# Spectral responsivity

Fabian Plag, Physikalisch-Technische Bundesanstalt (PTB), Bundesallee 100, 38116, Braunschweig, Germany

## Introduction

This page introduces spectral responsivity (SR) measurements of full-size photovoltaic (PV) modules and emphasizes its importance for performance measurements and energy rating.

An overview of typical measurement facilities for the characterization of PV modules’ spectral responsivity is presented. The standard procedures for measurements of the spectral responsivity and subsequent spectral mismatch correction procedures are explained in a comprehensible manner, so that one should be able to implement laboratory measurements and apply spectral mismatch corrections in accordance to the standard guides.

## Description of spectral responsivity measurements

The spectral responsivity of solar cells is commonly used in the field of cell development to analyze the charge carrier recombination, current generation and other processes occurring inside the cell material systems. The SR describes the ratio between the output short-circuit current density of the device and the incident irradiance in dependence of the photon energy (wavelength):

(1): $\displaystyle{ s\left(\lambda\right)=\frac{I_{\mathrm{SC}}(\lambda)}{A\bullet E_\lambda(\lambda)}, }$

where

s(λ) is the SR of the device under test (DUT) at the wavelength λ;

ISC(λ) is the short-circuit current of the DUT at the wavelength λ;

Eλ(λ) is the irradiance of the DUT at the wavelength λ;

A is the active area of the DUT.

Note that crystalline silicon PV modules consist of electrically interconnected solar cells that are encapsulated by several layers including sheets of ethylene vinyl acetate (EVA) and front glass. These additional materials affect the SR.

For high-accuracy measurements of PV module performance parameters the SR of the PV module and the reference device is of vital importance. When the incident solar spectral irradiance (spectrum) differs from that of the reference spectral irradiance defined in the standard IEC 60904‑3 [1] the difference must be considered and compensated. PV module performance parameters are commonly determined under simulated or natural sunlight whose irradiance is measured with a calibrated reference device (see Module 1 – Lesson 3). If the SR of the DUT PV module differs from that of the reference device, a spectral mismatch needs to be considered and the short-circuit current measurement of the DUT needs to be corrected appropriately. The correction procedure is given in the standard IEC 60904-7 [2]. To follow the procedures of the standard, the SRs of both devices need to be determined experimentally. The IEC standard 60904-8 [3] includes three different techniques to for the determination of the SR:

1) Measurement of the SR using a constant light source and a grating monochromator

2) Measurement of the SR using a constant light source and bandpass (interference) filters

3) Measurement of the SR using a flash light source and bandpass (interference) filters

Commonly, for PV module SR measurements facilities with constant light and a grating monochromator or facilities with a flash light source and bandpass filters are used.

Both facility types provide advantages and disadvantages in terms of the accuracy of the measured PV module SR. These are summarized in the following table:

 Facilities using constant bias light Advantages Disadvantages High accuracy (consideration of non-linearities). Time consuming measurement procedure if the differential spectral responsivity (DSR) method is applied. Technically complex setup and complex evaluation procedure for the determination of the SR. If simplifications are applied → Risk of uncertainties (i.e. due to interpolation errors). Enormous effort for the thermo unit to keep the device at 25°C. High power consumption due to continuous bias light. Facilities using pulsed monochromatic light only Advantages Disadvantages Fast measurement procedure. Comparably easy to perform and evaluate SR measurements. Lower requirements for instrumentation (electrical measurement and temperature control). Combination of SR measurements and performance measurement using the same instrumentation (broadband flash light of the solar simulator instead of filtered light). Larger uncertainties (due to simplifications in the method). Non-linearities of the device cannot be considered in accordance with the standard without using bias light.

## Common equipment and components for spectral responsivity measurements

A SR measurement setup consists of a monochromatic light source and electrical instrumentation for the short-circuit current measurement. An optional continuous broadband bias light source is used to vary the DUT’s short-circuit current level, which facilitates to consider non-linearities of the spectral responsivity dependent on the irradiance level. If continuous bias light is irradiating the DUT, the monochromatic light must be modulated by a chopper. A mounting assembly capable to mount the DUT PV module and the reference device including a temperature control system (thermo unit) is required. Fluctuations such as instabilities of the chopped monochromatic light can be monitored and compensated by an optional beam splitter assembly and a monitor detector system. When a continuous bias irradiation is used, the electrical instrumentation should be consistent of transimpedance amplifiers and lock-in amplifiers, one for the monitor detector and one for the device positioned in the designated test area (DUT or reference device). The lock-in technique is commonly used to separate the alternating current signal generated by the monochromatic light from the steady current signal from the continuous bias light that is measured using a volt meter. An exemplary spectral responsivity measurement system for full-size PV modules that is commercially available, is shown in Figure 1.

Figure 1: Spectral responsivity measurement system for PV modules that uses continuous bias light and a grating monochromator; the monochromatic light (green illuminated area) is generated by a grating monochromator and a broadband light source. Due to the low power output of grating monochromator systems commonly only one single solar cell out of the full-size module is illuminated. Additional bias lamps provide continuous broadband bias irradiance (bias lamps are switched off in this figure); ©Enli Technology Co., Ltd. [4].

The monochromatic irradiance can be also generated by applying bandpass (interference) filters to large area solar simulators. One major advantage of this technique is that entire PV modules can be illuminated by the monochromatic irradiance. Commonly this technique is applied to large area flash type solar simulators, driven by Xenon discharge lamps. Figure 2 shows the transmittance of 15 different bandpass filters covering a wavelength range from 400 to 1100 nm. An advantage of the large area monochromatic irradiance is that the reference device can be positioned within the designated test area next to the DUT PV module if the irradiance is uniform. Both devices short-circuit currents must be measured simultaneously by using a trigger with a peak detection unit. Hence, there is no need for a monitor detector system in this case. Note that the use of large filters can introduce large non-uniformities of the monochromatic irradiance that cause additional errors in the measurement. Also, the bandwidth of the wavelength covered by each filter affects the SR measurement. The standard requirements for the Full Width at Half Maximum FWHM of the filter’s bandwidth shall not exceed 20 nm between 300 nm and 1200 nm.

Figure 2: Transmittance of 15 interference (or bandpass) filters used to filter the broadband irradiance of a commercially available pulsed solar simulator (flasher) ©TÜBITAK UME, 2018.

Further information and schematics of the setups used for PV module SR measurements are included in the standard [3].

## Procedure for spectral responsivity measurements according to the standard guideline

In accordance with the standard IEC 60904-8 [3] the measurement of the SR of PV modules is performed by irradiating the DUT with narrow-bandwidth monochromatic light; either by using a grating monochromator or a set of bandpass filters. A series of measurements must be taken at different wavelengths covering the wavelength range of the DUT. This section includes a comprehensive description of the relevant methods for PV module SR measurements specified in the standard [3] and discusses details on simplifications that can be applied when using continuous bias light.

Excursus to theory:

The quantity that is actually measured with systems described in the first section of this lesson, 1) and 2), is the differential spectral responsivity (DSR). The DSR is dependent on the wavelength λ and on the bias irradiance E. If the PV module is linear with the irradiance, the DSR is equal to the SR sSTC(λ) under standard test conditions (STC). In the case that the non-linearity of the PV module is not negligible the DSR measurement must be performed to determine the correct SR under STC using a sufficient number of bias light levels ranging from 5 % to 110 % of STC.

Measurements of the DSR presume an adjustable continuous bias light level. Hence, facilities using flash lamps and bandpass filters to generate the monochromatic irradiance, are only appropriate for SR measurements if non-linearities are negligible or if simplifications causing larger uncertainties are acceptable. More details on the DSR method can be found in [5] and in the Module 1 – Lesson 3 on calibration procedures of reference cells. Simplifications on SR measurements of PV modules in accordance with the standard IEC 60904-8 are discussed later in this E-learning lesson. These simplifications often represent a reasonable tradeoff between accuracy and effort in the laboratory applications that are technically feasible under consideration of a realistic throughput.

## Procedure for spectral responsivity measurements under continuous bias light

In the first step the reference device with a given DSR $\displaystyle{ {\widetilde{s}}_{ref}(\lambda,I_{ref,DC}) }$ is used for the setup calibration in the following way:

1.1. Mount the reference device in the designated test area; Connect the electrical instrumentation appropriately by using 4-wire leads (current and voltage separated).

1.2. Adjust the temperature control of the reference device to 25 °C or to the temperature given in the calibration certificate.

1.3. Ensure that the irradiation of the reference device is larger than the active area of the device (over illumination), because light falling onto the non-active area (edges or the encapsulant) may also contribute to the generated short-circuit current of the device via multiple reflections in the material system.

1.4. Measure the alternating part of the reference device’s short-circuit current Iref(λ, Iref,DC) at the bias light level with the irradiance E generating the continuous part of the reference device’s short-circuit current Iref,DC for each wavelength of the monochromatic light.

Non-uniformities in the monochromatic light field shall be considered as a contribution to the measurement uncertainty by scanning the illuminated area with the (smaller) reference device and using the average short-circuit current. Both, the temporal fluctuations and the non-uniformity of the monochromatic light should be below 2 %. In a second step the DUT PV module is measured under the calibrated setup:

2.1. Follow the same procedure than in 1.1. for the DUT PV module.

2.2. Follow the same procedure than in 1.2.

2.3. Adjust the temperature of the DUT to 25°C.

2.4. Measure the alternating part of the DUT’s short-circuit current I(λ, Ibias(E)) at the bias light level with the irradiance E generating the continuous part of the DUT’s short-circuit current Ibias for each wavelength of the monochromatic light.

The steps one and two can be also performed simultaneously if the size of the illuminated area allows both devices to be placed next to each other and the non-uniformity of the irradiance is considered. If the measurement facility doesn’t provide a sufficiently large illuminated area, a monitor detector shall be used to compensate temporal fluctuations of the monochromatic light that impact the measured current of the DUT I(λ, Ibias(E)).

Measure the DSR at least for five different bias light levels that generate different short-circuit currents Ibias(E) ranging from 5 % to 110 % of the DUT under STC.

Calculate the DSR for each wavelength and for each individual bias level with the following equation:

(2): $\displaystyle{ \widetilde{s}\left(\lambda,I_{bias}\left(E\right)\right)=\frac{I\left(\lambda,I_{\mathrm{bias}}\left(E\right)\right)}{I_{\mathrm{ref}}\left(\lambda,I_{\mathrm{ref,DC}}\right)}\bullet{\widetilde{s}}_{ref}\left(\lambda,I_{ref,DC}\right). }$

The calculation steps from the DSR to the SR under STC conditions can be found in Module 1 – Lesson 3.

If the DSR method cannot be performed completely, several steps simplifying the technical requirements and the procedure can be applied in accordance with the standard [3]. Here, the most relevant steps for simplifications of PV module SR measurements are briefly summarized.

The following reasonable (but still complex) simplification can be applied if a complete DSR measurement is not possible or feasible to apply for PV modules: The DSR can be determined by measuring the white light responsivity In this case modulated white light is used instead of monochromatic light. The modulated white light shall provide at least a Class B spectrum in accordance with the solar simulator requirements in IEC60904-9 [6]. This simplification should be applied in the following way:

Measure the white light responsivities at least for 3, better for 5 bias light levels ranging from 5 % to 110 % of the DUT’s approximated short-circuit current ISTC,approx under STC. The ISTC,approx can be determined by using a solar simulator method without consideration of the spectral mismatch.

Calculate the responsivity of the DUT with the following equation:

(3): $\displaystyle{ s\left(I_{STC,\ approx}\right)=\frac{I_{STC,approx}}{\int_{0}^{I_{\mathrm{STC,approx}}}\frac{1}{\widetilde{s}\left(I_{\mathrm{bias}}\right)}\mathrm{d}\ I_{\mathrm{bias}}}. }$

Determine the bias irradiance E0 for the case that the calculated $\displaystyle{ s\left(I_{STC,approx}\right) }$ equals the measured $\displaystyle{ \widetilde{s}\left(I_{bias}(E_0)\right) }$ . Therefore, solve the following integral by iteratively increasing the upper boundary of the integral.

(4): $\displaystyle{ E_{bias}=\int_{0}^{I_{\mathrm{bias}}}{\frac{1}{\widetilde{s}(I)}dI\ } }$

Measure the DSR at one specific bias irradiance E0 by assuming that $\displaystyle{ \widetilde{s}\left(\lambda,\ E_0\right)\approx\ s_{STC}(\lambda) }$

An additional simplification can be applied by measuring the DSR at bias light conditions generating approximately 30 % ‑ 40 % of the $\displaystyle{ I_{STC,approx}. }$ . Then, the DSR at this bias light level is assumed to be equal to the $\displaystyle{ s_{STC}(\lambda) }$ . This approximation should only be used for crystalline silicon PV modules.

The simplest procedure given in the standard that uses continuous bias light specifies that a minimum bias light level shall generate at least 10 % of the ISC of the PV module under STC. The non-linearity of the DUT shall not vary more than 2 % when the measurement is performed under bias irradiances 50 % decreased and increased than before. If not, the two additional measurements indicate the non-linearity of the DUT PV module. In practice the complete DSR or white light responsivity method, both considering possible non-linearities of the devices, are rarely applicable for full size PV modules for the two following reasons:

Firstly, continuous bias light at high levels (in the range of 1 sun or more) cause enormous heat load onto the PV module that is difficult to stabilize at 25°C without an additional costly thermo unit. The additional temperature fluctuation impacts the DSR and contributes significantly to the uncertainty in the wavelength regions close to the band gap of the DUT solar cells in the PV module. Secondly, the determination of the non-linearity using these methods require complex setups and are time consuming. Hence, the complete DSR method is used only for reference cell calibrations on a very high-accuracy level.

## Procedure for spectral responsivity measurements under pulsed light

Measurements of PV modules SR are more accomplishable by using flasher-based facilities equipped with bandpass filters. The procedure presumes that the DUT is sufficiently linear with the irradiance, so that systematic errors in the SR are acceptably low.

The calibration of the setup and the subsequent measurement of the DUT’s SR requires the same steps 1.1 to 2.4 abovementioned, but without bias light. If the illuminated area is sufficiently large, the measurements of the reference and the DUT can be taken simultaneously without using a monitor detector.

Note that a fast data acquisition system is required to perform measurements under pulsed light.

Determine the SR by using the simplified version of equation (2) for each wavelength with instead of and without the bias light level dependency:

(5): $\displaystyle{ s\left(\lambda\right)=\frac{I\left(\lambda\right)}{I_{\mathrm{ref}}\left(\lambda\right)}\bullet\ s_{ref}\left(\lambda\right). }$

For most of the applications, where the SR of PV modules is required to perform a spectral mismatch correction, the additional uncertainties introduced by the measurements without bias light are acceptable. It is recommended to evaluate the measurement uncertainty for specific cases to estimate its impact on the spectral mismatch correction factor.

Note that non-uniformities of the monochromatic irradiance have significant impact onto the measured total current of a PV module because the solar cells are connected in series within the module and the solar cells generating the lowest current limit the total current. Differences in the conversion efficiency of single cells (current mismatch) may also contribute additional errors in the SR measurement. The standard [3] provides more information on measurement procedures and gives details on measurement of single cells in series connected modules that are beyond the scope of this lesson.

The spectral responsivity is needed for the determination of the spectral mismatch correction.

## References

[1] IEC 60904-3:2008, Photovoltaic devices - Part 3: Measurement principles for terrestrial photovoltaic (PV) solar devices with reference spectral irradiance data.

[2] IEC 60904-7:2008, Photovoltaic devices - Part 7: Computation of the spectral mismatch correction for measurements of photovoltaic devices.

[3] IEC 60904-8:2014, Photovoltaic devices - Part 8: Measurement of spectral responsivity of a photovoltaic (PV) device.

[4] Enli Technology Co., Ltd., 2019 https://www.enlitechnology.com/uploadfiles/402/ing001.png

[5] Metzdorf, 1987, Calibration of solar cells. 1: The differential spectral responsivity method, Applied Optics Vol. 26, pp 1701 -1708.

[6] IEC 60904-9:2007, Photovoltaic devices - Part 9: Solar simulator performance requirements.

[7] IEC 61853-3:2018, Photovoltaic (PV) module performance testing and energy rating - Part 3: Energy rating of PV modules.