Reciprocity relation between photovoltaic quantum efficiency and electroluminescent emission of solar cells

Light emitting diodes LEDs and solar cells are important optoelectronic devices. Because of their complementary physical action, the transformation of electrical energy into light and transformation of radiation energy into electricity, one would intuitively expect a certain reciprocity between the theoretical laws that determine the physical action of both devices. In fact, a solar cell that has the theoretical maximum power conversion efficiency will also act as an LED with the maximum possible luminescence efficiency. This is because light absorption by the generation of electron-hole pairs is linked via the principle of detailed balance to the complementary action, emission of light by radiative recombination. This restriction of the solar cell concept to the basic physical processes of detailed balance between light absorption and radiative recombination makes the elegance of the Shockley-Queisser SQ approach1 for the calculation of the limiting efficiency of photovoltaic power conversion. Although a perfect solar cell would also be a perfect LED, in reality neither device exists. However, excellent devices that come relatively close to the respective ideal limits are to be found. It is interesting to note that high-efficiency silicon solar cells, i.e., those which approach the SQ radiative limit, can be used as LEDs with essentially the same design.2 These highly sophisticated devices achieve an external LED quantum efficiency EQELED 1%, where EQELED is defined as the ratio between the number of photons emitted from the surface of the sample and the number of recombining electron-hole pairs. In contrast, the photovoltaic EQEPV E of a solar cell is a spectral quantity defined as the ratio of collected charge carriers to the number of photons with energy E incident on the cell’s surface. EQELED 1% is a highly respectable value for silicon devices but small when compared to LEDs made from organic semiconductors3 with EQELED 15%.4 In contrast, solar cells made from organic materials5 have power conversion efficiencies hardly exceeding 2% compared to 25% of the best silicon solar cell6 . Clearly, at a practical level, below the idealized SQ case, quality requirements for solar cells and LEDs diverge considerably. The present paper gives a detailed balance theory that embraces also less idealized solar cells and LEDs by adding the aspect of electronic transport to the SQ theory. The central result is a reciprocity theorem that relates the carrier collection properties of a solar cell to its spectral electroluminescence EL emission. This reciprocity approaches the SQ identity of an LED and a solar cell in the limit of infinite charge carrier mobility p and of an infinite nonradiative lifetime nr. An additional relation connects the open circuit voltage VOC of a solar cell and the external quantum efficiency EQELED for the same device operating as an LED.