Improving the efficiency of solar cells: hot carrier photovoltaics
As the efficiency of the first-generation solar cells asymptotically approaches an efficiency limit of 32%, it is necessary to broaden our search for methods to harness the power of the sun.
Author(s): James A.R. Dimmock
We discuss the cause of this fundamental efficiency limit and methods to overcome it, with particular reference to the hot carrier solar cell. The hot carrier solar cell operates as a heat engine between a hot and a cold population of electrons; by operating a solar cell in this way it is theoretically possible to reach a far higher limiting efficiency of 85%. This mechanism is no longer just a theoretical possibility, with recent experimental work pointing the way to a future of highly efficient hot carrier solar cells.
Solar cells allow us to harness the renewable and virtually unlimited power that reaches us from the sun, significantly reducing our dependence on non-renewable energy sources such as fossil fuels. Photovoltaic cells convert the sun's power into electricity, but at a loss due to various intrinsic and extrinsic loss mechanisms that are present in the current first generation of cells.
Extrinsic cell losses are, in principle, avoidable. These are familiar mechanisms, like series resistance, for which one can imagine methods, however expensive and contrived, which could reduce them to zero. By contrast intrinsic losses are those which are unavoidable and would still exist in some hypothetical, perfect, Platonic solar cells, existent only in our imaginations. These intrinsic loss mechanisms have been previously studied in great detail [ 1 ] to show the highest efficiency that such a Platonic solar cell could reach is 32.5% under single-sun illumination or 42% under maximally concentrated sunlight. While it is beyond the scope of this article to go into each of the intrinsic loss mechanisms in detail, it is instructive to understand that the biggest contribution to these losses is from what could be termed ‘spectral losses’. While approximately one-third of the sun's power can be converted into useful energy, almost 60% of the light incident on the cell is wasted purely because sunlight comprises a broad spectrum of wavelengths rather than being a single monochromatic source.
The broad spectral nature of sunlight results in this large efficiency penalty because a solar cell operates as a two-level system, with an energy gap (or band gap) separating a mobile (conduction band) and non-mobile (valence band) energy level. Light with energy equal to, or in excess of the band gap can be absorbed, promoting an electron to the mobile level for extraction, but any light with energy below the band gap is not able to be used by the cell. Similarly, because it is a two-level system, only the difference in energy between the two levels is able to be exploited. Light with energy in excess of the band gap is absorbed and contributes to the current, but the extra energy is lost as heat to the rest of the cell in a process termed ‘thermalisation’. These two loss mechanisms and the broad solar spectrum that gives rise to them are illustrated in Fig 1, with the energy gap plotted at the optimum value of 1.31 eV, which results in a maximum efficiency of 32.5% under single-sun illumination. All incident light which is of too low energy to be absorbed is shaded in red, and all light which is absorbed, but with a thermalisation loss, is shaded in blue. An illustration of how light with these energies interacts with our two-level system is shown below the spectral plot.
Fig 1: Top: Spectrum of sunlight plotted as a function of photon energy. Bottom: Energy–momentum diagrams for electrons in a semiconductor showing the effect of absorption of light with different energies
a No absorption of light with energy less than the band gap (red)
b Absorption of light with energy in excess of the band gap (blue) followed by energy loss to thermalisation
This limit represents a fundamental limit on conversion efficiency, with many groups approaching this limit and any further gains being made subject to a law of diminishing returns. With Sharp  and Panasonic  achieving efficiencies in excess of 25% in silicon photovoltaic cells and Alta devices of nearly 29%  in GaAs, if we want to achieve significantly higher efficiencies, it will be necessary to change the way solar cells operate. It is the aim of this paper to outline a few of the methods that could lead to higher efficiency cells and present a particular case study of our own work in developing a hot carrier photovoltaic cell.
Next generation concepts
Next generation solar cell concepts seek to remove or reduce the intrinsic energy losses already discussed by reformulating how a cell operates. As previously mentioned the largest energy losses are from not absorbing light beneath the band gap and from thermalisation of electrons generated by light with energy in excess of the cell's energy gap.
Fig 2 shows how much more efficient a solar cell can be if this extra energy can be used in the cell. In this figure, the efficiency of a cell under maximally concentrated solar illumination is plotted against the cell's energy gap, demonstrating that the maximum efficiency of 42% for a single junction cell is achieved at a band gap which balances the low-energy non-absorption loss with the high-energy thermalisation loss. However, if the thermalisation loss could be circumvented, then the optimum energy gap would be zero and an efficiency of 85% could, in principle, be achieved if we found some new way to exploit absorption in a material with no energy gap.
Fig 2: Efficiency of a single junction solar cell under full concentration as a function of its energy gap, with and without the loss of energy to thermalisation
Essentially, all the next generation concepts are methods to solve this issue and seek to either minimise or use this extra energy rather than waste it. The most prominent next generation concepts are briefly discussed in the following subsections and separate into two categories. Those which seek to minimise the extra energy given to the system on absorption, such as the multi-junction and intermediate band cells, and those which seek to exploit the extra energy given to the system, such as the multiple-exciton generating and hot carrier cells.
Multi-junction solar cells
The most successful next generation concept in photovoltaics to date has been the multijunction cell. This addresses the thermalisation loss by splitting the cell into a multitude of sub-cells, with the intention that light of different wavelengths is absorbed in the sub-cell most closely matched to it in energy. This reduces the thermalisation loss by effectively narrowing the spectrum of light for which each sub-cell is optimised. In the limit of an infinite number of sub-cells, this technology has an efficiency limit of 85% and in practice efficiencies of up to 46% [ 5 ] have been achieved by splitting light absorption over four sub-cells. Such technology finds a place in satellites and also terrestrially in concentrator photovoltaic systems. However, price is still an issue with this technology, to compete with Silicon, and efficiency gains have slowed due to the complications associated with stacking or growing multiple single junction cells on top of one another.
Intermediate band solar cell
A related concept to the multijunction solar cell is the intermediate band solar cell, in which a third level is introduced into the energy gap of the previous two-level system. In this way, the energy gap can be widened and the intermediate energy level acts as a stepping stone for absorption of lower energy light, allowing it to contribute to the current. With a single intermediate level the efficiency of a solar cell could increase to 63.2%  and in the case of infinitely many intermediate bands the limit is again 85% .
In practice, the intermediate band cell has proved difficult to achieve, essentially due to reciprocity; any intermediate states which absorb light necessarily emit light. This means that adding such a state needs to be carried out exceptionally carefully unless it is to be a net detriment to the cell and act as a way for electrons to be removed from the conduction band. One possible method has been proposed to overcome this by inserting a non-radiative ‘ratchet’ state in addition to the intermediate energy level , though this work is at an early stage.
Multiple exciton generation
It has been noticed that in some materials, rather than the excess energy generated by high-energy light being lost to thermalisation it can instead be used to generate further electrons via so-called multiple-exciton generation. The extra electrons provide extra current in the cell under higher energy illumination and can increase the efficiency from 32% to 42%  under single-sun illumination. While not as high an efficiency increase as the previous methods, the idea of simply using a different material and generating more current is appealing. In common materials, this process has been found to be generally of low efficiency with only a 5% efficiency gain in Silicon when illuminated at 4 eV although with possibly higher efficiencies in quantum dots .
Hot carrier solar cell concept
Prior to thermalisation, the electrons in the conduction band of our two-level system have an energy in excess of the conduction band minimum, which in a first generation cell would be lost as heat. The distribution of energies present in this electron system is akin to the distribution of energies present in a population of gas molecules and analogously it can be represented by a characteristic temperature, which defines the distribution. The temperature of these electrons can be thousands of Kelvin and significantly higher than the lattice temperature of the cell, which is defined by the spread of energies of the phonons in the system, hence the term hot carriers. In the hot carrier solar cell, we directly use this higher temperature of electrons by setting up a heat engine between a hot part of the cell, where light absorption takes place, and a cold part of the cell, which is held at ambient temperature.
To further understand the concept, it is useful to compare the hot carrier cell with the thermophotovoltaic (TPV) system , another next generation concept which addresses the thermalisation loss, with both concepts schematically illustrated in Fig 3.
Fig 3: Comparison of the working scheme of a TPV setup (top) with a hot carrier solar cell (bottom)
In a TPV system, light from the sun is absorbed by an intermediate body, causing it to heat up and radiate. The radiation from the intermediate body is filtered such that only light optimally matched to the band gap of an adjacent solar cell is allowed to pass to it. The rest of the radiation is reflected back to the intermediate body and reheats it. This scheme has an efficiency limit of 85% as well , since it deals comprehensively with the thermalisation loss in the cell. However, to reach this efficiency limit, it presents several complex engineering challenges, not least to find an intermediate body and a filtering mechanism which can withstand temperatures up to 2500 K and avoid any other heat losses, such as to convection.
The hot carrier solar cell is similar to the TPV system, but instead of holding this energy as a lattice temperature it is held as an electron temperature after absorption of light from the sun. Electrons at an optimum energy are then allowed to leave this absorption region to a cooler region, while electrons at non-optimum energies are reflected back to reheat the rest of the electrons and repopulate the optimum energy level. In this way, it was shown as long ago as 1982 that this concept could reach 85% efficiency too .
This theoretically sets out the promise of the hot carrier solar cell; however, in order for the hot carrier cell to operate correctly two key criteria must be met:
- The interaction between the hot electrons and the phonons (lattice) in the absorber must be minimised so that the extra electron energy is not lost as heat
- The electrons in the cold part of the cell must be maintained at a lower temperature so that the heat engine has a driving force (the temperature gradient)
It can be understood, with reference to the TPV cell, that criterion two is achieved by energy selective extraction, or filtering. Without energy selective extraction, this concept cannot work and the electron population simply reaches an equilibrium temperature as heat is transferred to the cold part of the cell and the thermalisation loss is reintroduced.
To achieve criterion one requires that electrons must be removed from the hot part of the cell to the cold part faster than they can interact with phonons. This necessitates an ultrafast extraction method and/or a method to reduce the coupling between the electrons and phonons. Specific methods to achieve this are detailed in the following section, but more generally some design rules have been set out by Takeda . Takeda's rules specify constraints on the loss rate from electrons to the phonons and its relationship to other rates in the system, such as the rate of redistribution of electron energy after non-optimum energy carriers are reflected. In particular, he specifies that for an efficient hot carrier cell the rate of energy redistribution between the electrons must be >100 times faster than the loss rate from electrons to phonons.
These two criteria, and the design rules that follow, show where research efforts must be concentrated to develop a highly efficient cell. We will overview the status of this research effort in the following section, followed by our own experimental realisation of a hot carrier cell.
Hot carrier solar cell status and challenges
The current research direction of the majority of the hot carrier photovoltaic cell community is focused on reducing the interaction between electrons and phonons in the absorbing region of the cell. The electron–phonon interaction is very fast and efficient at removing heat from the electron population and thermalising it to the lattice, occurring on a picosecond timescale. To frustrate this mechanism and maintain a hot population of electrons long enough for extraction, there are several design and material improvements which can be made.
From a design perspective, using quantum wells as the absorbing region shows great promise. Quantum wells have been shown to slow the energy relaxation of hot carriers from picoseconds to nanoseconds . This finding has been exploited by several groups to show the promise of a quantum well absorber region for a variety of materials systems [16–18], and recently a hot carrier photocurrent has been observed from a quantum well absorber . While promising, this approach is not without its challenges, as using thin quantum well layers as the absorber region will limit the total absorption in any device that uses them.
In terms of materials research, several groups are investigating whether certain materials inherently block the transfer of energy from electrons to phonons. In particular, compounds with large differences in mass between the constituent atoms have been shown to frustrate this energy transfer , with HfN one promising candidate .
As a complement to the materials research and design aimed at increasing the hot carrier lifetimes in the absorber region, our work concentrates on building prototypes to demonstrate a working device within the limitations of currently existing absorber materials, this is presented in the following section.
Case study – realisation of a hot carrier solar cell
We have realised a hot carrier photovoltaic cell  by placing a quantum well between two semiconductor regions with different band gaps. The narrower band gap material is used as the absorber region, where hot electrons are photogenerated, and the wider band gap region is used as the collector region, with the electrons maintained at ambient temperature. The difference in band gap ensures that carriers can be photogenerated in only the absorber region, while the quantum well that separates the two regions gives ultrafast and energy selective transfer, through tunnelling, between them.
A schematic of our hot carrier photovoltaic cell design is presented in Fig 4, in which hot electrons are photogenerated in the absorber before being rapidly, and selectively, removed by tunnelling over an energy range Δ E. The energy range Δ E is the spread of energies around the confined state of the quantum well for which the transmission probability from the absorber to the collector is greater than 1/ e.
Fig 4: A schematic of the band structure of the hot carrier solar cell, showing extraction of carriers after photogeneration in an absorber region by fast tunnelling of a carrier to a collector region
This cell was realised in a prototype system in which GaAs was used as the absorber region and AlGaAs was used as the collector region, grown by molecular beam epitaxy. We then demonstrated that electrons could be extracted before they thermalised by illuminating the device with various different monochromatic wavelengths of incident light. Changing the wavelength of light changes the extra energy that the electrons have after being photogenerated, so demonstrating a wavelength-dependent signature in the current–voltage (IV) characteristics is important evidence of hot carrier operation.
Fig 5 shows the IV characteristic of our cell at 93 K under illumination from 790 to 810 nm. Its characteristic peak and valley shape is similar to a resonant tunnelling diode, with the difference being that a current exists at zero bias in this device and thus power can be extracted from it. The IV curves in Fig 5 demonstrate two key effects showing evidence that hot electrons are being extracted. The current peak location and the current peak-to-valley ratio (PVR) in these curves are dependent on the electron temperature, with higher temperatures giving rise to a peak at a higher forward bias and also a lower PVR. The shift of the current peak to a higher forward bias for a higher temperature (shorter wavelength) is shown most clearly in Fig 5 b, which shows a magnification of the peak current region of the IV characteristic shown in Fig 5 a.
Fig 5: Experimental IV characteristics for the hot carrier cell
a The IV characteristic of our prototype hot carrier cell showing a wavelength dependence that indicates extraction of hot carriers
b A magnified section of the IV characteristic at the peak current region, highlighting the wavelength dependence of the bias of the peak current point
If the temperature of the electrons was the same, independent of wavelength of illumination, the IV characteristics would be identical and we could conclude that electrons were thermalising before extraction. The fact that we see a shift in the peak and the PVR with wavelength demonstrates that electrons are being extracted before they can thermalise fully in this device.
This demonstrates that a hot carrier cell is experimentally achievable and has recently been extended to study the carrier transfer processes in more detail and to use the hot carrier effect as a supplement to a standard field driven solar cell .
At this stage this work acts as an important proof of principle, but with several key issues and obstacles to overcome before a practical cell emerges. In particular, the GaAs absorber region must be thin to allow photogenerated electrons to reach the extraction region before thermalising. This places a constraint on the cell's total absorption and is a barrier to achieving a high-efficiency cell in this materials system, but other materials systems with longer thermalisation times are currently under investigation and would allow thicker absorber regions. In addition to these other semiconductor materials systems, it is possible to get particularly high absorption in thin films of metal . We believe that metallic absorbers may be a natural next step for the hot carrier solar cell, and have carried out work towards realising this , since not only is strong absorption possible but metals also have the required zero band gap, shown in Fig 2, to achieve the highest possible efficiencies.
Conclusions and future perspectives
After nearly 35 years of research effort, the hot carrier solar cell has transitioned from a theoretical possibility into an experimental reality, with research efforts intensifying to create new, highly efficient cells. A prototype hot carrier solar cell in GaAs/AlGaAs has been realised and this can be extended by using other materials systems, which are currently under investigation. Indeed, there is a growing research interest in designing materials with bespoke properties, in what is termed ‘inverse design’ , which would bring a great boost to the hot carrier solar cell and its stringent materials requirements.
Promising future directions are the use of metals to provide enhanced absorption in thin films and using this technology for other optoelectronic devices, such as ultrafast photodetectors.
J. Dimmock gratefully acknowledges a Royal Commission for the Exhibition of 1851 Industrial Fellowship.
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