The Voltage Boost Enabled by Luminescence Extraction in Solar Cells

Over the past few years, the application of the physical principle, i.e., “luminescence extraction,” has produced record voltages and efficiencies in photovoltaic cells. Luminescence extraction is the use of optical design, such as a back mirror or textured surfaces, to help internal photons escape out of the front surface of a solar cell. The principle of luminescence extraction is exemplified by the mantra “a good solar cell should also be a good LED.” Basic thermodynamics says that the voltage boost should be related to concentration ratio C of a resource by ΔV = (kT/q) ln{C }. In light trapping (i.e., when the solar cell is textured and has a perfect back mirror), the concentration ratio of photons C = {4n²}; therefore, one would expect a voltage boost of ΔV = (kT/q) ln{4n² } over a solar cell with no texture and zero back reflectivity, where n is the refractive index. Nevertheless, there has been ambiguity over the voltage benefit to be expected from perfect luminescence extraction. Do we gain an open-circuit voltage boost of ΔV = (kT/q ) ln{n²}, ΔV = (kT/q) ln{2 n²}, or ΔV = (kT/q) ln{4 n²}? What is responsible for this voltage ambiguity ΔV = (kT/q) ln{4}≍36 mV? We show that different results come about, depending on whether the photovoltaic cell is optically thin or thick to its internal luminescence. In realistic intermediate cases of optical thickness, the voltage boost falls in between: ln{n² } < (qΔV/kT) < ln{4n ²}.