# ASTM E973-16

Designation E973 16Standard Test forDetermination of the Spectral Mismatch Parameter Betweena Photovoltaic Device and a Photovoltaic Reference Cell1This standard is issued under the fixed designation E973; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon indicates an editorial change since the last revision or reapproval.1. Scope1.1 This test provides a procedure for the determi-nation of a spectral mismatch parameter used in perancetesting of photovoltaic devices.1.2 The spectral mismatch parameter is a measure of theerror introduced in the testing of a photovoltaic device that iscaused by the photovoltaic device under test and the photovol-taic reference cell having non-identical quantum efficiencies,as well as mismatch between the test light source and thereference spectral irradiance distribution to which the photo-voltaic reference cell was calibrated.1.2.1 Examples of reference spectral irradiance distributionsare Tables E490 or G173.1.3 The spectral mismatch parameter can be used to correctphotovoltaic perance data for spectral mismatch error.1.4 Temperature-dependent quantum efficiencies are used toquantify the effects of temperature differences between testconditions and reporting conditions.1.5 This test is intended for use with linear photo-voltaic devices in which short-circuit is directly proportional toincident irradiance.1.6 The values stated in SI units are to be regarded asstandard. No other units of measurement are included in thisstandard.1.7 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards2E490 Standard Solar Constant and Zero Air Mass SolarSpectral Irradiance TablesE772 Terminology of Solar Energy ConversionE948 Test for Electrical Perance of Photovol-taic Cells Using Reference Cells Under Simulated Sun-lightE1021 Test for Spectral Responsivity Measurementsof Photovoltaic DevicesE1036 Test s for Electrical Perance of Noncon-centrator Terrestrial Photovoltaic Modules and ArraysUsing Reference CellsE1125 Test for Calibration of Primary Non-Concentrator Terrestrial Photovoltaic Reference Cells Us-ing a Tabular SpectrumE1362 Test s for Calibration of Non-ConcentratorPhotovoltaic Non-Primary Reference CellsG138 Test for Calibration of a SpectroradiometerUsing a Standard Source of IrradianceG173 Tables for Reference Solar Spectral Irradiances DirectNormal and Hemispherical on 37 Tilted SurfaceSI10 Standard for Use of the International System of UnitsSI The Modern Metric System3. Terminology3.1 DefinitionsDefinitions of terms used in this test may be found in Terminology E772.3.2 Definitions of Terms Specific to This Standard3.2.1 test light source, na source of illumination whosespectral irradiance will be used for the spectral mismatchcalculation. The light source may be natural sunlight or a solarsimulator.3.3 Symbols The following symbols and units are used inthis test 1This test is under the jurisdiction of ASTM Committee E44 on Solar,Geothermal and Other Alternative Energy Sources and is the direct responsibility ofSubcommittee E44.09 on Photovoltaic Electric Power Conversion.Current edition approved July 1, 2016. Published August 2016. Originallyapproved in 1983. Last previous edition approved in 2015 as E973 15. DOI10.1520/E0973-16.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume ination, refer to the standards Document Summary page onthe ASTM website.Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States13.3.1 wavelength m or nm.3.3.2 Das a subscript, refers to the device to be tested.3.3.3 Ras a subscript, refers to the reference cell.3.3.4 Sas a subscript, refers to the test light source.3.3.5 0as a subscript, refers to the reference spectralirradiance distribution.3.3.6 Aactive area, m2.3.3.7 Eirradiance Wm2.3.3.8 ESspectral irradiance, test light sourceWm2m1or Wm2nm1.3.3.9 E0spectral irradiance, to which the reference cellis calibrated Wm2m1or Wm2nm1.3.3.9.1 DiscussionFollowing normal SI rules for com-pound units see Practice SI10, the units for spectralirradiance, the derivative of irradiance, with respect towavelength, dE/d, would be Wm3. However, to avoidpossible confusion with a volumetric power density unit andfor convenience in numerical calculations, it is commonpractice to separate the wavelength in the compound unit. Thiscompound unit is also used in Tables G173.3.3.10 Ishort-circuit current A.3.3.11 JLlight-generated photocurrent density Am2.3.3.12 Mspectral mismatch parameter dimensionless.3.3.13 Q,Tquantum efficiency electrons per photon or.3.3.14 partial derivative of quantum efficiency withrespect to temperature electrons per photonC1or C1.3.3.15 Rspectral responsivity AW1.3.3.16 Ttemperature C.3.3.17 TR0temperature, at which the reference cell iscalibrated C.3.3.18 TD0temperature, to which the short-circuit currentof the device to be tested will be reported C.3.3.18.1 DiscussionWhen reporting photovoltaic perfor-mance to Standard Reporting Conditions SRC, it is commonfor TR0 TD0 25C.3.3.19 qelectron charge C.3.3.20 hPlanck constant Js.3.3.21 cspeed of light ms1.3.3.22 Ttemperature difference C.3.3.23 measurement error in short-circuit current di-mensionless.4. Summary of Test 4.1 Spectral mismatch error occurs when a calibrated refer-ence cell is used to measure total irradiance of a test lightsource such as a solar simulator during a photovoltaic deviceperance measurement, and the incident spectral irradianceof the test light source differs from the reference spectralirradiance distribution to which the reference cell is calibrated.4.2 The magnitude of the error depends on how the quantumefficiencies of the photovoltaic reference cell and the device tobe tested differ from one another; these quantum efficienciesvary with temperature.4.3 Determination of the spectral mismatch parameter Mrequires six spectral quantities.4.3.1 The spectral irradiance distribution of the test lightsource ES.4.3.2 The reference spectral irradiance distribution to whichthe photovoltaic reference cell was calibrated E0.4.3.3 Photovolatic Reference Cell4.3.3.1 The quantum efficiency at the temperature corre-sponding to its calibration constant, QRT04.3.3.2 The partial derivative of the quantum efficiency withrespect to temperature, RQR/T.4.3.4 Device to be Tested4.3.4.1 The quantum efficiency at the temperature at whichits perance will be reported, QD,TD0.4.3.4.2 The derivative of the quantum efficiency with re-spect to temperature, RQD/T4.4 Temperatures of both devices are measured, and M iscalculated using Eq 1 and numerical integration.5. Significance and Use5.1 The calculated error in the photovoltaic device currentdetermined from the spectral mismatch parameter can be usedto determine if a measurement will be within specified limitsbefore the actual measurement is pered.5.2 The spectral mismatch parameter also provides a meansof correcting the error in the measured device current due tospectral mismatch.5.2.1 The spectral mismatch parameter is ulated as thefractional error in the short-circuit current due to spectral andtemperature differences.5.2.2 Error due to spectral mismatch is corrected by multi-plying a reference cells measured short-circuit current by M,atechnique used in Test s E948 and E1036.5.3 Because all spectral quantities appear in both the nu-merator and the denominator in the calculation of the spectralmismatch parameter see 8.1, multiplicative calibration errorscancel, and therefore only relative quantities are neededalthough absolute spectral quantities may be used if avail-able.5.4 Temperature-dependent spectral mismatch is a moreaccurate to correct photovoltaic current measurementscompared with fixed-value temperature coefficients.36. Apparatus6.1 Quantum Effciency Measurement ApparatusAs re-quired by Test E1021 for spectral responsivity mea-surements.6.2 Spectral Irradiance Measurement EquipmentA spec-troradiometer as defined and required by Test G138and calibrated according to Test G138.3Osterwald, C. R., Campanelli, M., Moriarty, T., Emery, K.A., and Williams, R.,“Temperature-Dependent Spectral Mismatch Corrections,” IEEE Journal ofPhotovoltaics, Vol 5, No. 6, November 2015, pp. 16921697. DOI10.1109/JPHOTOV.2015.2459914E973 1626.2.1 The wavelength resolution shall be no greater than 10nm.6.2.2 It is recommended that the wavelength pass-bandwithbe no greater than 6 nm.6.2.3 The wavelength range should be wide enough toinclude the quantum efficiencies of both the photovoltaicdevice to be tested and the photovoltaic reference cell.6.2.4 The spectroradiometer must be able to scan therequired wavelength range in a time period short enough suchthat the spectral irradiance at any wavelength does not varymore than 65 during the entire scan.6.2.5 Test s E948, E1036, and E1125 provide addi-tional guidance for spectral irradiance measurements.6.3 Temperature Measurement EquipmentAs required byTest E948 or Test s E1036.7. Procedure7.1 Obtain the reference spectral irradiance distribution,E0, to which the photovoltaic reference cell is calibrated,such as Tables E490 or G173.7.2 Obtain the quantum efficiency of the photovoltaic ref-erence cell at its calibration temperature, QR,TR0.7.2.1 An expression that converts spectral responsivity toquantum efficiency is provided in Test s E1021.NOTE 1Test s E1125 and E1362 require the spectral respon-sivity to be provided as part of the reference cell calibration certificate.7.3 Obtain the partial derivative of quantum efficiency withrespect to temperature, R, for the photovoltaic referencecell see 8.1.7.3.1 If R is not provided with the calibration certificateof the photovoltaic reference cell, the derivatiave function mustbe calculated from a series of quantum efficiency measure-ments at several temperatures. An acceptable procedure isgiven in Annex A1.7.4 Measure the quantum efficiency of the photovoltaicdevice to be tested at the temperature to which its perancewill be reported, QD,TD0, and its partial derivative ofquantum efficiency with respect to temperature, D, usingthe procedure given in Annex A1see also 8.1.7.5 Measure the spectral irradiance, ES, of the test lightsource, using the spectral irradiance measurement equipmentsee 6.2.1.7.6 Measure the temperature of the photovoltaic referencecell, TR, using the temperature measurement equipment.7.7 Measure the temperature of the photovoltaic device tobe tested, TD, using the temperature measurement equipment.8. Calculation of Results8.1 Calculate the spectral mismatch parameter with3M 5*12QD,TD0ESd1TD*12D ESd*34QR,TR0ESd1TR*34RESd3*34QR,TR0E0d*12QD,TD0E0d, 1where TR TR TR0and TD TDTD0. Use anappropriate numerical integration scheme such as that de-scribed in Tables G173. Appendix X1 provides the derivationof Eq 1.IfTR 0.5C and TD 0.5C, then R andD may be omitted and Eq 1 simplified toM 5*12QD,TD0ESd*34QR,TR0ESd3*34QR,TR0E0d*12QD,TD0E0d, 28.1.1 The wavelength integration limits 1 and 2 shallcorrespond to the spectral response limits of the photovoltaicdevice.8.1.2 The wavelength integration limits 3 and 4 shallcorrespond to the spectral response limits of the photovoltaicreference cell.8.2 OptionalCalculate the measurement error due to spec-tral mismatch using 5M 2 139. Precision and Bias9.1 PrecisionImprecision in the spectral irradiance andthe spectral response measurements will introduce errors in thecalculated spectral mismatch parameter.9.1.1 It is not practicable to specify the precision of thespectral mismatch test using results of an interlabora-tory study, because such a study would require circulating atleast six stable test light sources between all participatinglaboratories.9.1.2 Monte-Carlo perturbation simulations4using precisionerrors as large as 5 in the spectral measurements have shownthat the imprecision associated with the calculated spectralmismatch parameter is no more than 1 .9.1.3 Table 1 lists estimated maximum limits of imprecisionthat may be associated with spectral measurements at any onewavelength.9.2 BiasBias associated with the spectral measurementsused in the spectral mismatch calculation can be either inde-pendent of wavelength or can vary with wavelength.9.2.1 Numerical calculations using wavelength-independentbias errors of 2 added to the spectral quantities show theerror introduced in the spectral mismatch parameter to be lessthan 1 .9.2.2 Estimates of maximum bias that may be associatedwith the spectral measurements are listed in Table 2. Theselimits are listed for guidance only and in actual practice willdepend on the calibration of the spectral measurements.4Emery, K. A., Osterwald, C. R., and Wells, C. V., “Uncertainty Analysis ofPhotovoltaic Efficiency Measurements,” Proceedings of the 19th IEEE Photovolta-ics Specialists Conference1987, pp. 153159, Institute of Electrical and Electron-ics Engineers, New York, NY, 1987.TABLE 1 Estimated Limits of Imprecision in SpectralMeasurementsSource of Imprecision Estimated Limit, Spectral response measurement 2.0Spectral irradiance measurement 5.0E973 16310. Keywords10.1 cell; mismatch; photovoltaic; reference; solar; spectral;testingANNEXMandatory InationA1. DETERMINATION OF THE TEMPERATURE DEPENDENCE OF PHOTOVOLTAIC DEVICE QUANTUM EFFICIENCYA1.1 Accurate reporting of photovoltaic device perfor-mance over temperature requires knowledge of the thermalbehavior of short-circuit current, which is a function of theincident spectral irradiance and the quantum efficiency of thedevice. The quantum efficiency is the device property thatvaries with temperature, and its temperature dependence can bemapped with multiple measurements over a range of tempera-tures.A1.2 Select a series of temperatures at which the devicequantum efficiency will be measured.A1.2.1 The first must be the temperature at which the deviceto be tested will be reported, TD0. For Standard ReportingConditions SRC, this will typically be 25C