In a standard photovoltaic cell, a device made of layered semiconductors is exposed to sunlight in order to generate electricity. At the fundamental level, these devices harness the energy from the sun by absorbing photons to raise the energy levels of electrons in the semiconductor. Semiconductors like silicon have the property that the allowed energy states of electrons in the material split into two bands, separated by a gap of energy states which are not attainable.  The lower energy band is known as the valence band, where electrons behave as if they were bound to nuclei, and the higher band is known as the conduction band, where electrons are able to move freely. The aforementioned gap, or difference, between these two energy levels is called the band gap.
When a photon with energy Ep enters the semiconductor and is absorbed, it excites an electron from the valence band, which then jumps up into the higher-energy conduction band. Since energy must be conserved in this interaction, an absorbed photon must satisfy Ep > Eg where Eg is the band gap energy. Lower energy photons are not absorbed because this would require an electron to obtain an impossible energy state (i.e. one within the band gap).  Once an electron is in the conduction band energy state, it can move freely as if in a conductor to create an electrical current. Though the full devices and processes involved in generating current in a photovoltaic cell are much more complicated, the basic conversion from light energy to electrical energy is through this process of excitation into the conduction band. However, there are two important inefficiencies inherent in photovoltaic cells that rely on this effect.
The first problem with standard photovoltaic cells has to do again with the relationship between Ep the incoming photon energy and Eg the band gap energy. When a photon is absorbed with Ep > Eg, the difference in the two energies is lost as heat. This is because the electron always ends up in the lowest energy state of the conduction band in a process known as thermalization.  Thus the total energy gained by the electron is equal to the band gap energy. The loss of the excess photon energy as heat is a serious problem in photovoltaic cells. In fact, as much as half of the total solar energy entering a cell can be lost this way. 
As it turns out, this loss of heat energy causes a second major problem in photovoltaic cells: high temperature greatly reduces the energy conversion efficiency. That is, the fraction of electrons that, after being excited by photons, actually produce electrical energy is greatly reduced. For example in a silicon based cell, solar conversion efficiency at 25° C is nearly 20% while at 200° C it is less than 8%.  This also makes it difficult to make up for the lost heat energy by attaching a heat engine to a solar cell, because the high temperatures required for the heat engine to be efficient would render the photovoltaic cell nearly useless.  This combination of lost heat energy and inefficiency at high temperature is a major barrier to increasing solar cell efficiency.
Photon-enhanced Thermionic Emission (PETE) is a technique that seeks to overcome the heat-related drawbacks of standard solar cells. At its core, PETE is a combination of two effects: the first is the photovoltaic effect described above for standard solar cells, and the second is thermionic emission. Thermionic emission is a technique of converting heat energy into electric energy by placing a hot cathode and a cold anode near each other in a vacuum. Electrons with high enough heat energy at the surface of the cathode will jump across the vacuum to the anode, creating a current.  In practice these devices are designed as large parallel plates separated by small vacuum gap.
A full PETE cell is designed almost identically to a thermionic cell, except that the top plate is actually a semiconductor. The dynamics of a PETE cell are then simply a combination of those in a photovoltaic and a thermionic cell. First, a photon is absorbed, exciting an electron into the conduction band, and giving off heat energy equal to Ep - Eg. Then, these newly freed electrons move through the material, and, when they encounter the surface with sufficient energy, make the jump across the vacuum to the anode.  In particular, these electrons must have thermal energy greater than the semiconductor's electron affinity in order to leave the surface. Thus, a PETE cell uses the photoelectric energy from overcoming the band gap to create free electrons, and the extra heat energy from thermalizing electrons to leave the surface of the semiconductor into the vacuum. 
PETE cells have an advantage in efficiency over purely thermionic cells because the presence of electrons in the conduction band from photovoltaic effects reduces the effective work function of the material, making it easier for electrons to escape into the vacuum.  Similarly, PETE cells do not suffer from the problem of low efficiency at high temperatures as standard photovoltaic cells do. This is because the degradation effect is specific to the two-layer semiconductor junction design of standard photocells. Further, since a PETE cell can operate efficiently at high temperature, it can be run in conjunction with a heat engine attached to the anode.  Excess heat from the electrons transmitted across the vacuum to the anode is collected and sent into the heat engine. A steam turbine, for example, could be driven with the anode heating the water. Again, this relies on the fact that PETE cells can operate at high temperatures where heat engines are efficient.
The number to take away from all of this discussion of improved efficiency is 53%. That is, the calculated idealized maximum efficiency of a PETE cell hooked up to a thermal engine is 53%.  Of course this number comes with a long list of caveats. First of all, an anode temperature of 285° C and a heat engine efficiency of 31.5% are assumed in these calculations.  Though the temperature requirement of 285° C may seem high, it is actually quite reasonable. This is because PETE cells are designed to be used in existing concentrated solar power plants, where the sun's power is amplified 1000x using large collecting mirrors.  The most important thing to be concerned about with PETE is that all these calculations are theoretical, and the devices face real world technical challenges before any can actually be constructed.
First of all, though the computations in  show a much higher peak theoretical efficiency of PETE cells as compared to the peak theoretical efficiencies of existing solar technologies, a fully functioning PETE device has yet to be produced. Schwede et. al. built a proof-of-concept device that experimentally demonstrated that the photo-enhanced thermionic effect could be produced, but their device was not made to measure efficiency. Essentially what was constructed for the experiments in  was a semiconductor cathode isolated in a large vacuum chamber. It did show that the effect existed and the experimental results matched theoretical predictions for electron emission rates from PETE devices. However, the calculated theoretical efficiency relied on a much different structure of two large plates with a very thin vacuum gap between them, in order to maximize the collection of emitted electrons by the anode, while exposing a large surface area of the semiconductor cathode to the sun.  Thus, in order to even hope to come close to the promised 53% efficiency, one would have to precisely manufacture large plates with very thin vacuum gaps between them, a difficult engineering problem in its own right. In short, it would be very premature to declare PETE as the savior of solar energy with promises of high theoretical efficiencies. Nonetheless, it is a novel effect which could fit in well with existing technology, and is certainly worth exploring further.
© Jonah Brown-Cohen. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.
 J. L. Gray, "The Physics of the Solar Cell," in Handbook of photovoltaic Science and Engineering, edited by A. Luque and S. Hegedus (Wiley, 2003), pp. 61-98.
 J. W. Schwede et. al., "Photon-Enhanced Thermionic Emission for Solar Concentrator Systems," Nature Materials 9, 762 (2010).
 J. J. Wysocki and P. Rappaport, "Effect of Temperature on Photovoltaic Solar Energy Conversion," J. Appl. Phys. 31, 571 (1960).