Introduction
Since Edison’s bulb invented in 1879, lighting engineering has developed rapidly in the past few decades. And improving output power and reducing the size is the tendency with the series evolution of lights [1–5]. On account of the long lifetime, energy savings, environment-friendly characteristics, wide color temperatures, quick startup, light emitting diode (LED) has penetrated into every aspect of daily life, including automobile headlamps, street lamps and general lighting [6–9]. Since LED will benefit society even more widely and deeply in the future, three scientists gained the Nobel Prize in physics in 2014 for inventing efficient blue LEDs based on GaN [10].
There are three methods that are available to realize white LED. The first method is to combine three monochromatic LED showing red, green and blue [11]. However, this method of color mixing brought about low efficiency because of the poor radiant efficiency of green light sources [12,13]. In addition, the different degradation dynamic and temperature management of each light source will result in the color shift during working. Recalibrating mechanism to adapt the color mixing is a way to avoid this problem [14]. But this way makes the system more costly and complex. The second method is the near-ultraviolet (N-UV) LED chips exciting the blue, green, and red phosphor, which changes the wavelength of incident light [15,16]. The third method is using the blue LED to exciting single-phased yellow phosphor or mixed green and red phosphors. This way is practical applications and the major approach in the academic studies [11]. As the third method, the package way for phosphor layer coated on the structure is called phosphor-converted LEDs (PC-LEDs). However, optical energy loss will happen during the process of color conversion, which including light absorption, Stokes shift, and the non-unity quantum efficiency of phosphors particles. The loss of optical energy is converted into heat which can increase the chip junction temperature and the phosphor temperature.
Temperature is the key factor in LEDs system which will influence the lifetime, the luminance output and the correlated color temperature (CCT) [17,18]. What’s more, more than 60% of the electronic power is generated into heat because of non-radioactive recombination of electron-hole pairs, absorption of back-scattered light and low light extraction [19]. Generally, the heat generated by phosphor compared to the heat generated by chip is quite small. Yan et al. [19] revealed that phosphor temperature is a critical factor affecting the lifetime and the performance of LEDs. Luo et al. [20] claimed that the maximum phosphor temperature can attain 315.9°C, leading to the phosphor quenching even silicone carbonization. To sum up, high phosphor temperature will induce the local stress, material property deterioration. Then it will result in the reduction of the phosphors quantum conversion efficiency and the decrease of luminous efficiency attributed to the thermal quenching effect. Consequently, effects on the photometric electric and thermal performance of the PC-LEDs device need more studies. Thermal model is regarded as an effective tool to predict temperature for PC-LEDs device. Moreover, part of the light is absorbed by the packaging material and converted into heat during the process of optical propagation. Well-designed optical components and optical interface structure also play an important role in reducing the light absorption in the packaging material loss.
Recently, numerous studies have been reported on the optical design for reducing the light absorption, refraction, scattering, and reflection. Similarly, researchers all over the world have conducted plenty of research on the thermal model. Also, there are several outstanding reviews on the LEDs phosphors development. However, the development of optical-thermal coupled model for PC-LEDs is still lacked until now. This paper is intended to give a brief review of the development of optical-thermal coupled model for PC-LEDs. The review is structured as follows: at first, we discussed the optical model design in PC-LEDs, introduced the influence of the optical parameters in the chips and the phosphor silicone through software simulation in detail. Secondly, we summarized the thermal models to predict the phosphor temperature and the junction temperature. Finally, we summed up optical-thermal coupled model for phosphors and summarized future optical-thermal issues exploring the light quality for LEDs.
Optical design in PC-LEDs
The radiation of the chips and the emitting light of the phosphor exposed to the ambient after coming through the optical components. Because of the light absorption by the material, it is the key to reduce the optical path of light in the packaging material to improve the LED light efficiency. Therefore, it is necessary to design the structure of each optical element to reduce unnecessary scattering, refraction and total reflection. As for the judgment criteria of the optical element, luminous efficiency, angular color uniformity and color rendering index are crucial to evaluate LED light quality. At present, the influence of the optical components such as the chips and the phosphor silicone matrix was analyzed based on optical ray tracing using the commercial software ASAPTM or software LightTools and the scattering model. The software support customized device geometries and optical properties such as refractive index, reflectance, transmissivity and scattering properties of each device component. The optical models for LED devices could be divided into two parts: phosphor layer and LED chip, which will be described in details below.
Effect of phosphor parameters on optical properties
Phosphor is a necessary element for LED devices and plays a crucial role in the quality of LED [11]. The phosphor is excited by a high-density photon energy and heat energy from the chips in the circumstance of operating. Due to the heat, the phosphor crystal is in a highly-excited state and results in the LED excitation energy to convert into more thermal radiation via lattice relaxation rather than optical radiation. Such process is known as Stokes shift, thereby further decreasing the luminous efficiency [21,22]. Moreover, the heat energy generated by phosphor is hard to dissipate. Then the phosphor temperature increases greatly and reduces the optical characteristics of phosphor [23]. It has argued that the phosphor temperature is maximum among the temperature distribution [24–26]. Therefore, many researchers made many studies for the phosphor parameters on the optical properties.
Influence of phosphors parameters on angular homogeneity of PC-LED
Angular color uniformity is a key optical property of PC-LEDs. The energy distribution of the blue light emitted by the chip and the yellow light emitted by the phosphor is also different on account of the different luminescent properties of the chip and the phosphor. The different energy distribution eventually leads to a difference in CCT received at different viewing angles. Non-uniformity light color distribution not only reduces the LED quality but also affects the user’s feelings. Therefore, the angular color uniformity of the LED must be evaluated.
Fig.1 Sketch of the simulation model: (a) LED die with a phosphor-layer placed on its top, (b) LED light source with a hemispherical detector, and (c) LED light source with a segmented detector configuration. For the phosphor-layer the height h, the width b and the concentration c of the phosphor particles in the silicone matrix are varied throughout the simulations. Both the hemispherical and the segmented detector have a radius of 1 cm. The hemispherical detector is divided into 101 pixels along the principle axes while the segmented detector consists of 61 segments (Adapted from Ref. [27], Copyright 2008, Elsevier) |
According to the scattering model of Mie, the scattering process of the model is simulated. Based on the model as illustrated in Fig. 1, the blue LED light is 460 nm and the converted yellow light is 565 nm. Two wavelengths are supposed that only blue light is absorbed and each absorbed blue photon is translated into a yellow photon during the simulation process. To gain the optimized method of three parameters h, b, c, using control variable method throughout simulation run, namely two of these parameters are kept constant while the third one is varied. The results of ray tracing simulations show that the center of the phosphor layer is more bluish than the border for the lower phosphor-layer heights. With regard to further increased heights, the phenomenon is reversed, namely more yellowish in the center with a bluish fringe at the border. With the phosphor concentration change, the light emission also has a non-homogenous phenomenon which is resemble to the height variation. What is more, the phosphor concentration as an important parameter determines the absorption rate and the scattering rate. It makes the blue LED light initially forward directed radiation properties homogenize [27–30]. Phosphor particles with average diameter of 7.8 mm and a standard deviation of 4.2 mm are regarded as reference particles. A strong deviation from angular homogeneity could be found when particle diameters are varied. Namely, the particle diameter larger than the reference one leads to a yellowish fringe with a bluish center. And the smaller one results in a bluish fringe with a yellowish center. The phenomenon for the larger one could be explained that the blue light is too much forwardly directed and are not in harmony with the converted yellow light. As for the smaller particles, the behavior can be explained that the entire number of phosphor particles per unit volume is comparably larger because phosphor layer having the same phosphor concentration but lower diameters of the phosphor particles. Similarly, the entire number is lower for the larger one. The change in the number of phosphor particles per unit volume is related to the change in the number of scattering events per unit volume. It also denotes that the radiant intensity of both the blue and the converted yellow light is in harmony with the one at different heights of the phosphor layer. Furthermore, it is found that there is a clear correlation giving a straight line between the optimal height and the particle diameter [31–33].
As shown in Fig. 2, three types of surface shapes can be formed by the dispensing process, which is characterized by
R is the radius of the spherical cap. Define k= 0, when phosphor layer surface is flat. Meanwhile, k>0 when it is convex and k<0 when it is concave. At the same phosphor concentration, simulation results display that mean CCT reduces with the phosphor surface curvature increases. The amount of phosphor increases with increasing convex surface curvature at the same phosphor density. The increase of phosphor will result in a higher ratio of blue to yellow and a lower mean CCT output. Regarding the situation of the concave phosphor layer surface, the CCT output increases with the total value of the convex surface curvature increase due to the decrease of phosphor amount. The convex phosphor contributes to the light extraction of directional blue light from chips. Compared to the isotropic yellow light of phosphor particles, the convex phosphor comes to higher CCT output and higher ∆CCT. To make the CCT output unchanged, phosphor particle concentration decreases with the surface curvature increases. Yellow and blue light assume angles of 0° and 180° with convex phosphor structures without the typical geometrical boundaries of the reflective cup, resulting in forward light pattern. In addition, the steadiness of the ∆CCT shows that various factors are neutral to each other with the surface curvature increasing. Same ways are used to explain the consequences of concave phosphor structures. In contrast to the convex state, the ∆CCT increases as the totally valued of the surface curvature increases because a narrower light escaping cone is formed. The reason for the narrower light escaping cone is the overall internal reflection and the critical angle. As a result, the concave surface curvature prevents light from reaching angles of 0° and 180°. The light extraction is shortened by the surface of the concave phosphor layer. Therefore, for purpose of obtaining superior CCT angular uniformity, the phosphor surface curvature of 3.5 cm−1 is chosen as the optimal solution among the LED packages. Liu et al. [80] claimed that the color deviation and YAG:Ce phosphor particle sizes show a linear growth relationship. 2–8 mm particles are more easily to achieve uniform white light than 10–20 mm particles. In other words, 2–8 mm particles is a better choice for high angular color uniformity. If using 10–20 mm particles, it is a good choice to use low phosphor concentration at low color temperature or high phosphor concentration at high color temperature.
To sum up, the manufacture of LED that excel by an optimized angular homogeneity proves to be influenced by lots of factors, including blue LED light source, phosphor concentration, phosphor surface curvature, package types, phosphor-layer thickness and phosphor particle size distribution. All of these factors have to be controlled exactly.
Effect of the phosphors parameters on luminous efficacy of PC-LED
As shown in Fig. 3(a), the phosphor layer of in-cup phosphor package is mixed with silicone and phosphor. What is more, the phosphor-silicone mix is dispersed throughout the cup. The remote phosphor package forms a thin phosphor layer which separates from the chip as shown in Fig. 3(b). The outcome shows that the lumen output decreases as the particle size of phosphor increases from nanoparticles to submicron dimensions (between 0.1 and 0.5 μm). Then the luminous flux still increases with the particle size increase to micron size. The cause of this phenomenon is the extent of light scattering. The extent of light scattering is complex in the particle-encapsulant complex material. Moreover, the extent of light scattering is determined by the phase function of particle size, the degree of mismatch in refractive index between particles and encapsulating material, the wavelength and the concentration of particle in suspension. It is common knowledge that nanoparticle composite transmits larger amounts of visible light. It implies that the nanoparticle composite has a low trapping efficiency. Therefore, the luminous flux decreases with the particle size increases from a nano-size to submicron size. In addition, the particle size increase from the submicron size is corresponding to the minimal luminous flux and the complex material produces more transparent to the visible light [34,36,37]. The addition of light transparency diminishes trapping efficiency due to the particles scattering. The luminous flux thus increases with particle size increases from the particle size matching to the minimal luminous flux.
The remote phosphor package (shown in Fig. 3(b)) reduces the amounts of yellow and backscattered light emitted backward into the LED chip. What is more, the luminous flux increases and then decreases with the CCT increases for the two types of packages with the micron particle size. The reason for the phenomenon is that the luminous flux is a function of the full power and the power distribution of the light spectrum. In the light spectrum with a lower CCT, the power ratio of yellow to blue light is higher. Because yellow light has a higher luminous efficacy than blue one and the luminous efficacy increases as the CCT decreases. To increase luminous efficacy, it is necessary to enhance the phosphor concentration to improve the absorption of blue light and the emission of yellow light by phosphorus particles. The increasing of phosphor concentration results in a raising of trapping efficiency and thus increases the light absorption by packaging materials [38]. When the concentration reaches to a certain value, the light absorption is higher than the positive effect of yellow light on the luminous efficacy. Thus the luminous flux begins to decrease. Higher phosphor thickness has higher luminous flux. And the luminous flux shifts to lower CCT with the addition of phosphor thickness [33]. Under the same conditions for CCT and phosphor size, the luminous flux of the remote phosphor package compared to the in-cup one, is less sensitive to phosphor size and higher [35]. For particle size as a constant, the lumen efficiency increases with the reduction of phosphor concentration because of less light trapping [28]. In addition, the lumen efficiency increased with convex surface curvature due to the improvement of light extraction and the decrease of the phosphor density.
In conclusion, three factors affect lumen output: the relationship between luminous efficiency and wavelength, the phosphor concentration, and the trapping efficiency of phosphor particles. Furthermore, the amount of absorbed blue light increase with phosphor concentration increases, which results in high luminous efficacy. The process of blue light converts to the yellow light makes the luminous efficacy increase because the luminous efficacy of yellow light is higher than the blue one. However, with phosphor concentration increases, the trapping efficiency also increases and becomes a dominant factor at high phosphor concentration [38]. Lower phosphor concentration and higher thickness have lower trapping efficiency and less backscattering of light which lead to the higher luminous efficacy. The luminous efficacy and CCT are strongly influenced by the combination of phosphor concentration, thickness, particles, packages, and so on.
Effect of blue chip
The larger width is compensated by higher phosphor layer due to the blue and yellow light are conducive to white light generation. The blue LED chip has a Lambertian radiation pattern.
where n1 is the refractive index of the low refractive index material, n2 is the refractive index of the high refractive index material, q is the critical angle when total reflection occurs. Usually, the refractive index of the chip is about 2.5, and the refractive index of the phosphor powder is about 1.4 and 1.7. The difference between the refractive indexes of the two materials causes the light propagation and the chip-phosphor interface total reflection. According to Eq. (2), the critical angle of total reflection is 34°−43°. Therefore, the large lattice mismatch between sapphire and GaN impacts LEDs internal quantum efficiency. And a serious total reflection between sapphire and GaN reduce the light extraction efficiency [39,40]. There are two main methods to improve internal quantum efficiency. One is making epitaxial wafers have low crystal defect density and adopting advanced epitaxial structures. The other one is increasing the carrier radiant recombination-rate and reducing carrier leakage [40–43]. So it is the key to improve light extraction efficiency in various ways, such as patterned sapphire substrate, surfacing roughing. These proposed methods play a significant role in the enhancement of LED luminous efficiency. To find out the optimal methods, researchers have to routinely perform lots of experiments to evaluate the results of varying parameters. However, the manufacturing process and characteristics of LED devices must be performed completely, which is time-consuming and not profitable. In addition, this long process and many steps largely increase the possibility of mistakes, leading to inaccurate and uncertain results. Based on the above disadvantages, a new methodology by computer simulations is hence used in the study.
Chip surface roughening or patterning
Roughening or patterning the top surface of chip is a way to improve the light extraction. The roughed or patterned surface lessens the internal light reflection and outward light scatters [44]. The way to realize surface roughening and patterning includes chemical etching, deposition, etching or printing. The surface of the chip forms a regular or irregular microstructure [44–46]. As shown in Fig. 4, the light can be randomly refracted and reflected at the chip-phosphor interface. More light escapes from the chip and improves the light extraction efficiency of the chip when the chip surface is roughened or patterned. As shown in Fig. 5, Tsai et al. [47] prepared a hemispherical patterned chip surface structure. According to the experimental results, the structure improves the light extraction efficiency by 65% at a driving current of 350 mA compared to the flat chip surface. Cho et al. [45], according to the 3D finite-difference-time-domain (FDTD) simulation, claimed that the extraction efficiency of the PC-LEDs increases steadily with the etch-depth. However, the increment lessens with the etch-depth becomes larger than ~l/n. So the farther optimization of factors such as the lattice constant and the filling factor could pledge the better LEDs.
Substrate patterning
The basic principle of the substrate patterning is to make a patterned structure on the top surface or the bottom surface of the substrate, for example, a regularly arranged hemispherical array, a columnar array or a conical array [48–50]. As shown in Fig. 6, compared with the flat surface, the patterned substrate can realize the diffuse reflection of the reflected light. Also, the patterned substrate changes the direction and the path of the light propagating so as to improve the light extraction efficiency. TracePro, the optical software, is used to run the simulation. The first step of simulation is building the chip model, as shown in Fig. 7. All the parameters are set according to the actual LED devices data to assure the accuracy of the model. The second step is to make the top and bottom surfaces of the “active layer” as Lambertian light sources [40,41]. After setting all the geometry and parameters of the model, TracePro will reveal the luminous flux of each surface based on its math function.
Through Wang et al. work, various patterned sapphire substrates have been systematically optimized [40]. According to the simulation results, as shown in Fig. 8, the dome-patterned sapphire substrates LED (D-LED) with 10 in the generatrix’s central angle exhibits the highest brightness and the lowest luminous intensity. What is more, its total luminous flux is relative high. In addition, as shown in Fig. 9, the EL feature of the chip shows that the luminescence intensity of an optimal dome-patterned sapphire substrates LED is improved 19% compared to the cone-patterned sapphire substrates LED (C-LED) with the same dimensions. These conclusions straightforwardly confirm the availability of optimal dome-patterned sapphire substrates for improving LED luminous efficiency [42,43,51–54].
Thermal design in PC-LEDs
At present, about 65% of the LED input energy is changed into heat. Temperature has a crucial impact on luminous efficacy, lifetime, and color temperature of the LED device and system [55–57]. The heat transfer needs to pass through multiple standards because the LEDs have small size and high power. Thermal design has always been a difficult problem for LED packaging. Besides, the quantum efficiency of LED chips and phosphors are closely related to temperature. So accurately measuring or evaluating LED chip junction temperature and phosphor temperature are the key to thermal design. Heat is generated because of the light absorption and Stokes shift. What is more, the heat increases the chip junction temperature and the phosphor temperature [58–60].
Phosphor temperature
Phosphor temperature will reduce the conversion efficiency, resulting in decrease in the luminous flux, which is called thermal quenching effect [61–63]. The reduction of phosphor emission lows LED lumen efficiency and changes the CCT. In addition, phosphor temperature also causes the peak wavelength shift and the CCT changes [63]. Therefore, it is a challenge to quantify the heat generated in the phosphor layer and analyze how much luminous flux reduces during the LED package. However, the way to measure phosphor temperature is a difficult problem to solve. Thermal model is testified to be an available method to estimate the phosphor temperature. Kang et al. [64] proposed a one-dimensional model for white LED with phosphor layers. The model predicts the blue and yellow light intensities on condition that the phosphor thickness, the boundary’s yellow light reflectivity and phosphor particles characteristic parameters are available. But they did not publish details about how to estimate yellow light reflection coefficient for complicated package geometry. Yan et al. [19] found through the simulation that the phosphor temperature is always higher than the chip junction temperature regardless of the position of the phosphor. And the model showed that about 8% of the input energy is changed to heat in phosphor layer. Juntunen et al. [17] proposed a model and considered the heat generated in the phosphor layer. However, this model only laid emphasis on junction temperature estimation and ignored the phosphor temperature calculation.
Three packaging structures are as shown in Fig. 10. The structure for LED chip without any coating has been built unidimensional thermal resistance model, as shown in Fig. 11(I). The model only considers the chip with the die attaches adhesive. The heat transfer path is only from the junction layer to the ambient. As shown in Fig. 11(II), a bidirectional thermal resistance model displays two heat flow branches from the junction to the ambient. The two branches are defined as the upper branch and the lower branch. The lower branch is from junction to the substrate to the ambient. The relevant thermal resistance is Rj-s-a. While the upper branch is from the junction pass silicone layer to the ambient and the relevant thermal resistance is Rsili. As for the LED chip with phosphor coating showing in the Fig. 11(III), a modified bidirectional thermal resistance model has two heat source, namely chip heat source Qchip and phosphor heat source Qphos. For purpose of evincing the new heat source, the phosphor node Tph is established as the highest temperature in the phosphor layer. Then Qphos is divided into two heat transfer paths. In another word, one is between phosphor node and the ambient Qph-a across Rph-a, and the other is between the phosphor node and the junction node Qph-j across Rph-j. Therefore, the heat flux part Qph-j and Qchip converge into Qj-a, then continues conducting downward to the ambient node [59]. Based on the model, the junction temperature Tj and the phosphor temperature Tph can be acquired as follows:
where Ta is the ambient temperature.
Figure 12 displays the calculated Qphos and Qchip for packaging structure (III) under different driving current. It obviously found that Qchip is always higher than Qphos. Namely, most of energy is converted into heat in the chip for PC-LEDs [18]. According to Fig. 13, the Tph is always higher than the Tj. Besides, the rising rate of Tph is obviously higher than Tj. It means that phosphor temperature is more sensitive compared to the Tj. What is more, calculated Tj agrees pretty well with measured Tj by comparing with the simulation and experiment. Figures 12 and 13 verified that a part of energy are converted into heat in the phosphor. As a result, phosphor temperature should be focused on LED package and design process.
An accurate model of PC-LEDs was built in two different ways of package, as shown in Fig. 14. Figure 14(a) revealed phosphor layer is covered on the blue-chip directly; which called direct phosphor coating. Meanwhile, Fig. 14(b) showed the phosphor layer is isolated from chip by silicone encapsulant, which called remote phosphor coating. The phosphor thickness was 80 mm and the ambient temperature was 25°C. In the model, the temperature field was simulated. At the same time, optical simulation was conducted and the light flux absorbed by the phosphor and the chip were calculated.
Figure 15 shows that the heat generation of both the phosphor coating increased significantly with the enhancement of phosphor concentration. The reason for the phenomenon is that more light is absorbed by the phosphor particles with the phosphor concentration increased. The heat generated in chip with direct phosphor coating enhanced. However, the heat generated in the chip with remote phosphor coating hardly changed. Due to the phosphor layer was coated on the chip directly, more blue light emitted from the chip would be back-scattered to the chip, which increased the heat generated by chip. Hence, the heat generated by chip in the direct coating package was higher than the one in remote coating package. Figure 16 demonstrated that as the phosphor concentration increases, the three temperatures in both LED packages increase. The chip temperature is lower than the phosphor temperature and the maximum temperature coincide with the phosphor temperature. It shows that for the direct coating package, the location of hotspot is the phosphor layer, regardless of the phosphor concentration. Since the thermal conductivity of the phosphor is relatively low, the heat in phosphor is hard to be dissipated into the air, so the temperature is slightly higher than that of the chip. For the remote coating package, as shown in Fig. 17, when the phosphor concentration is lower than 0.20 g/cm3, the chip temperature is higher than the phosphor temperature, the hot spot is on the chip; when the phosphor concentration is over 0.20 g/cm3, the phosphor temperature is higher than the chip temperature, and the hot spot is transferred to the phosphor layer [65].
As shown in the Fig. 18, silicone layer with yellow phosphor coated on blue-chip to produce white light. The phosphor particles have different sizes. In the simulation, the phosphor particles are regarded as two different sizes, 5 and 7 mm, respectively. Based on the above model, the phosphor temperatures of three cases with different phosphor particle configurations were simulated. Figure 19(a) indicated that the larger phosphor particles are in the upper layer of Case 1 and Fig. 19(c) indicated the larger phosphor particles are distributed in the lower layer in Case 3. The larger and smaller phosphor particles are mixed in the Case 2 (see Fig. 19(b)). The simulation result shows that the heat tends to conduct along the phosphor particles due to the phosphors have larger thermal conductivity than the silicone matrix. The phosphor particles which close to the chip have higher temperature and the phosphor particles which is far from the chip have lower temperature. Comparing the phosphor temperatures in the three cases, it is found that the highest temperature in Case 1 is 116.9°C, while he highest temperature in Case 3 is 116.78°C [66]. Case 1 has largest temperature and Case 3 has lowest temperature. The temperature in Case 2 is the middle one [66]. So the heat is harder to be dissipated into the air for the larger phosphors particles.
Junction temperature
In PC-LEDs, the purpose of continuously reducing the package thermal resistance is to control the temperature of the p-n junction in the LED. As a light emitting device, the junction temperature greatly impacts the performance of the LED. The increase in junction temperature will result in a decrease in the electron-hole recombination probability in the p-n junction. Then the decreasing will affect the chip’s internal quantum efficiency and make the brightness of the chip significantly lower after a period of operating [67–69]. As shown in Fig. 20, its optical attenuation speeds up significantly when the junction temperature rises. The higher LED junction temperature will also accelerate the degradation of the packaging material and weak its optical, mechanical, and thermal properties at the package interface, such as yellowing of the silicone, cracks, delamination and so on [70,71]. Further, the degradation of the packaging material makes the LED product reliability decreases and life decreases [72]. Figure 21 shows the relationship between the lifetime of an XLamp XR-E white LED from Cree and the junction temperature. As can be seen from the figure, its service life is significantly reduced when the LED junction temperature rises. In addition, an augment in junction temperature shifts the peaks of LED luminescence and affects the correlated color temperature of the light, resulting in unstable light colors [73].
The model of spiral LED bulb was shown in Fig. 22. Other faces are open boundaries for ambient temperature and environmental pressure. The junction temperature of chips was taken as the monitoring point. Other coefficients of heat transfer could be calculated under the condition of coupling between solid and fluent. The ambient temperature is set as 25°C. According to the color of the filament in Fig. 23(a), the highest temperature was in the center of the spiral PC-LEDs. The temperature gradually decreased with the radius increased. In summary, the shape of flexible LED filament has a great influence on the heat dissipation of flexible LED filament. The chip junction temperature was related to the stretching height closely.
LED junction temperature can be measured in many ways. However, most of them require special instruments or destructive measurement. The measurement process is often complicated and requires a certain amount of time. Therefore, rapid measurement of LED junction temperature by simple measurement is significant. The work in this area has only begun to progress in recent years. Luo et al. [74] proposed a thermal model as shown in Fig. 24, only considering the heat which generated by the chip. Figures 24(b) and 24(c) are the heat flat path and the thermal resistances network, respectively. In this model, Rcop, Ralu, and RTIM respectively represent the thermal resistances of copper heat sink, aluminum stage and TIM layer. is the temperature of the bottom surface of the copper heat sink and hequ is the equivalent heat transfer coefficient at the bottom surface of the aluminum stage. The junction temperature is obtained as follows:
where A is the bottom surface of the heat sink. Based on the equitation, it realizes the prediction of the junction temperature of a single LED chip. The copper heat sink in the package bracket was divided into several parts of different diameters for processing. Different parts were connected through the equivalent convection heat transfer coefficient and combined with the measured average temperature of the heat sink fins to realize the prediction of the LED junction temperature. However, in practical applications, there are relatively few products with a single LED as a light source. And it is more common to pack multiple LED chips in an array. The prediction of junction temperature in multi-chip array packages is still in the missing stage.
Optical-thermal coupled model in PC-LEDs
Heat comes from light and affects light. On the microscopic point of view, luminescence is a radiative transition and heat is a non-radioactive transition. The two factors compete and interact with each other. Actually, the thermal and photometric factors of LED systems are closely linked together. However, most of the existing research studies light and heat alone, ignoring the nature of optical-thermal conversion. Therefore, the optical and thermal aspects of LED devices need to be coupled to study and the light-heat interaction between the photoluminescence was analyzed in depth to improve the light-to-heat conversion efficiency.
Phosphor is a kind of photoluminescence material. The energy conversion process includes radiative transition process and non-radioactive transition process. In the process of radiative transition, phosphor stimulates yellow light while non-radiative transition process generates heat. The energy generated during the non-radiative transition will dissipate in the crystal lattice. The crystal lattice will raise the temperature of the phosphor, resulting in problems such as decreased luminous efficiency and reduced lifetime of the phosphor. Therefore, it is necessary to suppress this non-radiative transition and improve the probability of the occurrence of radiative transitions. The radiative transition process and the non-radioactive transition process compete with each other under the premise of energy conservation. And the luminescence and heating processes are coupled with each other. Luo and Hu [75] modified the Kubelka–Munk theory by taking into account the light conversion process during propagation of light in phosphor mixed with silicone. What is more, based on the light scattering model of the phosphor particles, they established a photo-thermal coupling model of phosphor particles and calculated the photo-induced heating of phosphors. They also analyzed the effects of phosphor parameters (thickness, particle size, concentration, conversion efficiency, etc.) on the photo-induced heating of phosphors.
As shown in Fig. 25, the blue and yellow backscattering light energy F(z) can be expressed FB(z) and FY(z). The blue and yellow forward scattering light energy E(z) can be expressed EB(z) and EY(z). z is meant invasion depth and E0 is the input energy. The heat generated by phosphor Qphos(z) could be calculated as follows.
where is phosphor particle conversion efficiency, and are respectively expressed as absorption coefficient of blue and yellow light by phosphor particles. Qphos-total is defined as the total heat generation, which can be calculated by
It can be seen from Fig. 26 that as the depth of light intrusion increases, the phosphor heat generation is significantly reduced. The phenomenon means that a small invasion depth generates more heat and a large invasion depth generates less heat. The reason for this phenomenon is that the phosphor layer is closer to the chip (a small invasion depth), more light will be scattered, absorbed and converted. Figure 26 can also be found that the phosphor heat generation decreases with the quantum efficiency increases. Namely, more absorbed blue light is changed to yellow light led to less heat. As shown in Fig. 27, the total heat generated in phosphor increase with the addition of phosphor thickness and concentrations. Both two factors have the similar effect on the phosphor heat generation. Above that, phosphor concentration and thickness determine the phosphor amount. In other words, the greater phosphor amount is, more light will scatter, absorb and transform resulting in more heat. As shown in Fig. 28, a peak occurs in the phosphor heat generation and then gradually decreases when the phosphor particles size increases. The peak value corresponds to the critical size of the phosphor. The reason for this critical dimension is that the phosphor scattering coefficient changes with the phosphor particles size [75]. However, by modifying the traditional theory, an optical-thermal coupled model of the phosphor was established to calculate the phosphor heat generation. But their research was limited to the macroscopic level and there was no mutual penetration of optics and thermology into the phosphor photoluminescence and heat generation. Besides, it also lacks research on microscopic energy conversion of phosphors. It is crucial to depth to the microscopic level of the phosphor material, which truly improve the phosphor photoluminescence and heat generation through the material modification. Furthermore, Hui and Qin [76] conducted a theory that connects the electrical, photometric and thermal behaviors of whole LED system. This theory determines the best operating point for an LED system in order to achieve maximum luminous flux for a given thermal design. What is more, the theory demonstrated that thermal design is an integral part of the electrical circuit design. However, the theoretical model is focused on the electrical circuit design. And the model ignores the phosphor temperature, also not mentioned the relationship between the thermal and optical. Therefore, an LED device model has been established to predict the junction temperature and light output, which ignoring the phosphor temperature [77]. An electrical-thermal-luminous-chromatic model was derived to predict the optical performance with thermal management. It can be used to analyze optical quality and thermal performance due to thickness and particle density variation of phosphors [78].
Ma et al. [79] proposed an optical-thermal coupling model to calculate the phosphor temperature and evaluated the thermal quenching effects of laser-excited remote phosphor by further taking into account the temperature dependence of phosphor quantum efficiency. As shown in Fig. 29, the optical-thermal model consists of phosphor scattering model and settled thermal resistance model. What is more, they are linked through the interaction between phosphor heating power Qph and phosphor temperature Tph. As shown in Fig. 29(a), when the laser beat down on the phosphor layer parallelly, light absorption, conversion and scattering processes happen at the same time. In this situation, four light parts can be derived as forward-scattering and back-scattering energy for yellow and blue light EY(z), EB(z), FY(z) and FB(z), respectively. The overall thermal resistance from the ambient temperature Ta to Tph consist of a series of thermal resistance, as shown in Fig. 29(b), which can be expressed as
where Rph, Rbond, Rmir and Rhs are respectively represented conductive thermal resistance of phosphor layer, bonding layer, mirror layer and heat sink, respectively. Rconv is convective thermal resistance from heat sink to the ambient. All heat generated in phosphor layer Qph can be calculated by the equation as follows:
Tph can be calculated by
where Rs,ph is the relative thermal resistance between pump spot with the plate, Rs,hs is the relative thermal resistance between the bonding layer with the heat sink. The temperature dependence of phosphor quantum efficiency (Tph), which can be calculated as
The temperature dependence of is calculated by
According to the modified Kubelka–Munk theory and the energy conservation law, the optical-thermal model was calculated step by step as shown in Fig. 30.
The result of simulation shows that coinstantaneous lower phosphor heating and overall thermal resistance are effective to improve Critical incident power Plimit, and finally enhance the optical-thermal performance of LERPs [79]. However, the optical-thermal coupling model is to study the laser-excited remote phosphor the boundary conditions are not suitable for that of PC-LEDs.
Conclusion and perspectives
Compared with traditional lamps, white LEDs have the advantages of high luminous efficiency, environmental protection, high reliability and long lifetime which have penetrated into our daily life. LED packages based on blue LED chip and yellow phosphors with silicone are the most widely used scheme to produce white light. In this review, we have discussed the optical model and the thermal model for LED devices. First, we discussed the effect of phosphor parameters on optical properties in details via the software simulation. The final optical performance of the phosphor layer is the result of a combination of these parameters: phosphor material, phosphor particle size and particle distribution, phosphor layer concentration, phosphor layer thickness, geometry and spatial location of the phosphor layer. Predictive model is a crucial way to improve the properties of phosphor. To acquire the optimized balance between high color rendition index and luminous efficacy in LED devices, it is needed to explore the balance between the rational phosphor materials and the anticipated luminescence efficiency. The desired emission position and thermal stability need in accordance with the requirements of phosphor. Secondly, we introduced how to improve light extraction efficiency in various ways, such as patterned sapphire substrate, surfacing roughing. However, the design of chip and improve the light extraction efficiency is still a challenge. Because the effects of complicated geometrical characteristics are hardly possible to methodically analyze by experiments only. Thus, computer simulation is a very effective and reliable way to systematically study. Therefore, varieties of novel geometry chips can be optimized and designed with a rational time span. The field of chip with various ways still needs special attention because innovative chip designed by this computer simulation have potential for further enhancement of the light extraction efficiency of LEDs in the near future. Then, the thermal models are described in details to predict the junction temperature and phosphor temperature. To make the optical performance of PC-LEDs steady, many methods has been made to reduce the junction temperature of the chips. The phosphor temperature as a crucial reliability concern for PC-LEDs should be aroused academic interest. Finally, we summed up optical-thermal coupled model. Looking forward to the future work should pay more attention to the interaction between PC-LED electrons, photons, and phonons to study the transformation between their microscopic energies. Coupling the light and heat of PC-LEDs establish an optical-thermal coupling model and calculate its photo-thermal expression is predictable. There are still many research areas that need further study, including not limited to (1) At present, the packaging technology for single-chip or small-sized LED chip has matured, but the future of LED will inevitably move toward multi-chip high-power integrated development. (2) The new phosphor materials are crucial to the improvement of LED luminous efficiency. The new materials provide the possibility of improving the heat dissipation performance of LEDs. (3) The active layer of the LED chip converts electrical energy into light energy, but a large part of the light energy is absorbed by chips, phosphors, encapsulating glue, and lenses during the propagation process. Therefore, increasing the light extraction efficiency is crucial for the improvement of the photothermal performance of the LED. However, to achieve a major breakthrough in any of the above three aspects, the establishment of an optical-thermal coupled model for LED devices is inseparable, and the mechanism of photo-thermal conversion is studied microscopically.