Category Advances in Photovoltaics Part 2

ANALYTICAL SOLUTIONS OF THE MINORITY CHARGE CARRIER PROFILES

With respect to luminescence characterization of silicon solar cells, two general excitation scenarios exist: (a) the EL case where carriers are injected across the pn-junction into the solar cell base in the dark by applying a forward voltage and (b) the PL case where the solar cell is illuminated and held at a specific electrical working point (wp). In order to obtain the minor­ity charge carrier profile Dn(z) for the different excitation scenarios, we solve the differential equation given in Eq. (5.12) for the boundary conditions
defined in Section 3.3.2. Details about the mathematical derivation are given in Hinken et al. (2009a).

Подпись: A«drk(z) = «1 Подпись: z - Asinh z Lb Leff Lb Подпись: (A.1)

For the EL case, where _geh(z, l) = 0, we have to solve a linear differential equation to obtain the homogeneous solution

image411 image412

For the PL c...

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Comparison of global series resistance values

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)...

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Averaging of series resistance images

Different procedures have been used for the averaging of series resistance images. Trupke et al. (2007) suggested using the harmonic average of the RseriI – values, Ramspeck et al. (2007) used the arithmetic average, and Michl et al. (2008) utilized the independent series resistance model similar to the LIA approach as shown above to calculate the current-voltage char­acteristics and subsequently extract from these characteristics the global series resistance value. In order to find a procedure to calculate the global series resistance from series resistance images, Michl evaluated all three averaging

procedures. The harmonic-averaging approach is dominated by low Re­values...

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Current-voltage curve comparison

For the industrial screen-printed solar cell of Table 5.3, where the series resistance image was shown in Fig. 5.27, we first compare the calculated and measured global IV curves.

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Figure 5.31A shows the measured global IVcurve (green circles) and the calculated curve using the two-diode model (solid line). For this calculation, the parameters as given in Table 5.3 are used. The parameters J01, J02, and Rsh were determined with a least-square regression of the two-diode model to the measured data of the Jsc-Voc characteristics, the series resistance Rser, FF followed from the light-IV and Jsc – Voc characteristics and Jsc directly from the measured light-IV characteristics...

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Measurements

7.1.1.1 Efficiency comparison

We analyzed seven monocrystalline silicon solar cells which suffer from locally high series resistances. We carried out light-IV, Jsc-Voc, and PL-Rs measurements and compared the solar cell efficiency which follows
directly from the light – IV characteristics to the efficiency which follows from LIA (using the measured series resistance image). The local and global parameters needed for LIA are determined as explained in the previous section.

image404The result of this comparison is shown in Fig. 5.30. For the investigated solar cells, the values obtained with the LIA approach deviate from the mea­sured efficiencies by less than 1.6%rel.

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Simulations using SPICE

We prepare an electrical network simulation as already used in Section 5.3 to further analyze if the independent diode model used in the LIA approach holds. We focus on a monocrystalline solar cell, which suffers from a high local series resistance due to a broken finger. For the simulation, we cut the finger at a specific distance from the busbar. By varying this distance, the solar cell suffers globally and locally from different series resistance values. Table 5.2 summarizes all parameters inserted into the simulation.

The simulation is carried out for different applied voltages and illumina­tion intensities to obtain the light-IVand the Jsc – Voc characteristics...

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Parameter determination

The presented analysis can be performed with all parameters given as local parameters in a parameter mapping. Here, we analyze industrial monocrys­talline silicon solar cells, which suffer from high local series resistance. In this case, an image of the effective series resistance Rerii is of interest (see previ­ous sections); for all other parameters global parameters are used.

From the light-IV characteristics, we determine the short circuit current density Jsc which in good approximation equals the photocurrent density Jph for moderate series resistance. For monocrystalline solar cells, the assump­tion holds that the local photocurrent density Jphi equals the global photo­current density Jph.

The Jsc-Voc characteristic is used to determine the saturation current densities of the fir...

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Technical implementation

To carry out the calculations as indicated in Eq. (5.79), all parameters which are available as mappings have to be matched by means of scaling, rotation and translation. Note that Aloc is limited by the measurement technique hav­ing the lowest resolution.

Since the local two-diode model (see Eq. 5.56) is given implicitly for Vappl we apply Newton-Raphson’s method. Already, after a few iterations, a value forJextr, i follows with a very high precision. As indicated in Eq. (5.79), we add up all local currents to the global current and thus obtain one IVdata pair. IV data pairs with a typical resolution as used for standard IVmeasurements have to be calculated to obtain a complete IV characteristic.

The calculated light-IV characteristics from the LIA approach has to be compared to the ex...

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