Current-limiting behavior in multijunction solar cells

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Jun 3, 2011 - concentrator photovoltaics, with the subcells invariably con- nected in series rather than ... Solar: A solar fiber-optic mini-dish concentrator de-.
APPLIED PHYSICS LETTERS 98, 223506 共2011兲

Current-limiting behavior in multijunction solar cells Avi Braun,1 Nadine Szabó,2 Klaus Schwarzburg,2 Thomas Hannappel,2 Eugene A. Katz,1,3 and Jeffrey M. Gordon1,4,a兲 1

Department of Solar Energy and Environmental Physics, Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Sede Boqer Campus 84990, Israel 2 Helmholtz-Zentrum Berlin für Materialien und Energie GmbH, Hahn-Meitner-Platz 1, D–14109 Berlin, Germany 3 The Ilse Katz Institute for Nanoscale Science and Technology, Ben-Gurion University of the Negev, Beersheva 84105, Israel 4 The Pearlstone Center for Aeronautical Engineering, Department of Mechanical Engineering, Ben-Gurion University of the Negev, Beersheva 84105, Israel

共Received 10 February 2011; accepted 10 May 2011; published online 3 June 2011兲 Experimental measurements on tandem GaInAsP/InGaAs concentrator solar cells are presented that demonstrate how the short-circuit current can shift from that of the higher current subcell to that of the lower current subcell as irradiance increases. Theoretical modeling illustrates how this can occur when the current-limiting subcell has a noticeably nonzero slope in its current-voltage curve near short-circuit, and should be general to all series-connected multijunction cells of this nature. © 2011 American Institute of Physics. 关doi:10.1063/1.3596444兴 Multijunction solar cells comprise a core technology for concentrator photovoltaics, with the subcells invariably connected in series 共rather than in parallel兲 for reasons of both practicality and minimizing resistive losses. The operating voltage V is then the sum of the subcell voltages, and the short-circuit current Isc is taken to be that of the currentlimiting subcell, proportional to the solar power input Pin 共for a given illumination spectrum兲. Here, we demonstrate and model the anomalous case, where Isc can be significantly higher than that of the currentlimiting subcell,1,2 with a pronounced irradiance dependence that is unrelated to series resistance losses. Such behavior can occur when the cell’s current-voltage 共I-V兲 curve near short-circuit is noticeably nonhorizontal, which can derive from shunt losses or a voltage-dependent photocurrent.1–4 Measurements were conducted separately with concentrated solar and laser light at equivalent flux concentration values ranging from the order of 100 to 102 suns on two types of tandem GaInAsP/InGaAs cells of the same nominal architecture 共full details on the materials and architecture were reported in Refs. 5–7兲, both 3.4⫻ 3.4 mm2 in photoactive area, differing only in their metallization grid density. This tandem cell comprises the two lower band gap junctions of a planned four-junction concentrator cell.5–7 Solar: A solar fiber-optic mini-dish concentrator described previously8,9 irradiated the solar cells with flux maps ranging from 共a兲 strongly localized via a 1.0 mm diameter optical fiber 共hence with a given Pin restricted to ⬃7% of the cell’s active area兲 to 共b兲 uniform via a kaleidoscope flux homogenizer. First, delivered solar power Pin was measured with a spectrum-neutral pyrometer of 3% accuracy, and was confirmed to have approximately the same spectrum as the AM1.5D ambient solar beam radiation. Then, the transmitted solar spectrum that accounts for absorption by the future two higher band gap junctions5–7 was mimicked by placing an 850 nm 共wavelength兲 long-pass spectral filter 共RG850, a兲

Author to whom correspondence should be addressed. Electronic mail: [email protected].

0003-6951/2011/98共22兲/223506/3/$30.00

Schott AG, Mainz, Germany兲 over the concentrator’s entry aperture. The equivalent flux concentration 共in suns兲 corresponding to the measured Pin values refers to the solar irradiance within the filtered spectral range. Lasers: The power of two laser diodes of wavelengths 808 and 1560 nm 共slightly below those of the respective band gaps of the subcells兲 was adjusted to maintain a constant current mismatch between the top and bottom subcells 共with current mismatch denoting Isc_Top / Isc_Bottom兲. In all instances, the I-V curves were traced from shortcircuit to open-circuit with a picoscope of accuracy 0.3%. Cells were thermally bonded to a thermoelectrically cooled copper heat sink maintained at 25⫾ 0.5° C. A plot of the cell’s gain factor—defined as Isc / Pin—as a function of Pin 关Fig. 1共a兲兴 revealed significantly inconstant behavior that depends on absolute power rather than power density 共i.e., with no discernible effect of a severely localized flux distribution兲. The gain factor decreased by ⬃30% as averaged irradiance increased from a few suns to a few tens of suns, and then became constant. The laser diode results graphed in Fig. 1共b兲 confirm the same trend as in the solar experiments, and show that the relative decrease in gain factor 共as Pin increases兲 is proportional to the degree of current-mismatch, with an approximately irradiance-independent gain factor for currentmatched subcells. 关Because of the markedly different spectra in solar versus laser diode experiments, their respective gain factors cannot be compared directly; hence the relative— rather than absolute—gain factor ordinate in Fig. 1共b兲.兴 A decrease in gain factor with concentration can derive from high series resistance losses that limit short-circuit current.3 The signature of this behavior is a considerably low fill factor 共FF兲. However, the decrease in gain factor occurred at FF values exceeding 0.5. Furthermore, the fact that the gain factor again became constant at sufficiently high Pin 共rather than continuing to decrease兲 is incommensurate with Isc being limited by series resistance. These observations enjoin an alternative explanation, unrelated to series resistance, and rooted in the additivity of the I-V curves of the subcells.

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FIG. 1. 共Color online兲 Measured gain factor Isc / Pin as function of Pin for the tandem cell 共semilog plots兲. 共a兲 In the solar concentrator, under uniform and localized irradiation. Averaged irradiance denotes the ratio of the spectrumadjusted Pin to the cell’s photoactive area 共vide supra兲. The corresponding model calculation described in the text 共for uniform cell irradiation兲 is also shown for both the tandem cell and its individual subcells. The error bars for the calculated curves stem from the experimental uncertainty in the external quantum efficiency input data. 共b兲 Uniform cell irradiation from two laser diodes was adjusted to produce varying degrees of current mismatch Isc_Top / Isc−Bottom 共curve labels兲 at which the tandem cell’s gain factor relative to current matching, Isc / 具I典, could be determined. 具I典 = 共Isc_Top + Isc_Bottom兲 / 2.

The sample calculation in Fig. 2共a兲 illustrates how the voltages of series-connected subcells sum for a given current. The current-limiting subcell was purposely chosen to have a conspicuously nonzero slope near short-circuit. For clarity in what follows, we distinguish between Isc−tandem 共the current at short-circuit for the tandem device, at which there is a nonzero voltage on the subcells兲 versus Isc−1 and Isc−2 共the short-circuit current for the subcells were they operated individually as single-junction cells兲. The determination of Isc−tandem—and its unusual behavior as irradiance is increased—is sharpened in Fig. 2共b兲. Current-limiting 共bottom兲 subcell 1 is under reverse bias, while 共upper兲 subcell 2 is in forward bias, with V1 + V2 = 0. At short-circuit in the lower irradiance regime, subcell 1 is at a reverse bias 关points k in Fig. 2共b兲兴 that generates a current

FIG. 2. 共Color online兲 Illustration for summing voltages in serially connected bottom subcell 1 and upper subcell 2, where the I-V curve of currentlimiting subcell 1 is noticeably nonhorizontal near V = 0. 共a兲 Simplistic summing of voltages, Vtandem = V1 + V2. 共b兲 Determining Isc−tandem: the modeled I-V curves of the individual subcells and the tandem are plotted at 3 and 10 suns 共for an AM1.5D solar spectrum兲. For 3 suns, at I = Isc−tandem, subcell 1 is under reverse bias 共k兲 and subcell 2 experiences a forward bias of equal magnitude 共k⬘兲. Isc−tandem is then not limited by subcell 1. At 10 suns 共and greater兲, the required compensating forward bias of subcell 2 is beyond its I-V curve. Consequently, Isc−tandem decreases to Isc−1.

equal to that of subcell 2 at forward bias 共points k⬘兲. Then Isc−tandem = Isc−2 and hence is not limited by the lower current subcell. When the irradiance reaches a level where the negative bias at points k cannot be compensated by the positive bias at points k⬘, Isc−tandem decreases below Isc−2. As irradiance is further increased, Isc−tandem will eventually reach 共and level off at兲 Isc−1. The fact that the experiments show these trends to be independent of flux distribution follows from Fig. 2共b兲, i.e., it is cell voltage that limits performance, and voltage is essentially insensitive to flux map. The calculated curves in Fig. 2共b兲 adopt a lumpedparameter model for each subcell,

冋 冉

I = I ph − Io exp

冊 册

IRs + V q共V + IRs兲 −1 − , nkT Rsh

共1兲

where I, I ph, and Io are the current, photocurrent, and reverse saturation current, respectively. V is the applied voltage, k is

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Boltzmann’s constant, T is the junction temperature, and n is the diode quality factor. Rs and Rsh are the effective series and shunt resistances, respectively. I ph was calculated by convolving the measured external quantum efficiency of the subcells with the filtered solar spectrum 共not shown兲. At 1 sun irradiance, I ph is 1.30⫾ 0.06 and 0.96⫾ 0.05 mA for the top and bottom subcells, respectively. As explained above, their ratio of 1.37⫾ 0.10 should be 共and is兲 the same as that of the high-to-low gain factors in Fig. 1共a兲. For the top and bottom subcells, respectively, Io values of 1.2⫻ 10−9 mA and 1.7⫻ 10−6 mA were estimated based on the measured open-circuit voltage Voc and band gap values. Rs and Rsh were estimated from the laser-generated I-V curves as Rsh_Top = 21000 ⍀, Rsh_Bottom = 210 ⍀, and Rs_Top = Rs_Bottom = 1 ⍀. A diode quality factor n = 3.0 for the tandem 共taken as 1.5 per junction兲 was deduced from the measured linear dependence of Voc on the logarithm of flux concentration. The I-V curves of the subcells were then summed 共as portrayed above兲 to calculate the tandem’s I-V curve at assorted irradiance levels. The model calculations indicate that although the gain factor of each of the two subcells is essentially irradianceindependent, the gain factor of the tandem cell transitions from the value of the top subcell to that of the limiting subcell—consistent with the experimental results 关Fig. 1共a兲兴. The model also accounts for the change in gain factor being proportional to the degree of current mismatch 关Fig. 1共b兲兴. In summary, in cases where the current-limiting subcell exhibits a noticeably nonhorizontal I-V curve near zero voltage 共e.g., non-negligible shunt losses兲, Isc−tandem transitions from the short-circuit current of the higher photocurrent subcell to that of the nominally current-limiting subcell.

The ostensible anomaly of the dependence of gain factor on irradiance stems from the increased current of the currentlimiting subcell under reverse bias. Model calculations account for the key experimental observations from GaInAs/ GaInAsP tandem cells. The trends identified in the measurements reported here for III-V alloy multijunction concentrator cells should apply to all serially connected multijunction cells with nonhorizontal I-V curves near short-circuit 共especially thin film,10 amorphous semiconductor,11 and organic multijunction cells1,2兲, and may have consequences for cell characterization and design. Avi Braun is the recipient of a Howard and Lisa Wenger graduate scholarship. A. Hadipour, B. de Boer, and P. Blom, Org. Electron. 9, 617 共2008兲. J. Gilot, M. M. Wienk, and R. A. Janssen, Adv. Mater. 共Weinheim, Ger.兲 22, E67 共2010兲. 3 M. Wolf and H. Rauschenbach, Adv. Energy Conv. 3, 455 共1963兲. 4 D. Gupta, S. Mukhopadhyay, and K. Narayan, Sol. Energy Mater. Sol. Cells 94, 1309 共2010兲. 5 B. E. Sağol, U. Seidel, N. Szabó, K. Schwarzburg, and T. Hannappel, Chimia 61, 775 共2007兲. 6 N. Szabó, B. E. Sağol, U. Seidel, K. Schwarzburg, and T. Hannappel, Phys. Status Solidi 共RRL兲 2, 254 共2008兲. 7 U. Seidel, B. Sağol, N. Szabó, K. Schwarzburg, and T. Hannappel, Thin Solid Films 516, 6723 共2008兲. 8 E. A. Katz, J. M. Gordon, W. Tassew, and D. Feuermann, J. Appl. Phys. 100, 044514 共2006兲. 9 J. M. Gordon, E. A. Katz, D. Feuermann, and M. Huleihil, Appl. Phys. Lett. 84, 3642 共2004兲. 10 T. Nakada, S. Kijima, Y. Kuromiya, R. Arai, Y. Ishii, N. Kawamura, H. Ishizaki, and N. Yamada, Proceedings of IEEE Fourth World Conference on Photovoltaic Energy Conversion, 7–12 May 2006, Waikoloa, HI, Vol. 1, p. 400. 11 J. Yang, A. Banerjee, T. Glatfelter, K. Hoffman, X. Xu, and S. Guha, Proceedings of IEEE First World Conference on Photovoltaic Energy Conversion, 5–9 December 1994, Waikoloa, HI, Vol. 1, p. 380. 1 2

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