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Saturday, January 5, 2019

Dye-sensitized solar cell

From Wikipedia, the free encyclopedia

A selection of dye-sensitized solar cells.
 
A dye-sensitized solar cell (DSSC, DSC, DYSC or Grätzel cell) is a low-cost solar cell belonging to the group of thin film solar cells. It is based on a semiconductor formed between a photo-sensitized anode and an electrolyte, a photoelectrochemical system. The modern version of a dye solar cell, also known as the Grätzel cell, was originally co-invented in 1988 by Brian O'Regan and Michael Grätzel at UC Berkeley and this work was later developed by the aforementioned scientists at the École Polytechnique Fédérale de Lausanne until the publication of the first high efficiency DSSC in 1991. Michael Grätzel has been awarded the 2010 Millennium Technology Prize for this invention.

The DSSC has a number of attractive features; it is simple to make using conventional roll-printing techniques, is semi-flexible and semi-transparent which offers a variety of uses not applicable to glass-based systems, and most of the materials used are low-cost. In practice it has proven difficult to eliminate a number of expensive materials, notably platinum and ruthenium, and the liquid electrolyte presents a serious challenge to making a cell suitable for use in all weather. Although its conversion efficiency is less than the best thin-film cells, in theory its price/performance ratio should be good enough to allow them to compete with fossil fuel electrical generation by achieving grid parity. Commercial applications, which were held up due to chemical stability problems,[6] are forecast in the European Union Photovoltaic Roadmap to significantly contribute to renewable electricity generation by 2020.

Current technology: semiconductor solar cells

In a traditional solid-state semiconductor, a solar cell is made from two doped crystals, one doped with n-type impurities (n-type semiconductor), which add additional free conduction band electrons, and the other doped with p-type impurities (p-type semiconductor), which add additional electron holes. When placed in contact, some of the electrons in the n-type portion flow into the p-type to "fill in" the missing electrons, also known as electron holes. Eventually enough electrons will flow across the boundary to equalize the Fermi levels of the two materials. The result is a region at the interface, the p-n junction, where charge carriers are depleted and/or accumulated on each side of the interface. In silicon, this transfer of electrons produces a potential barrier of about 0.6 to 0.7 V.

When placed in the sun, photons of the sunlight can excite electrons on the p-type side of the semiconductor, a process known as photoexcitation. In silicon, sunlight can provide enough energy to push an electron out of the lower-energy valence band into the higher-energy conduction band. As the name implies, electrons in the conduction band are free to move about the silicon. When a load is placed across the cell as a whole, these electrons will flow out of the p-type side into the n-type side, lose energy while moving through the external circuit, and then flow back into the p-type material where they can once again re-combine with the valence-band hole they left behind. In this way, sunlight creates an electric current.

In any semiconductor, the band gap means that only photons with that amount of energy, or more, will contribute to producing a current. In the case of silicon, the majority of visible light from red to violet has sufficient energy to make this happen. Unfortunately higher energy photons, those at the blue and violet end of the spectrum, have more than enough energy to cross the band gap; although some of this extra energy is transferred into the electrons, the majority of it is wasted as heat. Another issue is that in order to have a reasonable chance of capturing a photon, the n-type layer has to be fairly thick. This also increases the chance that a freshly ejected electron will meet up with a previously created hole in the material before reaching the p-n junction. These effects produce an upper limit on the efficiency of silicon solar cells, currently around 12 to 15% for common modules and up to 25% for the best laboratory cells (33.16% is the theoretical maximum efficiency for single band gap solar cells).

By far the biggest problem with the conventional approach is cost; solar cells require a relatively thick layer of doped silicon in order to have reasonable photon capture rates, and silicon processing is expensive. There have been a number of different approaches to reduce this cost over the last decade, notably the thin-film approaches, but to date they have seen limited application due to a variety of practical problems. Another line of research has been to dramatically improve efficiency through the multi-junction approach, although these cells are very high cost and suitable only for large commercial deployments. In general terms the types of cells suitable for rooftop deployment have not changed significantly in efficiency, although costs have dropped somewhat due to increased supply.

Dye-sensitized solar cells

Type of cell made at the EPFL by Grätzel and O'Regan
 
Operation of a Grätzel cell.
 
In the late 1960s it was discovered that illuminated organic dyes can generate electricity at oxide electrodes in electrochemical cells. In an effort to understand and simulate the primary processes in photosynthesis the phenomenon was studied at the University of California at Berkeley with chlorophyll extracted from spinach (bio-mimetic or bionic approach). On the basis of such experiments electric power generation via the dye sensitization solar cell (DSSC) principle was demonstrated and discussed in 1972. The instability of the dye solar cell was identified as a main challenge. Its efficiency could, during the following two decades, be improved by optimizing the porosity of the electrode prepared from fine oxide powder, but the instability remained a problem.

A modern DSSC is composed of a porous layer of titanium dioxide nanoparticles, covered with a molecular dye that absorbs sunlight, like the chlorophyll in green leaves. The titanium dioxide is immersed under an electrolyte solution, above which is a platinum-based catalyst. As in a conventional alkaline battery, an anode (the titanium dioxide) and a cathode (the platinum) are placed on either side of a liquid conductor (the electrolyte). 

Sunlight passes through the transparent electrode into the dye layer where it can excite electrons that then flow into the titanium dioxide. The electrons flow toward the transparent electrode where they are collected for powering a load. After flowing through the external circuit, they are re-introduced into the cell on a metal electrode on the back, flowing into the electrolyte. The electrolyte then transports the electrons back to the dye molecules. 

Dye-sensitized solar cells separate the two functions provided by silicon in a traditional cell design. Normally the silicon acts as both the source of photoelectrons, as well as providing the electric field to separate the charges and create a current. In the dye-sensitized solar cell, the bulk of the semiconductor is used solely for charge transport, the photoelectrons are provided from a separate photosensitive dye. Charge separation occurs at the surfaces between the dye, semiconductor and electrolyte.

The dye molecules are quite small (nanometer sized), so in order to capture a reasonable amount of the incoming light the layer of dye molecules needs to be made fairly thick, much thicker than the molecules themselves. To address this problem, a nanomaterial is used as a scaffold to hold large numbers of the dye molecules in a 3-D matrix, increasing the number of molecules for any given surface area of cell. In existing designs, this scaffolding is provided by the semiconductor material, which serves double-duty.

Construction

In the case of the original Grätzel and O'Regan design, the cell has 3 primary parts. On top is a transparent anode made of fluoride-doped tin dioxide (SnO2:F) deposited on the back of a (typically glass) plate. On the back of this conductive plate is a thin layer of titanium dioxide (TiO2), which forms into a highly porous structure with an extremely high surface area. The (TiO2) is chemically bound by a process called sintering. TiO2 only absorbs a small fraction of the solar photons (those in the UV). The plate is then immersed in a mixture of a photosensitive ruthenium-polypyridine dye (also called molecular sensitizers) and a solvent. After soaking the film in the dye solution, a thin layer of the dye is left covalently bonded to the surface of the TiO2. The bond is either an ester, chelating, or bidentate bridging linkage.

A separate plate is then made with a thin layer of the iodide electrolyte spread over a conductive sheet, typically platinum metal. The two plates are then joined and sealed together to prevent the electrolyte from leaking. The construction is simple enough that there are hobby kits available to hand-construct them. Although they use a number of "advanced" materials, these are inexpensive compared to the silicon needed for normal cells because they require no expensive manufacturing steps. TiO2, for instance, is already widely used as a paint base.

One of the efficient DSSCs devices uses ruthenium-based molecular dye, e.g. [Ru(4,4'-dicarboxy-2,2'-bipyridine)2(NCS)2] (N3), that is bound to a photoanode via carboxylate moieties. The photoanode consists of 12 μm thick film of transparent 10–20 nm diameter TiO2 nanoparticles covered with a 4 μm thick film of much larger (400 nm diameter) particles that scatter photons back into the transparent film. The excited dye rapidly injects an electron into the TiO2 after light absorption. The injected electron diffuses through the sintered particle network to be collected at the front side transparent conducting oxide (TCO) electrode, while the dye is regenerated via reduction by a redox shuttle, I3/I, dissolved in a solution. Diffusion of the oxidized form of the shuttle to the counter electrode completes the circuit.

Mechanism of DSSCs

The main processes that occur in a DSSC to convert photons(light) to current are:
  1. The incident photon is absorbed by Ru complex photosensitizers adsorbed on the TiO2 surface.
  2. The photosensitizers are excited from the ground state (S) to the excited state (S). The excited electrons are injected into the conduction band of the TiO2 electrode. This results in the oxidation of the photosensitizer (S+).
    S+hν→S


  3. The injected electrons in the conduction band of TiO2 are transported between TiO2 nanoparticles with diffusion toward the back contact (TCO). And the electrons finally reach the counter electrode through the circuit.
  4. The oxidized photosensitizer (S+) accepts electrons from the I ion redox mediator leading to regeneration of the ground state (S), and two I-Ions are oxidized to elementary Iodine which reacts with I to the oxidized state, I3.
    S++e→S

  5. The oxidized redox mediator, I3, diffuses toward the counter electrode and then it is reduced to I ions.
    I3+2e→3I

The efficiency of a DSSC depends on four energy levels of the component: the excited state (approximately LUMO) and the ground state (HOMO) of the photosensitizer, the Fermi level of the TiO2 electrode and the redox potential of the mediator (I/I3) in the electrolyte.

Nanoplant-like morphology

In DSSC, electrodes consisted of sintered semiconducting nanoparticles, mainly TiO2 or ZnO. These nanoparticle DSSCs rely on trap-limited diffusion through the semiconductor nanoparticles for the electron transport. This limits the device efficiency since it is a slow transport mechanism. Recombination is more likely to occur at longer wavelengths of radiation. Moreover, sintering of nanoparticles requires a high temperature of about 450 °C, which restricts the fabrication of these cells to robust, rigid solid substrates. It has been proven that there is an increase in the efficiency of DSSC, if the sintered nanoparticle electrode is replaced by a specially designed electrode possessing an exotic 'nanoplant-like' morphology.

Operation

Sunlight enters the cell through the transparent SnO2:F top contact, striking the dye on the surface of the TiO2. Photons striking the dye with enough energy to be absorbed create an excited state of the dye, from which an electron can be "injected" directly into the conduction band of the TiO2. From there it moves by diffusion (as a result of an electron concentration gradient) to the clear anode on top. 

Meanwhile, the dye molecule has lost an electron and the molecule will decompose if another electron is not provided. The dye strips one from iodide in electrolyte below the TiO2, oxidizing it into triiodide. This reaction occurs quite quickly compared to the time that it takes for the injected electron to recombine with the oxidized dye molecule, preventing this recombination reaction that would effectively short-circuit the solar cell.

The triiodide then recovers its missing electron by mechanically diffusing to the bottom of the cell, where the counter electrode re-introduces the electrons after flowing through the external circuit.

Efficiency

Several important measures are used to characterize solar cells. The most obvious is the total amount of electrical power produced for a given amount of solar power shining on the cell. Expressed as a percentage, this is known as the solar conversion efficiency. Electrical power is the product of current and voltage, so the maximum values for these measurements are important as well, Jsc and Voc respectively. Finally, in order to understand the underlying physics, the "quantum efficiency" is used to compare the chance that one photon (of a particular energy) will create one electron. 

In quantum efficiency terms, DSSCs are extremely efficient. Due to their "depth" in the nanostructure there is a very high chance that a photon will be absorbed, and the dyes are very effective at converting them to electrons. Most of the small losses that do exist in DSSC's are due to conduction losses in the TiO2 and the clear electrode, or optical losses in the front electrode. The overall quantum efficiency for green light is about 90%, with the "lost" 10% being largely accounted for by the optical losses in the top electrode. The quantum efficiency of traditional designs vary, depending on their thickness, but are about the same as the DSSC.

In theory, the maximum voltage generated by such a cell is simply the difference between the (quasi-)Fermi level of the TiO2 and the redox potential of the electrolyte, about 0.7 V under solar illumination conditions (Voc). That is, if an illuminated DSSC is connected to a voltmeter in an "open circuit", it would read about 0.7 V. In terms of voltage, DSSCs offer slightly higher Voc than silicon, about 0.7 V compared to 0.6 V. This is a fairly small difference, so real-world differences are dominated by current production, Jsc

Although the dye is highly efficient at converting absorbed photons into free electrons in the TiO2, only photons absorbed by the dye ultimately produce current. The rate of photon absorption depends upon the absorption spectrum of the sensitized TiO2 layer and upon the solar flux spectrum. The overlap between these two spectra determines the maximum possible photocurrent. Typically used dye molecules generally have poorer absorption in the red part of the spectrum compared to silicon, which means that fewer of the photons in sunlight are usable for current generation. These factors limit the current generated by a DSSC, for comparison, a traditional silicon-based solar cell offers about 35 mA/cm2, whereas current DSSCs offer about 20 mA/cm2

Overall peak power conversion efficiency for current DSSCs is about 11%. Current record for prototypes lies at 15%.

Degradation

DSSCs degrade when exposed to ultraviolet radiation. In 2014 air infiltration of the commonly-used amorphous Spiro-MeOTAD hole-transport layer was identified as the primary cause of the degradation, rather than oxidation. The damage could be avoided by the addition of an appropriate barrier.

The barrier layer may include UV stabilizers and/or UV absorbing luminescent chromophores (which emit at longer wavelengths which may be reabsorbed by the dye) and antioxidants to protect and improve the efficiency of the cell.

Advantages

DSSCs are currently the most efficient third-generation (2005 Basic Research Solar Energy Utilization 16) solar technology available. Other thin-film technologies are typically between 5% and 13%, and traditional low-cost commercial silicon panels operate between 14% and 17%. This makes DSSCs attractive as a replacement for existing technologies in "low density" applications like rooftop solar collectors, where the mechanical robustness and light weight of the glass-less collector is a major advantage. They may not be as attractive for large-scale deployments where higher-cost higher-efficiency cells are more viable, but even small increases in the DSSC conversion efficiency might make them suitable for some of these roles as well. 

There is another area where DSSCs are particularly attractive. The process of injecting an electron directly into the TiO2 is qualitatively different from that occurring in a traditional cell, where the electron is "promoted" within the original crystal. In theory, given low rates of production, the high-energy electron in the silicon could re-combine with its own hole, giving off a photon (or other form of energy) which does not result in current being generated. Although this particular case may not be common, it is fairly easy for an electron generated by another atom to combine with a hole left behind in a previous photoexcitation. 

In comparison, the injection process used in the DSSC does not introduce a hole in the TiO2, only an extra electron. Although it is energetically possible for the electron to recombine back into the dye, the rate at which this occurs is quite slow compared to the rate that the dye regains an electron from the surrounding electrolyte. Recombination directly from the TiO2 to species in the electrolyte is also possible although, again, for optimized devices this reaction is rather slow. On the contrary, electron transfer from the platinum coated electrode to species in the electrolyte is necessarily very fast.

As a result of these favorable "differential kinetics", DSSCs work even in low-light conditions. DSSCs are therefore able to work under cloudy skies and non-direct sunlight, whereas traditional designs would suffer a "cutout" at some lower limit of illumination, when charge carrier mobility is low and recombination becomes a major issue. The cutoff is so low they are even being proposed for indoor use, collecting energy for small devices from the lights in the house.

A practical advantage which DSSCs share with most thin-film technologies, is that the cell's mechanical robustness indirectly leads to higher efficiencies at higher temperatures. In any semiconductor, increasing temperature will promote some electrons into the conduction band "mechanically". The fragility of traditional silicon cells requires them to be protected from the elements, typically by encasing them in a glass box similar to a greenhouse, with a metal backing for strength. Such systems suffer noticeable decreases in efficiency as the cells heat up internally. DSSCs are normally built with only a thin layer of conductive plastic on the front layer, allowing them to radiate away heat much easier, and therefore operate at lower internal temperatures.

Disadvantages

The major disadvantage to the DSSC design is the use of the liquid electrolyte, which has temperature stability problems. At low temperatures the electrolyte can freeze, ending power production and potentially leading to physical damage. Higher temperatures cause the liquid to expand, making sealing the panels a serious problem. Another disadvantage is that costly ruthenium (dye), platinum (catalyst) and conducting glass or plastic (contact) are needed to produce a DSSC. A third major drawback is that the electrolyte solution contains volatile organic compounds (or VOC's), solvents which must be carefully sealed as they are hazardous to human health and the environment. This, along with the fact that the solvents permeate plastics, has precluded large-scale outdoor application and integration into flexible structure.

Replacing the liquid electrolyte with a solid has been a major ongoing field of research. Recent experiments using solidified melted salts have shown some promise, but currently suffer from higher degradation during continued operation, and are not flexible.

Photocathodes and tandem cells

Dye sensitised solar cells operate as a photoanode (n-DSC), where photocurrent result from electron injection by the sensitized dye. Photocathodes (p-DSCs) operate in an inverse mode compared to the conventional n-DSC, where dye-excitation is followed by rapid electron transfer from a p-type semiconductor to the dye (dye-sensitized hole injection, instead of electron injection). Such p-DSCs and n-DSCs can be combined to construct tandem solar cells (pn-DSCs) and the theoretical efficiency of tandem DSCs is well beyond that of single-junction DSCs. 

A standard tandem cell consists of one n-DSC and one p-DSC in a simple sandwich configuration with an intermediate electrolyte layer. n-DSC and p-DSC are connected in series, which implies that the resulting photocurrent will be controlled by the weakest photoelectrode, whereas photovoltages are additive. Thus, photocurrent matching is very important for the construction of highly efficient tandem pn-DSCs. However, unlike n-DSCs, fast charge recombination following dye-sensitized hole injection usually resulted in low photocurrents in p-DSC and thus hampered the efficiency of the overall device. 

Researchers have found that using dyes comprising a perylenemonoimide (PMI) as the acceptor and an oligothiophene coupled to triphenylamine as the donor greatly improve the performance of p-DSC by reducing charge recombination rate following dye-sensitized hole injection. The researchers constructed a tandem DSC device with NiO on the p-DSC side and TiO2 on the n-DSC side. Photocurrent matching was achieved through adjustment of NiO and TiO2 film thicknesses to control the optical absorptions and therefore match the photocurrents of both electrodes. The energy conversion efficiency of the device is 1.91%, which exceeds the efficiency of its individual components, but is still much lower than that of high performance n-DSC devices (6%–11%). The results are still promising since the tandem DSC was in itself rudimentary. The dramatic improvement in performance in p-DSC can eventually lead to tandem devices with much greater efficiency than lone n-DSCs.

Development

"Black Dye", an anionic Ru-terpyridine complex
 
The dyes used in early experimental cells (circa 1995) were sensitive only in the high-frequency end of the solar spectrum, in the UV and blue. Newer versions were quickly introduced (circa 1999) that had much wider frequency response, notably "triscarboxy-ruthenium terpyridine" [Ru(4,4',4"-(COOH)3-terpy)(NCS)3], which is efficient right into the low-frequency range of red and IR light. The wide spectral response results in the dye having a deep brown-black color, and is referred to simply as "black dye". The dyes have an excellent chance of converting a photon into an electron, originally around 80% but improving to almost perfect conversion in more recent dyes, the overall efficiency is about 90%, with the "lost" 10% being largely accounted for by the optical losses in top electrode. 

A solar cell must be capable of producing electricity for at least twenty years, without a significant decrease in efficiency. The "black dye" system was subjected to 50 million cycles, the equivalent of ten years' exposure to the sun in Switzerland. No discernible performance decrease was observed. However the dye is subject to breakdown in high-light situations. Over the last decade an extensive research program has been carried out to address these concerns. The newer dyes included 1-ethyl-3 methylimidazolium tetrocyanoborate [EMIB(CN)4] which is extremely light- and temperature-stable, copper-diselenium [Cu(In,GA)Se2] which offers higher conversion efficiencies, and others with varying special-purpose properties. 

DSSCs are still at the start of their development cycle. Efficiency gains are possible and have recently started more widespread study. These include the use of quantum dots for conversion of higher-energy (higher frequency) light into multiple electrons, using solid-state electrolytes for better temperature response, and changing the doping of the TiO2 to better match it with the electrolyte being used.

New developments

2003

A group of researchers at the Swiss Federal Institute of Technology has reportedly increased the thermostability of DSC by using amphiphilic ruthenium sensitizer in conjunction with quasi-solid-state gel electrolyte. The stability of the device matches that of a conventional inorganic silicon-based solar cell. The cell sustained heating for 1,000 h at 80 °C. 

The group has previously prepared a ruthenium amphiphilic dye Z-907 (cis-Ru(H2dcbpy)(dnbpy)(NCS)2, where the ligand H2dcbpy is 4,4′-dicarboxylic acid-2,2′-bipyridine and dnbpy is 4,4′-dinonyl-2,2′-bipyridine) to increase dye tolerance to water in the electrolytes. In addition, the group also prepared a quasi-solid-state gel electrolyte with a 3-methoxypropionitrile (MPN)-based liquid electrolyte that was solidified by a photochemically stable fluorine polymer, polyvinylidenefluoride-co-hexafluoropropylene (PVDF-HFP).

The use of the amphiphilic Z-907 dye in conjunction with the polymer gel electrolyte in DSC achieved an energy conversion efficiency of 6.1%. More importantly, the device was stable under thermal stress and soaking with light. The high conversion efficiency of the cell was sustained after heating for 1,000 h at 80 °C, maintaining 94% of its initial value. After accelerated testing in a solar simulator for 1,000 h of light-soaking at 55 °C (100 mW cm−2) the efficiency had decreased by less than 5% for cells covered with an ultraviolet absorbing polymer film. These results are well within the limit for that of traditional inorganic silicon solar cells. 

The enhanced performance may arise from a decrease in solvent permeation across the sealant due to the application of the polymer gel electrolyte. The polymer gel electrolyte is quasi-solid at room temperature, and becomes a viscous liquid (viscosity: 4.34 mPa·s) at 80 °C compared with the traditional liquid electrolyte (viscosity: 0.91 mPa·s). The much improved stabilities of the device under both thermal stress and soaking with light has never before been seen in DSCs, and they match the durability criteria applied to solar cells for outdoor use, which makes these devices viable for practical application.

2006

The first successful solid-hybrid dye-sensitized solar cells were reported.

To improve electron transport in these solar cells, while maintaining the high surface area needed for dye adsorption, two researchers have designed alternate semiconductor morphologies, such as arrays of nanowires and a combination of nanowires and nanoparticles, to provide a direct path to the electrode via the semiconductor conduction band. Such structures may provide a means to improve the quantum efficiency of DSSCs in the red region of the spectrum, where their performance is currently limited.

On August 2006, to prove the chemical and thermal robustness of the 1-ethyl-3 methylimidazolium tetracyanoborate solar cell, the researchers subjected the devices to heating at 80 °C in the dark for 1000 hours, followed by light soaking at 60 °C for 1000 hours. After dark heating and light soaking, 90% of the initial photovoltaic efficiency was maintained – the first time such excellent thermal stability has been observed for a liquid electrolyte that exhibits such a high conversion efficiency. Contrary to silicon solar cells, whose performance declines with increasing temperature, the dye-sensitized solar-cell devices were only negligibly influenced when increasing the operating temperature from ambient to 60 °C.

April 2007

Wayne Campbell at Massey University, New Zealand, has experimented with a wide variety of organic dyes based on porphyrin. In nature, porphyrin is the basic building block of the hemoproteins, which include chlorophyll in plants and hemoglobin in animals. He reports efficiency on the order of 5.6% using these low-cost dyes.

June 2008

An article published in Nature Materials demonstrated cell efficiencies of 8.2% using a new solvent-free liquid redox electrolyte consisting of a melt of three salts, as an alternative to using organic solvents as an electrolyte solution. Although the efficiency with this electrolyte is less than the 11% being delivered using the existing iodine-based solutions, the team is confident the efficiency can be improved.

2009

A group of researchers at Georgia Tech made dye-sensitized solar cells with a higher effective surface area by wrapping the cells around a quartz optical fiber. The researchers removed the cladding from optical fibers, grew zinc oxide nanowires along the surface, treated them with dye molecules, surrounded the fibers by an electrolyte and a metal film that carries electrons off the fiber. The cells are six times more efficient than a zinc oxide cell with the same surface area. Photons bounce inside the fiber as they travel, so there are more chances to interact with the solar cell and produce more current. These devices only collect light at the tips, but future fiber cells could be made to absorb light along the entire length of the fiber, which would require a coating that is conductive as well as transparent. Max Shtein of the University of Michigan said a sun-tracking system would not be necessary for such cells, and would work on cloudy days when light is diffuse.

2010

Researchers at the École Polytechnique Fédérale de Lausanne and at the Université du Québec à Montréal claim to have overcome two of the DSC's major issues:
  • "New molecules" have been created for the electrolyte, resulting in a liquid or gel that is transparent and non-corrosive, which can increase the photovoltage and improve the cell's output and stability.
  • At the cathode, platinum was replaced by cobalt sulfide, which is far less expensive, more efficient, more stable and easier to produce in the laboratory.

2011

Dyesol and Tata Steel Europe announced in June the development of the world's largest dye sensitized photovoltaic module, printed onto steel in a continuous line.

Dyesol and CSIRO announced in October a Successful Completion of Second Milestone in Joint Dyesol / CSIRO Project. Dyesol Director Gordon Thompson said, "The materials developed during this joint collaboration have the potential to significantly advance the commercialisation of DSC in a range of applications where performance and stability are essential requirements. Dyesol is extremely encouraged by the breakthroughs in the chemistry allowing the production of the target molecules. This creates a path to the immediate commercial utilisation of these new materials."

Dyesol and Tata Steel Europe announced in November the targeted development of Grid Parity Competitive BIPV solar steel that does not require government subsidised feed in tariffs. TATA-Dyesol "Solar Steel" Roofing is currently being installed on the Sustainable Building Envelope Centre (SBEC) in Shotton, Wales.

2012

Northwestern University researchers announced a solution to a primary problem of DSSCs, that of difficulties in using and containing the liquid electrolyte and the consequent relatively short useful life of the device. This is achieved through the use of nanotechnology and the conversion of the liquid electrolyte to a solid. The current efficiency is about half that of silicon cells, but the cells are lightweight and potentially of much lower cost to produce.

2013

During the last 5–10 years, a new kind of DSSC has been developed — the solid state dye-sensitized solar cell. In this case the liquid electrolyte is replaced by one of several solid hole conducting materials. From 2009 to 2013 the efficiency of Solid State DSSCs has dramatically increased from 4% to 15%. Michael Grätzel announced the fabrication of Solid State DSSCs with 15.0% efficiency, reached by the means of a hybrid perovskite CH3NH3PbI3 dye, subsequently deposited from the separated solutions of CH3NH3I and PbI2.

The first architectural integration was demonstrated at EPFL's new convention center in partnership with Romande Energie. The total surface is 300 m2, in 1400 modules of 50 cm x 35 cm. Designed by artists Daniel Schlaepfer and Catherine Bolle.

2018

Researchers have investigated the role of surface plasmon resonances present on gold nanorods in the performance of dye-sensitized solar cells. They found that with an increase nanorod concentration, the light absorption grew linearly; however, charge extraction was also dependent on the concentration. With an optimized concentration, they found that the overall power conversion efficiency improved from 5.31 to 8.86% for Y123 dye-sensitized solar cells.

The synthesis of one-dimensional TiO2 nanostructures directly on fluorine-doped tin oxide glass substrates was successful demonstrated via a two-stop solvothermal reaction. Additionally, through a TiO2 sol treatment, the performance of the dual TiO2 nanowire cells was enhanced, reaching a power conversion efficiency of 7.65%.

Stainless steel based counter-electrodes for DSSCs have been reported which further reduce cost compared to conventional platinum based counter electrode and are suitable for outdoor application.

Researchers from EPFL have advanced the DSSCs based on copper complexes redox electrolytes, which have achieved 13.1% efficiency under standard AM1.5G, 100 mW/cm2 conditions and record 32% efficiency under 1000 lux of indoor light.

Market introduction

Several commercial providers are promising availability of DSCs in the near future:
  • Dyesol officially opened its new manufacturing facilities in Queanbeyan Australia on 7 October 2008. It has subsequently announced partnerships with Tata Steel (TATA-Dyesol) and Pilkington Glass (Dyetec-Solar) for the development and large scale manufacture of DSC BIPV. Dyesol has also entered working relationships with Merck, Umicore, CSIRO, Japanese Ministry of Economy and Trade, Singapore Aerospace Manufacturing and a joint Venture with TIMO Korea (Dyesol-TIMO).
  • Solaronix, a Swiss company specialized in the production of DSC materials since 1993, has extended their premises in 2010 to host a manufacturing pilot line of DSC modules.[57]
  • SolarPrint was founded in Ireland in 2008 by Dr. Mazhar Bari, Andre Fernon and Roy Horgan. SolarPrint was the first Ireland-based commercial entity involved in the manufacturing of PV technology. SolarPrint's innovation was the solution to the solvent-based electrolyte which to date has prohibited the mass commercialization of DSSC. The company went into receivership in 2014 and was wound up.
  • G24innovations founded in 2006, based in Cardiff, South Wales, UK. On 17 October 2007, claimed the production of the first commercial grade dye sensitized thin films.
  • Sony Corporation has developed dye-sensitized solar cells with an energy conversion efficiency of 10%, a level seen as necessary for commercial use.
  • Tasnee Enters Strategic Investment Agreement with Dyesol.
  • H.Glass was founded 2011 in Switzerland. H.Glass has put enormous efforts to create industrial process for the DSSC technologie - the first results where shown at the EXPO 2015 in Milano at the Austrian Pavilion. The milestone for DSSC is the Science Tower in Austria - it is the largest installation of DSSC in the world - carried out by SFL technologies.

Friday, January 4, 2019

Hybrid solar cell

From Wikipedia, the free encyclopedia
 
Hybrid solar cells combine advantages of both organic and inorganic semiconductors. Hybrid photovoltaics have organic materials that consist of conjugated polymers that absorb light as the donor and transport holes. Inorganic materials in hybrid cells are used as the acceptor and electron transporter in the structure. The hybrid photovoltaic devices have a potential for not only low-cost by roll-to-roll processing but also for scalable solar power conversion.

Theory

Solar cells are devices that convert sunlight into electricity by the photovoltaic effect. Electrons in a solar cell absorb photon energy in sunlight which excites them to the conduction band from the valence band. This generates a hole-electron pair, which is separated by a potential barrier (such as a p-n junction), and induces a current. Organic solar cells use organic materials in their active layers. Molecular, polymer, and hybrid organic photovoltaics are the main kinds of organic photovoltaic devices currently studied.

Hybrid solar cell

Figure 1. Energy diagram of the donor and acceptor. The conduction band of the acceptor is lower than the LUMO of the polymer, allowing for transfer of the electron.
 
In hybrid solar cells, an organic material is mixed with a high electron transport material to form the photoactive layer. The two materials are assembled together in a heterojunction-type photoactive layer, which can have a greater power conversion efficiency than a single material. One of the materials acts as the photon absorber and exciton donor. The other material facilitates exciton dissociation at the junction. Charge is transferred and then separated after an exciton created in the donor is delocalized on a donor-acceptor complex.

The acceptor material needs a suitable energy offset to the binding energy of the exciton to the absorber. Charge transfer is favorable if the following condition is satisfied:
where superscripts A and D refer to the acceptor and donor respectively, EA is the electron affinity, and U the coulombic binding energy of the exciton on the donor. An energy diagram of the interface is shown in figure 1. In commonly used photovoltaic polymers such as MEH-PPV, the exciton binding energy ranges from 0.3 eV to 1.4 eV.

The energy required to separate the exciton is provided by the energy offset between the LUMOs or conduction bands of the donor and acceptor. After dissociation, the carriers are transported to the respective electrodes through a percolation network.

The average distance an exciton can diffuse through a material before annihilation by recombination is the exciton diffusion length. This is short in polymers, on the order of 5–10 nanometers. The time scale for radiative and non-radiative decay is from 1 picosecond to 1 nanosecond. Excitons generated within this length close to an acceptor would contribute to the photocurrent. 

Figure 2. Two different structures of heterojunctions, a) phase separated bi-layer and b) bulk heterojunction. The bulk heterojunction allows for more interfacial contact between the two phases, which is beneficial for the nanoparticle-polymer compound as it provides more surface area for charge transfer.
 
To deal with the problem of the short exciton diffusion length, a bulk heterojunction structure is used rather than a phase-separated bilayer. Dispersing the particles throughout the polymer matrix creates a larger interfacial area for charge transfer to occur. Figure 2 displays the difference between a bilayer and a bulk heterojunction.

Types of interfaces and structures

Controlling the interface of inorganic-organic hybrid solar cells can increase the efficiency of the cells. This increased efficiency can be achieved by increasing the interfacial surface area between the organic and the inorganic to facilitate charge separation and by controlling the nanoscale lengths and periodicity of each structure so that charges are allowed to separate and move toward the appropriate electrode without recombining. The three main nanoscale structures used are mesoporous inorganic films infused with electron-donating organic, alternatining inorganic-organic lamellar structures, and nanowire structures.

Mesoporous films

Mesoporous films have been used for a relatively high-efficiency hybrid solar cell. The structure of mesoporous thin film solar cells usually includes a porous inorganic that is saturated with organic surfactant. The organic absorbs light, and transfers electrons to the inorganic semiconductor (usually a transparent conducting oxide), which then transfers the electron to the electrode. Problems with these cells include their random ordering and the difficulty of controlling their nanoscale structure to promote charge conduction.

Ordered lamellar films

Recently, the use of alternating layers of organic and inorganic compounds has been controlled through electrodeposition-based self-assembly. This is of particular interest because it has been shown that the lamellar structure and periodicity of the alternating organic-inorganic layers can be controlled through solution chemistry. To produce this type of cell with practical efficiencies, larger organic surfactants that absorb more of the visible spectrum must be deposited between the layers of electron-accepting inorganic.

Films of ordered nanostructures

Researchers have been able to grow nanostructure-based solar cells that use ordered nanostructures like nanowires or nanotubes of inorganic surrounding by electron-donating organics utilizing self-organization processes. Ordered nanostructures offer the advantage of directed charge transport and controlled phase separation between donor and acceptor materials. The nanowire-based morphology offers reduced internal reflection, facile strain relaxation and increased defect tolerance. The ability to make single-crystalline nanowires on low-cost substrates such as aluminum foil and to relax strain in subsequent layers removes two more major cost hurdles associated with high-efficiency cells. There have been rapid increases in efficiencies of nanowire-based solar cells and they seem to be one of the most promising nanoscale solar hybrid technologies.

Fundamental challenge factors

Hybrid cell efficiency must be increased to start large-scale manufacturing. Three factors affect efficiency. First, the bandgap should be reduced to absorb red photons, which contain a significant fraction of the energy in the solar spectrum. Current organic photovoltaics have shown 70% of quantum efficiency for blue photons. Second, contact resistance between each layer in the device should be minimized to offer higher fill factor and power conversion efficiency. Third, charge-carrier mobility should be increased to allow the photovoltaics to have thicker active layers while minimizing carrier recombination and keeping the series resistance of the device low.

Types of hybrid solar cells

Polymer–nanoparticle composite

Nanoparticles are a class of semiconductor materials whose size in at least one dimension ranges from 1 to 100 nanometers, on the order of exciton wavelengths. This size control creates quantum confinement and allows for the tuning of optoelectronic properties, such as band gap and electron affinity. Nanoparticles also have a large surface area to volume ratio, which presents more area for charge transfer to occur.

The photoactive layer can be created by mixing nanoparticles into a polymer matrix. Solar devices based on polymer-nanoparticle composites most resemble polymer solar cells. In this case, the nanoparticles take the place of the fullerene based acceptors used in fully organic polymer solar cells. Hybrid solar cells based upon nanoparticles are an area of research interest because nanoparticles have several properties that could make them preferable to fullerenes, such as:
  • Fullerenes are synthesized by a combination of a high temperature arc method and continuous gas-phase synthesis, which makes their production difficult and energy intensive. The colloidal synthesis of nanoparticles by contrast is a low temperature process.
  • PCBM (a common fullerene acceptor) diffuses during long timespans or when exposed to heat, which can alter the morphology and lower the efficiency of a polymer solar cell. Limited testing of nanoparticle solar cells indicates they may be more stable over time.
  • Nanoparticles are more absorbent than fullerenes, meaning more light can be theoretically absorbed in a thinner device.
  • Nanoparticle size can affect absorption. This combined with the fact that there are many possible semiconducting nanoparticles allows for highly customizable bandgaps that can be easily tuned to certain frequencies, which would be advantageous in tandem solar cells.
  • Nanoparticles with size near their Bohr radius can generate two excitons when struck by a sufficiently energetic photon.

Structure and processing

Figure 3. Four different structures of nanoparticles, which have at least 1 dimension in the 1–100 nm range, retaining quantum confinement. Left is a nanocrystal, next to it is nanorod, third is tetrapod, and right is hyperbranched.
 
For polymers used in this device, hole mobilities are greater than electron mobilities, so the polymer phase is used to transport holes. The nanoparticles transport electrons to the electrode.

The interfacial area between the polymer phase and the nanoparticles needs to be large. This is achieved by dispersing the particles throughout the polymer matrix. However, the nanoparticles need to be interconnected to form percolation networks for electron transport, which occurs by hopping events.

Efficiency is affected by aspect ratio, geometry, and volume fraction of the nanoparticles. Nanoparticle structures include nanocrystals, nanorods, and hyperbranched structures. Figure 3 contains a picture of each structure. Different structures change the conversion efficiency by effecting nanoparticle dispersion in the polymer and providing pathways for electron transport.

The nanoparticle phase is required to provide a pathway for the electrons to reach the electrode. By using nanorods instead of nanocrystals, the hopping event from one crystal to another can be avoided.

Fabrication methods include mixing the two materials in a solution and spin-coating it onto a substrate, and solvent evaporation (sol-gel). Most of these methods do not involve high-temperature processing. Annealing increases order in the polymer phase, increasing conductivity. However, annealing for too long causes the polymer domain size to increase, eventually making it larger than the exciton diffusion length, and possibly allowing some of the metal from the contact to diffuse into the photoactive layer, reducing the efficiency of the device.

Materials

Inorganic semiconductor nanoparticles used in hybrid cells include CdSe (size ranges from 6–20 nm), ZnO, TiO, and PbS. Common polymers used as photo materials have extensive conjugation and are also hydrophobic. Their efficiency as a photo-material is affected by the HOMO level position and the ionization potential, which directly affects the open circuit voltage and the stability in air. The most common polymers used are P3HT (poly (3-hexylthiophene)), and M3H-PPV (poly[2-methoxy, 5-(2′-ethyl-hexyloxy)-p-phenylenevinylene)]). P3HT has a bandgap of 2.1 eV and M3H-PPV has a bandgap of ~2.4 eV. These values correspond with the bandgap of CdSe, 2.10 eV. The electron affinity of CdSe ranges from 4.4 to 4.7 eV. When the polymer used is MEH-PPV, which has an electron affinity of 3.0 eV, the difference between the electron affinities is large enough to drive electron transfer from the CdSe to the polymer. CdSe also has a high electron mobility (600 cm2·V−1·s−1).

Performance values

The highest demonstrated efficiency is 3.2%, based upon a PCPDTBT polymer donor and CdSe nanoparticle acceptor. The device exhibited a short circuit current of 10.1 mA·cm−2, an open circuit voltage of .68 V, and a fill factor of .51.

Challenges

Hybrid solar cells need increased efficiencies and stability over time before commercialization is feasible. In comparison to the 2.4% of the CdSe-PPV system, silicon photodevices have power conversion efficiencies greater than 20%. 

Problems include controlling the amount of nanoparticle aggregation as the photolayer forms. The particles need to be dispersed in order to maximize interface area, but need to aggregate to form networks for electron transport. The network formation is sensitive to the fabrication conditions. Dead end pathways can impede flow. A possible solution is implementing ordered heterojunctions, where the structure is well controlled.

The structures can undergo morphological changes over time, namely phase separation. Eventually, the polymer domain size will be greater than the carrier diffusion length, which lowers performance.

Even though the nanoparticle bandgap can be tuned, it needs to be matched with the corresponding polymer. The 2.0 eV bandgap of CdSe is larger than an ideal bandgap of 1.4 for absorbance of light.

The nanoparticles involved are typically colloids, which are stabilized in solution by ligands. The ligands decrease device efficiency because they serve as insulators which impede interaction between the donor and nanoparticle acceptor as well as decreasing the electron mobility. Some, but not complete success has been had by exchanging the initial ligands for pyridine or another short chain ligand.

Hybrid solar cells exhibit material properties inferior to those of bulk silicon semiconductors. The carrier mobilities are much smaller than that of silicon. Electron mobility in silicon is 1000 cm2·V−1·s−1, compared to 600 cm2·V−1·s−1 in CdSe, and less than 10 cm2·V−1·s−1 in other quantum dot materials. Hole mobility in MEH-PPV is 0.1 cm2·V−1·s−1, while in silicon it is 450 cm2·V−1·s−1.

Carbon nanotubes

Carbon nanotubes (CNTs) have high electron conductivity, high thermal conductivity, robustness, and flexibility. Field emission displays (FED), strain sensors, and field effect transistors (FET) using CNTs have been demonstrated. Each application shows the potential of CNTs for nanoscale devices and for flexible electronics applications. Photovoltaic applications have also been explored for this material.

Mainly, CNTs have been used as either the photo-induced exciton carrier transport medium impurity within a polymer-based photovoltaic layer or as the photoactive (photon-electron conversion) layer. Metallic CNT is preferred for the former application, while semiconducting CNT is preferred for the later.

Efficient carrier transport medium

Device diagram for CNT as efficient carrier transport medium.
 
To increase the photovoltaic efficiency, electron-accepting impurities must be added to the photoactive region. By incorporating CNTs into the polymer, dissociation of the exciton pair can be accomplished by the CNT matrix. The high surface area (~1600 m2/g)  of CNTs offers a good opportunity for exciton dissociation. The separated carriers within the polymer-CNT matrix are transported by the percolation pathways of adjacent CNTs, providing the means for high carrier mobility and efficient charge transfer. The factors of performance of CNT-polymer hybrid photovoltaics are low compared to those of inorganic photovoltaics. SWNT in P3OT semiconductor polymer demonstrated open circuit voltage (Voc) of below 0.94 V, with short circuit current (Isc) of 0.12 mA/cm2.

Metal nanoparticles may be applied to the exterior of CNTs to increase the exciton separation efficiency. The metal provides a higher electric field at the CNT-polymer interface, accelerating the exciton carriers to transfer them more effectively to the CNT matrix. In this case, Voc = 0.3396 V and Isc = 5.88 mA/cm2. The fill factor is 0.3876%, and the white light conversion factor 0.775%.

Photoactive matrix layer

CNT may be used as a photovoltaic device not only as an add-in material to increase carrier transport, but also as the photoactive layer itself. The semiconducting single walled CNT (SWCNT) is a potentially attractive material for photovoltaic applications for the unique structural and electrical properties. SWCNT has high electric conductivity (100 times that of copper) and shows ballistic carrier transport, greatly decreasing carrier recombination. The bandgap of the SWCNT is inversely proportional to the tube diameter, which means that SWCNT may show multiple direct bandgaps matching the solar spectrum.

A strong built-in electric field in SWCNT for efficient photogenerated electron-hole pair separation has been demonstrated by using two asymmetrical metal electrodes with high and low work functions. The open circuit voltage (Voc) is 0.28 V, with short circuit current (Isc) 1.12 nA·cm−2 with an incident light source of 8.8 W·cm−2. The resulting white light conversion factor is 0.8%.

Challenges

Several challenges must be addressed for CNT to be used in photovoltaic applications. CNT degrades over time in an oxygen-rich environment. The passivation layer required to prevent CNT oxidation may reduce the optical transparency of the electrode region and lower the photovoltaic efficiency.
Challenges as efficient carrier transport medium
Additional challenges involve the dispersion of CNT within the polymer photoactive layer. The CNT is required to be well dispersed within the polymer matrix to form charge-transfer-efficient pathways between the excitons and the electrode
Challenges as photoactive matrix layer
Challenges of CNT for the photoactive layer include its lack of capability to form a p-n junction, due to the difficulty of doping certain segments of a CNT. (A p-n junction creates an internal built-in potential, providing a pathway for efficient carrier separation within the photovoltaic.) To overcome this difficulty, energy band bending has been done by the use of two electrodes of different work functions. A strong built-in electric field covering the whole SWCNT channel is formed for high-efficiency carrier separation. The oxidation issue with CNT is more critical for this application. Oxidized CNTs have a tendency to become more metallic, and so less useful as a photovoltaic material.

Dye-sensitized

Dye-sensitized solar cells consists of a photo-sensitized anode, an electrolyte, and a photo-electrochemical system. Hybrid solar cells based on dye-sensitized solar cells are formed with inorganic materials (TiO2) and organic materials.

Materials

Hybrid solar cells based on dye-sensitized solar cells are fabricated by dye-absorbed inorganic materials and organic materials. TiO2 is the preferred inorganic material since this material is easy to synthesize and acts as a n-type semiconductor due to the donor-like oxygen vacancies. However, titania only absorbs a small fraction of the UV spectrum. Molecular sensitizers (dye molecules) attached to the semiconductor surface are used to collect a greater portion of the spectrum. In the case of titania dye-sensitized solar cells, a photon absorbed by a dye-sensitizer molecule layer induces electron injection into the conduction band of titania, resulting in current flow. However, short diffusion length (diffusivity, Dn≤10−4cm2/s) in titania dye-sensitized solar cells decrease the solar-to-energy conversion efficiency. To enhance diffusion length (or carrier lifetime), a variety of organic materials are attached to the titania.

Fabrication scheme

Dye-sensitized photoelectrochemical cell (Grätzel cell)
Fig. 5. Schematic representation of electron-hole generation and recombination
 
TiO2 nanoparticles are synthesized in several tens of nanometer scales (~100 nm). In order to make a photovoltaic cell, molecular sensitizers (dye molecules) are attached to the titania surface. The dye-absorbed titania is finally enclosed by a liquid electrolyte. This type of dye-sensitized solar cell is also known as a Grätzel cell. Dye-sensitized solar cell has a disadvantage of a short diffusion length. Recently, supermolecular or multifunctional sensitizers have been investigated so as to enhance carrier diffusion length. For example, a dye chromophore has been modified by the addition of secondary electron donors. Minority carriers (holes in this case) diffuse to the attached electron donors to recombine. Therefore, electron-hole recombination is retarded by the physical separation between the dye–cation moiety and the TiO2 surface, as shown in Fig. 5. Finally, this process raises the carrier diffusion length, resulting in the increase of carrier lifetime.
Solid-state dye sensitized solar cell
Mesoporous materials contain pores with diameters between 2 and 50 nm. A dye-sensitized mesoporous film of TiO2 can be used for making photovoltaic cells and this solar cell is called a ‘solid-state dye sensitized solar cell’. The pores in mesoporous TiO2 thin film are filled with a solid hole-conducting material such as p-type semiconductors or organic hole conducting material. Replacing the liquid electrolyte in Grätzel’s cells with a solid charge-transport material can be beneficial. The process of electron-hole generation and recombination is the same as Grätzel cells. Electrons are injected from photoexcited dye into the conduction band of titania and holes are transported by a solid charge transport electrolyte to an electrode. Many organic materials have been tested to obtain a high solar-to-energy conversion efficiency in dye synthesized solar cells based on mesoporous titania thin film.

Efficiency factors

Efficiency factors demonstrated for dye-sensitized solar cells are:

Parameters Types of dye sensitized solar cells
Grätzel cell Solid-state
Efficiency (%) ~ 10–11 ~ 4
Voc (V) ~ 0.7 ~ 0.40
Jsc (mA/cm2) ~ 20 ~ 9.10
Fill factor ~ 0.67 ~ 0.6

Challenges

Liquid organic electrolytes contain highly corrosive iodine, leading to problems of leakage, sealing, handling, dye desorption, and maintenance. Much attention is now focused on the electrolyte to address these problems. 

For solid-state dye sensitized solar cells, the first challenge originates from disordered titania mesoporous structures. Mesoporous titania structures should be fabricated with well-ordered titania structures of uniform size (~ 10 nm). The second challenge comes from developing the solid electrolyte, which is required to have these properties:
  1. The electrolyte should be transparent to the visible spectrum (wide band gap).
  2. Fabrication should be possible for depositing the solid electrolyte without degrading the dye molecule layer on titania.
  3. The LUMO of the dye molecule should be higher than the conduction band of titania.
  4. Several p-type semiconductors tend to crystallize inside the mesoporous titania films, destroying the dye molecule-titania contact. Therefore, the solid electrolyte needs to be stable during operation.

Nanostructured inorganic — small molecules

In 2008, scientists were able to create a nanostructured lamellar structure that provides an ideal design for bulk heterojunction solar cells. The observed structure is composed of ZnO and small, conducting organic molecules, which co-assemble into alternating layers of organic and inorganic components. This highly organized structure, which is stabilized by π-π stacking between the organic molecules, allows for conducting pathways in both the organic and inorganic layers. The thicknesses of the layers (about 1–3 nm) are well within the exciton diffusion length, which ideally minimizes recombination among charge carriers. This structure also maximizes the interface between the inorganic ZnO and the organic molecules, which enables a high chromophore loading density within the structure. Due to the choice of materials, this system is non-toxic and environmentally friendly, unlike many other systems which use lead or cadmium.

Although this system has not yet been incorporated into a photovoltaic device, preliminary photoconductivity measurements have shown that this system exhibits among the highest values measured for organic, hybrid, and amorphous silicon photoconductors, and so, offers promise in creating efficient hybrid photovoltaic devices.

Inequality (mathematics)

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