# ASTM E973-16

Designation: E973 − 16Standard Test Method 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 method provides a procedure for the determi-nation of a spectral mismatch parameter used in performancetesting 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 performance 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 method 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 Standards:2E490 Standard Solar Constant and Zero Air Mass SolarSpectral Irradiance TablesE772 Terminology of Solar Energy ConversionE948 Test Method for Electrical Performance of Photovol-taic Cells Using Reference Cells Under Simulated Sun-lightE1021 Test Method for Spectral Responsivity Measurementsof Photovoltaic DevicesE1036 Test Methods for Electrical Performance of Noncon-centrator Terrestrial Photovoltaic Modules and ArraysUsing Reference CellsE1125 Test Method for Calibration of Primary Non-Concentrator Terrestrial Photovoltaic Reference Cells Us-ing a Tabular SpectrumE1362 Test Methods for Calibration of Non-ConcentratorPhotovoltaic Non-Primary Reference CellsG138 Test Method 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 Units(SI): The Modern Metric System3. Terminology3.1 Definitions—Definitions of terms used in this testmethod may be found in Terminology E772.3.2 Definitions of Terms Specific to This Standard:3.2.1 test light source, n—a 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 method:1This test method 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. DOI:10.1520/E0973-16.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at service@astm.org. For Annual Book of ASTMStandards volume information, refer to the standard’s 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 λ—wavelength (µm or nm).3.3.2 D—as a subscript, refers to the device to be tested.3.3.3 R—as a subscript, refers to the reference cell.3.3.4 S—as a subscript, refers to the test light source.3.3.5 0—as a subscript, refers to the reference spectralirradiance distribution.3.3.6 A—active area, (m2).3.3.7 E—irradiance (W·m–2).3.3.8 ES(λ)—spectral irradiance, test light source(W·m–2·µm–1or W·m–2·nm–1).3.3.9 E0(λ)—spectral irradiance, to which the reference cellis calibrated (W·m–2·µm–1or W·m–2·nm–1).3.3.9.1 Discussion—Following normal SI rules for com-pound units (see Practice SI10), the units for spectralirradiance, the derivative of irradiance, with respect towavelength, dE/dλ, would be W·m–3. 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 I—short-circuit current (A).3.3.11 JL—light-generated photocurrent density (A·m–2).3.3.12 M—spectral mismatch parameter (dimensionless).3.3.13 Q(λ,T)—quantum efficiency (electrons per photon or%).3.3.14 Θ(λ)—partial derivative of quantum efficiency withrespect to temperature (electrons per photon·°C–1or %·°C–1).3.3.15 R(λ)—spectral responsivity (A·W–1).3.3.16 T—temperature (°C).3.3.17 TR0—temperature, at which the reference cell iscalibrated (°C).3.3.18 TD0—temperature, to which the short-circuit currentof the device to be tested will be reported (°C).3.3.18.1 Discussion—When reporting photovoltaic perfor-mance to Standard Reporting Conditions (SRC), it is commonfor TR0= TD0= 25°C.3.3.19 q—electron charge (C).3.3.20 h—Planck constant (J·s).3.3.21 c—speed of light (m·s–1).3.3.22 ∆T—temperature difference (°C).3.3.23 ɛ—measurement error in short-circuit current (di-mensionless).4. Summary of Test Method4.1 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 deviceperformance 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(λ).4.3.2 The reference spectral irradiance distribution to whichthe photovoltaic reference cell was calibrated E0(λ).4.3.3 Photovolatic Reference Cell:4.3.3.1 The quantum efficiency at the temperature corre-sponding to its calibration constant, QR(λT0)4.3.3.2 The partial derivative of the quantum efficiency withrespect to temperature, ΘR(λ)=∂QR/∂T(λ).4.3.4 Device to be Tested:4.3.4.1 The quantum efficiency at the temperature at whichits performance will be reported, QD(λ,TD0).4.3.4.2 The derivative of the quantum efficiency with re-spect to temperature, ΘR(λ)=∂QD/∂T(λ)4.4 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 performed.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 formulated 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 cell’s measured short-circuit current by M,atechnique used in Test Methods 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 needed(although absolute spectral quantities may be used if avail-able).5.4 Temperature-dependent spectral mismatch is a moreaccurate method to correct photovoltaic current measurementscompared with fixed-value temperature coefficients.36. Apparatus6.1 Quantum Effıciency Measurement Apparatus—As re-quired by Test Method E1021 for spectral responsivity mea-surements.6.2 Spectral Irradiance Measurement Equipment—A spec-troradiometer as defined and required by Test Method G138and calibrated according to Test Method 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. 1692–1697. DOI:10.1109/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 Methods E948, E1036, and E1125 provide addi-tional guidance for spectral irradiance measurements.6.3 Temperature Measurement Equipment—As required byTest Method E948 or Test Methods E1036.7. Procedure7.1 Obtain the reference spectral irradiance distribution,E0(λ), 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(λ,TR0).7.2.1 An expression that converts spectral responsivity toquantum efficiency is provided in Test Methods E1021.NOTE 1—Test Methods 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, ΘR(λ), for the photovoltaic referencecell (see 8.1).7.3.1 If ΘR(λ) 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 performancewill be reported, QD(λ,TD0), and its partial derivative ofquantum efficiency with respect to temperature, ΘD(λ), usingthe procedure given in Annex A1(see also 8.1).7.5 Measure the spectral irradiance, ES(λ), of the test lightsource, using the spectral irradiance measurement equipment(see 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 with:3M 5*λ1λ2λQD~λ,TD0!ES~λ!dλ1∆TD*λ1λ2λΘD~λ! ES~λ!dλ*λ3λ4λQR~λ,TR0!ES~λ!dλ1∆TR*λ3λ4λΘR~λ!ES~λ!dλ3*λ3λ4λQR~λ,TR0!E0~λ!dλ*λ1λ2λQD~λ,TD0!E0~λ!dλ, (1)where ∆TR= TR– TR0and ∆TD= TD–TD0. Use anappropriate numerical integration scheme such as that de-scribed in Tables G173. Appendix X1 provides the derivationof Eq 1.If?∆TR? ≤ 0.5°C and ?∆TD? ≤ 0.5°C, then ΘR(λ) andΘD(λ) may be omitted and Eq 1 simplified to:M 5*λ1λ2λQD~λ,TD0!ES~λ!dλ*λ3λ4λQR~λ,TR0!ES~λ!dλ3*λ3λ4λQR~λ,TR0!E0~λ!dλ*λ1λ2λQD~λ,TD0!E0~λ!dλ, (2)8.1.1 The wavelength integration limits λ1 and λ2 shallcorrespond to the spectral response limits of the photovoltaicdevice.8.1.2 The wavelength integration limits λ3 and λ4 shallcorrespond to the spectral response limits of the photovoltaicreference cell.8.2 Optional—Calculate the measurement error due to spec-tral mismatch using:ε 5?M 2 1?(3)9. Precision and Bias9.1 Precision—Imprecision 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 method 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 Bias—Bias 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 Conference—1987, pp. 153–159, 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;testingANNEX(Mandatory Information)A1. 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 25°C