After carefully reviewing the assumptions made in deriving the SQ limit (previous post), we can begin to list opportunities for exceeding the limit. All these efforts of overcoming the limit are classified as ‘third-generation’ PV cells.
1) Each incoming photon excites only one electron-hole pair: When a photon successfully excites an electron across the band-gap and into a certain region of the conduction band, the electron loses the excess energy through thermalization and falls down to the lowest energy level in the conduction band. When this lost energy is equal to or more than the band-gap energy, we are losing energy that is theoretically sufficient to excite a second electron. There are two ways to prevent this loss:
a) Multiple exciton generation: In certain materials, the phonons from the lost energy can be re-absorbed to excite another electron across the bandgap. MEG can also take place through other mechanisms. This behaviour was first exhibited in PbSe quantum dots (2004). It was later also observed in quantum dots of lead, cadmium and indium compounds, silicon, single-walled carbon nanotubes, graphene, and organic pentacene derivatives. Such materials show a quantum yield > 100% and upto 300%. The biggest challenge in quantum dots is the collection of these carriers before they recombine. During excitation, the electron-hole pair exists as ‘excitons’ and are bounded by coloumbic forces. Excitons have to be split into free charges to do useful work.
b) Down conversion: Certain luminescent materials can absorb high energy photons and emit a higher number of lower energy photons. These emitted photons can be energetic enough to excite electrons and thus, quantum yield > 100% can be achieved. The process is often through auger recombination and de-excitation of all excited electrons. Such luminescence has been famously exhibited in quantum dots and even has applications in ligh-emitting technologies. The size of quantum-dots/nanocrystals can be tuned to obtained desired wavelengths of emitted light. Generally, smaller quantum-dots have larger band-gaps and emit light of shorter wavelengths. The drawback of using QDs is that they lead to many interfaces and hence recombinations.
Colloidal quatum dots produced in a kg scale at PlasmaChem GmbH
Image courtesy: commons.wikimedia.org, user: antipof
2) Photovoltaic material consists of a single band gap energy: This restriction leads to either thermalization losses (if band-gap is too low) or absorption losses (if band-gap is too high) as shown in the illustration below.
Image courtesy: commons.wikimedia.org, user: Sbyrnes321
The solution to this problem is the use of multi-junction cells incorporating 2 or more different band-gap materials which can together, absorb the solar spectrum more efficiently. Multi-junction cells (upto 4 layers) are often made with III-V group elements (tunable band-gap) or amorphous silicon-microcrystalline silicon junctions (high and low band-gap respectively).
Spectral utilization of multi-junction solar cells
Image courtesy: commons.wikimedia.org, Fraunhofer ISE
3) Photons with energy lower than band gap energy are not absorbed: This limit can also be addressed in two ways:
a)Intermediate band gap: Materials can be added which provide an energy level in the forbidden band-gap. Thus, electrons do not necessarily need photons of band-gap energy but can also be excited to the intermediate state with lower energy photons. From this state, they can be further excited to the conduction band with low energy photons. This behaviour has been demonstrate in InAs quantum dots embedded in a InGaAs matrix.
The severe draw-back of this method is that it is similar to having defects/impurities in a materials and leads to high rates of SRH recombination.
b) Upconversion: Certain rare-earth ions can absorb low energy radiation and emit light with lesser photons, but more energy. Thus, low-energy photons undergo ‘up-conversion’ and can excite electrons across a band-gap, which they otherwise could not do.
4) Illumination of the solar cell is by unconcentrated sunlight: Concentrators can be used to greatly increase the amount of incident light. This often leads to higher efficiency in a solar cell but can make the module setup more expensive.
It’s best to conclude with some perspective on this topic. While solar cells have a bad reputation for low efficiency, and the best solar cells have been pegged at 46% (4-junction cell at Fraunhofer ISE), it is also important to remember that most thermal power stations have an operating efficiency of 33% to 48%!
 Schaller, R.; Klimov, V. (2004). “High Efficiency Carrier Multiplication in PbSe Nanocrystals: Implications for Solar Energy Conversion”. Physical Review Letters 92 (18): 186601
 X D Pi et al 2008 Nanotechnology 19 245603
Ramiro, I. et al., “Wide-Bandgap InAs/InGaP Quantum-Dot Intermediate Band Solar Cells,” in Photovoltaics, IEEE Journal of , vol.5, no.3, pp.840-845, May 2015
 Jan Goldschmidt et al. “Record efficient upconverter solar cell devices”, PV solar energy conference and exhibition, 2014