The voltage boost enabled by luminescence extraction in solar cells

A new physical principle has emerged to produce record voltages and efficiencies in photovoltaic cells, "luminescence extraction." This is exemplified by the mantra "a good solar cell should also be a good LED." Luminescence extraction is the escape of internal photons out of the front surface of a solar cell. 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={4n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> }, so one would expect a voltage boost of Δν=kT ln{4n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> } 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{n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> }, ΔV=(kT/q)ln{2n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> }, or ΔV=(kT/q)ln{4n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> }? What is responsible for this voltage ambiguity ΔV=(kT/q)ln{4}=36mVolts? 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{n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> }qΔV/kT)<;ln{4n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> }.