IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 65, NO. 7, JULY 2018 2899

Determining External Quantum EfficiencyFrom Energy Conversion Efficiency

for Light-Emitting DiodesSiqi Lin , Tien-Mo Shih, Yijun Lu , Yue Lin , Richard Rugin Chang, and Zhong Chen

Abstract— We propose a convenient method for esti-mating external quantum efficiency (EQE) of light-emittingdiode directly from the energy conversion efficiency, basedon two facts. One lies in that the EQE approximately reachesits maximum when the power source provides the amountof energy that equals the electroluminescence peak energy(EELp) to every electron. For the other, an electron carryinghigher electrical energy than EELp will release its excessiveportion to lattice vibration during radiative recombination,thus emitting a photon with the energy around EELp. In com-parison with traditional methods, our approach maintains adecent accuracy of mostly 0.4%.

Index Terms— External quantum efficiencies (EQEs),light-emitting diodes (LEDs).

I. INTRODUCTION

L IGHT-EMITTING diodes (LEDs) convert electricalenergy to optical radiation energy during

operations [1]–[8]. The efficiency of this conversion processis of paramount importance for engineers in lighting industryas well as scientists devoted for optoelectronic devices.“Conversion efficiency” has so far been defined from variousaspects. The luminous efficacy, which is the ratio of luminousflux to electrical power, is what light source manufacturers andconsumers mostly care about. Apart from luminous efficacy,

Manuscript received March 21, 2018; revised April 25, 2018; acceptedApril 27, 2018. Date of publication May 11, 2018; date of currentversion June 19, 2018. This work was supported in part by the NationalNatural Science Foundation of China under Grant 61504112 andGrant 51605404, in part by the International Science and TechnologyCooperation Program of China under Grant 2015DFG62190, in part bythe Fundamental Research Funds for the Central Universities underGrant 20720150026, in part by the Natural Science Foundation ofFujian Province under Grant 2016R0091, and in part by the Institutefor Complex Adaptive Matter, University of California, Davis, under GrantICAMUCD 13-08291. The review of this paper was arranged by EditorE. G. Johnson. (Corresponding authors: Yue Lin; Zhong Chen.)

S. Lin, Y. Lu, Y. Lin, and Z. Chen are with the Department of ElectronicScience, Fujian Engineering Research Center for Solid-State Lighting,Collaborative Innovation Center for Optoelectronic Semiconductors andEfficient Devices, Xiamen University, Xiamen 361005, China (e-mail:yue.lin@xmu.edu.cn; chenz@xmu.edu.cn).

T.-M. Shih is with the Department of Physics, Xiamen University,Xiamen 361005, China, and also with the Research and Develop-ment Department, Tianming Physics Research Institute, Fujian 363900,China.

R. R. Chang is with the Research and Development Department,Shineraytek Optoelectronics Co., Ltd., Shanghai 200000, China.

Color versions of one or more of the figures in this paper are availableonline at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TED.2018.2832118

there are two other parameters. One is the energy conversionefficiency (ECE), which is the ratio between the total opticalpower emitted from the device and the injected electricalpower. The other one is external quantum efficiency (EQE),which concerns the photons and carriers that, respectively, bearthe optical and electrical energies, and is defined as the ratiobetween number of photons emitted out of the device and thenumber of injected electrons. Researchers in laboratories aremore interested in EQE, because it is proven to be associatedwith some intrinsic properties of the devices [9]–[11]. Thevalue of EQE has been considered a key parameter of devices.In addition, the dependence of EQE upon injection density(forward current) has attracted many attentions. In particular,the EQE exhibit monotonically decreases after injectiondensity surpasses a certain value, which is called EQE droopeffect, has been under intense investigations [12]–[14]. Severalorigins, e.g., Auger effect [15]–[17], carrier leakage [18]–[20],and carrier delocalization [21], [22], have been reported andbelieved to be responsible for it. By imposing minoradjustment on device structure, the EQE droop couldbe suppressed significantly. All this research rests on areliable measurement of EQE. However, the measurementprocess of EQE requires high precision instruments such asphotomultiplier tube incorporated with integrating sphere andspectrometer to capture absolute electroluminescence (EL)spectra, making it more complicated compared with thatof ECE.

In this paper, we introduce an approach for EQE estimation.Benefited from the carrier relaxation theory, this solutionavoids repeated measuring EL spectra, and can yield equallyprecise EQE results from values of ECEs, EL peak energy,and forward voltage. Relative to EL spectra, it is convenientfor these parameters to be acquired. Between our solution andtraditional ones, differences lie within mostly 0.4%, indicatinga high reliability of the former.

II. THEORY

When an LED is driven by a power source, the Fermi levelwill be split, forming two quasi-Fermi levels for electrons andholes, denoted as Efn and Efp, respectively. The electric poten-tial difference between them is denoted by �E f . Since thesmall ohmic contact resistance in LED can be ignored, we cansafely assume �E f = qV f , where q denotes the elementary

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2900 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 65, NO. 7, JULY 2018

Fig. 1. (a) Measurements of EQE versus voltage. Values of EQE reach maxima at 1.89 V for red LED, 2.32 V for green LED, 2.72 V for blue LED,and 3.36 V for UV LED. (b) Voltages that correspond to EQE maxima for different types of LEDs, with each of them equaling VELp.

TABLE ICOMPARISON OF EQES AT VELP AND MAXIMUM EQE

charge. As injection density increases, the separation in quasi-Fermi levels increases. When Efn and Efp reach the bottomof conduction band and top of valence band, the voltage canbe determined as

VELp = �E f /q = EELp/q (1)

where EELp denotes the EL peak energy, which approximatesthe bandgap energy.

Curves of EQE versus V f for several types of LEDs areplotted in Fig. 1(a). Here, we defined the Vmax as the voltagewhen the EQE reaches its peak. It is interesting to find thatthe experimentally measured Vmax approximately equals VELp[Fig. 1(b)]. The EQEs at VELp and maximum EQEs measuredby spectrometer for four kinds of LEDs (Table I) are almostequal to each other, demonstrating that most portion of carriersparticipate the radiative recombination when (1) is satisfied.Similar effects have been reported in [23] and [24].

For low voltages V f < VELp, since an electron occupying alow-energy level is incapable of releasing a photon, it will gainenergy from the surroundings. For high voltages V f > VELp,the separation in quasi-Fermi levels becomes severe, thus,the energy an electron has gained exceeds the amount releasedby electron–hole recombination in quantum wells (QWs).In this case, the extra portion is transferred in the form ofphonons to the lattice during relaxation (Fig. 2).

This energy loss during down-conversion is inevitable eventhough all electron–hole pairs with energies above the EELpcan recombine radiatively. After carrier relaxation and recom-bination, the energy power transferred to photons (Pph) canbe calculated as

Pph =∫

n(hν)hνdν (2)

Fig. 2. Schematic energy band diagram of QW LED. Once the carrierenergy becomes larger than EELp, the carrier releases the excessiveenergy in the form of phonon.

Fig. 3. Typical spectra of LED samples.

where n(hν) denotes the density of photons carrying energyof hν per unit time, h is the Planck constant, and ν is thephoton’s frequency. The average photon energy of the wholespectrum hν can be defined as

hν = Pph

Nph=

∫n(hν)hνdν∫

n(hν)dν(3)

LIN et al.: DETERMINING EQE FROM ENERGY CONVERSION EFFICIENCY 2901

Fig. 4. Comparison of EQEs between mathematic calculation (red lines) and measurement (blue line) for (a) red LED, (b) green LEDs, (c) blueLEDs, and (d) UV LED. Satisfactory agreement is observed.

where Nph denotes the total photon number per unittime. Note that the energy distributions of most EL spec-tra are approximately symmetric with respect to EELp(Fig. 3) and EELp varies little as current changes at roomtemperature [25], [26]. Consequently, we assume that (1) hνcan be substituted with EELp, and (2) EELp is a constantparameter.

On the other hand, the electrical power (Pele) provided bythe sources could be calculated as

Pele = I f V f = q N eleV f (4)

where Nele denotes the number of injected electrons per unittime. With the preparation in (2)–(4), and hν ≈ EELp, we areable to establish a bridge connecting ECE and EQE as

ηECE = Pph

Pele= Nphhυ

q N eleV f= Nph

Nele× hυ

qV f=ηEQE× EELp

qV f(5a)

or

ηEQE = ηECE × qV f

EELp. (5b)

Since EELp serves as a key parameter for commercialLEDs, (5.b) allows us to calculate the EQE directly fromthe ECE, with the help of the forward voltage V f and EELp,without knowing the detailed shape of EL spectra.

III. EXPERIMENTAL DETAILS

According to the theory introduced above, we conducteda measurement to verify the accuracy of (5b), as describedbelow. To ensure the reliability of experimental result,we select four kinds of quantum-well LEDs [AlGaInP red

LEDs, InGaN green LEDs, InGaN blue LEDs, and AlGaNultraviolet (UV) LEDs] as our experimental samples, whichdiffer significantly in bandgap. All the samples are mountedon a heat sink, and the junction temperature can be controlledmanually. An integrating sphere (ISP 500) in conjunction witha spectrometer (Spectro 320) is utilized to capture EL spectra,from which the EQE can be calculated in the traditional waywhile the VELp can be derived from the peak wavelength.Using a current source (YOKOGAWA GS610) to drive thesamples and capture the voltage (V f ) at the same time.Increasing I f from zero until the value of V f reaches VELp,measure the ηECE as the maximum ηEQE. Continually increasethe I f , all data of V f , EQE, and EL spectra are captured atthe same time.

IV. RESULTS AND DISCUSSION

Plots of ηECE versus forward current for four types ofsamples are illustrated in Fig. 4. The ηEQE measured inthe traditional way are also illustrated, which varies moreslightly than ηECE. In high current region, the decrease ofECE is attributed to EQE droop and excessive-energy waster.Comparing different contributions of these two factors, wedeem that the loss in excess energy leads to the reductionin ECE. Especially for the red LED, whose EQE remainsconstant in large voltage regions, the reduction in ECE iscaused by the loss in excess energy only. Therefore, optimalregulations of voltage can eliminate the unnecessary excessiveenergy waste of LEDs.

We employ EELp at currents of 100 mA as our parametersin (5.b). The relative percent error between EELp and hυ is

2902 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 65, NO. 7, JULY 2018

Fig. 5. (a) Relative percent error between calculated EQE and experi-ment EQE. (b) Relative percent error between EELp and hυ.

plotted in Fig. 5(a). According to (5.b), we calculate ηEQE atvarious currents and plot them in red lines (Fig. 4). As it hasindicated, the model predicts the values of EQE with goodaccuracies. The relative error εEQE between experimental dataηEQEe and calculated data ηEQEc is defined in the followingequation:

εEQE =∣∣∣∣ηEQEc − ηEQEe

ηEQEc

∣∣∣∣ × 100%. (6)

The varieties in εEQE with respect to the current are plotted inFig. 5(b). In general, the relative errors are limited to 1.4%.With increasing current, relative errors of red, Green, andblue samples decrease, while that of the UV sample barelychanges. When the current increases, the excessive carriersscreen the electric field that otherwise tilts the band edgesof QWs, canceling the quantum confinement stark effect, andchanging the bandgap [27]. Meanwhile the junction tempera-ture of device will rise as the current increases, narrowing thebandgap. Both of two mechanism lead to variation of averagephoton energy [28]. We calculated the relative error εE of theaverage photon energy upon current with respect to the valueat 100 mA, which we employed for EQE calculation in (5.b),defined as

εE =∣∣∣∣hυ − EELp (100 mA)

EELp(100 mA)

∣∣∣∣ × 100%. (7)

Fig. 5(b) illustrates εE at different currents for four kinds ofLEDs. The current dependence of εE highly resembles that ofεEQE, showing that the slight variation upon current of εE Q E

are account for the shifts in EL spectra. Notwithstanding, suchvariation is so tiny that could be ignored in most cases.

V. CONCLUSION

We propose a practical method for estimating the EQEfrom ECE. This method abandons the repeat processes ofcapturing EL spectra. Just with a value of peak energy (or peakwavelength), EQEs can be obtained with a decent accuracy.Although the shift in EL spectra at higher currents wouldslightly modify the outcomes, measuring errors are limited to∼1%, which proves the reliability of this new method. We findthat the excessive energy leads to the reduction of ECE.

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Siqi Lin received the B.S. degree in microelec-tronics from Xiamen University, Xiamen, China,in 2011, where he is currently pursuing the Ph.D.degree in electronic science.

Tien-Mo Shih received the Ph.D. degree fromthe University of California at Berkeley, Berkeley,CA, USA.

He held a Post-Doctoral Fellowship at HarvardUniversity, Cambridge, MA, USA, in 1978. Heis currently a Professor with Xiamen University,Xiamen, China, the University of Maryland, Col-lege Park, MD, USA, and the Tianming PhysicsResearch Institute, Fujian, China.

Yijun Lu received the B.S. and Ph.D. degrees incondensed matter physics from Xiamen Univer-sity, Xiamen, China, in 1995 and 2000, respec-tively.

He is currently a Professor with the FujianEngineering Research Center for Solid-StateLighting, Xiamen University.

Yue Lin received the B.S. degree in appliedphysics from Southeast University, Nanjing,China, in 2007, and the Ph.D. degree in wirelessphysics from Xiamen University, Xiamen, China,in 2012.

He currently serves as an Associate Professorwith the Department of Electronics Science, Xia-men University.

Richard Rugin Chang received the Ph.D.degree from Southern Methodist University, Dal-las, TX, USA, in 1985.

He is with Shineraytek Optoelectronics Co.,Shanghai, China.

Zhong Chen received the M.Sc. and Ph.D.degrees from Xiamen University, Xiamen, China,in 1988 and 1993, respectively.

He has been a Full Professor with XiamenUniversity since 2000, where he is currently theVice Dean of the Electronic Science and Tech-nology College and the Director of the FujianEngineering Research Center for Solid- StateLighting.