We report the use of a rapid flux calculation method using incomplete Riemann zeta functions as a replacement for the {Bose-Einstein} integral in detailed balance calculations to study the efficiency of tandem solar cell stacks under the terrestrial {AM1.5G} spectrum and under maximum concentration. The maximum limiting efficiency for unconstrained and constrained tandem stacks of up to eight solar cells, under the {AM1.5G} spectrum and maximum concentration, are presented. The results found agree well with previously published results with one exception highlighting the precautions necessary when calculating for devices under the {AM1.5G} spectrum. The band gap sensitivities of two tandem solar cell stack arrangements of current interest were also assessed. In the case of a three solar cell tandem stack the results show a large design space and illustrate that the constrained case is more sensitive to band gap variations. Finally, the effect of a non-optimum uppermost band gap in a series constrained five solar cell tandem stack was investigated. The results indicate that a significant re-design is only required when the uppermost band gap is greater than the optimum value with a relatively small effect on the limiting efficiency. It is concluded that this rapid flux calculation method is a powerful tool for the analysis of tandem solar cells and is particularly useful for the design of devices where optimum band gaps may not be available. Copyright © 2007 John Wiley & Sons, Ltd.

1 aBremner, S P1 aLevy, M Y1 aHonsberg, Christiana, B uhttp://dx.doi.org/10.1002/pip.79900519nas a2200169 4500008004100000020001800041245002600059210002600085260002600111300000800137520001100145100001600156700002100172700001400193700001500207856012700222 2007 eng d a1-84407-401-300aApplied Photovoltaics0 aApplied Photovoltaics aLondon, UKbEarthscan a3173 a1 aWenham, S R1 aGreen, Martin, A1 aWatt, M E1 aCorkish, R uhttp://www.amazon.com/Applied-Photovoltaics-Stuart-R-Wenham/dp/1844074013/ref=sr_1_1?ie=UTF8&s=books&qid=1279558328&sr=8-100396nas a2200109 4500008004100000245006400041210006300105260003900168300001100207100002400218856004400242 2005 eng d00aApproaching the 29% limit efficiency of silicon solar cells0 aApproaching the 29 limit efficiency of silicon solar cells aLake buena Vista, FL, USAb01/2005 a889-941 aSwanson, Richard, M uhttps://www.pveducation.org/ru/node/39300398nas a2200109 4500008004100000245006300041210006300104260003400167490002800201100001500229856004400244 2000 eng d00aAluminium Back Surface Field in Buried Contact Solar Cells0 aAluminium Back Surface Field in Buried Contact Solar Cells bUniversity of New South Wales0 vBachelor of Engineering1 aAnwar, K K uhttps://www.pveducation.org/ru/node/27500294nas a2200085 4500008004100000245005500041210005400096100001400150856004400164 1994 eng d00aAttaining Thirty-Year Photovoltaic System Lifetime0 aAttaining ThirtyYear Photovoltaic System Lifetime1 aDurand, S uhttps://www.pveducation.org/ru/node/30201006nas a2200157 4500008004100000022001300041245008400054210006900138260001600207300000900223490000700232520051500239100002700754700002300781856004400804 1993 eng d a0021897900aAccurate measurements of the silicon intrinsic carrier density from 78 to 340 K0 aAccurate measurements of the silicon intrinsic carrier density f cJan-01-1993 a32930 v743 aThe intrinsic carrier density in silicon has been measured by a novel technique based on low‐frequency capacitance measurements of a p+‐i‐n+ diode biased in high injection. The major advantage of the method is its insensitivity to uncertainties regarding the exact values of the carrier mobilities, the recombination parameters, and the doping density. The intrinsic carrier density was measured in the temperature range from 78 to 340 K. At 300 K the value of ni was found to be (9.7±0.1)×10^9 cm−3.1 aMisiakos, Konstantinos1 aTsamakis, Dimitris uhttps://www.pveducation.org/ru/node/54200803nas a2200253 4500008004100000245013700041210006900178260000800247300001400255490000700269653002100276653002700297653002200324653001800346653001200364653002400376653002300400653002100423653001300444653001100457100001900468700001800487856004400505 1987 eng d00aAnalysis of the interaction of a laser pulse with a silicon wafer: Determination of bulk lifetime and surface recombination velocity0 aAnalysis of the interaction of a laser pulse with a silicon wafe bAIP a2282-22930 v6110acarrier lifetime10aLASERRADIATION HEATING10aMINORITY CARRIERS10aRECOMBINATION10aSILICON10aSILICON SOLAR CELLS10aSURFACE PROPERTIES10aTHEORETICAL DATA10aVELOCITY10aWAFERS1 aLuke, Keung, L1 aCheng, Li-Jen uhttp://link.aip.org/link/?JAP/61/2282/100368nas a2200109 4500008004100000245006700041210006700108300001200175490000600187100002100193856004400214 1982 eng d00aAccuracy of Analytical Expressions for Solar Cell Fill Factors0 aAccuracy of Analytical Expressions for Solar Cell Fill Factors a337-3400 v71 aGreen, Martin, A uhttps://www.pveducation.org/ru/node/32101923nas a2200157 4500008004100000022001400041245007000055210006900125300001400194490000700208520145500215100001801670700001601688700001701704856004401721 1979 eng d a0018-938300aApplication of the superposition principle to solar-cell analysis0 aApplication of the superposition principle to solarcell analysis a165–1710 v263 aThe principle of superposition is used to derive from fundamentals the widely used shifting approximation that the current-voltage characteristic of an illuminated solar cell is the dark current-voltage characteristic shifted by the short-circuit photocurrent. Thus the derivation requires the linearity of the boundary-value problems that underlie the electrical characteristics. This focus on linearity defines the conditions that must hold if the shifting approximation is to apply with good accuracy. In this regard, if considerable photocurrent and considerable dark thermal recombination current both occur within the junction space-charge region, then the shifting approximation is invalid. From a rigorous standpoint, it is invalid also if low-injection concentrations of holes and electrons are not maintained throughout the quasi-neutral regions. The presence of sizable series resistance also invalidates the shifting approximation. Methods of analysis are presented to treat these cases for which shifting is not strictly valid. These methods are based on an understanding of the physics of cell operation. This understanding is supported by laboratory experiments and by exact computer solution of the relevant boundary-value problems. For the case of high injection in the base region, the method of analysis employed accurately yields the dependence of the open-circuit voltage on the short-circuit current (or the illumination level).1 aLindholm, F A1 aFossum, J G1 aBurgess, E L uhttps://www.pveducation.org/ru/node/34400311nam a2200109 4500008004100000245002500041210002500066260003400091100001600125700001600141856004400157 1976 eng d00aApplied Solar Energy0 aApplied Solar Energy bAddison Wesley Publishing Co.1 aMeinel, A B1 aMeinel, M P uhttps://www.pveducation.org/ru/node/35200407nas a2200121 4500008004100000022001400041245004800055210004400103300001400147490000700161100001600168856010100184 1969 eng d a0038-092X00aThe absorption of radiation in solar stills0 aabsorption of radiation in solar stills a333 - 3460 v121 aCooper, P I uhttp://www.sciencedirect.com/science/article/B6V50-497BD6C-27/2/a4ca2069fe8c8b0cfa571de016d93cc500488nas a2200133 4500008004100000022001300041245013000054210006900184260001600253300001400269490000800283100001900291856004400310 1934 eng d a0003380400aAbsolutwerte der optischen Absorptionskonstanten von Alkalihalogenidkristallen im Gebiet ihrer ultravioletten Eigenfrequenzen0 aAbsolutwerte der optischen Absorptionskonstanten von Alkalihalog cJan-01-1934 a434 - 4640 v4111 aBauer, Gerhard uhttps://www.pveducation.org/ru/node/52900319nas a2200121 4500008004100000245003600041210003200077300000800109490000800117100001500125700001300140856004400153 1877 eng d00aThe Action of Light on Selenium0 aAction of Light on Selenium a1130 vA251 aAdams, W G1 aDay, R E uhttps://www.pveducation.org/ru/node/273