The effects described in this literature review are known to
• generate dark IV characteristics, which do not obey the two diode model or
• result in ideality factors higher than one in case of the first diode or higher than two in case of the second diode or
• result in IV characteristics, whose adjustment by one of the diode models results in misinterpretations.
8.2.1 Laterally varying properties of the solar cell
Different laterally varying properties of solar cells, which affect the shape of the IV characteristics, were found in the literature:
• Laterally inhomogeneous contact resistance: Van der Heide et al. [31]
showed that a laterally inhomogeneous contact resistance can result in ideality factors greater than 2, if the one diode model is adjusted to the illuminated IV characteristic. If the two diode model with ideality factor n2 = 2 is adjusted to the illuminated IV characteristic of a solar cell with laterally inhomogeneous contact resistance, the saturation current density in the depletion region J02 seems to be increased instead of the series resistance.
• Laterally inhomogeneous diffusion lengths of the minority carriers:
Mijnarends et al. [94] showed, that laterally inhomogeneous diffusion lengths may suggest an increased series resistance and increased saturation current J02 of the second diode instead of an increased J01, when the two diode model is adjusted to the according IV characteristic.
• Resistance limited enhanced recombination: This effect was analyzed by two authors/author-groups: Hernando et al. [95] and McIntosh [33], chapter 4.
Hernando et al. [95] show that shoulders/”humps”1 in the dark IV characteristic with ideality factors n2 > 2 may be caused by a small region with very high saturation current J02 of the second diode, which is separated by a high series resistance from the other parts of the solar cell. In real solar cells this effect can be caused by broken pyramids of the front texturization.
The effect is shown to diminish, if pyramids with a height of 3 µm are used instead of 15 µ m as the lower pyramids break less often.
McIntosh [33], chapter 4.3, explains shoulders in the dark IV characteristics of small buried contact solar cells with cell areas of less than about 4 cm2 in case of usual buried contact solar cells and with cell areas of less than about 6 cm2 in case of double sided buried contact solar cells by resistance limited enhanced recombination. In the analyzed cases the enhanced recombination occurs at the cell edge, which is separated by the emitter sheet resistance from the peripheral finger. The hump in the local ideality factor characteristics (see chapter 2.6.2) of the analyzed solar cells becomes lower
1 In the literature shoulders in the dark IV characteristics are also often called „humps.“
and shifts to higher voltages, if the distance between peripheral finger and cell edge and therefore also the according effective emitter resistance becomes smaller. In chapter 4.4 of his PhD-thesis, McIntosh explains humps in the local ideality factor characteristics with local Schottky contacts between the fingers and the p-type base of buried contact solar cells.
• Laterally inhomogeneous distributed coupled defect levels: see chapter 8.2.4.
8.2.2 Recombination saturation effects
Solar cells with defects, which obey the Shockley-Read-Hall (SRH) statistic (see chapters 2.3.3 and 2.3.4) and which have asymmetrical capture cross sections for electrons and holes, may have dark IV characteristics with a shoulder in the low voltage range. The effect is called recombination saturation as the recombination in the specific voltage range is limited by the supply of one kind of charge carriers due to the asymmetric capture cross sections.
One of the first publications found describing saturation recombination effects is [96], in which III-V materials are analyzed.
In case of silicon solar cells, recombination saturation effects were analyzed by several authors (e.g. [97], [98], [99], [100], [101]) who attributed the effect to different kinds of defects:
• Defect levels in the space charge region: Beier et al. [97] showed that
“humps” or shoulders, which were observed in the dark IV characteristics of high efficiency silicon solar cells, can be caused by SRH-defects in the space charge region with asymmetrical capture cross sections and with energy levels, which are not positioned in the middle of the band gap. Robinson et al. [98] confirmed this thesis.
• Defect levels at the rear surface: Robinson et al. [98] furthermore showed that shoulders or “humps” in the dark IV characteristic also occur if the defects are located at the rear surface. They were able to attribute the shoulders, which occur in the dark IV characteristics of high efficiency solar cells, to their silicon-silicon oxide interface at the rear as this interface is characterized by defects with asymmetrical capture cross sections [99].
• Defect levels in the base material: Robinson et al. [98] also simulated the effect of defect levels with asymmetrical capture cross sections in the base
material using PC1D. The resulting dark IV characteristics also show a shoulder.
As the boron oxygen defect complex, which often occurs in boron doped Czochralski silicon (see e.g. [102]), has strongly asymmetric capture cross sections for electrons and holes in its active state [103], this also results in dark IV characteristics with a shoulder. This effect is analyzed in [100] by Schmidt et al.
Macdonald et al. [101] analyzed the effect of interstitial iron in silicon solar cells. The defect caused by interstitial iron, which mostly occurs in multicrystalline silicon, also has asymmetric capture cross sections. This results in a reduction of the fill factor of the solar cell compared to one without this defect.
• Coupled defect-levels: see chapter 8.2.4.
8.2.3 Surface charges on p-doped silicon
Kühn et al. [104] analyzed the effect of positive surface charges on p-doped silicon on the dark and illuminated IV characteristics. Such surface charges may occur at p-doped silicon, which is passivated by a silicon dioxide or silicon nitride layer. The positive surface charges create a depletion or even inversion region within the p-doped silicon.
Kühn et al. simulated, that the dark IV characteristics of solar cells with positive charges on a p-doped surface can have a shoulder or “hump”.
8.2.4 Coupled defect-level recombination
Coupled defect-level recombination was analyzed by Schenk and Krumbein [105] and by Breitenstein et al. [106], [107]. Coupled defect-levels may occur in regions with high defect density as e.g. badly passivated surfaces or regions with high impurity density. The cases, which were found by both author-groups to result in dark IV characteristics with increased local ideality factors, are an extension of the saturation recombination effect described in chapter 8.2.2 to more than one defect level. Furthermore Breitenstein et al. showed that these kinds of defects cause increased local ideality factors also when they are distributed laterally inhomogeneously across the solar cell.
• Schenk and Krumbein [105] analyzed the effect of two coupled defect-levels on the dark IV characteristic and the corresponding local ideality factors. Therefore they derived a theory for different kinds of coupling and implemented their models into the device simulator DESSIS (a two and three dimensional device simulator, which is now distributed by Synopsis, Inc.,
under the name Sentaurus Device). Hereby they analyzed possible reasons for the observed increased local ideality factors of liquid phase epitaxial grown diodes with weak intrinsic fields. They found two scenarios, which result in increased local ideality factors. The first one is a shallow donor level, which is coupled to a recombination center, whose energy level is positioned in the middle of the band gap, under the assumption of a not-limiting interlevel rate. The second scenario is the one of a coupled donor-acceptor pair recombination in conjunction with direct tunneling into both shallow levels.
• Breitenstein et al. [106], [107] also used DESSIS simulations to explain the increased local ideality factors, which often occur in industrially fabricated silicon solar cells. In one approach they applied one of the coupled defect-level models as described by Schenk and Krumbein [105]: one defect-level, which can be occupied by tunneling, in combination with another defect level, to which the tunneled charge carrier is transferred immediately. As in industrially fabricated solar cells defects as e.g. shunts often occur locally they implemented this defect locally in their cell model assuming a shunted region with a cross section of 10 µm x 10 µm. In this way they were able to generate dark IV characteristics with local ideality factors up to 6.5 by decreasing the lifetime to 2 x 10-8 s and increasing the energy distance between the defect levels and the according band edges to 190 meV. In their second approach Breitenstein et al. used two deep recombination levels, a donor-acceptor-pair. For both levels unequal capture cross sections for electrons and holes were chosen. With varying transfer coefficient, which describes the charge carrier transfer between both levels, they were able to generate dark IV characteristics with increased local ideality factors.
8.3 Structure of the analyzed solar cells
The solar cells analyzed in this chapter consist of a p-doped float zone base with a resistivity of 0.5 Ohm cm. At the rear a highly boron doped region is integrated. This region provides for a low effective surface recombination velocity, which is lower than e.g. the one of a solar cell with a screen printed aluminum back surface field [108].
Furthermore a highly boron doped region at the rear is not known to result in non-linear effects, when different illumination intensities are applied. Such effects occur for example in solar cells, which have a SiO2-passivation layer at the rear (see e.g. [109], [110], [111]). Another advantage of a highly doped region at the rear is the resulting
decrease in contact resistance [58]. The back contact of the solar cells consists of an aluminum layer, which is followed by a Ti-, Pd- and Ag-layer, as aluminum is more difficult (or not at all) to solder than silver [112]. At the front inverted pyramids, which have an approximate height of 13 µm, and an anti-reflection coating consisting of SiO2
allow for a high rate of the incident light to enter the solar cell. The emitter consists of a shallow phosphorus doped layer with an emitter sheet resistance of approximately 100 Ohm/sq. As front contacts a thin Ti-, Pd-, Ag-layer is used, which is thickened with plated silver. The solar cells are approximately 260 µm thick. A solar cell has an active cell area of 2 cm x 2 cm. Seven cells are produced on one 4 inch wafer. Fig. 8.2 shows a schematic cross section of the analyzed solar cells.
Usually the measurements shown in this work were performed while the solar cells were still integrated into the wafer.
Fig. 8.2: Schematic of the profile of the analyzed solar cells.