# Differential spectral responsivity (DSR) method

*Ingo Kroeger*

###### The differential spectral responsivity method (DSR)

The DSR-method is a spectral method using quasi monochromatic light as a light source. Hence, for this method a reference is needed with calibrated differential spectral irradiance responsivity. This could be a reference solar cell or a photodiode. The optical setup of a DSR-facility is typically built up the following way: A white light source such as a Xe arc lamp or a halogen lamp is coupled into a monochromator system that selects the desired wavelength. Following the monochromator there is an optical chopper that modulated the monochromatic light with a given frequency *f*. Subsequently the monochromatic light passes an imaging optics that generates a uniform irradiance distribution in the measurement plane. Within this optics there is a beam splitter that couples a fraction of the monochromatic light onto a monitor photodiode. Finally, there are white light bias lamps that can generate a bias irradiance between 0 – 1100 W/m² in the measurement plane additionally to the monochromatic irradiance. The DUT and the reference must be temperature controlled and kept at 25°C. Both reference device and DUT shall be connected to a transimpedance amplifier, that coverts the currents into voltages and keeps the solar cell in short circuit state. The AC modulated voltage generated by the monochromatic spectral irradiance shall be then measured by a Lock-In amplifier, the DC voltage generated by the bias irradiance shall be measured by a calibrated multimeter. Also the Monitor current should be converted into a voltage using a shunt or a transimpedance amplifier and measured by a Lock-In-amplifier. The calibration procedure would be as follows:

- Place the reference device in the centre (i.e. location of the best uniformity) of the monochromatic light field, wait until the temperature reading is stable within 25°C ± 1°C and measure the monitor corrected voltage of the reference for all wavelengths of interest (i.e. from 280 nm – 1200 nm if the DUT is made from c-Si): [math]\displaystyle{ \frac{I_{Ref}\left(\lambda\right)}{I_{MD,Ref}\left(\lambda\right)} }[/math]
- Place the DUT at the identical position as i), set the bias irradiance to a fixed level, wait until the temperature reading is stable within 25°C ± 1°C and measure the monitor corrected voltage of the DUT for all wavelengths of interest. Repeat this measurement for at least 7 different bias irradiance levels between 0 and 1100 W/m² and measure the bias current [math]\displaystyle{ I_{Bias} }[/math] of the DUT: [math]\displaystyle{ \frac{I_{SZ}\left(\lambda,I_{Bias}\right)}{I_{MD,SZ}\left(\lambda\right)} }[/math]
- Calculate the absolute differential spectral irradiance responsivity [math]\displaystyle{ {\widetilde{s}}_{SZ}\left(\lambda,I_{Bias}\right) }[/math] using the calibration values [math]\displaystyle{ {\widetilde{s}}_{Ref}\left(\lambda\right) }[/math] of the reference: [math]\displaystyle{ {\widetilde{s}}_{SZ}\left(\lambda,I_{Bias}\right)=\frac{\frac{I_{SZ}\left(\lambda,I_{Bias}\right)}{I_{MD,SZ}\left(\lambda\right)}}{\frac{I_{Ref}\left(\lambda\right)}{I_{MD,Ref}\left(\lambda\right)}}\bullet{\widetilde{s}}_{Ref}\left(\lambda\right) }[/math]
- Calculate the AM1.5g weighted absolute differential spectral irradiance responsivity using the tabulated AM1.5g spectral irradiance data from IEC 60904-3: [math]\displaystyle{ {\widetilde{s}}_{AM1.5g}\left(I_{SC}\left(E_b\right)\right)=\frac{\int_{0}^{\infty}{\widetilde{s}\left(\left.\ \lambda,\ I_{SC}\ (E_B\right)\right)\bullet E_{\lambda,\ AM1.5g}\left(\lambda\right)d\lambda}}{\int_{0}^{\infty}{E_{\lambda,\ AM1.5g}\left(\lambda\right)d\lambda}} }[/math]
- Calculate the short circuit current under standard test conditions by approximating the upper integration limit, such that the following equation is fulfilled. [math]\displaystyle{ 1000=\int_{0}^{I_{STC}}\frac{1}{{\widetilde{s}}_{AM1.5g}\left(I_{SC}\right)}dI_{SC} }[/math]
- Additionally, the absolute spectral irradiance responsivity of the DUT can be calculated by firstly calculating the irradiance level of each measurement [math]\displaystyle{ E_{b,\ AM1.5g}=\int_{0}^{I_{SC}\left(E_b\right)}\frac{1}{{\widetilde{s}}_{AMx}\left(I_{SC}\right)}dI_{SC} }[/math] and secondly solving the following equation: [math]\displaystyle{ s_{STC,\ AM1.5g}\left(\lambda\right)=\frac{1}{E_{STC}}\int_{0}^{E_{STC}}{\widetilde{s}\left(\lambda,E_{b,\ AM1.5}\right)\partial E_{b,\ AM1.5}} }[/math]

In addition to this calibration procedure the following sources of uncertainty should carefully be evaluated and eventually corrected/accounted for: non-uniformity of the spectral irradiance, temperature deviation from 25°C, bandwidth and wavelengths of the monochromatic spectral irradiance, non-linearity of the measurement electronics, positioning of DUT and reference in the same position and measurement plane and reproducibility. More detailed information on this method can be found in Ref. [21-23].

## References

[4] IEC 60904-4:2009, Photovoltaic devices - Part 4: Reference solar devices - Procedures for establishing calibration traceability

[21] J. Metzdorf “Calibration of solar cells. 1: The differential spectral responsivity method”, *Appl. Optics* **26** (9) (1987) 1701-1708.

[22] J. Metzdorf, S. Winter, T. Wittchen “Radiometry in photovoltaics: calibration of reference solar cells and evaluation of reference values” *metrologia* **37** (2000) 573-578.

[23] S. Winter, T. Wittchen, J. Metzdorf “Primary Reference Cell Calibration at the PTB Based on an Improved DSR Facility” in “Proc. 16th European Photovoltaic Solar Energy Conf.”, ed. by H. Scherr, B. Mc/Velis, E. Palz, H. A. Ossenbrink, E. Dunlop, P. Helm (Glasgow 2000) James & James (Science Publ., London), ISBN 1 902916 19 0.