Category Advances in Photovoltaics Part 2

Local impact analysis

For the LIA, we use the model of independent diodes and the local two – diode model, as shown in Fig. 5.18A and B and explained in Section 5.2. By combining Eqs. (5.47) and (5.48) the local voltage

Vi = Vappl + Rserpjextr,! (5-78)

is determined by Vappl, the voltage applied to the terminals, the local series resistance Rser, i, and the current density Jextr>i extracted from the local ele­ment of size Aloc.

Within the model of independent diodes all locally extracted currents Jextr iAloc add up to the globally extracted current

fextr = /extr, iAloc) (5-79)


which corresponds to the current which would be measured in a standard current-voltage measurement.

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The characterization technique most often applied to solar cells is the measurement of the global current-voltage (IV) characteristics under one-sun illumination (light-IV). The analysis of this characteristic yields fundamental solar cell parameters such as the energy conversion efficiency Г, the open circuit voltage Voc, the short circuit current density Jsc, and the fill factor FF. If additionally the Jsc-Voc characteristic is analyzed (Wolf and Rauschenbach, 1963), parameters of the two-diode model such as the saturation current densities of the first J01 and second diode J02, the series resistance Rer, and the shunt resistance Rsh can be extracted (Kunz et al., 2005). Table 5.3 exemplarily shows these parameters for an industrial screen-printed monocrystalline silicon solar cell.


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Glatthaar J0i compared to other methods

To investigate if the determined J0i values using Glatthaar’s method are physically relevant, we compare them with values obtained by a combined approach based on local SR-LBIC and global Jsc-Voc measurements. First, we determine a J0b image using spectrally resolved light beam-induced cur­rent (SR-LBIC) (Warta et al., 1998). Therefore, SR-LBIC is carried out on a multicrystalline silicon solar cell and an Leff image is extracted (not shown here). In combination with the dopant concentration, which we determine using capacitance-voltage analysis (Hinken et al., 2010a; Schutze et al.,


Подпись: J0b,i Подпись: qDn2 NALeff Подпись: (5.77)

, the J0b image follows for each pixel using

Note that this saturation current density yields the base contribution J0b only; the emitter is not included...

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Global J0 versus J0i as a fit parameter (PL imaging)

One might ask how the assumption of a global J0 value (Trupke et al., 2007) affects the determination ofthe series resistance compared to the case where local Jo; values are used (Glatthaar et al., 2010b).

Figures 5.22E and 5.23A show resulting series resistance images of Trupke’s (using the 538 mV image) and Glatthaar’s (using the 526 and the 568 mV image) method for a multicrystalline silicon solar cell. Good qualitative agreement is obtained. However, while Trupke’s method gives an averaged value of 1.06 O cm2, Glatthaar’s method yields 0.82 O cm2. Comparing the saturation current densities, a value of5000 fA/cm2 was cal­culated for Trupke’s method (using the Jsc and the Voc of the low – illumination image) and Glatthaar’s method gives the image shown in Fig. 5...

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Voltage dependence of the local series resistance

It was shown in Section 5.2 that the independent diode model is not valid for all working points (i. e., all applied voltages). Thus, a voltage dependence of the local series resistance is expected beyond a certain voltage, which is important to determine. Here, we investigate the voltage-dependence of the local series resistance for all PL-based methods. In addition, we analyze if the results of an absolute and a differential local series resistance vary.

We take PL images of a monocrystalline silicon solar cell. The images are taken with applied voltage between 500 and 620 mV in 10 mV steps. The series resistance analysis is then carried out for a certain region between the busbars. In Fig. 5.24A, which shows the PL-wp image of 1/2 suns and

Подпись: A PL-wp (counts) В 1.0 CT 0.50 0.52 0.54 0.56 0.58 0.60 0.62 0.Є4 Working point V, (V) Figure 5.24 Local series resistance as a function of the applied voltage for various PL-based series resistance determination methods.

540 mV of this solar cell, the region is...

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Series resistance imaging of a monocrystalline silicon solar cell

Figure 5.21 shows the series resistance analysis of a monocrystalline silicon solar cell. Figure 5.21A shows the EL image in counts at an applied voltage of



Figure 5.21 Luminescence and series resistance images of a monocrystalline silicon solar cell. (A) EL, 610 mV (counts). (B) PL-mpp, 520 mV, 1/2 sun (counts). (C) AV,, PL, 1/2 suns (mV). (D) J,, PL, 1/2 suns, J0 — 900 fA/cm2 (mA/cm2). (E) Rser/, PL, J0 — 900 fA/cm2, Trupke (O cm2). (F) Rser /, EL, 620 mV, Haunschild (O cm2).


610 mV. The two busbars and the fingers appear dark since they shade the emission of luminescence photons. Clearly visible is a certain structure orig­inating from the transport belt of the firing furnace...

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For an experimental demonstration, a number of different series resis­tance approaches are applied to mono – and multicrystalline silicon solar cells. Resulting series resistance images are shown and compared with each other. For various PL-based methods we measure the voltage dependence of the local series resistance of the center region of a monocrystalline silicon solar cell. Moreover, images of the saturation current density are generated using the CCDR approach of Glatthaar et al. (2010b) and compared with results from LBIC measurements as well as to global values extracted from the Jsc-Voc characteristics of the solar cell.

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Approach by Breitenstein et al

Breitenstein et al. (2010) published in October 2009 an EL-based method which determines the local series resistance and the local recombination properties. For this method, at least two EL images are required. Breitenstein uses Eqs. (5.54) and (5.39) and also replaces Ci =//J0i using Fuyuki’s assump­tion (Fuyuki et al., 2005b). Then, the following equation is obtained:

Подпись: (5.75)Подпись: Rabs,iVappl – Vt – Ц Si/



Assuming that the Fuyuki approximation holds, the latter equation allows for separating the local series resistance Rser, i and the local saturation current density J0i also for EL-based methods, since J0i appears twice on the right-hand side of Eq. (5.75). Breitenstein proposes an iterative approach to adapt the latter equation to measured (Vappl, Si) values...

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