Efficiency limits for multi-junction coloured photovoltaics

Coloured photovoltaic cells are of interest for product or building-integrated photovoltaics. Limiting efficiencies have previously been reported for single-junction semitransparent and opaque cells; in this work, we expand this analysis to multi-junction devices with up to six junctions, with opaque colours produced through reflection of the incident Sunlight. We introduce a multi-objective optimization framework in Python which uses differential evolution to find parameters (e.g. central wavelength and width of reflection peaks, sub-cell bandgaps) which maximize both efficiency and colour accuracy. We find that for the 18 standard chromatic ColorChecker colours, the limiting efficiencies for cells up to six junctions are within 18% (relative) of those of a black cell with the same number of junctions, while achromatic white or light grey cells with high luminance (lightness) are much less efficient. We find that, as reported previously for single-junction cells, only two box-shaped reflection peaks are sufficient for reaching the highest efficiencies and producing any target colour which can be formed by reflecting Sunlight. Generally, colours with higher luminance cause a redshift in the optimal bandgap of the top junction to compensate for the loss of photons (and thus current) required to produce colour. However, as the number of junctions increases to five or more, one or more of the optimal bandgaps must be placed in the visible wavelength range (380-750 nm) near the reflection peaks, which affects the placement of the optimal bandgap beyond the expected redshift. Finally, we will consider technologically relevant material combinations such as perovskite or III-V materials on silicon tandems, and III-V multi-junction cells, and assess their suitability for use as a platform for coloured PV.