The spectral p-n junction model for tandem solar-cell design

Tandem solar cells can have significantly higher efficiencies than single-junction solar cells because they convert a larger fraction of the incident solar spectrum to electricity. For the design of tandem solar cells the spectral p-n junction model is proposed. It is based on tabulated standard spectra, on the fit of experimentally achieved open-circuit voltages, and assumes a quantum efficiency of unity. By consistent treatment of the energy gap in the diode equation, the model can be quantitatively applied to all tandem solar-cell systems. The special form and use of the reverse saturation current density is discussed in detail. The spectral p-n junction model is rigorously applied based on accepted standard spectra. The tandem solar-cell performance limits based on the model are calculated. A quantitative expression for the increase in efficiency under concentration is derived. Choosing materials with optimum bandgaps, a two-solar-cell two-terminal tandem system can achieve a theoretical maximum efficiency of 38.2-percent (AM1.5 global). A two-solar-cell four-terminal tandem system can have a maximum efficiency of 39.1 percent at the same spectrum. This four-terminal system allows more freedom in choosing the most efficient bandgap combinations. Assuming realistic losses, a configuration consisting of a Si solar cell on the bottom and a solar cell with a bandgap, Eg= 1.85 eV on the top, a maximum efficiency of 32.1 percent (AM1.5 global) can be predicted. Increased efficiency can be obtained from a three-solar-cell six-terminal tandem system. With an optimum bandgap combination the theoretical maximum efficiency is 44.5 percent (AM1.5 global) for the three-solar-cell system. The limits predicted by the model are discussed for tabulated standard spectra. The highest achievable efficiency is 57.3 percent (AM1.5 global) without concentration of the incident light. The increase in efficiency under concentration is evaluated, and it is found that the relative change of the efficiency at any concentration X is linear with In (X).