PAPER PRESENTED AT 28TH EU PVSEC, PARIS, FRANCE, 2013

Temperature-dependent electroluminescence andvoltages of multi-junction solar cellsChristian Karcher*, Henning Helmers, Michael Schachtner, Frank Dimroth and Andreas W. Bett

Fraunhofer Institute for Solar Energy Systems ISE, Heidenhofstr. 2, 79110 Freiburg, Germany

ABSTRACT

The spectral electroluminescence of a monolithic triple-junction solar cell reveals the sub-cell open-circuit voltages under var-iation of temperature and carrier concentration. We present an electroluminescence set-up that is able to acquire a full spectrumin less than 10 s and give insight into the voltage-extraction process. The sum of the sub-cell voltages is in excellent agreement toopen-circuit voltages acquired under concentrated illumination. The temperature-induced voltage losses are investigated andexplained by a bandgap dependent increase in intrinsic carrier concentration. Finally, the accurate extraction of the sub-cellbandgaps helps to identify a temperature rise with increasing current density. Copyright © 2013 John Wiley & Sons, Ltd.

KEYWORDS

III–V semiconductors; multi-junction solar cells; electroluminescence; temperature dependence; CPV; space

*Correspondence

Christian Karcher, Fraunhofer Institute for Solar Energy Systems ISE, Heidenhofstr. 2, 79110 Freiburg, Germany.E-mail: christian.karcher@ise.fraunhofer.de

Received 28 June 2013; Revised 2 September 2013; Accepted 18 September 2013

1. INTRODUCTION

Multi-junction solar cell devices comprising III–V com-pound semiconductors are nowadays widely applied asphotovoltaic converters. These converters are usedterrestrially in concentrator systems to maximize theirpower-to-cost ratio. Additionally, extraterrestrial applica-tions are of great importance. Here, highly efficient solarcells are required. Both fields of application span a broadrange of operation parameters such as a variance in temper-ature and irradiance conditions. In order to tap the fullpotential of these cells with regard to current matching andpower extraction under different conditions of operation, afull set of parameters under temperature and irradiancevariation is of great interest.

In this paper, we present a sophisticated study of atriple-junction solar cell typically applied in state-of-the-artconcentrator systems. In particular, this structure is alattice-matched triple-junction solar cell (tripLM) made ofGa0.50In0.50P (top cell), Ga0.99In0.01As (middle cell), andGe (bottom cell) connected with tunnel diodes to enableseries-connected operation. This cell design is able to reachrecord efficiencies of up to 41.6% [1]. In order to character-ize monolithically stacked multi-junction cells, proven solarcell characterization techniques such as current–voltagecharacteristics under different illumination conditions

are, for the most part, limited to the superimposedbehavior of all individual sub-cells. An extraction of therespective single cell performance under varying photo-generated carrier concentration is rather difficult and timeconsuming.

In order to bypass this problem, we performed spectralelectroluminescence (EL) measurements to get access tothe important sub-cell parameters. This technique utilizesthe detection of photons which are generated uponradiative recombination of injected carriers into the multi-junction device under forward bias. Each sub-cell junctionemits photons distributed at energies close to its bandgap.Because the semiconductors are stacked in a way that thebandgaps are decreasing from top to bottom, the generatedluminescence does not get reabsorbed due to band-to-bandrecombination on its way out of the cell’s front side.Additional absorbance from defect and interface states inhigh-quality crystal reaching external quantum efficiencies(EQEs) of more than 90% only weakly impacts thephotoluminescence intensity [2]. Hence, we are able todetect the superimposed luminescence of all contributingcells with externally placed detectors. This approachis not limited to the investigated tripLM structure butis instead easily scalable to investigate the emissionof monolithic cell designs with an arbitrary numberof junctions.

PROGRESS IN PHOTOVOLTAICS: RESEARCH AND APPLICATIONSProg. Photovolt: Res. Appl. 2014; 22:757–763

Published online 23 October 2013 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/pip.2431

Copyright © 2013 John Wiley & Sons, Ltd. 757

The superimposed luminescence of all junctions yieldstwo important pieces of information with regard to thecell’s performance:

(i) The emission energy: peaks within the EL spectrumlie close to the bandgap of the correspondingsemiconductor [3]. Hence, the different contributingsub-cells are observable and clearly distinguishablein the superimposed emission.

(ii) The relative intensity: each junction emits a pho-ton flux, which is directly related to its respectiveEQE [4]. The relation is given by

ϕEL ¼ EQE�ϕBB� expqV

kbT

� �� 1

� �(1)

where ϕEL is the total emitted EL photon flux, ϕBB is theblack body photon flux, V is the internal voltage appliedto the pn-junction, q is the electron charge, kb is theBoltzmann constant, and T is the temperature of the cell.Thus, the spectral EL is connected to the EQE via thevoltages of the sub-cells.

This relationship enables us to extract the internal open-circuit voltage VOC, which is generated across each sub-cellwhen operating under an injection carrier density equivalentto the photo-generated carrier density under illumination.

Hence, this measurement technique results in a fastextraction of sub-cell voltages and bandgaps without theneed of additional component cells as already demonstratedin Refs. [5–7]. The new EL set-up combined with a versatile

and easy-to-use extraction of the VOC delivers an extremelyfast and cost-efficient way to characterize all kinds ofmulti-junction solar cells.

2. MATERIALS AND EXPERIMENT

Figure 1 shows a schematic of the investigated lattice-matched triple-junction structure and the fundamentalbandgaps of the contributing semiconductors at T=298K.The top, middle, and bottom sub-cells are composed ofGa0.50In0.50P, Ga0.99In0.01As, and Ge, respectively.

The device under test has a concentrator front gridmetallization, which enables the investigation at highcurrent densities. The designated cell area amounts to0.0547 cm2. In order to control the temperature, wesoldered the cell to a copper plate, which itself is mountedonto a Peltier element. The temperature controller of thePeltier element used a Pt100 RTD thermocouple mountedon the copper plate adjacent to the solar cell, where thetemperature is close to the cell temperature. Hence, wewere able to regulate the cell’s temperature accurately from298 to 443K (25–170 °C) with an error of less than 1K.

A complete data set of EQE and light I–V curves, thelatter under various irradiances, has already been acquiredin another study focusing on the characterization of thesolar cell by the utilization of component cells. Thecovered temperatures and irradiances ranged from 273 to443K and up to a concentration ratio of 3000. Thus, adetailed description of this part of the experimental proce-dure can be found elsewhere [2,8].

In order to detect the spectral EL, we have designed anew custom set-up. Although we already have a fullyfunctional EL set-up at our disposal [6,7,9], this measure-ment technique is slow because of the time required forthe mechanical switching of wavelengths within themonochromator. This resulted in typical measurementtimes of around 20min. A full concentration and tempera-ture dataset, spanning more than 100 highly resolvedmeasurements over a large spectral range covering all threejunctions thus would have resulted in an unreasonably longmeasurement time of more than 30 h.

The newly designed set-up, shown in Figure 2, reducesthe measurement time of a full spectrum (300–2000 nm) to

Figure 1. Schematic structure of the investigated device (left)and the individual fundamental bandgaps at T=298K within

the triple-junction solar cell (right).

Figure 2. Photos of our custom set-up to detect the spectral electroluminescence. Left: The four fibers that are connected to individ-ual spectrometers are guided via a motor-driven stage above the cell. Right: Detailed view of the four-fiber holder.

EL and voltages of multi-junction solar cells C. Karcher et al.

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less than 10 s under high concentration. This extremeacceleration of the measurement process primarily originatesfrom the utilization of four compact mini spectrometers. Thespectral equipment consists of two Si and two GaInAsdetector arrays, covering a part of the visible and the nearinfrared spectrum, respectively.

All four spectrometers are equipped with a fiber opticsthat couples the emitted light from the cell into thespectrometers. To minimize errors due to fiber positioningand grid shadowing, the fiber tips are placed perpendicularand close to the cell’s surface. The measurement isperformed consecutively, i.e., each fiber is placed individ-ually over the small concentrator cell, adjusted by a motor-driven linear stage with a positioning error of less than15μm. To annihilate the detection of parasitic surroundinglight during the measurement, a dark spectrum of the cell istaken. Subsequently, a forward bias voltage is applied tothe cell by a source meter unit covering an electronic rangeof up to 3A and 10V. The detected EL signal has avarying spectral resolution depending on the responsiblespectrometer; it varies from 1 nm in the visible up to3 nm in the infrared spectral range. The spectrometerset-up was calibrated via a tungsten lamp with a knownspectral emission determined at the German nationalmetrology institute Physikalisch-Technische Bundesanstalt.The lamp spectrum was detected via a white calibrationstandard. Hence, we are able to correct the spectral responseof the fiber, the grating, and the detector array in order toderive the unperturbed emission spectrum of the multi-junction device. Furthermore, a linearity test of the detectorarrays assured the correctness of the calibration with varyingluminescence intensity.

3. RESULTS AND DISCUSSION

We will now present our experimental results as well asthe computer-aided extraction of the sub-cell parameters.Finally, we will discuss the internal temperature of thesolar cell.

3.1. Temperature-dependent spectra

An excerpt of the temperature-dependent EL spectra forthe highest injection current density of 11A/cm2 is shownin Figure 3. It is tempting to identify the three dominatingemission centers around 1.2, 1.4, and 1.8 eV as the activejunctions within the solar cell. This approach is correctfor the upper junctions Ga0.99In0.01As and Ga0.50In0.50P,which possess a direct bandgap and thus an efficientradiative recombination. The third luminescence distribu-tion at 1.2 eV, however, is not originating from the bottomjunction but from a tunnel junction within the structure.

Ge, which acts as the bottom junction in the device,exhibits an indirect bandgap, in which radiative combinationcan only occur with the assistance of a phonon. Carriersgenerated across the direct bandgap around 0.8 eV arequickly scattered towards the energetically lower conduction

band minimum at 0.66 eV. Hence, the overall luminescencefor semiconductors with an indirect bandgap is generallyreduced drastically compared with direct bandgap materials.Consequently, we observe only a very weak luminescenceshoulder from the direct bandgap superimposed by the broadluminescence originating from the indirect transition at lowerenergy. Though an extended GaInAs detector array with abroadened spectral range up to 2000nm is part of our four-spectrometer set-up, the spectral response of this device istoo low and its dark current is too high to obtain satisfyingdata from the emission of the indirect Ge bandgap. For thatreason, only spectra down to 0.7 eV were examined, whichcorresponds to the detection limit of the first IR-spectrometerequipped with a standard GaInAs detector.

The spectral features of the individual emission peaksof the triple-junction device change as expected with risingtemperature: due to an enhanced electron–phonon interac-tion in combination with a dilation of the crystal latticethe bandgaps of the semiconductors energetically drop.The respective shift in emission energy can be clearlyidentified for the top and middle cells. The luminescence ofthe bottom cell is strongly distorted by interference oscilla-tions caused by overlapping reflections in the multi-layeredstack. Hence, an extraction of a local peak is not necessarilycorresponding to the direct bandgap of Ge. One way toovercome this problem would be to measure and subtractthe reflectance of the solar cell. Another approach is todirectly extract the bandgap from the sub-cell EQEs [10].

Besides the energy shift of the luminescence, anotherfeature of the emission peaks is exponentially droppingedges. While the energetically lower slope remainsconstant, the energetically higher one gets flatter withincreasing temperature. The reason for this different devel-opment can be explained by their respective origins:

The low-energy luminescence is emitted by energeticstates in the band tails below the fundamental bandgap ofthe semiconductor, which is a temperature-independentdensity of states [11]. This slope can be identified as wellin the EQE spectra.

Figure 3. Spectral emission of the triple-junction cell at aninjection current density of 11 A/cm2 under variation of temper-ature. The emission bands can be related to the sub-cellmaterials Ge (0.8 eV, direct bandgap), Ga0.99In0.01As (1.4 eV)

and Ga0.50In0.50P (1.8 eV).

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The high-energy luminescence is emitted fromBoltzmanndistributed carriers,

N∼ expΔEkbT

� �(2)

where N is the number of occupied states, and ΔE is thedifference in carrier energy with respect to the Fermi energyof the semiconductor.

Hence, both the exponentially rising and the falling edgeof the luminescence can be identified in the reciprocityrelation (Eq. (1)): the low-energy slope by the EQE and thehigh-energy slope by the black body photon flux.

3.2. Current-dependent spectra

We also investigated the influence of carrier concentrationon the EL emission. In this study, we applied currentdensities from 1mA/cm2 up to 11A/cm2. The investigatedtriple-junction solar cell generates a one sun currentdensity of 13.6mA/cm2 under an AM1.5d spectrum(1000W/m2). Consequently, this variation corresponds tosun concentrations of 0.1–800.

Figure 4 shows the EL of the solar cell at room temper-ature under variation of applied current densities. Apartfrom an overall and nearly homogeneous rise in overallluminescence intensity, no drastic changes in the spectralshape are observed. Slight temperature-induced changesin the peak emission energy are discussed further in thesucceeding text.

This set of both temperature-dependent and current-dependent spectra is the first half of the required data to getaccess to the temperature and irradiance-dependent sub-cellvoltages. The second half is the extraction of the EQE ofthe sub-cells under variation of temperature. As mentionedpreviously, these data have been presented elsewhere [2,10].

3.3. Determination of open-circuit voltage

Having extracted both the EL and the EQE, we are nowable to use the reciprocity relation to derive the internal

voltages of the sub-cells. As the calculation of Eq. (1) isenergy-dependent and the EQE is measured with a differ-ent spectral resolution than the EL, the extraction of thevoltage becomes rather time consuming. Additionally, thereciprocity relation requires an unperturbed luminescencespectrum of the respective sub-cell. This is only the casenear the bandgap of the semiconductor. A few 100meVaway from the luminescence peak, the emission is alreadysuperimposed by energetically neighboring cells or tunneljunctions. Because of this, we developed a fully graphicalvoltage-extraction procedure, which greatly simplifies thecomplete process.

Figure 5 illustrates the graphical user interface. On theleft hand side, the imported experimental data is shown,i.e., the EL spectra under variation of current (top left)and the EQEs of the sub-cells (bottom left). Dependingon the number of junctions within the device, spectral re-gions of interest are automatically selected around thebandgaps of the cells and are presented in vertical stripes.

On the top right in Figure 5 the result of the reciprocitycalculation is shown for each sub-cell at various currentdensities. Within one spectral region of interest data pointsare only taken into account where both the EQE and the ELare known. To account for the sensitivity limit of the spec-trometers, a noise limit is introduced, below which EL dataare ignored. You can observe the effect of this limit in thediagonal cuts within the derived voltages.

One of the major benefits of this graphical extractionprocedure is the instant feedback of the chosen spectral re-gion of interest. We can directly tell whether the reciproc-ity relation holds by looking at the calculated data. Becausethe generated sub-cell voltage should be independent fromenergy, we expect constant values at a given current. Thisshould be reflected in horizontal lines for the voltagesextracted from different spectral ranges at a given currentdensity. Deviation from constancy indicates that eitherthe spectral region was chosen incorrectly, e.g., by takinginto account an overlapping neighboring emission, or thatthe temperature of the cell differs from the assumed value.

Finally, the mean voltage for each sub-cell is calculatedand plotted in the bottom right as a function of current density.

It should be noted that the calculation of the voltagewith Eq. (1) necessitates scaling by one remaining un-known constant in the reciprocity relation, which basicallyis the absolute photonic irradiance of the cell. Conse-quently, the sum of the derived sub-cell voltages featuresa constant offset with regard to the actual voltage. This off-set δV, which remains constant under variation of currentdensity, is determined from an automated comparison witha measured I-V curve of the sample under known illumina-tion condition:

δV ¼ 13

∑3

i¼1V�i JEL;i ¼ JPhoto;i� �� VOC;3J

� �(3)

where V�i is the calculated sub-cell voltage for a current

density JEL,i equal to the current density JPhoto,i generated

Figure 4. Spectral emission of the triple-junction cell at 298Kunder variation of current density. While the total electrolumines-cence intensity rises homogenously with exponentially growingcurrent densities, the overall spectral shape remains unchanged.

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under illumination. A detailed description of this process isgiven in Ref. [6].

The final results of the analysis, namely the total VOC ofthe solar cell and the individual VOC of the sub-cells, areshown in Figures 6 and 7. We achieve excellent agreementbetween measured I-V curves under concentrated illumina-tion and the sum of the calculated sub-cell voltages basedon EQE and EL measurements and the reciprocity relation.Because the EQE of the bottom cell collapses at temperaturesabove 398K, an investigation of the high temperature regimeby means of the reciprocity relation was not accessible.

As expected and observable in Figure 7, all three junc-tions show a logarithmic raise in voltage with increasingcurrent density. Minor deviations from perfect logarithmicbehavior are observable in the top and middle junctions,where the curves show a slight kink around 30–100 suns.This behavior might be related to non-radiative recombina-tion in the space charge region or at the perimeter of thesolar cell. For both mechanisms, the losses saturate at highcurrent densities and, therefore, become negligible for higherconcentrations. Furthermore, all junctions lose VOC withincreasing temperature. This trend is well known and canbe explained by the rising saturation current of the semicon-ductor diode. The saturation current depends strongly on thetemperature through its proportionality to the square of theintrinsic carrier density [12], which again is connected tothe temperature via the Boltzmann distribution (Eq. (2)).

We are able to gain a deeper insight into the VOC develop-ment by taking a look at its derivative with respect to

temperature. Figure 8 shows the extracted linear slope ofΔVOC/ΔT for the investigated current densities. Up to 30 sunsa rather complex behavior of both middle and bottom cellscan be observed. This non-linearity presumably originatesfrom crystal defects discussed previously. For higher currentdensities, all sub-cells show a linear decreasing VOC losswith regard to temperature. The magnitude of this lossdepends on the number of thermally activated carriersand—consequently—on the energy of the sub-cell bandgap.

Figure 5. Layout of the graphical user interface to extract the internal voltages of multi-junction solar cells. The top left figure showselectroluminescence spectra taken at constant temperature and at different current densities. A voltage value for each sub-cell can beextracted for each current density and for each spectral interval that is analyzed. This is shown in the top right graph. The focus on

graphical evaluation enables a quick access to the validity of the chosen spectral region of interest.

Figure 6. Comparison of the open-circuit voltages measureddirectly via flash illumination (Flash) and the sum of the voltagesextracted from the sub-cells using the reciprocity relation(electroluminescence). We observe an excellent agreement

over the entire investigated range.

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Hence, we observe the largest remaining temperature-induced VOC losses in the sub-cell with the smallestbandgap, i.e., the Ge bottom cell.

3.4. Current-induced temperature shift

As a final aspect of this study, we want to briefly take alook at the spectral features of Figure 4 again. Althoughwe mentioned previously that there are no drastic changesin the spectral distribution with rising current density, thisis not entirely true when looking at very small changes inemission energy. A closer look reveals that there is a slightdecrease in the peak emission energy with increasinginjection current density.

Before further investigating these small changes, let usrevisit Figure 3. A linear red shift of the peak emission isobserved with increasing temperature for the top andmiddle cells, as shown in Figure 9. The respective slopesare denoted below the linear regressions plotted in Figure 9.Such a linear decrease of bandgap energy with increasing

temperature is a typical feature of semiconductors fortemperatures above roughly 100K [13].

Coming back to the small emission peak shifts withincreasing current density, we can use the linear slopes toestimate temperature variations in the sample as a functionof current density from the measured peak shifts. In the topsection of Figure 10, we show the extracted energetic shiftat 298K over all investigated carrier concentrations. Pleasenote the energy scale of the top plot in Figure 10, which isless than 3meV. As can be clearly seen, there is a mono-tonic decrease in emission energy, i.e., bandgap energy,for both cells. We explain this shift by a temperature risedue to enhanced carrier–carrier and carrier–latticecollisions. By using the extracted temperature slopes inFigure 9, the bottom section of Figure 10 illustrates thederived temperature rise within the cells. This rise isroughly linear with a slope of 5 · 10�4 K/(A/cm2).

Both sub-cells reach a relative temperature rise of about6K at a concentration of 800 suns. We note that this valueheavily depends on the thermal interface between cell andheat sink (or measurement chuck), on the ambient temper-ature, and, depending on the thermal capacitance, dependspossibly even on the time of the duration of the applied

Figure 7. Internal sub-cell voltages extracted with Eq. (1) and asubsequent flash I–V calibration (see text). The negative impactof the rising temperature with regard to the voltage is almostequally distributed over all contributing sub-cells. Yet, increasingconcentration reduces the temperature-induced voltage drop.

Figure 8. Linear ΔVOC/ΔT slopes of the solar cell stack and theextracted sub-cell characteristics under variation of injection

current density.

Figure 9. Plot of the electroluminescence emission peakenergy as a function of temperature for top and middle cells.The shift originates from the decrease in bandgap energy as

the temperature rises.

Figure 10. Top: Bandgap drop of top and middle cells with risingcarrier concentration. Bottom: Calculated corresponding tempera-

ture rise within both cells.

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current, which was as little as ~10ms for high currents.The corresponding change in VOC amounts to less than30mV in total or 10mV in sub-cell voltage (Figure 8).Even though this voltage loss due to the temperature riseis not negligible, other studies of flash I-V curves haveshown a similar increase of temperature with increasingconcentration [14]. Hence, we did not perform a correctionof this temperature deviation with regard to the extractedvoltages. However, the possibility of this in situ extractionof the cell temperature once more underlines the versatilityof this fast characterization process by means of spectral EL.

4. SUMMARY

We have developed a tool to quickly extract the spectralEL of monolithically stacked multi-junction solar cells.By means of the reciprocity relation in combination withEQE measurements, we are able to extract the I–V charac-teristics of all contributing sub-cells within this stack. Weprogrammed a powerful and easy-to-use graphical user inter-face, which visualizes the voltage extraction of the reciproc-ity relation, enabling the user to quickly validate the data.

We used the combination of the new experimentalset-up and the new GUI to extract the sub-cell I–Vcharacteristics of a triple-junction lattice-matched structureunder variation of both concentration and temperature. Wefind excellent agreement between our results and VOCextracted from illuminated I–V characteristics. Hence, weare able to get a full set of sub-cell voltages without thefabrication of additional component cells. These voltagesreveal a concentration and bandgap dependent loss withincreasing temperature, which can be understood by therespective rise in intrinsic carrier density.

Finally, we used the highly resolved EL spectra toextract the internal sub-cell temperature. We revealed acarrier concentration-dependent temperature rise, whichwas explained by increasing carrier–carrier and carrier–lattice interaction.

ACKNOWLEDGEMENTS

This work has been partly supported by the Federal Ministryfor the Environment, Nature Conservation and NuclearSafety (BMU) under the CPV-Magnus project, contractnumber 0325485D. The authors are responsible for thecontent of this work.

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