 mm×255 mm Substrate Al+Cu+PI 205 255 mm×3 mm×0.15 mm

Table 1. Filament module component size and thermal property parameters of packaging materials. .

Insulated-metal-substrate (IMS) was used as the power electronic substrate of this LED filament. The flip chips were attached on the substrate through Au–Si eutectic bonding. Finally, the flip chips were attached on the substrate through solder and protected by the phosphor glue. A glass bar was used to support the shape of the flexible filament.

The following conditions were fulfilled to simplify the calculation process for numerical analysis: (i)

The calculation has a major emphasis on the steady state of thermal system.

Conservation of mass, energy, and momentum is the basic equation to solve the energy equation describing the heat and mass transfer of the system. In the calculating model, the mass conservation equation is

The momentum equation is as follows (−y is the direction of gravity):

The air density is calculated by the approximate method of Boussinesq

Heat can be delivered by convection, radiation, and thermal conduction. Heat is delivered by thermal conduction mainly in solid state. In the interfacial region, heat is delivered in the way of convection. In fluids, both thermal conduction and convection exist at the same time. Radiation could be emitted from solid surface to the colder outside by means of electromagnetic wave. The packaging model and boundary conditions are shown in Fig. 3. The other faces are open boundaries for environmental temperature and environmental pressure. The junction temperature of chips is taken as the monitoring point. The other coefficients of heat transfer could be calculated under the coupling condition between solid and fluid. Assuming that T_a is the environmental temperature at 25 °C, τ is the direction of heat transfer, then the Fourier's law is

Fig. 3.

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	Fig. 3. (color online) Flexible filament module and boundary conditions.

Convection exists in the region between filament model and air. Newton cooling formula is

Figure 4 shows the numerical model of solder, single chip, substrate, and phosphor layer of the package module. These models are designed in real size. The temperature field and heat transfer process at working state are calculated.

Fig. 4.

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	Fig. 4. (a) Solder, (b) chip, (c) substrate, and (d) phosphor layer.

As shown in Fig. 4, there are four sub-domains included in the computational domain; i.e., chips, aluminum substrate (Al substrate), phosphor layer (glue), and also gas outside the filament. The outside cuboid enveloping the filament is included to simulate the heat change between the filament and the ambient. Heat conduction, natural convection, and radiation heat transfer are involved in the problem. Standard heat conduction equation is used for heat transfer in solid domains such as chips, substrate, and glue. Navier–Stokes equations with buoyancy force term are used for natural convection outside the filament. Figures 5(a) and 5(b) show the multi-block unstructured meshes which are generated by FLOEFD 15.0 in all domains. Chips are distributed on the filament substrate evenly. Figure 5(c) shows the physical model of the computational domain clearly according to the side view.

Fig. 5.

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	Fig. 5. (color online) Numerical simulation model: (a) mesh, (b) side view, and (c) the physical model of the computational domain.

Figure 6 shows the thermal distribution of the spring-like LED filaments at different pitches. In Fig. 6, we have demonstrated that the highest filament temperature decreases widely by increasing the stretching pitch while the lowest temperature is almost constant. Compared with straight filament, the heat generated by the multi-chips of cylinder screw distribution is more severe owing to the closer distribution, which prevents heat from spreading outward.

Fig. 6.

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	Fig. 6. (color online) Thermal distribution of filaments at different stretching pitches by simulation.

The result of the thermal distribution of the filament at different stretching pitches by infrared test is shown in Fig. 7. It can be seen that the highest filament temperature decreases widely by increasing the stretching pitch while the lowest temperature is almost constant, which agrees with the simulation result as shown in Fig. 6. The thermal conductivity of the substrate is higher than that of the silica. Thus, it is expected that this will result in the higher temperature of substrate than that of phosphor silica.

Fig. 7.

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	Fig. 7. (color online) Thermal distribution of filaments at different stretching pitches by infrared test.

By combining Figs. 6 and 7, we can draw the conclusion that the highest temperature point is the upper part on the filament, but not the top. The larger the pitch, the longer the high temperature part, and the lower the air heat density. This indicates that a larger pitch results in a lower filament temperature.

Figure 8 further illustrates the highest temperature and lowest temperature of the filament by simulation and infrared test under different pitches (measured at a typical injected power of 3.5 W) from 11 mm to 19 mm. It is evident that the highest temperature of both simulation and infrared test decreases with the increase of the filament pitch, while it is opposite for the lowest temperature. This indicates that a larger pitch benefits the heat dissipation, whereas it simultaneously increases the heat exchange area surface between air and filament. Furthermore, the ambient temperature is responsible for the lowest temperature of filament. Some reasonable reasons behind these results are provided.

Fig. 8.

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	Fig. 8. (color online) Highest temperature and lowest temperature of filament by simulation and infrared test under different pitches.

The spiral line can be understood as a complex movement of the particle, together with circular motion and straight motion, as shown in Fig. 9. The ratio of pitch to radius eventually affects the helix angle. The temperature distribution of simulated straight filaments at different inclination angles is depicted in Fig. 10. It can be seen that the highest filament temperature increases widely by increasing the inclination angle, while the lowest temperature is almost constant.

Fig. 9.

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	Fig. 9. (color online) Sketch of spiral filament expansion.

Fig. 10.

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	Fig. 10. (color online) (a) Schematic diagram of the inclination angle. (b)–(f) Thermal distribution of filaments at different inclination angles by simulation.

Figure 11 shows the corresponding relation of the highest temperature under different inclination angles, in which the black squares correspond to the maximum temperatures in Figs. 10(b)–10(f).

Fig. 11.

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	Fig. 11. Corresponding relation of the highest temperature under different inclination angles.

Thermal resistance is an important parameter to measure the performance of heat dissipation. The model can be calculated under the total power of 3.5 W through Eq. (9). The thermal resistance of the filament is the thermal resistance of multi-chips ranging in parallel. The total thermal resistance is reduced with the increase of the number of chips. Multi-chips in parallel increase the contact area, resulting in the reduction of the thermal resistance. It means that at a constant input power, the more chips, the better the heat dissipation, which can be calculated through Eq. (10).

There are 4 basic steps of the heat transfer: (I) from chips to glue; (II) from chips to substrate; (III) from glue to ambient; (IV) from substrate to ambient. Each step is closely related to one or more thermal resistance models.

There may be thermal contact resistance at the interface between chips and glue, chips and substrate in step (I), and also a spreading thermal resistance when heat is transferred from chips to glue or from chips to substrate. It is difficult to accurately analyze the spreading thermal resistance owing to the complex structure of the filament. The thermal resistances concerning step (I) are not covered in the discussed thermal resistance network and, therefore, the suggested model is only capable of predicting the average filament temperature.

When heat is transferred from the glue or substrate to the ambient in step (II), it is partly transferred by natural convection and partly through radiation, associated with the convective resistance and radiative resistance, respectively. There is only conduction in the heat transfer process of glue and substrate, corresponding to the conductive resistance.

The thermal resistant network, beginning from the junction temperature and ending at the ambient temperature, is shown in Fig. 12, where T_a is the ambient temperature, R_NC is the convective resistance, R_rad is the radiative resistance, R_{glue, cond} is the conductive resistance of glue, T_j is the temperature of PN junction, R_{Al, cond} is the conductive resistance of substrate, and R_{c − p} is the thermal resistance of chip.

Fig. 12.

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	Fig. 12. Schematic diagram of thermal resistance model for LED filament.

The total thermal resistance R is