1. Introduction

The invention of efficient blue light-emitting diodes (LEDs) brought worldwide attention to solid state lighting, which, based on its advantages with respect to ecological aspects and the possibility of new lighting effects, is expected to dominate the lighting market in the future [1, 2]. Nevertheless, for a widespread penetration of white LEDs into the general lighting market, design and development of LED light sources are still facing several challenges, for which reduction of costs, efficacy enhancement as well as the improvement of the white light quality are the most important. While the first two aspects are essential from the ecological and economical points of view, the latter is relevant for convincing people to abandon conventional lighting sources. In this context, for example, it has been concluded that for white LEDs to be commonly accepted for general lighting the color variation among individual LEDs should become of the order of a 2–step MacAdam ellipse [3].

For several reasons it is hard to meet this demand with today’s most common approach for white LEDs, which relies on the excitation of a phosphor by a blue or UV emitting LED. The phosphor is part of the color conversion element (CCE), which typically consists of phosphor particles embedded in a silicone matrix and which is placed in the direction of the light emitted from the blue LED die. For a given set of excitation and fluorescence wavelengths, their intensity ratio determines the overall color temperature of the output light. Generally, the larger the amount of phosphor particles the lower are the LED’s (correlated) color temperatures (CCT). While this concept seems to be rather trivial, recent studies have shown that the performances of LEDs in terms of light output and white light quality also critically depend on the shape, composition and arrangement of such CCEs within the LED package [4–12] as well as on materials parameters, like the extinction coefficient and the quantum efficiency of the phosphor [13]. For example, referring to a reference system, that was defined by an LED package consisting of an LED die and a square-shaped CCE, the latter having a width b of 1040 µm, a height h of 400 µm and a phosphor concentration c of 10 vol. % (in the following named “LED with a thick phosphor layer”), it was concluded that a reduction of the quantum efficiency of the phosphor by about 6% would result in a deviation from the initial CCT value that matches the outer limits of a MacAdam ellipse of step 2, similarly for a reduction of the extinction coefficient of about 5% [13].

Generally, phosphors are prone to decreasing luminescence intensity with increasing temperature, which therefore may severely affect the color temperature constancy of LEDs under operation. Therefore, care should be taken, that the temperature increase and variation within the LED package and in particular in the CCE upon device operation remains as small as possible. Using one specific Ce-doped yttrium aluminum garnet (YAG) as a reference phosphor and based on the above mentioned valuation of permissible reductions of the quantum efficiency, it has been concluded that a temperature variation of about 40 K [13] might be just tolerable for CCT variations which do not exceed a MacAdam ellipse of step 2, however, assuming that this would be the only source for color deviation. In reality, in order to give leeway to the other potential sources for color deviation, and to keep the luminescence intensity of the phosphor at a high level, care should be taken that the temperature increase and variation within the CCE remains at the lowest possible value.

This is of particular relevance, since, as shown in some recent studies [14–16], the highest temperatures within phosphor converted LED packages may be located within the CCE. The reason for this is the low thermal conductivity of the silicone matrix, which gives reason for a high thermal load of the CCE. In this regard, in a recent study [17] we presented a combined optical and thermal simulation procedure which allows us to enter into a detailed discussion of the correlation of the materials properties, in particular the quantum efficiency of the phosphor and the thermal conductivity of the CCE, and the temperature increase within the CCE. Both parameters should be as high as possible, which, in case of the thermal conductivity of the CCE, e.g., can be achieved by increasing the phosphor concentration in the silicone matrix.

In the following we show that, besides such compositional aspects, also different LED driving schemes have a notable impact on the thermal load of the CCEs, which have to be considered for in strategies to keep the CCT values of phosphor converted LEDs under operation as constant as possible. The LED assemblies investigated (see Fig. 1) comprise the LED with the thick phosphor layer and an LED with a thin phosphor layer (a CCE with a height h of 200 µm, a width b of 1040 µm and a concentration of c = 16 vol.% of phosphor particles) in order to deduce the impact of a higher phosphor concentration and therefore a higher thermal conductivity of the CCE. The specific height and phosphor concentration for the latter CCE geometry were chosen in order to get a similar overall CIE x value of 0.33 as observed for the LED with the thick phosphor layer.

 

Fig. 1 Top, left side: The model of the LED assembly consists of a blue emitting LED die with a square-shaped CCE placed on top of it. The sketches refer to an LED with a thick phosphor layer (CCE having a height h of 400 μm, a width b of 1040 µm and a concentration of the phosphor particles in the silicone matrix of 10 vol. %) and an LED with a thin phosphor layer (CCE with a height h of 200 μm, a width b of 1040 µm and a concentration of the phosphor particles in the silicone matrix of 16 vol. %). Right side: Sketch of the different operational conditions: PWM with duty cycles of 25% and 50%). Bottom, left side: 3D sketch of the model for the LED with a thick phosphor layer. The CCE (0 µm to 400 µm) is placed on top of the silicon substrate (0 µm to −100 µm) of the LED die. The printed circuit board consists of an aluminum substrate with a height of 1500 µm (below −260 µm) and a dielectric layer (−180 µm to −260 µm) as well as a copper layer on top of it. Latter and the adhesive layer range from −100 µm to −180 µm. Right side: Temperature distribution as determined for one exemplary operational condition superposed on the 3D model.

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The most common driving techniques for LEDs are DC current and pulse width modulation (PWM), the latter one in particular in case of dimming applications [18]. Several studies have discussed the differences of these two driving schemes for the constancy of CCT values of phosphor converted white LEDs [19–21]. E.g., an increase of the driving current results in a blue shift of the emission spectrum of the LED die [21]. On the other hand, an increase of the junction temperature at constant driving current results in a red-shift of the emission spectrum. Such a shift of the emission spectrum of the blue exciting wavelength may have a notable impact on variations of the CCT values. On the one hand it changes the amount of phosphor excitation and on the other hand the blue LED light directly contributes to the spectrum of the white light. As suggested by Loo et al. [21], under DC conditions and using an appropriate thermal design, the different impacts of current and junction temperature increase in principle could be compensated and a shift of the exciting wavelength can be suppressed. This is not possible under PWM conditions, for which the amplitude of the current is fixed. In this regard, a bilevel current driving approach, in which the current pulsates between two different current levels and the average current is determined by the duty cycle provides some benefits [21].

Besides such a current-dependent shift of the excitation wavelength, one has also to consider that the emission intensity of LEDs varies linearly with the forward current for small currents, but there is a tendency for saturation at high currents [18]. Therefore, time varying current waveforms with large amplitudes are prone to lower the device efficacy. However, besides efficacy, as will be discussed in the following, this non-linearity has also to be considered for the respective thermal load of a CCE, which, due to its impact on the luminescence intensity of the phosphor, may also affect the constancy of a desired CCT value.

2. Experimental

The details of the combined optical and thermal simulation procedure can be found in a previous publication [17]. It relies on the set-up of an appropriate simulation model for a blue emitting LED die and the implementation of a CCE with a flat surface on top of the die (see Fig. 1 for a sketch of the LED assembly). The die’s active area (940 µm × 940 µm) is located on top of a silicon substrate. Its gold pads for wire bonding are in two neighboring corners, and the die itself is placed on a printed circuit board (PCB) by chip-on-board technology. The printed circuit board consists of an aluminum substrate with a height of 1500 µm and a dielectric layer (80 µm) as well as a copper layer (70 µm) on its top. The LED die is mounted on the PCB by an adhesive layer having a height of 10 µm. The silicon substrate of the LED die has dimensions of 990 μm × 990 μm and a height of 100 μm. This specific die design refers to a vertical thin film LED die like the EZ1000 (Gen I) from Cree [22]. From the data sheet of this chip also the electrical and optical characteristics (voltage, current, corresponding radiant flux etc.) for the LED die under operation were deduced.

Of particular importance with regard to the simulation of the thermal load of the CCEs of phosphor converted LEDs with high accuracy is the knowledge of the absorption profile of the blue LED light within the CCE, which is an essential input parameter for the subsequent thermal simulations. Due to the low thermal conductivity of the silicone the heat dissipation is strongly affected by the distance of a heat source (the phosphor particles) to heat dissipating elements like the LED die. As shown recently, such a consideration of the absorption profile of the blue LED light in the CCE is essential in order to get agreement between simulation and experimental investigation of the thermal load of a CCE [16].

In order to determine the absorption profile of the blue LED light within the CCE configurations, firstly ray-tracing simulations were carried out with the commercial software package ASAP^TM, which take two wavelengths, representing the blue LED light (460 nm) and the converted yellow light (565 nm) into consideration. It is assumed that only the blue LED light is absorbed by the yellow phosphor particles, therefore the extinction coefficient of the yellow phosphor particles is set to zero for 565 nm and to 1 × 10⁻³ for λ = 460 nm. Both the blue LED light and the yellow converted light are scattered throughout the CCE. The simulation of this scattering process is based on the scattering model of Mie and considers the particle size distribution of the phosphor, and the optical properties of both the matrix material and the phosphor. The refractive indexes of the silicone and the phosphor are kept constant at 1.4 and 1.63 for both wavelengths. Similarly, the mean diameter of the phosphor particles is kept constant at 7.8 µm with a standard deviation of 4.2 µm.

Dividing the CCEs in a number of voxels allows one to determine the absolute number of the blue radiant flux which is absorbed within each individual voxel from the respective overall blue radiant flux emitted from the LED die for a specific current as determined from the data sheet [17]. There are mainly two sources for heat generation due to the absorption of the blue LED light by the phosphor particles within the CCE, on the one hand heat generation due to the Stokes shift (for the two wavelengths taken into consideration which represent the blue LED light (460 nm) and the converted yellow light (565 nm)) and on the other hand heat generation from the absorption of blue photons and subsequent non-radiative recombination in case of a quantum efficiency smaller than unity. In the following we only consider the Stokes shift as a source for heat generation, this means, the phosphor is assumed to have a quantum efficiency of 100%. Lower quantum efficiencies would not change the overall findings as discussed in the following, but would only give reason for an even higher thermal load of the CCEs.

For simplicity, we also do not consider the thermal impact of this portion of light, which is backscattered from the CCE and absorbed in the LED die again. The data on the number of absorption and color conversion processes for the individual voxels are taken as input parameters for the subsequent thermal simulations in which three-dimensional models of the LED package were set-up using the GPL-software packages GetDP/Gmsh [23, 24]. In this case, the CCE is modeled as a block with a specific thermal conductivity and heat capacity. As the whole geometry of the model is symmetric with respect to 4 axes one principally can reduce the FEM calculation effort and time by simulating only one eighth of the whole sample with adiabatic boundary conditions at the cut surfaces. However, parameters like the local power sources or the absorption profile of the blue light in the CCE break this symmetry. Therefore, an equivalent, 4-axes-symmetrical CCE-power-source distribution was determined. Its validity was checked by comparing the results of full 3D-simulations with the results of the model having a reduced size.

Within the defined model the steady-state heat equation has been solved with the finite element method (GetDP). In order to satisfy heat transfer equations in steady state, the following boundary conditions were introduced: The bottom surface of the PCB is assumed to be mounted on a perfect cooler, which realizes a constant temperature Tcool (Dirichlet boundary condition) at the bottom surface. A cooler temperature of 300 K has been chosen at the bottom surface of the PCB for the present study. All other boundaries of the model are subject to natural convection in air. The exact value of the coefficient h for natural convection depends on many factors (size of the sample, orientation of the sample in space, ambient temperature, etc.). For the simulations presented in this study a value of h = 20 W/(m²K) [25] and an ambient temperature of 300 K have been selected. For the transient thermal simulations the simple, robust, and fairly accurate implicit Euler strategy (backward Euler scheme, Θ = 1) with fixed time-steps has been chosen. Several tests with different step-sizes have been performed to find optimized parameters for the subsequent series of transient simulations. For the simulation of the thermal response to power-on and power-off steps a combination of two pseudo-logarithmic series of time-steps has been chosen, which enables the description of the temperature versus time characteristic for the whole model-geometry with sufficient accuracy and acceptable computing time. For the simulations of the thermal response to a PWM-signal a constant step-size has been defined to create a thermal model which accepts different PWM duty-cycles as input parameters (see Fig. 1).

3. Results and discussion

The top images of Fig. 2 show the calculated steady state temperature profiles along the z direction of the LEDs with the thick and the thin phosphor layers for DC currents of 350 mA, 700 mA and 1000 mA.

 

Fig. 2 Top, left side: Line scans for the steady state temperature profiles along the vertical directions of the LED package with a thick phosphor layer assuming that the assembly is mounted on a cooler with a constant temperature of 300 K and that the quantum efficiency of the phosphor is 100%. The LED assembly is operated at currents which vary from 350 mA to 700 mA and 1000 mA. Right side: same as in the left side for the LED package with the thin phosphor layer. Bottom: Comparison of the thermal load of the CCEs of the LEDs with the thick and the thin phosphor layers for the three different currents investigated.

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As a consequence of the low thermal conductivity, the by far highest package temperatures are in any case located within the CCE, which, e.g., ranges from 0 µm to 400 µm in the top left image of Fig. 2. As evident from the top right side image of Fig. 2, the thermal load of the LED with the thin phosphor layer is lower than that of the LED with the thick phosphor layer. This is due to the lower height (lower distance for heat dissipation by the LED die) and the higher thermal conductivity of this CCE (0.31 W/mK vs. 0.26 W/mK as determined by thermal simulations) because of a higher phosphor concentration.

It has to be noted that for the present study the respective combinations of electrical powers and radiant fluxes of the LED package have been calculated from the data sheet [22], which provides these values for T_A = 25°C. These values have been taken for all the current driving conditions investigated in this study and no temperature induced variations of these parameters like a voltage shift with junction temperature have been considered, since they are of minor relevance for the discussions given in the following. In reality, the radiant flux of the blue LED light shows also some dependency on the junction temperature [18]. As evident from Fig. 2, for the assumed cooling conditions the temperature in the junction area increases by about 20 K when increasing the drive current from 350 mA to 1000 mA. According to the data sheet, such an increase of the junction temperature by 20 K gives reason for a reduction of the overall radiant flux by about 3%. In comparison with the non-linearity of the radiant flux and the driving current as discussed in the following, this is of minor relevance and therefore can be neglected for a general discussion of the phenomenon.

The low thermal conductivity of the CCE is also manifested in its thermal response to current turn on and turn off steps. As shown in Fig. 3, while the final temperatures within the PCB and the LED die (within the aluminum substrate, within the copper layer, and on top of the LED die) both after current turn on and turn off steps of 1000 mA are reached within milliseconds, it takes seconds till the final temperature within the CCE is reached. Again, due to the higher thermal conductivity of the CCE of the LED package with the thin phosphor layer, this CCE shows a somewhat faster thermal response.

 

Fig. 3 Top images: Thermal response of the LED with a thick phosphor layer on a power-on step (1000 mA, top left) and a power-off step (top right) for different positions within the LED package. Bottom images: Same as for the top images but for the LED with the thin phosphor layer.

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Figure 3 also highlights that there are differences in the thermal response along the vertical axes for both CCEs. In particular, nearby the LED die in the bottom part of the CCE, the final temperature is reached faster than in the top part of the CCE. This again can be attributed to the absorption profile of the blue LED light within the CCE. Most of the absorption and conversion processes, which are directly related to heat generation, take place in the bottom part of the CCE [17], while a comparably lower portion of the blue LED light is absorbed and converted in the top part of the CCE. Therefore, the bottom part of the CCE heats up faster during a pulse on step while, due to the low thermal conductivity of the CCE, it takes much longer till also the top part of the CCE heats up and reaches its final temperature. Contrarily, when the current is switched off, the temperature drops faster in the bottom part of the CCE, since it has a closer distance to the LED die that acts as a cooling unit.

Figure 4 shows the thermal response at different positions along the vertical axis of the LED package with the thick phosphor layer operated under PWM conditions. In this case, a duty cycle of 50% at 100 Hz and a current amplitude of 1000 mA is chosen for the operational condition.

 

Fig. 4 Left side: Thermal response of the LED package with the thick phosphor layer operated under PWM conditions (1000 mA, duty cycle 50% at 100 Hz) for three different positions within the LED package. Also shown is the thermal response under DC conditions for IF/2, PE/2, PB/2 and a combination of PE/2 and PB/2, (PE/2@PB/2). Right side: Thermal response of the LED package shown in the left side on a larger time scale. In addition, the thermal response within (z = 100 μm) and on the top of the CCE (z = 400 μm) is added in this image.

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As shown in the left side image, again, the final temperature within the PCB and on top of the LED die is reached within milliseconds. Also included in the image are the thermal responses for the operation of the LED package under DC current conditions (which means the response to a DC current turn-on step) of half of the PWM current amplitude (IF/2), half of the electrical power (PE/2) with regard to DC current operation of 1000 mA, half of the blue radiant flux (PB/2) with regard to DC current operation of 1000mA as well as a combination of PE/2 and PB/2, for which the blue radiant flux is hypothetically set to half of its value for 1000 mA at PE/2 (PE/2@PB/2). The right image shows the thermal responses within the PCB, the LED die and within the CCE on a larger time scale. Again, it takes seconds till the final temperature within the CCE is reached. In addition, the thermal response within the CCE by far does not show the pronounced dependency on pulse period and duration, as it can be observed, e.g., on top of the LED die (see the inset).

Figure 5 shows the thermal response within the CCE more in detail, both at z = 100 μm (left side) and z = 400 μm (right side). Again, the thermal responses for operating the LED package under DC current conditions of IF/2, PE/2, PB/2 as well as a combination of PE/2 and PB/2 are included in the images. A comparison of DC current operation at 1000 mA (see Fig. 2) and PWM operation with a current amplitude of 1000 mA and a duty cycle of 50% at 100 Hz shows, that the temperature in the junction area at the top of the LED die reduces from about 55°C to a mean temperature of about 40°C. The reduction in the thermal load of the CCE is even more pronounced. At z = 100 μm, which is the area most relevant for color conversion, the temperature reduces from about 80°C to about 50°C. Such a strong temperature difference may have a notable bearing on color temperature constancy with regard to a temperature dependent reduction of the luminescence intensity of the phosphor.

 

Fig. 5 Left side: Thermal response of the LED package with a thick phosphor layer operated under PWM operation conditions (1000 mA, duty cycle 50% at 100 Hz) at a position of z = 100 μm within the CCE. Also shown is the thermal response under DC conditions for IF/2, PE/2, PB/2 and a combination of PE/2 and PB/2, (PE/2@PB/2). Right side: Same as in the left side but at a position of z = 400 μm on the top of the CCE.

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Remarkably, and different from the thermal response within the PCB and the LED die (see Fig. 4), in comparison with operational conditions of IF/2 and PE/2 the temperature within and at the surface of the CCE remains notably lower under PWM conditions.

To explain this behavior, one has to consider that for operational conditions of IF/2 the blue radiant flux is still 61% of the blue radiant flux at 1000 mA [22], for operational conditions of PE/2, the blue radiant flux is even 65% of the blue radiant flux at 1000 mA [22]. Since the blue radiant flux is much higher than one half and since the thermal load of the CCE is related to the amount of blue light which is absorbed and converted to yellow light, the thermal load of the CCE under PWM conditions with a duty cycle of 50% is notably lower as it is for operational conditions of IF/2 or PE/2. Contrarily, a comparison with operational conditions corresponding to PB/2 gives reason for a notably lower thermal load. The reason for this is that for operational conditions of PB/2 the electrical power is only 33% of the electrical power at 1000 mA. With increasing electrical power the overall temperature within the PCB and the LED die increases (see Fig. 2) while the additional thermal load of the CCE by the absorption of the blue LED light and the color conversion process more or less adds to the temperature of the LED die. Therefore, a hypothetical combination of half of the electrical power at half of the blue radiant flux (both with respect to DC current operation of 1000 mA) gives the best match with the actual thermal response for PWM operation with a duty cycle of 50%. For a detailed comparison, one should consider, that, as shown in Fig. 4 the temperature on the top of the LED die, which is the junction area, is about 1 K lower for operational conditions of half of IF/2 in comparison with PWM operation. However, according to the data sheet, a variation of the junction temperature by about 1 K modifies the radiant flux only in a low sub-percent range. This means that in comparison with the impact of the non-linearity of the blue radiant flux for the different currents the variation of radiant flux with junction temperature is of minor relevance for the present discussion. In addition, a lower junction temperature means that the radiant flux and therefore the thermal load for IF/2 would become even slightly higher, which in addition would increase the difference in the thermal load between PWM operation and DC current operation of IF/2. A similar behavior also can be observed in case of PWM operation with a lower duty cycle of 25%, see Fig. 6 and also for the LED with the thin phosphor layer (Fig. 7, PWM with a duty cycle of 25%). As shown in Fig. 6, a reduction of the duty cycle from 50% to 25% further reduces the temperatures within the LED packages and therefore further increases the temperature difference with respect to DC current operation of 1000 mA. E.g., at z = 100 μm the temperature difference increases to about 40°C.

 

Fig. 6 Left side: Thermal response of the LED with a thick phosphor layer operated under PWM conditions (1000 mA, duty cycle 25% at 100 Hz) at a position of z = 100 μm within the CCE. Also shown is the thermal response under DC drive current for IF/2, PE/2, PB/2 and a combination of PE/2 and PB/2, (PE/2@PB/2). Right side: Same as in the left side but at a position of z = 400 μm on the top of the CCE.

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Fig. 7 Left side: Thermal response of the LED with a thin phosphor layer operated under PWM conditions (1000 mA, duty cycle 25% at 100 Hz) at a position of z = 100 μm within the CCE. Also shown is the thermal response under DC drive current for IF/2, PE/2, PB/2 and a combination of PE/2 and PB/2, (PE/2@PB/2). Right side: Same as in the left side but at a position of z = 200 μm on the top of the CCE.

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Due to the higher thermal conductivity of the assembly with the thinner phosphor layer and therefore an improved heat removal, the relative differences in the thermal load between PWM operation and DC drive current operation with IF/2 and PE/2 becomes somewhat lower than in case of the assembly with the thicker phosphor layer. This is due to the fact, that the heat generated in the CCE by the absorption of the blue LED light and the color conversion processes is better removed from the CCE. Contrarily, the relative differences between PWM operation and DC drive current operation with PB/4 slightly increase.

However, since such a CCE with an improved thermal conductivity still shows better thermal performance at a DC current of 1000 mA, and due to the fact, that the overall temperature of the system is also determined by the respective electric power the package is operated at (see Fig. 2), the temperature difference for the LED with the thin phosphor layer between DC current operation at 1000 mA and PWM operation with the same current amplitude remains almost at the same level as in case of the LED with the thicker phosphor layer.

4. Conclusion

The respective current driving scheme has a notable impact on the thermal load of the CCEs of phosphor converted LEDs. For the LED package and the cooling conditions investigated in the present study, a temperature difference of about 40 K has been observed within the CCE comparing DC drive current operation of 1000 mA and PWM operation with the same current amplitude and a duty cycle of 25% at 100 Hz. Recent valuations have shown that such a temperature difference may cause color variations which match with the outer limits of a MacAdam ellipse of step 2. Besides the electric power the LEDs are operated at, the thermal load of a CCE is strongly affected by the heat generated upon the absorption of the blue LED light by the phosphor particles and the color conversion process. Therefore, the temperature difference for DC current operation and PWM operation with the same current amplitude is much more pronounced within the CCE as for example in the junction area. In addition, the non-linearity of the radiant flux of the blue LED light and the drive current has also a strong bearing on the exact value of the thermal load of a CCE operated under PWM conditions and also has to be accounted for in any attempt to compensate the operation related impacts on the constancy of a desired CCT value, in particular in case that the CCE has low thermal conductivity, e.g., for configurations with lower concentrations of phosphor in silicone (like glob-top ones), or PWM operation with high current amplitudes for which saturation effects become the more dominant.