On a relationship among optical power, current density, and junction temperaturefor InGaN-based light-emitting diodesZi-Quan Guo, Tien-Mo Shih, Zhang-Bao Peng, Hai-Hua Qiu, Yi-Jun Lu, Yu-Lin Gao, Li-Hong Zhu, Jiang-HuiZheng, and Zhong Chen

Citation: AIP Advances 7, 015307 (2017); doi: 10.1063/1.4974877View online: http://dx.doi.org/10.1063/1.4974877View Table of Contents: http://aip.scitation.org/toc/adv/7/1Published by the American Institute of Physics

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AIP ADVANCES 7, 015307 (2017)

On a relationship among optical power, current density,and junction temperature for InGaN-basedlight-emitting diodes

Zi-Quan Guo,1,a Tien-Mo Shih,2 Zhang-Bao Peng,1 Hai-Hua Qiu,1 Yi-Jun Lu,1Yu-Lin Gao,1,b Li-Hong Zhu,1 Jiang-Hui Zheng,3 and Zhong Chen11Department of Electronic Science, Fujian Engineering Research Center for Solid-stateLighting, Xiamen University, Xiamen 361005, China2Department of Physics, Xiamen University, Xiamen 361005, China3School of Energy Research, Xiamen University, Xiamen 361005, China

(Received 22 October 2016; accepted 11 January 2017; published online 23 January 2017)

Theories of spontaneous emission rates and carrier recombination mechanisms formultiple-quantum-well InGaN-based blue light-emitting diodes (LEDs) have beencarefully studied. A relationship among the optical power, the current density, andthe temperature (heat-sink temperature or p-n junction temperature) is identified,and an optical-electrical-thermal model (OETM) is proposed. Thereafter, spec-tral measurements have been carried out to confirm the validity of this OETM.Results show that measured optical powers under various current densities andheat-sink temperatures agree satisfactorily with those determined by the OETM.Furthermore, the traditional forward-voltage method (FVM) has also been carriedout for comparison. Junction temperatures determined by this OETM is in accor-dance with those measured by the FVM. Therefore, this model can serve as analternative tool for fast estimating junction temperatures after relevant fitting coef-ficients having been determined. © 2017 Author(s). All article content, except whereotherwise noted, is licensed under a Creative Commons Attribution (CC BY) license(http://creativecommons.org/licenses/by/4.0/). [http://dx.doi.org/10.1063/1.4974877]

I. INTRODUCTION

Light-emitting diodes (LEDs) based on nitride (InGaN/GaN) compounds have recently becomepopular electronic components that serve lighting communities.1–3 In evaluation of LEDs’ perfor-mances, quantum efficiencies and temperatures (T ) (heat-sink temperatures, T s; or p-n junctiontemperatures, T j) at a certain electrical current are deemed as two critical criterions.4–8 In general,there are interactions among these photometric, electrical, and thermal aspects.9–12 In their works,the photo-electro-thermal theory has been presented by linking the luminous flux, thermal resistance,electrical current, junction temperature, heat dissipation coefficient, etc. Here, by studying theoriesof spontaneous emission rates and carrier recombination mechanisms, we derive a simple and usefulmodel only linking the optical powers, junction temperatures or heat-sink temperatures, and currentdensities. Correlations among these parameters have been considered as powerful tools for evaluatingsome key factors of optoelectronic devices, such as the optical power and the junction temperatureamong others.13

In this present study, we have developed an empirical model, in which experimental opticalpowers (P), temperatures, and current densities (J) for InGaN-based LEDs are interrelated. First,it is noted that the integral of the theoretical spontaneous emission rate (SER) of LEDs (Rspon,called as the theoretical optical power) is proportional to the well-known radiative recombination

aE-mail: zqguo@xmu.edu.cnbE-mail: ylgao@xmu.edu.cn

2158-3226/2017/7(1)/015307/6 7, 015307-1 © Author(s) 2017

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coefficient (B) as well as to the square of the free carrier concentration (n). Second, the carrierrecombination inside quantum wells by means of J/qd = An + Bn2 + Cn3 14 (the simple traditionalABC model in consideration of the Auger recombination) or other proposed complicated modelslike J/qd =An + Bn2 + Cn3 + f (n) (polynomial formula) in consideration of carrier losses and other“efficiency droop” mechanisms15 implies that n is a function of J. Therefore, theoretical Rspon canbe logically expressed in terms of J. Then, we infer that the electroluminescent (EL) optical powercan also be described as a function of J. But coefficients of A, B, C, or others are all functionsof temperatures.16 For purposes of separating temperatures from electrical currents, a referencestate is introduced such that all coefficients can be expressed by an exponential term containingtemperatures and their respective referenced values. Under such arrangements, we obtain the modelingequation for determining optical powers in terms of current densities and temperatures. Finally,spectral measurements are conducted to confirm the validity of this model.

II. THEORY

Our analysis starts from the theoretical SER of multiple-quantum-well (MQW) LEDs,17,18

namely,

γ(hυ)=1τrρ(hυ)fc(hυ)[1 − fv(hυ)], (1)

where τr is the lifetime of the electron-hole radiative recombination; hυ the photon energy; ρ(hυ) theoptical joint density of states; and fc(hυ)[1 − fv(hυ)] occupation probabilities of electron and holestates in conduction and valence bands. When this SER is integrated from the energy band-gap (Eg)to the infinity, we obtain

Rspon =

∫ +∞Eg

γ(hυ)d(hυ), (2)

which is known to be equal to Bn2.19 Eventually, we wish to derive an equation expressing Rspon interms of J. Let us analyze the carrier recombination process inside the quantum well by means of thetraditional ABC model for simplicity14 (although the traditional ABC model somewhat fails to explainthe “efficiency droop” phenomenon of InGaN-based MQW LEDs), namely J/qd = An + Bn2 + Cn3,where A and C represent Shockley-Read-Hall (SRH) and Auger coefficients; q the elementary charge;d the thickness of the MQW. Solving this ABC model directly for deriving a formula expressingn in terms of J, however, is quite complicated, prompting us to seek another approach instead.According to the carrier recombination process, at low current densities (typically smaller than5 A/cm2), the An term dominates, i.e., An�Bn2 and An�Cn3. Hence, J/qd =An=A

√Rspon/B,

which leads to Rspon =B(J/Aqd)2. Likewise, for large J values, the Cn3 term is known to dominate,yielding J/qd =Cn3 =C(Rspon/B)3/2, which subsequently becomes Rspon =B(J/Cqd)2/3. Omittingthe algebra for moderate J values, we combine terms for all three regimes and obtain,

Rspon = βaJ2 + βbJ + βcJ23 . (3)

Coefficients, βa ∝B(1/Aqd)2, βb ∝ 1/qd, and βc ∝B(1/Cqd)2/3 are all functions of temperatures,like three weighting factors. Experimentally, it is wise to strive for establishing a similar form as,

Po = ξaJ2 + ξbJ + ξcJ23 , (4)

where ξa, ξb, and ξc are fitting coefficients. Then, an exponential expression, P=Po exp[−ξd(T −To)],is considered,20 where To is the reference temperature taken to be 298.0 K in our study (it can also betaken as any other arbitrary temperature, such as 308.0 K, 318.0 K, 328.0 K, and 338.0 K, etc.); Po isthe EL optical power at T = To. Finally, we can find an optical-electrical-thermal model (OETM) as

P= (ξ1J2 + ξ2J + ξ3J23 )e−ξ4(T−To), (5)

where ξ1, ξ2, ξ3 and ξ4 = ξd are four fitting coefficients to be determined below.

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III. EXPERIMENT AND DISCUSSION

The MQW-structured blue InGaN-based packaged LED samples, with its chip size as 1 mm× 1 mm × 0.1 mm, are fabricated by the metal-organic chemical vapor deposition (MOCVD) onthe c-plane sapphire substrate. In this study, three samples, sample #1, #2, and #3, manufacturedby three well-established companies are used. During experiments, these LED samples are placedon a temperature-controlled heat sink (Keithley-2510, Keithley Inc.) with the heat-sink temperaturemaintained between 298.0 K and 338.0 K, varying with an increment of 5.0 K. They are drivenwith a direct current ranging from 0.25 A to 0.75 A with an increment of 0.05 A, correspondingto the current density ranging from 25 A/cm2 to 75 A/cm2, supplied by an electrical source meter(Keithley-2611, Keithley Inc.) with an accuracy of 0.1 nA. Finally, the emitted light is collected bya 500 mm-diameter integrating sphere (ISP-500, Instrument System Inc.), which is connected to aspectrometer (Spectro-320e, Instrument System Inc.) that provides measurements of spectra. Figure1(a) shows the schematic assembly of the InGaN-MQW LED, the copper base, and the heat sink,along with the optical instrumentation. Figure 1(b) shows the EL spectrum of the InGaN-MQW LED(driven at 0.25 A), with an emission peak wavelength locating at around 453 nm. Inset of Fig. 1(b)depicts the photograph of this assembly.

In Figs. 2(a) and 2(b), measured spectra of one representative InGaN-MQW LED with variousheat-sink temperatures and current densities are plotted versus the wavelength. Figure 2(a) showsthat the EL peak increases as the current density increases, due to the fact that a great amount ofelectrons are injected into the active region of LEDs. As the heat-sink temperature increases, theEL peak decreases oppositely, as shown in Fig. 2(b). The decrease of the emission is due to severalfactors, such as the non-radiative recombination via deep levels and carrier losses.20 From Eq. (5),we first realize that, as T is set to To, coefficients of ξi(i= 1∼ 3) in this equation can be determinedby fitting the curve of the optical power versus J at To. In Fig. 3(a), optical powers integrated over

FIG. 1. (a) The schematic assembly of the InGaN-MQW LED, the copper base, the heat sink, and the optical instrumentation.(b) The EL spectrum of the InGaN-MQW LED, with an emission peak wavelength locating at around 453 nm (driven at0.25 A). Inset: the photograph of this assembly.

FIG. 2. (a) The optical power of EL spectra versus the wavelength parameterized in the current density for sample #1 at 298 Kheat-sink temperature. (b) The optical power of EL spectra versus the wavelength parameterized in the heat-sink temperaturefor sample #1 driven at 0.25 A electrical current (Here, the temperature is heat-sink temperature).

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FIG. 3. (a) Optical powers integrated over the entire spectrum of sample #1, #2, and #3 versus the current density, with anaverage R-squared value of 0.9991. (b) Optical power integrated over the entire spectrum of sample #1, #2, and #3 versus theheat-sink temperature, with an average R-squared value of 0.9931.

the entire spectrum of sample #1, #2, and #3 are plotted versus J with an average R-squared value of0.9991, which indicates that data agree fairly with the model.

Second, we need to determine the coefficient of ξ4. Figure 3(b) shows optical powers of sample#1, #2, and #3 versus Ts at 25 A/cm2. We also fit the curve of the optical power versus the heat-sink temperature at this fixed J, and obtain ξ4. Therefore, average coefficients of ξi(i= 1∼ 4) forthree InGaN-MQW LED samples are determined as 1.00×10−8 W·cm4A−2, 5.20×10−3 W·cm2A−1,1.87×10−2 W·cm4/3A−2/3, and 1.85×10−3 K−1, respectively. These values differ in LEDs with varioustypes and structures, like InGaN, GaP, and AlGaInP LEDs, but are almost the same for LEDs withsame types and structures. The ξ1 value is so low that it could be ignored in this study, hence, thesimplified formula of OETM is expressed as follows,

P= (ξ2J + ξ3J23 )e−ξ4(T−To). (6)

Figure 4 shows the optical power measured by optical instrumentation (solid scatter) and calculatedby OETM (open scatter) for sample #1. It is observed that experimental results agree satisfactorilywith the computational counterpart. Therefore, this model can be adopted to concisely predict opticalpowers. We also expand our studied range of currents and temperatures, and observe the similaragreement.

So far, the junction temperature can be predicted through the OETM. We rearrange the Eq (6)and approach an expression of Tj with respect to J,

Tj =Tjo + [ln(ξ2J + ξ3J23 ) − ln(P)]/ξ4, (7)

FIG. 4. The optical power measured by the optical instrumentation (solid scatter) and calculated by OETM (open scatter) forone representative sample (sample #1).

015307-5 Guo et al. AIP Advances 7, 015307 (2017)

FIG. 5. (a) The voltage versus the temperature at Im = 2 mA. (b) The temperature rise versus the electrical current.

if we have measured the optical power and determined above relevant parameters, includingξi(i= 2∼ 4) and Tjo (in our case, Tjo represents the junction temperature at 25 A/cm2 and 298.0 Kheat-sink temperature). In order to prove the usefulness of this expression, we have carried out exper-iments as follows. The sample is driven at 35 A/cm2. The heat-sink temperature is maintained at298.0 K, 308.0 K, 318.0 K, 328.0 K, and 338.0 K, respectively. For comparison, we also adopt thetransient thermal tester (T3Ster, MicReD Ltd., with an accuracy resolution of 0.1 K) by employingthe widely-used forward-voltage method (FVM)6 to measure the junction temperature at steady statesparameterized in various current densities. In the calibration of the temperature-sensitive parameter(TSP, k) of voltage, we adopt a small measurement current (Im) of 2 mA, and apply it within thetemperature range from 298.0 K to 328.0 K, with an increment of 10.0 K. The TSP can be written as,

k =∆V∆T

, (8)

where ∆V is the voltage variation at Im = 2 mA. Figure 5(a) plots the voltage versus the temperatureat Im = 2 mA. A linear relationship between the voltage variation and the temperature rise can benoticed, along with R-squared value of 0.9963, suggesting an excellent agreement. Therefore, theaverage TSP for three samples is determined by least-squared methods as -1.227 mV/K. After thiscalibration, the temperature rise versus time at various current densities is measured by the T3Ster.Polynomial relationships between the temperature rise and the current can be observed in Fig. 5(b).In the present case, Tj,o is determined by the FVM as 300.7 K (at 298.0 K heat-sink temperature).Therefore, junction temperatures calculated by OETM (Equation 7) and measured by the FVM at35 A/cm2 and under five heat-sink temperatures for sample #1 are listed in Table I.

We also calculate the absolute value of the change of temperature (∆T ) determined by OETM andFVM. Results show that junction temperatures determined by OETM and FVM are in fair agreement(∆T ≤ 2 K). Here, we have re-calculated the parameter of ξ4 by determining the relationship betweenoptical power and junction temperature (measured by FVM), and have found that this value becomes1.80×10−3 K−1, which is close to 1.85×10−3 K−1. This small difference indicates that the parameterof ξ4 derived by the relationship between optical power and heat-sink temperature in our work canstill be used in the junction temperature calculation, and dose not affect the accuracy of this model.Therefore, this OETM proves useful in fast predicting the junction temperature of the InGaN-basedLED if we obtain its real-time optical power at an arbitrary current density and at an arbitraryambient temperature, after determining three coefficients of ξi(i= 2∼ 4) and only one referencejunction temperature value.

TABLE I. Junction temperatures determined at 35 A/cm2 by OETM and FVM for sample #1.

T s (K) 298.0 308.0 318.0 328.0 338.0

T j (K) by OETM 303.9 314.0 324.0 334.0 344.2T j (K) by FVM 302.5 312.4 322.4 332.4 342.4∆T (K) 1.4 1.6 1.6 1.6 1.8

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IV. CONCLUSION

In summary, based on theories of the spontaneous emission rate and the ABC model, we havederived a relationship among optical powers, current densities, and temperatures. Via measuring ELspectra, we confirm the validity of this model. Results show that computations and experiments arein satisfactory agreement. Future studies will focus on the application of OETM to the LED arrayand transient behaviors of this model.

ACKNOWLEDGMENTS

This work is supported in part by the International Science and Technology Cooperation Programof China under Grant No. 2015DFG62190, the National Natural Science Foundation of China underGrant Nos. 61504112, 11604285, and 51605404, and the Natural Science Foundation of FujianProvince under Grant No. 2016R0091.

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