Flash inhomogeneity and distributed circuit model

The illumination inhomogeneity of the QUANTUM Qflash x2 used with two diffusers QF64 mounted 87 cm above the measurement chuck was measured on the measurement chuck. Therefore an array of 64 1 x 1 cm² solar cells in a 2 cm pitch was used in order to perform the measurement during the decaying edge of one single photo flash. The measurement was performed by Jochen Hohl-Ebinger.

The maximum intensity of the spot is located slightly beside the geometrical centre of the measurement chuck. The intensity deviation between the brightest and darkest spot

was determined to be approximately 7.5%. Fig. 5.5 shows the measured intensity inhomogeneity.

Fig. 5.5: Measured illumination inhomogeneity of the suns-Voc flash (QUANTUM Qflash x2 with two diffusers QF64), which is mounted 87 cm above the measurement chuck, measured on the measurement chuck. The maximum measured value is normalized to one. The measurement was performed by Jochen Hohl-Ebinger. (from [78])

It is not possible to perform a distributed circuit simulation of a solar cell, which covers the whole measurement chuck (approx. 16 cm x 16 cm), with sufficiently high resolution of the underlying distributed circuit model using the currently for this work available personal computer (Intel®Core™2Quad CPU Q9550@ 2.83GHz, 2.83 GHz, 2.96 GB RAM). Therefore the measured illumination inhomogeneity was averaged between the four corresponding quarters. The result is shown in Fig. 5.6. The symmetry element used in the distributed circuit simulations is marked in red. The averaged illumination value of the symmetry element is 0.975, if the maximum value of the profile is set to one.

1 3 5 7 9 11 13 15 corresponding quarters. The maximum value is set to one. Marked in red is the symmetry element used in the distributed circuit simulations. Please note that the solar cell grid (dark cyan lines) does not represent the actually simulated grid dimensions. In the performed simulations 33 fingers are arranged on the symmetry element. Marked by x1, x2 and x3

are the different positions of the test prod, whose influence was analyzed.

The local IV characteristics

As local IV characteristics the same PC1D model as described in Tab. 5.1 was used with slightly adopted external reflection data.

To analyze the effect of a laterally varying illumination intensity as shown in Fig. 5.6 many local IV characteristics with different illumination intensities Ix are needed to perform one distributed circuit simulation. To simplify the calculation of the local IV characteristics of different illumination intensities in this chapter the local IV characteristic ^Jlocal^x

( )

suns of an illumination intensity of x suns is calculated using

( ) ( ) ( )

The difference between the resulting local IV characteristics compared to the ones received when the local illumination intensity is adapted directly in the PC1D model is low because the local IV characteristics are generated without external series

resistances. For example the difference in open circuit voltage comparing the results of both procedures for an illumination intensity of 0.8 suns is about 0.1 mV (see Fig. 5.7).

-100 0 100 200 300 400 500 600

-30 -20 -10 0 10

Illumination intensity: 0.8 suns PC1D model

J^{0.8 suns}_local = J^{1 sun}_local(V) - (0.8-1) J local,1sun sc

J [mA/cm2]

U [mV]

Fig. 5.7: Local IV characteristic using an illumination intensity of 0.8 suns, once generated by adopting the illumination intensity in the PC1D model directly and once calculated using formula (5.2).

The voltage increment of the local IV characteristics was set to 0.1 mV in the voltage range between 580 mV and 650 mV, which is the voltage range around the open circuit voltage.

The distributed circuit model

With an area of approximately 8 cm x 8 cm and 33 fingers the symmetry element used in the analysis of this chapter is comparatively big and complex in comparison to the symmetry elements chosen in the other chapters. To be able to perform the simulations all the same, the resolution of the distributed circuit model had to be chosen relatively low compared to the resolutions chosen in the other chapters. After all in the regarded case this is of minor influence, as the influence of the resolution on the simulated open circuit voltage is negligible compared to the influence of the analyzed illumination inhomogeneity. The chosen resolution parameters are given in Tab. 5.4.

Tab. 5.4: Resolution of the distributed circuit model used in the analysis presented in chapter 5.2.

Resolution chosen

Number of nodes:

• beneath the bus bar in direction perpendicular to the bus bar

1

• beneath the finger in direction parallel to the finger 5

• beneath the finger in direction perpendicular to the finger

2

• in the region without metallization in direction perpendicular to the finger

7

The resistance parameters of the distributed circuit model were chosen as given in Tab.

5.2. However the metallization had to be chosen higher because with a height of 12.5 µm the simulation was not performable on the available personal computers. To be able to estimate the effect of the metallization height all the same, the simulation results of three different metallization heights - 18 µm, 20 µm and 25 µm - are compared.

Furthermore the influence of the position of the test prod on the bus bar on the simulated open circuit voltage is analyzed. The three different positions, which are analyzed, are marked in Fig. 5.6 by crosses.

The voltage increment of the distributed circuit simulations in the voltage range around the open circuit voltage was set to 0.1 mV.