Energy Conversion Efficiency of the Bulk Photovoltaic Effect

The bulk photovoltaic effect (BPVE) leads to directed photo-currents and photo-voltages in bulk materials. Unlike photo-voltages in p-n junction solar cells that are limited by carrier recombination to values below the bandgap energy of the absorbing material, the BPVE photo-voltages have been shown to greatly exceed the bandgap energy. Therefore the BPVE is not subject to the Shockley-Queisser limit for sunlight to electricity conversion in single junction solar cells and experimental claims of efficiencies beyond this limit have been made. Here, we show that BPVE energy conversion efficiencies are, in practice, orders of magnitude below the Shockley-Queisser limit of single junction solar cells and are subject to different, more stringent limits. The name BPVE stands for two different fundamental effects, the shift current and the injection current. In both of these, the voltage bias necessary to produce electrical energy, accelerates both, intrinsic and photo-generated, carriers. We discuss how energy conservation alone fundamentally limits the BPVE to a bandgap-dependent value that exceeds the Shockley Queisser limit only for very small bandgaps. Yet, small bandgap materials have a large number of intrinsic carriers, leading to high conductivity which suppresses the photo-voltage. We discuss further how slightly more stringent fundamental limits for injection (ballistic) currents may be derived from the trade-off between high resistivity, needed for a high voltage, and long ballistic transport length, needed for a high current. We also explain how erroneous experimental and theoretical claims of high efficiency have arisen. Finally, we calculate the energy conversion efficiency for an example 2D material that has been suggested as candidate material for high efficiency BPVE based solar cells and show that the efficiency is very similar to the efficiency of known 3D materials.