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Measuring Photovoltages of III–V Multijunction Solar Cells by Electroluminescence Imaging

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2013 Appl. Phys. Express 6 102302

(http://iopscience.iop.org/1882-0786/6/10/102302)

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Measuring Photovoltages of III–V Multijunction Solar Cells

by Electroluminescence Imaging

Gia-Wei Shu1, Nai-Ning Ou1, Po-Yen Hsueh1, Tzu-Neng Lin1, Jyh-Shyang Wang1,

Ji-Lin Shen1�, Chih-Hung Wu2�, and Cheng-Hao Ko3

1Department of Physics and Center for Nanotechnology, Chung Yuan Christian University, Chungli 32023, Taiwan2Institute of Nuclear Energy Research, P. O. Box 3-11, Lungtan 32500, Taiwan3Graduate Institute of Automation and Control, National Taiwan University of Science and Technology, Taipei 10672, Taiwan

E-mail: jlshen@cycu.edu.tw; chung@iner.gov.tw

Received August 29, 2013; accepted September 18, 2013; published online October 3, 2013

A technique is presented that allows the determination of the photovoltages of subcells in an InGaP/InGaAs/Ge triple-junction solar cell utilizing

electroluminescence (EL) imaging. The EL intensity of a subcell was found to be quenched when the others’ subcells were illuminated by an extra

laser. From analysis of the EL intensity under variable spectral illumination conditions, we estimated the photovoltages of the individual subcells.

The measured photovoltages were successfully reproduced using the Simulation Program with Integrated Circuit Emphasis (SPICE) in an

equivalent electric network. # 2013 The Japan Society of Applied Physics

Among solar cell technologies, III–V multijunctionsolar cells for concentrator photovoltaic systemshave attracted increasing attention owing to their

very high conversion efficiencies and potential for spaceapplications.1–3) Conversion efficiencies over 40% have beenachieved in InGaP/InGaAs/Ge multijunction solar cells.4,5)

To implement higher efficiency, it is essential to characterizethe optical and electrical properties in multijunction solarcells. Electroluminescence (EL) spectroscopy is known to bea sensitive technique to detect optical, resistive, and recom-bination effects in solar cells.6–8) This technique has theadvantages of being nondestructive and not requiring specialsample preparation. For III–V multijunction solar cells, theuse of EL as a characteristic tool has been reported.9–11) Dueto the reciprocity theorem between EL emission and theexternal quantum efficiency of solar cells, the individualcurrent–voltage curves of all subcells in InGaP/InGaAs/Gesolar cells were obtained.9) Also, it was demonstrated thatcell parameters such as the diode quality factors and defectintroduction rates in multijunction solar cells can be deter-mined by using EL spectroscopy.10,11) Recently, spatiallyresolved EL imaging associated with a charge-coupleddevice (CCD) camera has emerged as a fast and powerfultool for analyzing the cell properties in solar cells.12–14)

It gives insight into the operation of solar cells and helpsto obtain the local diode properties and the spatial distri-butions of open-circuit voltages.12) Utilizing the lateralcurrent spreading of the EL imaging in subcells, the currentdensity distribution and the sheet resistance in multijunctionsolar cells have been derived.13) In addition, EL intensitymaps in the top subcell were investigated to demonstrate thesubcell coupling effect in multijunction solar cells.14)

The design and performance evaluation of a multijunctionsolar cell require characterization of each of the activejunctions to quantify the photocurrents. It would be useful toobtain the photovoltage of each junction, but this is difficultfor a two-terminal, series-connected multijunction solarcell. In this study, we describe an approach for determiningthe photovoltage of each junction in InGaP/InGaAs/Gesolar cells using EL imaging. It is found that the light biason the InGaAs middle subcell (the InGaP top subcell)strongly quenches the EL intensity of the InGaP top subcell(the InGaAs middle subcell). From the quenching of ELintensity, the photovoltage of each junction can be esti-

mated. The dependence of the photovoltage in each subcellon the illumination power was quantitatively analyzed on thebasis of the Simulation Program with Integrated CircuitEmphasis (SPICE) in an equivalent electric network.

The samples investigated here were composed of InGaP/InGaAs/Ge junctions connected in series. The details of thesample structure are described elsewhere.14) Briefly, the topIn0:51Ga0:49P, middle In0:01Ga0:99As, and bottom Ge subcellswere all lattice-matched and grown on a p-type Ge substrateby metal–organic chemical vapor deposition (MOCVD).The InGaP subcell was connected to the InGaAs subcell bya p-AlGaAs/n-InGaP tunnel junction. The InGaAs subcellwas connected to the Ge subcell by a p-GaAs/n-GaAs tunneljunction. EL images of the solar cell were obtained undera forward bias with a current density of 35mA/cm2 atroom temperature. To produce the EL images, a Keithley6430 source meter was used as the current source. Imagesof the top and middle regions of the solar cell were takenby a standard Si CCD camera. The 1024� 1024 pixelcamera yields a resolution of �6:5 �m on the 5:5� 5:5mm2

cell. Band-pass filters were mounted in front of the CCDcamera to reduce the disturbance of unwanted light. The dataacquisition time was chosen to be 1ms. Lasers with energiesof 2.38, 1.59, and 1.17 eV were used to excite the electron–hole pairs and produce light bias in the active layer of thetop, middle, and bottom subcells, respectively. A manuallyadjustable density filter was used to control the intensity ofthe laser reaching the cell sample.

Figure 1(a) shows the EL image of the top InGaP subcellin the dark. A homogenous image without any spatial varia-tions was observed. The emitted red light can be clearly seenby the naked eye in a normal office light environment. Toinvestigate the effect of the light bias from the middle(bottom) subcell on the EL of the top subcell, the energyof the laser was chosen to be 1.59 (1.17) eV, lower than theband gap of InGaP (InGaAs) but higher than that of InGaAs(Ge). Figures 1(b) and 1(c) display the EL images of thetop InGaP subcell upon irradiating the 1.59 and 1.17 eVIR lasers, respectively. Figure 1(b) shows a clear circularfeature with reduced EL intensity around the spot of the1.59 eV incident laser. For the 1.17 eV incident laser, a slightreduction of the EL intensity was observed [Fig. 1(c)]. Onthe other hand, Fig. 1(d) shows the EL image of the middleInGaP subcell in the dark, revealing a homogenous image.

Applied Physics Express 6 (2013) 102302

102302-1 # 2013 The Japan Society of Applied Physics

http://dx.doi.org/10.7567/APEX.6.102302

By irradiating a laser with energy (2.38 eV) above thebandgap of the InGaP layer, the EL image of the middleInGaAs subcell displays a reduction of EL around the laserspot [Fig. 1(e)]. By irradiating the 1.17 eV incident laser,with energy lower than the band gap of InGaAs but higherthan that of Ge, a similar decrease of the EL intensity wasobserved in the middle InGaAs subcell [Fig. 1(f)].

The EL intensity in solar cells is generally a measureof the excess minority carrier concentration, correlated tothe applied forward voltage or the nonradiative recombi-nation induced by defects.15,16) In order to investigatethe possible physical origin of the EL reduction in thesubcells, a reversibility test was performed. After stoppingthe laser irradiation, the dark area disappears immediatelyand the homogeneous EL image recovers completely. Thisindicates that the reduction of EL in the subcell owingto absorption of the incident laser is a reversible effect.Thus, the decreased EL intensity under illumination is notcaused by the defects in solar cells since the generation ofthe light-induced defects is an irreversible effect. Instead,a decrease of the applied forward voltage should beresponsible for the reduction of EL intensities in Figs. 1(b),1(c), 1(e), and 1(f ).

Figures 2(a) and 2(b) show the variations of the ELintensities of the top InGaP subcell with illumination of the1.59 and 1.17 eV incident lasers under different irradiationpowers, respectively. The EL intensities show a decreasewith increasing irradiation power, revealing an increasein the size of the dark region in the EL image. Figures 2(c)and 2(d) show the variations of the EL intensities of themiddle InGaAs subcell with illumination of the 2.38 and1.17 eV incident lasers under different irradiation powers,respectively. Similarly, as the irradiation power increases,EL intensity decreases accordingly. The EL intensity ofan image can be quantitatively obtained by integrating theluminescence intensity detected from the CCD camera. Theopen circles in Fig. 3 plot the dependence of the integratedEL intensities on the irradiation power. Figures 3(a)–3(d)correspond to Figs. 2(a)–2(d), respectively. In all cases, it isfound that the integrated EL intensity decays exponentiallywith increasing irradiation power.

The EL intensity provides information about the localvoltage, which can be used to estimate the photovoltage of asubcell in multijunction solar cells. The EL of solar cells iscaused by the radiative recombination of electrons injectedfrom the emitter into the base in the forward-bias condition.If we detect the EL image of a subcell with an appliedforward voltage Vapp, the EL intensity can be expressed asfollows:8)

IL ¼ I0 expqVapp

kT

� �; ð1Þ

where I0 is a constant and k is the Boltzmann constant.When the solar cell is illuminated by a laser, a photovoltageVph is produced which is oppositely oriented to the appliedforward voltage Vapp. Therefore, the effective forwardvoltage under illumination is represented by Veff ¼ Vapp �Vph. In this case, the EL intensity under spot illumination canbe expressed as follows:

Fig. 1. EL images of the InGaP/InGaAs/Ge solar cells. The EL images of

the top InGaP subcell (a) without irradiation, (b) with irradiation of the

1.59 eV laser, and (c) with irradiation of the 1.17 eV laser. The EL images of

the middle InGaAs subcell (d) without irradiation, (e) with irradiation of the

2.38 eV laser, and (f) with irradiation of the 1.17 eV laser.

(a) (b)

(c) (d)

Fig. 2. EL intensity profiles of line scans with different irradiation powers:

the top InGaP subcell with irradiation of the (a) 1.59 eV and (b) 1.17 eV

lasers; the middle InGaAs subcell with irradiation of the (c) 2.38 eV and

(d) 1.17 eV lasers.

(a) (b)

(c) (d)

Fig. 3. Integrated EL intensity from a line scan versus the irradiation

power of light: the top InGaP subcell with irradiation of the (a) 1.59 eV

and (b) 1.17 eV lasers; the middle InGaAs subcell with irradiation of the

(c) 2.38 eV and (d) 1.17 eV lasers. Solid lines are fitted by the least-squares

method.

G.-W. Shu et al.Appl. Phys. Express 6 (2013) 102302

102302-2 # 2013 The Japan Society of Applied Physics

IL ¼ I1 expqðVapp � VphÞ

kT

� �þ I2; ð2Þ

where I1 is the EL intensity for the dark region and I2 isthe EL intensity corresponding to the other region of theimage. According to Eqs. (1) and (2), Vph can be determinedby comparison of the EL intensity without and with thelaser illumination. The open circles in Figs. 4(a) and 4(b)show the dependence of Vph of the top InGaP subcell on theirradiation power with illumination of the 1.59 and 1.17 eVincident lasers, respectively. Similarly, the open circles inFigs. 4(c) and 4(d) show the dependence of Vph of themiddle InGaAs subcell on the irradiation power with illumi-nation of the 2.38 and 1.17 eV lasers, respectively. For allcases, we can determine Vph of a subcell as a function of theirradiation power. The advantage of this technique is thatit is nondestructive and it can selectively determine Vph

with a given photon energy. For example, by irradiatingthe light with a photon energy of 1.17 eV, the Vph values ofthe top InGaP and middle InGaAs subcells can be separatelyderived, as displayed in Figs. 4(b) and 4(d), respectively.

In order to demonstrate the validity of the above tech-nique, the SPICE calculation in an equivalent circuit wascarried out. The triple-junction solar cell can be modeled ingeneral as three diodes cascaded in series, as shown inFig. 5. The solar-cell diode equations with the two-diodelumped model are applied. In the calculations, the DCforward current JF and reverse current JR in the SPICEdiode model were modified from Ref. 17 as follows:

JF ¼ J01 expqðVapp � VphÞ

kT

� �� 1

� �

þ J02 expqðVapp � VphÞ

2kT

� �� 1

� �; ð3Þ

JR ¼ JBV exp � q½ðVapp � VphÞ þ VB�kT

� �; ð4Þ

where J01 is the diffusion current, J02 is the space-chargerecombination current, JBV is the reverse breakdown kneecurrent, and VB is the reverse breakdown knee voltage. Thephotocurrent is generated internally in the cell and expected

to be proportional to the illumination power. Parameters forthe photocurrents, diffusion currents, space-charge recom-bination currents, series and shunt resistances, and theequivalent resistance for the tunnel diodes were estimatedto fit the dark J–V curve. The obtained parameters wereutilized to determine Vph of each subcell in the equivalentcircuit model. The solid lines in Fig. 4 display the calculatedVph versus illumination power according to the SPICE diodemodel. The parameters used in the calculations, listed inTable I, are based on those in Ref. 18. As shown in Fig. 4,the calculated results obtained from the SPICE modeling arein good agreement with those obtained from measurements.This confirms the validity of the measured photovoltages ofindividual subcells using the EL-imaging technique.

The proposed technique using EL imaging is useful foroptimizing the cell design and analyzing the performance inthe multijunction solar cells. In the solar-cell physics, thereare two current mechanisms that flow in opposite directionin solar cells: the light-generated current that producespower, and the dark saturation current that dissipates energy.An understanding of these currents is important for theperformance and design in multijunction solar cells. It isknown that the open circuit voltage denotes the point in theilluminated current–voltage characteristics where the light-generated current equals the dark saturation current. Theopen circuit voltage has been estimated to be logarithmicallyproportional to the light-generated current and to thereciprocal of the dark saturation current.19) According to

0.00

0.02

0.04

0.06P

hoto

volt

age

(V)

Pho

tovo

ltag

e (V

)

Pho

tovo

ltag

e (V

)

Power(mW) Power(mW)

Pho

tovo

ltag

e (V

)

(d)(c)

(b)

Power(mW)Power(mW)

(a)

0.00

0.01

0.02

0.03

0.00

0.03

0.06

0.09

0.12

0 20 40 60 0 20 40 60

0 20 40 60 0 20 40 600.00

0.02

0.04

0.06

Fig. 4. Dependence of photovoltages of the subcells on the irradiation

power: the top InGaP subcell with irradiation of the (a) 1.59 eV and

(b) 1.17 eV lasers; the middle InGaAs subcell with irradiation of the

(c) 2.38 eV and (d) 1.17 eV lasers. Solid lines are the photovoltages

calculated from the SPICE modeling.

Fig. 5. Schematic of equivalent circuit model for the InGaP/InGaAs/Ge

solar cell. RS denotes the resistance due to the window layer and electrodes.

RiS denotes the series resistance of the subcells. Ri

Sh denotes the shunt

resistance of the subcells. R12T and R23

T denote the equivalent resistances of

the tunnel diodes.

Table I. Summary of cell parameters used in the SPICE modeling.

Subcell i/material Top/InGaP Middle/InGaAs Bottom/Ge

J i01 (A/cm2) 1:1� 10�28 2:2� 10�18 9:6� 10�6

J i02 (A/cm2) 2:2� 10�16 1:0� 10�10 7:9� 10�5

RiS (� cm2) 0.2 0.2 0.2

RiSh (� cm2) 106 106 500

R12T R23

T RS

(� cm2) (� cm2) (� cm2)

2:2� 10�16 1� 10�10 3.9

G.-W. Shu et al.Appl. Phys. Express 6 (2013) 102302

102302-3 # 2013 The Japan Society of Applied Physics

this relationship, if the open circuit voltage and the darksaturation current are determined, the light-generated currentcan be derived. In this study, the value of the effectiveforward voltage (Veff ¼ Vapp � Vph) is related to the opencircuit voltage.15) Also, the dark saturation current ineach subcell can be determined by employing the diffusioncurrent J01 and the space-charge recombination currentJ02 (Table I). Therefore, it is possible to extract the light-generated current in each subcell through the EL imagemeasurement and the SPICE calculation. Further, the light-generated current can be used to estimate the dependenceof fill factor on the ratio of the subcell current, which isimportant in the performance of the solar cell and thediagnosis whether a multijunction solar cell is operating ina current matched mode or mismatched mode.20) Thus,the EL imaging technique of determining the photovoltagedescribed here is helpful for the design and performanceof multijunction solar cells.

In summary, the photovoltages of the individual subcellsof InGaP/InGaAs/Ge solar cells have been extracted frommeasurements utilizing EL imaging. The EL intensityof a subcell was found to be quenched when an extralaser irradiates onto the others’ subcells. With increasingirradiation level of the excitation laser, the EL intensity isquenched exponentially. The photovoltages of the individualsubcells were extracted from the EL intensity of imagesunder different excitation energies and illumination levels.Using the SPICE program, the photovoltages in the subcellsof InGaP/InGaAs/Ge solar cells were calculated and werein good agreement with the experimental values. This ELimage technique for measuring photovoltage can be usefulfor the design and performance analysis of multijunctionsolar cells.

Acknowledgment This work was supported in part by the Institute of

Nuclear Energy Research under grant number 1022001INER018.

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