Opt Quant Electron (2012) 44:111–117DOI 10.1007/s11082-011-9528-x

The phosphor’s optical properties—chromaticitycoordinate relationship of phosphor converted whiteLEDs

C. Sommer · P. Hartmann · P. Pachler · H. Hoschopf ·F. P. Wenzl

Received: 29 September 2011 / Accepted: 15 December 2011 / Published online: 24 December 2011© Springer Science+Business Media, LLC. 2011

Abstract Based on optical ray-tracing simulations we discuss the effect of the extinctioncoefficient and the quantum efficiency of the phosphors on the angular homogeneity of thewhite light emitted from phosphor converted light-emitting diodes. In particular variationsof the extinction coefficient are prone to affect diverse CIE chromaticity coordinates for dif-ferent viewing angles. Contrarily, the impact of the quantum efficiency on angle dependentvariations of the chromaticity coordinates turns out to be of minor importance.

Keywords Solid state lighting · Optical simulation · Ray tracing · Colour conversion ·White LEDs

1 Introduction

Today’s most common approach for white light-emitting diodes (LEDs) relies on a combina-tion of blue LED light and excited emission from phosphor particles (Schubert et al. 2006),which are typically embedded in a silicone matrix. Although this concept seems to be rathertrivial, it recently turned out that the appropriate shape, composition and arrangement of sucha colour conversion element (CCE) within the LED package has a strong bearing on the lightoutput and the white light quality (Tran and Shi 2008; Liu et al. 2008; Sommer et al. 2009,2011).

In order to avoid the need for experimental realization and inspection of a plurality of dif-ferent CCE configurations and compositions, recent progress in numerical simulation allowsfor a time- and cost saving alternative. Besides geometrical and compositional aspects, such

C. Sommer · P. Hartmann · F. P. Wenzl (B)Institute of Surface Technologies and Photonics, Joanneum Research Forschungsgesellschaft mbH,Franz-Pichler Straße 30, 8160 Weiz, Austriae-mail: Franz-Peter.Wenzl@joanneum.at

P. Pachler · H. HoschopfTridonic Jennersdorf GmbH, Technologiepark 10, 8380 Jennersdorf, Austria

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simulations allow also to predict the impact of the optical properties of the CCE components,which will provide important input parameters for materials development.

Based on a simulation procedure for phosphor converted LEDs, we have recently discussedthe geometrical and compositional needs of the CCEs for improved white light emission(Sommer et al. 2009), in particular with respect to angular homogeneity of the chromaticitycoordinates. However, throughout this study, the extinction coefficient (EC) and the quantumefficiency (QE) of the phosphor were assumed to be constant.

A large number of new phosphors are developed nowadays in order to extend the numberof phosphors emitting at different wavelength ranges, improve the long-term stability upondevice operation and to optimize the EC and the QE values for device efficacy enhancement(Ye et al. 2010; Lin and Liu 2011). Nonetheless, for a systematic improvement of phosphorconverted LEDs it is imperative to gain a better understanding how variations of the EC andthe QE values affect the white light quality. Such variations originate from the temperatureincrease upon device operation, long-term materials degradation or slightly different pro-cessing conditions upon synthesis of different phosphor batches. Recently, we have reportedon permissible variations of the QE and the EC of a phosphor in order to limit the attendedoverall colour deviation to McAdam ellipses of small step size (Sommer et al. submitted).However, besides reproducibility of a targeted colour temperature, its constancy for differentviewing angles is also of relevance in the context of white light quality. Therefore, in thefollowing we extend our previous investigations and discuss the impact of variations of theoptical properties of a phosphor on angular homogeneous white light emission from a LED.

2 Simulation

The optical ray-tracing simulations were performed with the commercial software packageASAPT M and rely on the set-up of a model for a blue emitting LED die as well as the imple-mentation of a CCE and a detector element, see Fig. 1. The CCE has a square shaped baseand a flat surface. In combination with the phosphor concentration c in the matrix material,the height h and the width b of the CCE define a set of three key parameters, which have to beconcerted to each other in order to guarantee angular homogenous white light emission. Asone example for such an optimized CCE, a width of b = 1040 µm, a height of h = 400 µmand a phosphor concentration c of 10 vol. % has been identified previously (Sommer et al.2009), considering a phosphor mean particle diameter of 7.8 µm with a standard deviation

Fig. 1 The simulation model consists of a blue emitting LED die with a square-shaped CCE placed on topof it and a hemispherical detector. The hemispherical detector is divided into 101 × 101 pixels along the twoperpendicular main axes

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Fig. 2 CIE x values along the main axes of the hemispherical detector versus pixel number for a CCE havinga constant width b = 1040µm, a constant height h = 400µm and a constant concentration of phosphor particlesc = 10 vol. % in the matrix material, as well as a constant quantum efficiency of 100% (left side) and 50%(right side) while the extinction coefficient of the phosphor is varied from a 5 × 10−4, to b 1 × 10−3 andc 3 × 10−3

of 4.2 µm. For an extinction coefficient that is set to zero for λ = 565 nm and 1 × 10−3

for λ = 460 nm and assuming, that every absorbed blue photon is converted into a yellowone, which means that the QE of the phosphor is 100%, angular homogenous white lightemission can be achieved. Here, this system is taken as a reference system. A variation of thereference extinction coefficient and quantum efficiency allows one to determine their impacton the constancy of the chromaticity coordinates for different viewing angles.

The simulation of the colour conversion process considers two wavelengths, one repre-senting the blue LED light (460 nm) and the other one the converted yellow light (565 nm)and takes the absorption of the blue LED light by the phosphor particles, the re-emissionof yellow light as well as the scattering of the blue and the yellow light (Mie scattering)into account. The refractive indices of the silicone and the phosphor are kept constant at 1.4

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Fig. 3 CIE x values along the main axes of the hemispherical detector versus pixel number for a CCE havinga constant width b = 1040µm, a constant height h = 400 µm and a constant concentration of phosphor particlesc = 10 vol. % in the matrix material, as well as a constant quantum efficiency of 100% (top) and 50% (bottom)and an extinction coefficient of the phosphor of 1 × 10−4

and 1.63 for both wavelengths. When mixing the two wavelengths, the CIE coordinates arelocated on a straight line between 460 and 565 nm in the corresponding CIE 1931 colourspace. Therefore, a single chromaticity coordinate, e.g., CIE x is sufficient for defining theresult.

The CIE x values are determined by monitoring the irradiance distributions for the blueand the yellow light separately on a hemispherical detector with a radius of 4 cm that iscentrically placed above the LED chip (see Fig. 1). The surface of the detector is divided into101 × 101 pixels (in direction of the x and y principle axes). The projection of the detector’ssurface onto a flat plane gives a matrix consisting of 101 × 101 elements (pixels). Finally,the two data matrices containing the irradiance distributions for the blue and the yellow lightare converted into a single matrix of the corresponding CIE x values.

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3 Results and discussion

Figure 2 shows the angular dependency of the CIE x chromaticity coordinates along the mainaxes of the detector for three different EC values of the phosphor (5 × 10−4, 1 × 10−3 and3 × 10−3), while the QE is kept constant at 100 and 50 %.

As evident, despite a shift of the overall CIE x chromaticity coordinates, variations ofthe EC and the QE to values which are smaller than the reference ones, do not affect angledependent colour variations. This is also highlighted in Fig. 3, which depicts this dependencyfor an extremely small EC value, 1 × 10−4 and QE values of 100 and 50 %. In this casethe blue light already dominates the white light emission: the CIE x values are only slightlyhigher than 0.143, representing the blue LED emission at 460 nm.

Contrarily, deviations from an angular homogeneous emission occur for EC values whichare larger than the reference one: the light becomes comparably yellowish in the centre witha bluish fringe at the border, see Fig. 2c. This behaviour can be mainly attributed to thevariation of the extinction coefficient while, despite its impact on the overall CIE x valuesand some smaller ramifications on the shaping, the QE has basically no impact.

For a more detailed discussion, Figs. 4 and 5 compare the relative deviations of the blue andthe yellow irradiance distributions of the modified CCEs with respect to the reference system.The relative deviation of the irradiance distributions is calculated by (IV − IR)/(IV + IR),in which IV refers to the irradiance distributions of the CCE with varied optical parametersand IR are the irradiance distributions of the reference CCE. From Fig. 4, which compares aCCE with an extinction coefficient of 1 × 10−3 and a QE of 50% with the reference system,it becomes evident that for a lower QE the respective irradiance distributions of the blue andthe yellow light still coincide, which is also reflected in the angularly homogeneous CIE xvalues depicted in Fig. 2b.

Similarly, Fig. 5 compares the relative deviations of the irradiance distributions of the blueand the yellow light for CCEs having a QE of 100% and extinction coefficients of 5 × 10−4

and 3 × 10−3. While for the smaller EC value the relative deviations of the irradiance distri-butions of the blue and the yellow light again largely remain constant, a notable difference

Fig. 4 Relative deviation of the irradiance distributions along the main axis of a hemispherical detector forthe blue and yellow light for a CCE having an extinction coefficient of 1 × 10−3 and a quantum efficiency of50% with respect to the reference CCE (top line: 460 nm, bottom line: 565 nm)

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Fig. 5 Relative deviations of the irradiance distributions along the main axis of a hemispherical detectorfor the blue and yellow light for CCEs having a quantum efficiency of 100% and extinction coefficients of5 × 10−4 (top image, top line: 460 nm, bottom line: 565 nm) and 3 × 10−3 (bottom image, top line: 565 nm,bottom line: 460 nm) with respect to the reference CCE

becomes evident for the larger EC value. The blue light shows a comparably larger irradi-ance at the corners of the detector than at the centre, which finally causes the observed angledependent deviation of the corresponding CIE x values, see Fig. 2c.

Generally, for equal irradiance and/or radiant intensity distributions, which is the pre-req-uisite for angular homogeneous light emission, the different emission characteristics of theblue and the converted light have to be harmonized to one another by the scattering processwithin the CCE.

The QE basically determines the flux of yellow light and thereby the final colour temper-ature, however it has only a minor impact on angular variations of the colour temperature.This can be explained by the fact, that a reduction of the QE does not affect the overallabsorption profiles and scattering behaviours within a CCE consisting of a phosphor witha given EC value. Contrarily, the extinction coefficient, which affects the absorption profileand subsequently the scattering rate within the CCE, has a much stronger impact on angular

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colour temperature variation. In particular for larger extinction coefficients, for which mostof the absorption takes place in close proximity to the LED die, the absorption and scatteringprofiles differ from the reference CCE. Similarly, a variation of the phosphor concentration,which also modifies the respective absorption profile and the scattering rate, has shown amuch stronger dependency of the optimized CCE height (Sommer et al. 2009) for higherphosphor concentrations than for lower ones.

4 Conclusion

In particular variations of the extinction coefficient are prone to affect angular dependentcolour variations of the white light emitted from a LED package. Contrarily, despite somealterations of the overall colour temperature, the respective impact of the QE is negligible.

This highlights the importance of an accurate reproducibility as well as chemical and ther-mal stability of the extinction coefficient of a phosphor for white LED applications. Whileoverall deviations from a given colour temperature to some extend can be compensated byappropriate electronic driving schemes, variations of the extinction coefficient may also affectangular colour temperature deviations, which hardly can be compensated.

Acknowledgments The authors gratefully acknowledge financial support from the “Neue Energien 2020”program, project number 827784, of the Austrian Climate and Energy Fund.

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