We investigated the deviations of the global series resistance values determined either from series resistance images or from the global IVcurve. Therefore, the series resistance imaging methods introduced by Trupke, Kampwerth, and Glatthaar are applied to four silicon solar cells, as shown in Fig. 5.33. The solar cells in Fig. 5.33A and C are fabricated using monocrystalline wafers and the ones in Fig. 5.33B and D using multicrystalline wafers.
Using the series resistance images of Fig. 5.33, the harmonic and arithmetic means as well as the series resistance value of the LIA approach are determined. These values are compared to values extracted from global IV curves using the double-light level method (Wolf and Rauschenbach, 1963) as well as the fill-factor method (Green, 1995). The results are shown in Fig. 5.34.
Figure 5.34A and B demonstrate that for small series resistance values (smaller than 1 O cm2) all approaches yield similar results. The harmonic and the arithmetic averages give a sufficiently good value if compared to the global series resistance or the series resistance extracted with the LIA approach. The situation changes for solar cells with higher series resistance values (>2 O cm2), as shown in Fig. 5.34C and D. The simple averaging methods (harmonic and arithmetic) give a value which is about 20—30% smaller than the one obtained with a global Rer method. The LIA approach instead gives in both cases a more precise result; deviations are less than 15%. Thus, the experimental results confirm the findings and explanations of Michl et al. mentioned in the previous section.
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Figure 5.34 Comparison of global series resistances extracted with different methods. CDCR, Kampwerth, and Trupke are the spatially resolved series resistance methods used. Harmonic and arithmetic are two averaging methods. Also, the LIA approach transforms the series resistance image to a global IV characteristics, which is then evaluated using the fill-factor method (FF) or the double-light-level method (DLL). For example "CDCR > LIA> Rs-DLL" means that Rser,-data from CDCR was used in the LIA approach to calculate the global IVcurve and subsequently the global series resistance was extracted using the DLL method. Note that Rs-Kampwerth was not carried out for solar cell (B). |
8. CONCLUSION
This work covers a broad range of aspects relevant to understanding the potential and limitations of luminescence-based diagnostics of crystalline silicon solar cells. Starting from radiative recombination and the description ofthe luminescence emission, we studied the experimental requirements for the detection of luminescence light from silicon and finally discussed the extraction of physical parameters from luminescence measurements. Special attention was paid to the determination of the local series resistance since this is the prime application of luminescence imaging with respect to the analysis of the solar cell today.
With Eq. (5.8) we presented the central equation to model the luminescence photon emission per time and surface element. This equation is defined by the minority charge carrier profile An and the luminescence photon detection profilefout. The solution of the diffusion equation for the specific boundary condition of interest yielded the minority charge carrier profiles for the EL case and the photoluminescence (PL-wp, PL-oc, and PL-sc) cases under different electrical conditions. The luminescence photon detection profile fout(z, 1) as given in Eq. (5.30) was shown to follow when summing up all volume-elements V) contributing to the luminescence emitted from a surface element a. Interestingly, it turned out that/out(z, 1) is fully determined by the generation profile of minority charge carriers _geh(z, 1). Consequently, documented equations explicitly designed to describe the generation profile of minority charge carriers in solar cells can be used. We demonstrated that the EL spectrum of a solar cell can be modeled with the equations derived in this paper. Due to the numerous parameters entering the equations, we determined all, using additional characterization techniques.
It was shown analytically and by experiment that the luminescence photon emission is directly proportional to exp( V)/ VT), where V and VT are the local and the thermal voltages. Thus, luminescence measurements provide the required data for a camera-based determination of the local series resistance. In experiment, the detection wavelength ranges are often limited due to the use of specific types of camera sensors or due to optical filters: A silicon detector only collects photons in the short-wavelength range while an InGaAs detector in combination with an optical long pass filter detects the long-wavelength range. Therefore, for both wavelength-ranges, we derived approximations of the luminescence photon emission. As a result, we found that the short-wavelength detection range is more reliable for a voltage determination because the long-wavelength range also depends on the rear-surface reflectance Rb. However, if the local voltage is kept constant, the long-wavelength range allows some extraction of Rb and it is also proportional to the collection length LC. In addition, we could demonstrate that for both wavelength ranges a proportionality to the effective diffusion length Leff is only given for effective diffusion lengths well below the thickness of the solar cell.
The prime application of luminescence imaging on solar cells is the camera-based determination of the local series resistance Rser,). For this reason, we compared a variety of EL – and PL-based approaches by applying these techniques to mono – and multicrystalline silicon solar cells. We showed that all approaches are based on the same general equation which is a consequence of the underlying independent one-diode model. Numerical circuit simulations using SPICE revealed that this simple model is sufficient for the determination of Rerii and J0 i for applied voltages below the maximum power-point voltage.
Generally, PL-based approaches had been shown to have an advantage over EL-approaches since they are capable of separating recombination – related effects from series resistance effects. Consequently, a more detailed study focused on two PL approaches published by Trupke et al. and Glatthaar et al. The approach by Glatthaar can be regarded as an extension of the approach by Trupke with the advantage of being capable in determining not only Rser, i but also J0,;. However, for voltages well below the maximum power point, all techniques yield the same Rer value. Finally, area-averaged values had been shown to be consistent with global values determined by the double-light-level approach and values calculated from light current-voltage curves applying the fill-factor equation of Green. For small series resistance values (<1 O cm2), an arithmetic averaging procedure is sufficient. However, for higher series resistance values, a network approach (based on the independent series resistance model) to calculate the current-voltage characteristics and subsequently the global series resistance value is required.
ACKNOWLEDGMENT
The authors would like to thank R. Brendel for his continuous support and encouragement. Carsten Schinke is acknowledged for fruitfull discussions and his work on
