5.1 Effect of shading near the bus bar on the open circuit voltage and
5.1.2 The distributed circuit model
The distributed circuit simulations were performed using the symmetry element shown in Fig. 5.1.
Fig. 5.1: a)Schematic of the front of an industrial like silicon solar cell. Marked by the red rectangle is the symmetry element used to simulate the effect of an additionally shaded region near the bus bar.
b) Used symmetry element. Marked by x1 – x3 are three different positions of the simulated test prod, whose influence is analyzed.
c) Dimensions used in the distributed circuit simulations.
A PC1D model with industrial-like solar cell parameters was used to generate the local IV characteristics (see Tab. 5.1).
Tab. 5.1: Parameters used in the PC1D model which was used to generate the local IV characteristics of the distributed circuit model.
Surface texturing 3 µm Internal shunt elements
Surface charge Without Conductor No conductor
External
Emitter diffusion Compl. error funct.
Internal reflectance First bounce 90 diffuse Bulk recombination
Subsequent
Rear surface Recombination velocities
First bounce 70 diffuse Front surface
In order to generate the local IV characteristics used beneath the metalized regions in the distributed circuit simulations the front surface recombination velocity was adapted to 107 cm/s. For the local IV characteristics of the additionally shaded regions dark IV characteristics were used with the same front surface recombination velocity as in the illuminated areas. This means, that the additionally shaded region is totally shaded.
The short circuit current density of the whole symmetry element with additionally shaded region near the bus bar was kept at the level of the one sun short circuit current density achieved without additional shading. Therefore the illumination intensity Iwith shading used in the models to generate the local IV characteristics of the not metalized and not shaded region of the distributed circuit models with additional shading near the bus bar was increased according to
shading Amax: area without metallization
Iwithout shading: 0.1 W/cm2.
The properties of the symmetry element were chosen as given in Tab. 5.2.
Tab. 5.2: Parameters used in the distributed circuit model.
Height of the metallization
12.5 µm ρmetallization 3.2 x 10-6 Ohm cm
Rsheet 55 Ohm/sq ρcont 0.003 Ohm cm2
The effect of the additional shading on the fill factor is expected to be very low.
Therefore special care has to be taken to achieve as exact and comparable simulation results as possible. For this purpose the following aspects were taken into account:
• The voltage increment of the underlying local IV characteristics:
The voltage increment of the local IV characteristics was chosen to be 5 mV for the voltage range between -50 mV and 640 mV. It was decreased at voltages around the open circuit voltage (580 mV – 640 mV) and around the maximum power point (480 mV- 560 mV) to 0.1 mV. To determine the voltage ranges for which a decreased increment is needed, local voltage maps under open circuit and maximum power conditions were simulated.
The minimum and maximum voltage of these maps gives the range of decreased voltage increment of the underlying local IV characteristics.
• The resolution of the distributed circuit model (see also chapter 3.5):
The effect of the resolution of the distributed circuit model on the simulated fill factor was analyzed by varying the resolution with and without additionally shaded region. In the not shaded case always one resolution parameter was set to the value of the resolution named high in Tab. 5.3 while the others were kept at the values named chosen in Tab. 5.3. The difference of the simulated fill factors using the chosen resolution parameters compared to the ones using the high resolution is less than 0.002% without additionally
shaded region.
A similar analysis was performed for a solar cell with additionally shaded region resulting in a resolution of the distributed circuit model in the additionally shaded region in direction perpendicular to the bus bar of 9 nodes for widths of the shaded region up to 4 000 µm and of 25 nodes for a 18 250 µ m wide shaded region. The resolution of the not shaded region in this direction was kept at 41 nodes for an up to 4 000 µm wide additionally shaded region, which results in a higher resolution compared to the not shaded case. For an 18 250 µm wide shaded region, the resolution in this direction was also set to 25 nodes as in this case half of the not metalized region is shaded.
• The position of the test prod on the bus bar:
The effect of the position of the test prod on the bus bar on the simulated IV characteristic parameters was analyzed comparing the simulation results using three different contact positions on the symmetry element:
• on the upper end of the bus bar (x1 in Fig. 5.1),
• in the middle of the bus bar and (x2 in Fig. 5.1)
• on the lower end of the bus bar (x3 in Fig. 5.1),
in each case in the middle of the bus bar in direction perpendicular to it.
The maximum difference in fill factor between these three contact positions is less than 0.01% and therefore not relevant. In the following analysis the contact position at the lower end of the symmetry element x3 has been chosen.
• The voltage increment of the simulated IV characteristics:
In the following analysis the open circuit voltage and the voltage of the maximum power point were determined performing two consecutive distributed circuit simulations with different voltage increments. In the first simulation the whole IV characteristic between 0 mV and 610 mV was simulated with a coarse voltage increment of 5 mV. From these results the approximate open circuit voltage and maximum power point were determined. In the second simulation the open circuit voltage and the maximum power point were determined more precisely using a finer voltage increment of 0.1 mV around the before determined voltages.
Tab. 5.3: Resolutions of the distributed circuit model used to analyze the effect of the resolution on the simulated fill factor. The resolution called chosen is the one used in the further simulations of chapter 5.1.
Resolution chosen high
Number of nodes:
beneath the bus bar in direction perpendicular to the bus bar 5 10 beneath the finger in direction parallel to the finger 41 61 beneath the finger in direction perpendicular to the finger 5 21 in the region without metallization in direction perpendicular
to the finger
15 21