Article Novel Method for Estimating Phosphor Conversion Efficiency of Light-Emitting Diodes
Chih-Hao Lin 1 , Che-Hsuan Huang 1, Yung-Min Pai 1 , Chung-Fu Lee 1, Chien-Chung Lin 2, Chia-Wei Sun 1, Cheng-Huan Chen 1, Chin-Wei Sher 1,3,* and Hao-Chung Kuo 1,*
1 Department of Photonics and Institute of Electro-Optical Engineering, National Chiao Tung University, Hsinchu 30010, Taiwan; [email protected] (C.-H.L.); [email protected] (C.-H.H.); [email protected] (Y.-M.P.); [email protected] (C.-F.L.); [email protected] (C.-W.S.); [email protected] (C.-H.C.) 2 Institute of Photonic System, National Chiao Tung University, Tainan 711, Taiwan; [email protected] 3 Fok Ying Tung Research Institute, Hong Kong University of Science and Technology, Hong Kong 511458, China * Correspondence: [email protected] (C.-W.S.); [email protected] (H.-C.K.)
Received: 23 October 2018; Accepted: 26 November 2018; Published: 27 November 2018
Abstract: This study presents a novel method for estimating the phosphor conversion efficiency of white light-emitting diodes (WLEDs) with different ratios of phosphors. Numerous attempts have been made for predicting the phosphor conversion efficiency of WLEDs using Monte Carlo ray tracing and the Mie scattering theory. However, because efficiency depends on the phosphor concentration, obtaining a tight match between this model and the experimental results remains a major challenge. An accurate prediction depends on various parameters, including particle size, morphology, and packaging process criteria. Therefore, we developed an efficient model that can successfully correlate the total absorption ratio to the phosphor concentration using a simple equation for estimating the spectra and lumen output. The novel and efficient method proposed here can accelerate WLED development by reducing costs and saving fabrication time.
Keywords: light emitting diode; electro-optical devices
1. Introduction Recently, light-emitting diodes (LEDs) have gained considerable attention because of their long-lifetime, high-efficiency, and energy-saving properties which make them good candidates for solid-state lighting [1–3]. White LEDs (WLEDs) through epitaxy using GaN-based chips have demonstrated great improvements in efficiency [4–8]. The basic concept underlying WLED fabrication involves coating blue LEDs (BLEDs) with a yellow light-emitting color-conversion element, such as phosphors or organic dyes. This has become the most common approach for white light generation [9]. To achieve different color gamut, color rendering index (CRI), light quality, and efficiency specifications for various applications, many novel phosphors that increase the efficiency or color performance of LEDs have been developed [10–13]. Among the several phosphors for LED applications, yttrium aluminum garnet (YAG)-, silicate-, and nitride-based phosphors are used most widely in WLEDs because of their well developed fabrication processes and outstanding features. Several studies have focused on optimizing the package design of LEDs to improve their efficiency and color quality. The parameters of the LED packaging depend on the type of phosphor and dopant concentration used. These properties considerably affect the LEDs’ efficiency, correlated color temperature (CCT), and CRI [14–17]. For practical applications, simulating the spectrum or chromatic performance of LEDs
Crystals 2018, 8, 442; doi:10.3390/cryst8120442 www.mdpi.com/journal/crystals Crystals 2018, 8, x FOR PEER REVIEW 2 of 8 have investigated models based on Monte Carlo ray tracing combined with the Mie scattering theory [18–23]. However, accurate prediction results have been difficult to achieve, regardless of the parametersCrystals used,2018, 8, 442including the absorption coefficient, particle size distribution, phosphor2 of density, 9 scattering model, and phosphor morphology. Numerous attempts to develop an accurate simulation platformunder have various provided design conditionssuboptimal is necessary.results, thereby Many researchers indicating have that investigated accurate models simulation based onrequires substantialMonte effort Carlo and ray tracing experience combined because with the the Mie micros scatteringcope theory properties [18–23]. of However, phosphor accurate are unavoidable prediction for accurateresults simulation have been [24–28]. difficult toDe achieve,spite these regardless efforts, of the predicting parameters th used,e spectrum including precisely the absorption when the packagecoefficient, design particleor type size of distribution,phosphor phosphorchanges density,in real scatteringcases remains model, anddifficult. phosphor Different morphology. phosphors have differentNumerous crystal attempts phases, to develop particle an accurate size simulationdistributions, platform and have morphologies, provided suboptimal which results,are hard to thereby indicating that accurate simulation requires substantial effort and experience because the measured and define specifications for. The phosphor particle size distribution and morphology are microscope properties of phosphor are unavoidable for accurate simulation [24–28]. Despite these the mainefforts, factors predicting affecting the spectrum the accuracy precisely of whena simula the packagetion model. design However, or type of phosphor even when changes all the in real essential informationcases remains from the difficult. emitting Different materials phosphors is meas have differentured to crystalpredict phases, the performance particle size distributions, of WLEDs, the simulationand morphologies, remains restricted which are to harda narrow to measured range, and su definech as specificationssingle-package for. Thegeometry, phosphor as particle well as the fixed physicalsize distribution properties and morphology of phosphor. are theTherefore, main factors this affecting paper pres the accuracyents a novel of a simulation method model. based on a wavelengthHowever, conversion even when concept all the essential instead information of a traditional from the complex emitting simulation materials is measured in order toto predict increase the consistencythe performance between ofpredicted WLEDs, the results simulation and remainsexperime restrictedntal data. to a narrowThe proposed range, such wavelength as single-package conversion geometry, as well as the fixed physical properties of phosphor. Therefore, this paper presents a novel method is more suitable than microcosmic concepts involving complicated scattering cases, which method based on a wavelength conversion concept instead of a traditional complex simulation in lead toorder unpredictable to increase simulation the consistency results. between predicted results and experimental data. The proposed Awavelength novel method conversion based method on the is moredown-conversion suitable than microcosmic luminescence concepts efficiency involving (DCLE) complicated concept is employedscattering to predict cases, which the leadperformance to unpredictable of the simulation LED, including results. the pumping source and emitted photons forA novelany methodpackage based design. on the The down-conversion major difference luminescence between efficiency this model (DCLE) and concept traditional is simulationsemployed is that to predict it is easier the performance to measure of thethe LED, parameters including required the pumping when source using and out emitted method, photons and it is more straightforwardfor any package design. to correlate The major the difference total absorpti betweenon this ratio model to and the traditional phosphor simulations concentration is that it in real is easier to measure the parameters required when using out method, and it is more straightforward applications. We believe that this method will accelerate the development of WLED applications to correlate the total absorption ratio to the phosphor concentration in real applications. We believe becausethat of thisits simplicity, method will acceleratehigh accuracy, the development and lack ofof WLEDrigorous applications restrictions. because of its simplicity, high accuracy, and lack of rigorous restrictions. 2. DCLE Concept for Phosphor Conversion System 2. DCLE Concept for Phosphor Conversion System Figure 1 is the schematic of a WLED used for the novel model in this study. A dispensing Figure1 is the schematic of a WLED used for the novel model in this study. A dispensing package package was used as the template. In general, the white light emitted by a WLED comprises blue was used as the template. In general, the white light emitted by a WLED comprises blue photons and photonsfluorescent and fluorescent yellow rays yellow emitted rays from emitted the phosphor. from the Here, phosphor. the white lightHere, was the divided white into light two was parts divided into twoto analyzeparts to the analyze wavelength the conversionwavelength between conv theersion BLEDs between and the the phosphors. BLEDs Theand algorithm the phosphors. for the The algorithmphosphor for conversionthe phosphor system conversion was developed system by analyzing was thedeveloped wavelength by conversion analyzing between the thewavelength two conversionparts inbetween an emission the spectrumtwo parts of in white an emission light. spectrum of white light.
FigureFigure 1. 1.SchematicSchematic of aa WLEDWLED structure. structure. 3. Phosphor Conversion Model Based on the DCLE Concept 3. Phosphor Conversion Model Based on the DCLE Concept To develop an optical model of the WLED, the DCLE mechanism was identified as a Tophenomenological develop an optical approach. model Where of Ithe is theWLED fraction, the of leakageDCLE frommechanism the pumping was lightidentified source as a phenomenological approach. Where I is the fraction of leakage from the pumping light source (blue rays) and PB-LED is the radiant flux of the BLED in the package. Hence, the down-converted light could be reformulated and written as follows: Crystals 2018, 8, 442 3 of 9 Crystals 2018, 8, x FOR PEER REVIEW 3 of 8
(blue rays) and PB-LED is the radiant flux of the BLED in the package. Hence, the down-converted light Crystalscould be2018 reformulated, 8, x FOR DownPEER and REVIEW written converted light as follows: 1 I P E , 3 of 8 (1)
Down − converted light = (1 − I) × P × E (1) where E , represents the extraction efficienciesB−LED of blueλp− λlight,ph1,PKG emission light, and the Down converted light 1 I P E , (1) material. where Eλp−λph1,PKG represents the extraction efficiencies of blue light, emission light, and the material. where E , represents the extraction efficiencies of blue light, emission light, and the All calculationsAll calculations were were performed performed according according to thethe flowchart flowchart in in Figure Figure2. First, 2. First, two samples two samples were were material. prepared:prepared: A BLED A BLED without without phosphor phosphor coating coating and aa BLEDBLED with with phosphor phosphor coating coating (i.e., a(i.e., WLED). a WLED). All calculations were performed according to the flowchart in Figure 2. First, two samples were prepared: A BLED without phosphor coating and a BLED with phosphor coating (i.e., a WLED).
FigureFigure 2.2. FlowchartFlowchartof of the the singular singular phosphor phosphor model. model. Figure 2. Flowchart of the singular phosphor model. The spectrum ofof thethe BLEDsBLEDs wherewhere nono light light conversion conversion (I (I = = 1) 1) occurs, occurs, indicates indicates a a radiant radiant flux flux of of Theapproximately spectrum of7474 mW,themW, BLEDs as as illustrated illustrated where in no Figurein Figurelight3a. conversion Figure3a. Figure3b shows 3b (I shows= the 1) emissionoccurs, the emission spectrumindicates spectrum under a radiant total under flux of approximatelytotalconversion conversion 74 for mW, the for WLED asthe illustratedWLED (I = 0). (I The = 0). radiantin TheFigure radiant flux 3a was. fluxFigure approximately was 3bapproximately shows 66 mW the and 66emission all mW the and blue spectrum all light the was blue under total conversionlightabsorbed. was Theabsorbed. for efficiency the WLEDThe E λefficiencyp− λ(Iph1,PKG = 0). EThewasλp−λph1,PKG calculatedradiant was flux bycalculated dividing was approximately by the dividing radiant flux the 66 of radiant themW WLED and flux by allof the thethe blue difference in absorption powers of BLED and WLED, which was 0.72 (= 53.28/74). light wasWLED absorbed. by the difference The efficiency in absorption Eλp−λ powersph1,PKG ofwas BLED calculated and WLED, by whichdividing was 0.72the (=radiant 53.28/74). flux of the WLED by the difference in absorption powers of BLED and WLED, which was 0.72 (= 53.28/74).
FigureFigure 3.3. SpectraSpectra ofof leakedleaked blue blue rays: rays: ( a(a)) I I = = 1 1 (only (only blue blue light) light) and and (b ()b I) =I = 0 0 (no (no blue blue light). light).
Next, the value ofof thethe leakageleakage fractionfraction II waswas variedvaried by by changing changing the the blue-to-white-light blue-to-white-light ratio. ratio. The Figure spectraspectra 3. simulated simulatedSpectra accordingof leakedaccording blue to the to rays: DCLEthe (aDCLE) theorem I = 1 (onlytheorem can blue be usedcan light) tobe calculateandused (b )to I the =calculate 0 CIE1931(no blue thecoordinate light). CIE1931 coordinateand the luminous and the flux. luminous Figure 4flux. shows Figure the calculation4 shows the results calculation for different results I for values. different I values. Next, Tablethe value 1 presents of the the leakage calculation fraction results I wasfor differ variented byleakage changing fractions. the The blue-to-white-light distribution of the ratio. The spectravisual function simulated shows according that human to eyes the are DCLE more sensitivetheorem at can 550 nm;be usedthus, oneto partcalculate of the emissionthe CIE1931 coordinatespectrum and accounts the luminous for a predominant flux. Figure portion 4 shows of th thee luminous calculation flux. results The more for energy different the Ipart values. emits, the higher the value of luminous flux is. This type of wavelength conversion also leads to higher Table 1 presents the calculation results for different leakage fractions. The distribution of the values of color coordinates. visual function shows that human eyes are more sensitive at 550 nm; thus, one part of the emission spectrum accounts for a predominant portion of the luminous flux. The more energy the part emits, the higher the value of luminous flux is. This type of wavelength conversion also leads to higher values of color coordinates. Crystals 2018, 8, 442 4 of 9 Crystals 2018, 8, x FOR PEER REVIEW 4 of 8
FigureFigure 4. 4. CalculatedCalculated results results for for different different leakage leakage fractions. fractions.
Table1 presents theTable calculation 1. Calculated results results for differentfor different leakage leakage fractions. fractions. The distribution of the visual function shows that human eyes are more sensitive at 550 nm; thus, one part of the emission Leakage spectrum accounts0 for a 0.1 predominant 0.2 portion0.3 of0.4 the luminous0.5 flux.0.6 The0.7 more energy0.8 the0.9 part emits,1 Fraction theRadiant higher the value of luminous flux is. This type of wavelength conversion also leads to higher 53.3 55.4 57.4 59.5 61.6 63.6 65.7 67.78 69.9 72 74 valuesFlux (mW) of color coordinates. Luminous 24.7 22.5 20.2 17.9 15.7 13.4 11.1 8.9 6.6 4.3 2.1 Flux (lm) Table 1. Calculated results for different leakage fractions. CIE-x 0.439 0.384 0.340 0.304 0.273 0.247 0.224 0.204 0.167 0.172 0.158 LeakageCIE-y Fraction0.543 0.4410 0.10.359 0.20.291 0.30.234 0.40.186 0.50.143 0.60.107 0.7 0.075 0.8 0.046 0.9 0.021 1 Radiant Flux (mW) 53.3 55.4 57.4 59.5 61.6 63.6 65.7 67.78 69.9 72 74 Luminous Flux (lm) 24.7 22.5 20.2 17.9 15.7 13.4 11.1 8.9 6.6 4.3 2.1 To CIE-xverify the precision0.439 of 0.384 the DCLE 0.340 concept 0.304 of 0.273 phosphor 0.247 conversion 0.224 0.204 in the 0.167 LED package, 0.172 0.158 we investigatedCIE-y the relationship0.543 0.441between 0.359 the calculat 0.291ion 0.234 and experimental 0.186 0.143 results 0.107 at 0.075 various 0.046 phosphor0.021 concentrations. We applied a surface-mounted device (SMD) type 3030 (3.0 × 3.0 mm2) LED, with a configurationTo verify consisting the precision of 22 of× 35-mil the DCLE blue die concept operating of phosphor at 60 mA conversion(Lextar Electronics in the LEDCorporation, package, Hsinchu,we investigated Taiwan); the relationshipa YAG phosphor between mixture the calculation (NYAG4 and from experimental Intematix, results CA, USA) at various was phosphorused in varyingconcentrations. concentrations We applied from a surface-mounted 10% to 50%. deviceOptical (SMD) measurements type 3030 (3.0were× 3.0performed mm2) LED, using with a a spectrometer:configuration CAS consisting 140CT of (Instrument 22 × 35-mil System blue die GmbH operating, Munich, at 60 Germany), mA (Lextar with Electronics a 50-cm Corporation, integrating sphereHsinchu, and Taiwan); 0.5 nm resolution. a YAG phosphor Figure mixture 5 demonstrates (NYAG4 that from the Intematix, luminous CA, flux USA) depends was usedon the in leakage varying fraction.concentrations Our results from 10%demonstrated to 50%. Optical a high measurements linear correlation were performedunder 50% usingconcentration a spectrometer: and a CASlow junction140CT (Instrument temperature System of <60 GmbH, °C. It Munich,therefore Germany), should carefully with a 50-cmcontrol integrating the LED package sphere and design 0.5 nmto avoidresolution. concentration Figure5 demonstrates quench and thatphosphor the luminous thermal flux quench depends as onnot the to leakage cause fraction.a failed Ourprediction. results Accordingdemonstrated to our a high past linear experiences, correlation the underleakage 50% rati concentrationo should be not and lower a low than junction 0.2 as temperature not to cause of concentration<60 ◦C. It therefore quench should in a carefullynormal case, control and the lowe LEDr junction package temperature design to avoid of <100 concentration °C for the quench most commonlyand phosphor used thermal materials quench such as notYAG to and cause red a nitride failedprediction. phosphor in According lighting applications. to our past experiences, Therefore, DCLEthe leakage could ratiobe a shouldfavorable be notconcept lower for than application 0.2 as not without to cause difficult-to-measure concentration quench parameters in a normal or case,any limitationand lower on junction the package temperature or phosphor of <100 type◦C forused. the Moreover, most commonly the target used CIE materials coordination such asof YAGthe LED and packagered nitride for phosphordifferent applications in lighting applications. depends on Therefore,the phosphor DCLE concentration could be a applied favorable in conceptreal cases. for Hence,application we derived without the difficult-to-measure following equations parameters based on or the any weight limitation percentage on the packageof the phosphor, or phosphor instead type ofused. the leakage Moreover, fraction. the target We CIEused coordination the total absorption of the LED ratio package At, (which for different is equal applications to 1 − leakage depends fraction on (I))the for phosphor the subsequent concentration model applied derivation. in real cases. Hence, we derived the following equations based on Crystals 2018, 8, 442 5 of 9
the weight percentage of the phosphor, instead of the leakage fraction. We used the total absorption Crystals 2018, 8, x FOR PEER REVIEW 5 of 8 ratio At, (which is equal to 1 − leakage fraction (I)) for the subsequent model derivation.
Figure 5. Simulation and experimental results. Figure 5. Simulation and experimental results. 4. Novel Model for Phosphor Wavelength Conversion
4. NovelIn Model the proposed for Phosphor absorption Wavelength model, the totalConversion absorption ratio At can be written as:
In the proposed absorption model, the total absorption ratio At cann be written as: Total absorption ratio(At) = 1 − Asystem(1 − A) (2) Total absorption ratio A 1 A 1 A (2) where A is the absorption ratio of each particle from the emission material and n is the statistical mean whereaverage A is numberthe absorption of absorption ratio processes of each thatparticle the LED from beam the undergoesemission insidematerial the and phosphor n is the material. statistical meanIn additionaverage tonumber these parameters, of absorption the absorptionprocesses curvethat the is affected LED beam by the undergoes LED package; inside consequently, the phosphor material.the fixed In termaddition Asystem to isthese added parameters, to Equation the (2). Toabsorption analyze the curve parameters is affected of the by absorption the LED curve, package; Equation (2) can be rewritten as follows: consequently, the fixed term Asystem is added to Equation (2). To analyze the parameters of the absorption curve, Equation (2) can be rewritten as follows: ln(1 − At) = n ln(1 − A) + ln Asystem (3)
ln 1 A nln 1 A lnA (3) here, n is a key parameter supposed to be highly related to the weight index w, which represents the here,total n is weight a key ofparameter the phosphor supposed grains. Becauseto be highly the greater related the phosphorto the weight quantity, index the w, higher which the represents excitation the totalpossibility. weight of For the the phosphor purpose of gr performingains. Because this calculation, the greater an the assumption phosphor of thequantity, excitation the model higher is the presented in Equation (4). The excitation times of phosphor n is affected by the optic length (OL) and excitation possibility. For the purpose of performing this calculation, an assumption of the excitation the probability of pumping. The OL depends on the packaging system used, and the probability of model is presented in Equation (4). The excitation times of phosphor n is affected by the optic length pumping is related to the sum of the volume of the phosphor v within the system volume V. It is also (OL) and the probability of pumping. The OL depends on the packaging system used, and the proportional to the surface area of the phosphor, and hence, the fixed term 4πr2/ 4 πr3 is added to probability of pumping is related to the sum of the volume of the phosphor 3v within the system Equation (4): volume V. It is also proportional to the surface area of4 the phosphor, and hence, the fixed term n ∝ OL·(v/V)·4πr2/ πr3 (4) 4πr / πr is added to Equation (4): 3 4 n ∝ OL‧ v / V ‧ 4πr / πr (4) 3 where the effective radius of the phosphor r = (3v/4Nπ)1/3 and the parameter N is the number of phosphor particles. Then, Equation (4) can be arranged as Equations (5) and (6):
n ∝ OL‧ v / V ‧ 3 / r (5)