A discretisation mesh of the entire solar cell device volume could not be constructed, using state-of-the-art simulation software nor could the device equations be solved on such a huge mesh. Therefore, semiconductor device simulation as described in Section 3.2 is restricted to a symmetry element representing an irreducible section of the solar cell. Considering a solar cell with single sided contacts this symmetry element of the interior cell part typically consists of one Q- to S-contact finger distance multiplied by the wafer thickness for a 2D simulation.
Losses arising from the ohmic metal resistance and recombination losses at the cell perimeter can not be included using a symmetry element of the interior cell part. These losses can be accounted for by using the circuit simulation method [60].
An equivalent circuit of a solar cell with single sided interdigitated contact grid is shown in Fig. 3.10. It consists of elementary diodes (E) and perimeter diodes (P) which are connected by Ohmic resistors. Contact pads of the solar cell are located in the upper corners of the graph. The ,9 curve of each diode is simulated by semiconductor device simulation and tabulated. These tabulated ,9 curves are considered as voltage controlled current sources in the subsequent circuit simulation [41]. Each current density value of a diode is scaled by an associated area fraction shown as hatched areas in Fig. 3.10. For symmetry reasons only half of the metal grid has to be resolved in the circuit simulation in order to describe the ,9 curve of an entire solar cell.
PERIMETERDIODE ELEMENTARYDIODE
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Fig. 3.10: Electrical circuit for the circuit simulation consisting of half of the solar cell.
The small boxes denote the elementary diodes (E) and the perimeter diodes (P). The resistors are arranged in order to describe the interdigitated metal grid indicated as dark areas.
The total current flow causes a voltage drop along the metal grid. Thus, different cell regions (represented by the tabulated ,9 curves in the circuit) are driven by different voltages to that at the contact pads. The resulting losses are known as QRQJHQHUDWLRQORVVHV [61].
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This chapter has presented an overview of numerical methods of silicon solar cell simulation. It has briefly explained how the basic equations that govern carrier transport in solar cells can be solved numerically using a discretisation method.
One-dimensional numerical solutions of the semiconductor device equations using the program 3&' are presented for a SQ junction solar cell with a diffused emitter. The position dependent carrier- and current densites for short-circuit, maximum power and open-circuit conditions have been compared to the analytical Shockley model.
Early analytical light trapping investigations were performed for planar cells with ideal diffuse reflectors on the rear side of the wafer. Modelling light trapping in textured silicon solar cells requires numerical ray tracing techniques. This led B. Wagner and the author of this thesis to develop the ray tracing program 5$<1. This program is capable of handling textured surfaces, antireflection coatings, non-Lambertian surface roughness (Phong model), and spatially distributed absorption. 5$<1 represents an improvement compared to other ray tracing software as it has achieved a more realistic description of surface roughness: Modelled scattering patterns of rough silicon surfaces are observed to match those determined by experiment.
5$<1 was used to simulate the external reflection and absorption of silicon solar cells textured with inverted pyramids and random pyramids. In addition, the absorption enhancement due to structuring of cell interconnectors in solar modules has been investigated by R. Preu and P. Koltay using 5$<1.
Using 5$<1, the normalised generation function of a solar cell with textured surfaces can be simulated. This is essential in order to realistically simulate the short circuit current of textured cells, especially textured thin silicon solar cells. Furthermore, the normalised generation function calculated by 5$<1 provides the basis for modelling the differential spectral response of solar cells with injection level-dependent recombination mechanisms.
This feature is not provided by other ray tracing programs.
Distributed resistive losses in the metal grid can be accounted for by applying the circuit simulation method. Moreover, this method accounts for non-generation losses: when the entire cell is operating at maximum power, different cell parts work at different voltages.
Therefore, the maximum power point of the entire cell deviates from the maximum power point of the elementary diodes constituting the circuit.
Losses due to recombination of charge carriers at the solar cell perimeter can be quantified as well by introducing ,±9 curves of the perimeter region into the circuit simulation.
Both distributed Ohmic losses in the metal grid and perimeter losses influence the solar cell’s fill factor (this will be exemplified in Sections 7.7 and 7.8).
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A two- or three-dimensional computer simulation of a solar cell is often considered as an attempt to estimate the cell output parameters by feeding black boxes (executable programs) with several independent input parameters. The input parameters specify the optical properties of antireflection coatings, the surface texture, the device geometry, and the doping profiles.
Furthermore, details of physical models like those for carrier recombination and minority carrier mobility etc. have to be specified.
However, when solving a scientific problem, researchers communicate in abstract terms, rather than exchanging numerous lists of numbers.
Accordingly, how can our knowledge of the physical properties of solar cells be organised in terms of a hierarchy of categories reflecting the way we formulate problems when discussing them in a research group? In this study the problem is solved by using the REMHFW RULHQWHG SDUDGLJP,which is a new way of thinking about the process of decomposing problems and developing programming solutions.
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The design of 392EMHFWV allows us to examine a wide variety of solar cell-related problems. Some examples of this are outlined in the following:
• Reflection and absorption of a textured silicon wafer or encapsulated solar module can be simulated using ray tracing techniques.
• Models describing the solar cell physics can be accessed separately, HJ mobility, band gap, and recombination models. This is useful in gaining insight into the physical dependencies without having to perform a complete device simulation.
• The electrical symmetry element of device simulations is based on a simple set of two-and three-dimensional geometrical elements implemented as objects. All geometrical and doping parameters determining the topology of the device can be varied.
Solar cells are represented by complex objects (solar cell models), in which all of the above-mentioned objects are embedded. A solar cell model includes several interfaces with commercial device simulation programs.
All the standard measurement procedures of a characterisation laboratory for solar cell analysis can be simulated: the external reflection, the spectral response, the dark- and
illuminated ,9 curve, and the -VF9RF curve. This is achieved by passing a solar cell model to an object representing a measurement apparatus in a virtual laboratory.