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Saturday, September 25, 2021

Perovskite solar cell

From Wikipedia, the free encyclopedia
 
Perovskite solar cells

A perovskite solar cell (PSC) is a type of solar cell which includes a perovskite-structured compound, most commonly a hybrid organic-inorganic lead or tin halide-based material, as the light-harvesting active layer. Perovskite materials, such as methylammonium lead halides and all-inorganic caesium lead halide, are cheap to produce and simple to manufacture.

Solar cell efficiencies of laboratory-scale devices using these materials have increased from 3.8% in 2009 to 25.5% in 2020 in single-junction architectures, and, in silicon-based tandem cells, to 29.15%, exceeding the maximum efficiency achieved in single-junction silicon solar cells. Perovskite solar cells have therefore been the fastest-advancing solar technology as of 2016. With the potential of achieving even higher efficiencies and very low production costs, perovskite solar cells have become commercially attractive. Core problems and research subjects include their short- and long-term stability.

Advantages

Metal halide perovskites possess unique features that make them useful for solar cell applications. The raw materials used, and the possible fabrication methods (such as various printing techniques) are both low cost. Their high absorption coefficient enables ultrathin films of around 500 nm to absorb the complete visible solar spectrum. These features combined result in the possibility to create low cost, high efficiency, thin, lightweight and flexible solar modules. Perovskite solar cells have found use in powering low-power wireless electronics for the ambient powered internet of things applications 

Materials

Crystal structure of CH3NH3PbX3 perovskites (X=I, Br and/or Cl). The methylammonium cation (CH3NH3+) is surrounded by PbX6 octahedra.

The name 'perovskite solar cell' is derived from the ABX3 crystal structure of the absorber materials, which is referred to as perovskite structure and where A and B are cations and X is an anion. A cations with radii between 1.60 Å and 2.50 Å were found to form perovskite structures. The most commonly studied perovskite absorber is methylammonium lead trihalide (CH3NH3PbX3, where X is a halogen ion such as iodide, bromide or chloride), with an optical bandgap between ~1.55 and 2.3 eV depending on halide content. Formamidinium lead trihalide (H2NCHNH2PbX3) has also shown promise, with bandgaps between 1.48 and 2.2 eV. The minimum bandgap is closer to the optimal for a single-junction cell than methylammonium lead trihalide, so it should be capable of higher efficiencies. The first use of perovskite in a solid state solar cell was in a dye-sensitized cell using CsSnI3 as a p-type hole transport layer and absorber. A common concern is the inclusion of lead as a component of the perovskite materials; solar cells based on tin-based perovskite absorbers such as CH3NH3SnI3 have also been reported with lower power-conversion efficiencies.

Shockley-Queisser limit

Solar cell efficiency is limited by the Shockley-Queisser limit. This calculated limit sets the maximum theoretical efficiency of a solar cell using a single junction with no other loss aside from radiative recombination in the solar cell. Based on the AM1.5G global solar spectra, the maximum power conversion efficiency is correlated to a respective bandgap, forming a parabolic relationship.

This limit is described by the equation

Where

and u is the ultimate efficiency factor, and v is the ratio of open circuit voltage Vop to band-gap voltage Vg, and m is the impedance matching factor, and Vc is the thermal voltage, and Vs is the voltage equivalent of the temperature of the Sun.

The most efficient bandgap is found to be at 1.34 eV, with a maximum power conversion efficiency (PCE) of 33.7%. Reaching this ideal bandgap energy can be difficult, but utilizing tunable perovskite solar cells allows for the flexibility to match this value. Further experimenting with multijunction solar cells allow for the Shockley-Queisser limit to be surpassed, expanding to allow photons of a broader wavelength range to be absorbed and converted, without increasing thermalisation loss.

The actual band gap for formamidinium (FA) lead trihalide can be tuned as low as 1.48 eV, which is closer to the ideal bandgap energy of 1.34 eV for maximum power-conversion efficiency single junction solar cells, predicted by the Shockley Queisser Limit. More recently, the 1.3 eV bandgap energy has been successfully achieved with the (FAPbI
3
)
1−x
(CsSnI
3
)
x
hybrid cell, which has a tunable bandgap energy (Eg) from 1.24 – 1.41 eV.

Multi-junction solar cells

Multi-junction solar cells, are capable of a higher power conversion efficiency (PCE), increasing the threshold beyond the thermodynamic maximum set by the Shockley–Queissier limit for single junction cells. By having multiple bandgaps in a single cell, it prevents the loss of photons above or below the band gap energy of a single junction solar cell. In tandem (double) junction solar cells, PCE of 31.1% has been recorded, increasing to 37.9% for triple junction and 38.8% for quadruple junction solar cells. However, the metal organic chemical vapor deposition (MOCVD) process needed to synthesize lattice-matched and crystalline solar cells with more than one junction is very expensive, making it a less than ideal candidate for widespread use.

Perovskite semiconductors offer an option that has the potential to rival the efficiency of multijunction solar cells, but can be synthesized under more common conditions at a greatly reduced cost. Rivaling the double, triple, and quadruple junction solar cells mentioned above, are all-perovskite tandem cells with a max PCE of 31.9%, all-perovskite triple-junction cell reaching 33.1%, and the perovskite-Si triple-junction cell, reaching an efficiency of 35.3%. These multijunction perovskite solar cells, in addition to being available for cost-effective synthesis, also maintain high PCE under varying weather extremes – making them utilizable worldwide.

Chiral ligands

Utilizing organic chiral ligands shows promise for increasing the maximum power conversion efficiency for halide perovskite solar cells, when utilized correctly. Chirality can be produced in inorganic semiconductors by enantiomeric distortions near the surface of the lattice, electronic coupling between the substrate and a chiral ligand, assembly into a chiral secondary structure, or chiral surface defects. By attaching a chiral phenylethylamine ligand to an achiral lead bromide perovskite nanoplatelet, a chiral inorganic-organic perovskite is formed. Inspection of the inorganic-organic perovskite via Circular Dichroism (CD) spectroscopy, reveals two regions. One represents the charge transfer between the ligand and the nanoplatelet (300-350 nm), and the other represents the excitonic absorption maximum of the perovskite. Evidence of charge transfer in these systems shows promise for increasing power conversion efficiency in perovskite solar cells.

Other research and developments

In another recent development, solar cells based on transition metal oxide perovskites and heterostructures thereof such as LaVO3/SrTiO3 are studied.

Rice University scientists have discovered a novel phenomenon of light-induced lattice expansion in perovskite materials.

In order to overcome the instability issues with lead-based organic perovskite materials in ambient air and reduce the use of lead, perovskite derivatives, such as Cs2SnI6 double perovskite, have also been investigated.

Processing

Perovskite solar cells hold an advantage over traditional silicon solar cells in the simplicity of their processing and their tolerance to internal defects. Traditional silicon cells require expensive, multi-step processes, conducted at high temperatures (>1000 °C) under high vacuum in special cleanroom facilities. Meanwhile, the hybrid organic-inorganic perovskite material can be manufactured with simpler wet chemistry techniques in a traditional lab environment. Most notably, methylammonium and formamidinium lead trihalides, also known as hybrid perovskites, have been created using a variety of solution deposition techniques, such as spin coating, slot-die coating, blade coating, spray coating, inkjet printing, screen printing, electrodeposition, and vapor deposition techniques, all of which have the potential to be scaled up with relative ease except spin coating.

Deposition methods

The solution-based processing method can be classified into one-step solution deposition and two-step solution deposition. In one-step deposition, a perovskite precursor solution that is prepared by mixing lead halide and organic halide together, is directly deposited through various coating methods, such as spin coating, spraying, blade coating, and slot-die coating, to form perovskite film. One-step deposition is simple, fast, and inexpensive but it’s also more challenging to control the perovskite film uniformity and quality. In the two-step deposition, the lead halide film is first deposited then reacts with organic halide to form perovskite film. The reaction takes time to complete but it can be facilitated by adding Lewis-bases or partial organic halide into lead halide precursors. In two-step deposition method, the volume expansion during the conversion of lead halide to perovskite can fill any pinholes to realize a better film quality. The vapor phase deposition processes can be categorized into physical vapor deposition (PVD) and chemical vapor deposition (CVD). PVD refers to the evaporation of a perovskite or its precursor to form a thin perovskite film on the substrate, which is free of solvent. While CVD involves the reaction of organic halide vapor with the lead halide thin film to convert it into the perovskite film. A solution-based CVD, aerosol-assisted CVD (AACVD) was also introduced to fabricate halide perovskite films, such as CH3NH3PbI3, CH3NH3PbBr3, and Cs2SnI6.

One-step solution deposition vs two-step solution deposition

One-step solution deposition

In one-step solution processing, a lead halide and a methylammonium halide can be dissolved in a solvent and spin coated onto a substrate. Subsequent evaporation and convective self-assembly during spinning results in dense layers of well crystallized perovskite material, due to the strong ionic interactions within the material (The organic component also contributes to a lower crystallization temperature). However, simple spin-coating does not yield homogenous layers, instead requiring the addition of other chemicals such as GBL, DMSO, and toluene drips. Simple solution processing results in the presence of voids, platelets, and other defects in the layer, which would hinder the efficiency of a solar cell.

Another technique using room temperature solvent-solvent extraction produces high-quality crystalline films with precise control over thickness down to 20 nanometers across areas several centimeters square without generating pinholes. In this method "perovskite precursors are dissolved in a solvent called NMP and coated onto a substrate. Then, instead of heating, the substrate is bathed in diethyl ether, a second solvent that selectively grabs the NMP solvent and whisks it away. What's left is an ultra-smooth film of perovskite crystals."

In another solution processed method, the mixture of lead iodide and methylammonium halide dissolved in DMF is preheated. Then the mixture is spin coated on a substrate maintained at higher temperature. This method produces uniform films of up to 1 mm grain size.

Pb halide perovskites can be fabricated from a PbI2 precursor, or non-PbI2 precursors, such as PbCl2, Pb(Ac)2, and Pb(SCN)2, giving films different properties.

Two-step solution deposition

In 2015, a new approach for forming the PbI2 nanostructure and the use of high CH3NH3I concentration have been adopted to form high quality (large crystal size and smooth) perovskite film with better photovoltaic performances. On one hand, self-assembled porous PbI2 is formed by incorporating small amounts of rationally chosen additives into the PbI2 precursor solutions, which significantly facilitate the conversion of perovskite without any PbI2 residue. On the other hand, through employing a relatively high CH3NH3I concentration, a firmly crystallized and uniform CH3NH3PbI3 film is formed. Furthermore, this is an inexpensive approach.

Vapor deposition

In vapor assisted techniques, spin coated or exfoliated lead halide is annealed in the presence of methylammonium iodide vapor at a temperature of around 150 °C. This technique holds an advantage over solution processing, as it opens up the possibility for multi-stacked thin films over larger areas. This could be applicable for the production of multi-junction cells. Additionally, vapor deposited techniques result in less thickness variation than simple solution processed layers. However, both techniques can result in planar thin film layers or for use in mesoscopic designs, such as coatings on a metal oxide scaffold. Such a design is common for current perovskite or dye-sensitized solar cells.

Scalability

Scalability includes not only scaling up the perovskite absorber layer, but also scaling up charge-transport layers and electrode. Both solution and vapor processes hold promise in terms of scalability. Process cost and complexity is significantly less than that of silicon solar cells. Vapor deposition or vapor assisted techniques reduce the need for use of further solvents, which reduces the risk of solvent remnants. Solution processing is cheaper. Current issues with perovskite solar cells revolve around stability, as the material is observed to degrade in standard environmental conditions, suffering drops in efficiency.

In 2014, Olga Malinkiewicz presented her inkjet printing manufacturing process for perovskite sheets in Boston (US) during the MRS fall meeting – for which she received MIT Technology review's innovators under 35 award. The University of Toronto also claims to have developed a low-cost Inkjet solar cell in which the perovskite raw materials are blended into a Nanosolar ‘ink’ which can be applied by an inkjet printer onto glass, plastic or other substrate materials.

Scaling up the absorber layer

In order to scale up the perovskite layer while maintaining high efficiency, various techniques have been developed to coat the perovskite film more uniformly. For example, some physical approaches are developed to promote supersaturation through rapid solvent removal, thus getting more nucleations and reducing grain growth time and solute migration. Heating, gas flow, vacuum, and anti-solvent can all assist solvent removal. And chemical additives, such as chloride additives, Lewis base additives, surfactant additive, and surface modification, can influence the crystal growth to control the film morphology. For example, a recent report of surfactant additive, such as L-α-phosphatidylcholine (LP), demonstrated the suppression of solution flow by surfactants to eliminate gaps between islands and meanwhile the surface wetting improvement of perovskite ink on the hydrophobic substrate to ensure a full coverage. Besides, LP can also passivate charge traps to further enhance the device performance, which can be used in blade coating to get a high-throughput of PSCs with minimal efficiency loss.

Scaling up the charge-transport layer

Scaling up the charge-transport layer is also necessary for the scalability of PSCs. Common electron transport layer (ETL) in n-i-p PSCs are TiO2, SnO2 and ZnO. Currently, to make TiO2 layer deposition be compatible with flexible polymer substrate, low-temperature techniques, such as atomic layer deposition, molecular layer deposition, hydrothermal reaction, and electrodeposition, are developed to deposit compact TiO2 layer in large area. Same methods also apply to SnO2 deposition. As for hole transport layer (HTL), instead of commonly used PEDOT:PSS, NiOx is used as an alternative due to the water absorption of PEDOT, which can be deposited through room-temperature solution processing. CuSCN and NiO are alternative HTL materials which can be deposited by spray coating, blade coating, and electrodeposition, which are potentially scalable. Researchers also report a molecular doping method for scalable blading to make HTL-free PSCs.

Scaling up the back electrode

Evaporation deposition of back electrode is mature and scalable but it requires vacuum. Vacuum-free deposition of back electrode is important for full solution processibility of PSCs. Silver electrodes can be screen-printed, and silver nanowire network can be spray-coated as back electrode. Carbon is also a potential candidate as scalable PSCs electrode, such as graphite, carbon nanotubes, and graphene.

Toxicity

Toxicity issues associated with the Pb content in perovskite solar cells strains the public perception and acceptance of the technology. The health and environmental impact of toxic heavy metals has been much debated in the case of CdTe solar cells, whose efficiency became industrially relevant in the 1990s. Although, CdTe is a thermally and chemically very stable compound with a low solubility product, Ksp, of 10−34 and, accordingly, its toxicity was revealed to be extremely low, rigorous industrial hygiene programmes and recycling commitment programmes have been implemented. In contrast to CdTe, hybrid perovskites are very unstable and easily degrade to rather soluble compounds of Pb or Sn with KSP=4.4×10−9, which significantly increases their potential bioavailability and hazard for human health, as confirmed by recent toxicological studies. Although the 50 % lethal dose of lead [LD50(Pb)] is less than 5 mg per kg of body weight, health issues arise at much lower exposure levels. Young children absorb 4–5 times as much lead as adults and are most susceptible to the adverse effects of lead. In 2003, a maximum blood Pb level (BLL) of 5 μg/dL was imposed by the World Health Organization, which corresponds to the amount of Pb contained in only 5x5 mm2 of the perovskite solar module. Furthermore, the BLL of 5 μg/dL was revoked in 2010 after the discovery of decreased intelligence and behavioral difficulties in children exposed to even lower values.

Efforts in Reducing Lead Toxicity

Replacing Lead in Perovskites

Various studies have been performed to analyze promising alternatives to lead perovskite for use in PSCs. Good candidates for replacement, which ideally have low toxicity, narrow direct bandgaps, high optical absorption coefficients, high carrier mobility, and good charge transport properties, include Tin/Germanium-halide perovskites, double perovskites, and Bismuth/Antimony-halides with perovskite-like structures.

Research done on Tin halide-based PSCs show that they have a lower power conversion efficiency (PCE), with those fabricated experimentally achieving a PCE of 9.6%. This relatively low PCE is in part due to the oxidation of Sn2+ to Sn4+, which will act as a p-type dopant in the structure and result in higher dark carrier concentration and increased carrier recombination rates. Gemanium halide perovskites have proven similarly unsuccessful due to low efficiencies and issues with oxidising tendencies, with one experimental solar cells displaying a PCE of only 0.11%. Higher PCEs have been reported from some Germanium Tin alloy-based Perovskites, however, with an all-inorganic CsSn0.5Ge0.5I3 film having a reported PCE of 7.11%. In addition to this higher efficiency, the Germanium Tin alloy Perovskites have also been found to have high photostability.

Apart from the Tin and Germanium based perovskites, there has also been research on the viability of double-perovskites with the formula of A2M+M3+X6. While these double-perovskites have a favorable bandgap of approximately 2 eV and exhibit good stability, several issues including high electron/hole effective masses and the presence of indirect bandgaps result in lowered carrier mobility and charge transport. Research exploring the viability of Bismuth/Antimony halides in replacing lead perovskites has also been done, particularly with Cs3Sb2I9 and Cs3Bi2I9, which also have bandgaps of approximately 2 eV. Experimental results have also shown that, while Antimony and Bismuth halide-based PSCs have good stability, their low carrier mobilities and poor charge transport properties restrict their viability in replacing lead-based perovskites.

Encapsulation to Reduce Lead Leakage

Recent research into the usage of encapsulation as a method for reducing lead leakage has been conducted, particularly focusing on the utilization of self-healing polymers. Research has been done on two promising polymers, Surlyn and a thermal crosslinking epoxy-resin, diglycidyl ether bisphenol A:n-octylamine:m-xylylenediamine = 4:2:1. Experiments showed a substantial reduction in lead leakage from PSCs using these self-healing polymers under simulated sunny weather conditions and after simulated hail damage had cracked the outer glass encapsulation. Notably, the epoxy-resin encapsulation was able to reduce lead leakage by a factor of 375 times when heated by simulated sunlight.

Coatings to Adsorb Lead Leakage

Chemically lead-binding coatings have also been employed experimentally to reduce lead leakage from PSCs. In particular, Cation Exchange Resins (CERs) and P,P′-di(2-ethylhexyl)methanediphosphonic acid (DMDP) have been employed experimentally in this effort. Both coatings work similarly, chemically sequestering lead that might leak from a PSC module after weather damage occurs. Research into CERs has shown that, through diffusion-controlled processes, Pb2+ lead is effectively adsorbed and bonded onto the surface of CERs, even in the presence of competing divalent ions such as Mg2+ and Ca2+ that might also occupy binding sites on the CER surface.

To test the efficacy of CER-based coatings in adsorbing lead in practical conditions, researchers dripped slightly acidic water, meant to simulate rainwater, onto a PSC module cracked by simulated hail damage. Researchers found that by applying a CER coating onto the copper electrodes of damaged PSC modules, lead leakage was reduced by 84%. When the CER was integrated into a carbon-based electrode paste applied to PSC and on the top of the encapsulating glass, the lead leakage decreased by 98%. A similar test was also performed on a PSC module with DMDP coated on both the top and bottom of the module to study the efficacy of DMDP in reducing lead leakage. In this test, the module was cracked by simulated hail damage, and placed in a solution of acidic water containing aqueous Ca2+ ions, meant to simulate acidic rain with low levels of aqueous Calcium present. The lead concentration of acidic water was tracked, and researchers found that the lead sequestration efficiency of the DMDP coating at room temperature 96.1%.

Physics

An important characteristic of the most commonly used perovskite system, the methylammonium lead halides, is a bandgap controllable by the halide content. The materials also display a diffusion length for both holes and electrons of over one micron. The long diffusion length means that these materials can function effectively in a thin-film architecture, and that charges can be transported in the perovskite itself over long distances. It has recently been reported that charges in the perovskite material are predominantly present as free electrons and holes, rather than as bound excitons, since the exciton binding energy is low enough to enable charge separation at room temperature.

Efficiency limits

Perovskite solar cell bandgaps are tunable and can be optimised for the solar spectrum by altering the halide content in the film (i.e., by mixing I and Br). The Shockley–Queisser limit radiative efficiency limit, also known as the detailed balance limit, is about 31% under an AM1.5G solar spectrum at 1000 W/m2, for a Perovskite bandgap of 1.55 eV. This is slightly smaller than the radiative limit of gallium arsenide of bandgap 1.42 eV which can reach a radiative efficiency of 33%.

Values of the detailed balance limit are available in tabulated form and a MATLAB program for implementing the detailed balance model has been written.

In the meantime, the drift-diffusion model has found to successfully predict the efficiency limit of perovskite solar cells, which enable us to understand the device physics in-depth, especially the radiative recombination limit and selective contact on device performance. There are two prerequisites for predicting and approaching the perovskite efficiency limit. First, the intrinsic radiative recombination needs to be corrected after adopting optical designs which will significantly affect the open-circuit voltage at its Shockley–Queisser limit. Second, the contact characteristics of the electrodes need to be carefully engineered to eliminate the charge accumulation and surface recombination at the electrodes. With the two procedures, the accurate prediction of efficiency limit and precise evaluation of efficiency degradation for perovskite solar cells are attainable by the drift-diffusion model.

Along with analytical calculations, there have been many first principle studies to find the characteristics of the perovskite material numerically. These include but are not limited to bandgap, effective mass, and defect levels for different perovskite materials. Also there have some efforts to cast light on the device mechanism based on simulations where Agrawal et al. suggests a modeling framework, presents analysis of near ideal efficiency, and talks about the importance of interface of perovskite and hole/electron transport layers. However, Sun et al. tries to come up with a compact model for perovskite different structures based on experimental transport data.

Architectures

Schematic of a sensitized perovskite solar cell in which the active layer consist of a layer of mesoporous TiO2 which is coated with the perovskite absorber. The active layer is contacted with an n-type material for electron extraction and a p-type material for hole extraction. b) Schematic of a thin-film perovskite solar cell. In this architecture in which just a flat layer of perovskite is sandwiched between two selective contacts. c) Charge generation and extraction in the sensitized architecture. After light absorption in the perovskite absorber the photogenerated electron is injected into the mesoporous TiO2 through which it is extracted. The concomitantly generated hole is transferred to the p-type material. d) Charge generation and extraction in the thin-film architecture. After light absorption both charge generation as well as charge extraction occurs in the perovskite layer.

Perovskite solar cells function efficiently in a number of somewhat different architectures depending either on the role of the perovskite material in the device, or the nature of the top and bottom electrode. Devices in which positive charges are extracted by the transparent bottom electrode (cathode), can predominantly be divided into 'sensitized', where the perovskite functions mainly as a light absorber, and charge transport occurs in other materials, or 'thin-film', where most electron or hole transport occurs in the bulk of the perovskite itself. Similar to the sensitization in dye-sensitized solar cells, the perovskite material is coated onto a charge-conducting mesoporous scaffold – most commonly TiO2 – as light-absorber. The photogenerated electrons are transferred from the perovskite layer to the mesoporous sensitized layer through which they are transported to the electrode and extracted into the circuit. The thin film solar cell architecture is based on the finding that perovskite materials can also act as highly efficient, ambipolar charge-conductor.

After light absorption and the subsequent charge-generation, both negative and positive charge carrier are transported through the perovskite to charge selective contacts. Perovskite solar cells emerged from the field of dye-sensitized solar cells, so the sensitized architecture was that initially used, but over time it has become apparent that they function well, if not ultimately better, in a thin-film architecture. More recently, some researchers also successfully demonstrated the possibility of fabricating flexible devices with perovskites, which makes it more promising for flexible energy demand. Certainly, the aspect of UV-induced degradation in the sensitized architecture may be detrimental for the important aspect of long-term stability.

There is another different class of architectures, in which the transparent electrode at the bottom acts as cathode by collecting the photogenerated p-type charge carriers.

History

Perovskite materials have been well known for many years, but the first incorporation into a solar cell was reported by Tsutomu Miyasaka et al. in 2009. This was based on a dye-sensitized solar cell architecture, and generated only 3.8% power conversion efficiency (PCE) with a thin layer of perovskite on mesoporous TiO2 as electron-collector. Moreover, because a liquid corrosive electrolyte was used, the cell was only stable for a few minutes. Park et al. improved upon this in 2011, using the same dye-sensitized concept, achieving 6.5% PCE.

A breakthrough came in 2012, when Mike Lee and Henry Snaith from the University of Oxford realised that the perovskite was stable if contacted with a solid-state hole transporter such as spiro-OMeTAD and did not require the mesoporous TiO2 layer in order to transport electrons. They showed that efficiencies of almost 10% were achievable using the 'sensitized' TiO2 architecture with the solid-state hole transporter, but higher efficiencies, above 10%, were attained by replacing it with an inert scaffold. Further experiments in replacing the mesoporous TiO2 with Al2O3 resulted in increased open-circuit voltage and a relative improvement in efficiency of 3–5% more than those with TiO2 scaffolds. This led to the hypothesis that a scaffold is not needed for electron extraction, which was later proved correct. This realisation was then closely followed by a demonstration that the perovskite itself could also transport holes, as well as electrons. A thin-film perovskite solar cell, with no mesoporous scaffold, of > 10% efficiency was achieved.

In 2013 both the planar and sensitized architectures saw a number of developments. Burschka et al. demonstrated a deposition technique for the sensitized architecture exceeding 15% efficiency by a two-step solution processing, At a similar time Olga Malinkiewicz et al, and Liu et al. showed that it was possible to fabricate planar solar cells by thermal co-evaporation, achieving more than 12% and 15% efficiency in a p-i-n and an n-i-p architecture respectively. Docampo et al. also showed that it was possible to fabricate perovskite solar cells in the typical 'organic solar cell' architecture, an 'inverted' configuration with the hole transporter below and the electron collector above the perovskite planar film.

A range of new deposition techniques and even higher efficiencies were reported in 2014. A reverse-scan efficiency of 19.3% was claimed by Yang Yang at UCLA using the planar thin-film architecture. In November 2014, a device by researchers from KRICT achieved a record with the certification of a non-stabilized efficiency of 20.1%.

In December 2015, a new record efficiency of 21.0% was achieved by researchers at EPFL.

As of March 2016, researchers from KRICT and UNIST hold the highest certified record for a single-junction perovskite solar cell with 22.1%.

In 2018, a new record was set by researchers at the Chinese Academy of Sciences with a certified efficiency of 23.3%.

June 2018 Oxford Photovoltaics 1 cm² perovskite-silicon tandem solar cell has achieved a 27.3% conversion efficiency, certified by the Fraunhofer Institute for Solar Energy Systems ISE. This exceeds the 26.7% efficiency world record for a single-junction silicon solar cell.

In September 2019, a new efficiency record of 20.3% with a module of 11.2cm². This module was developed by the Apolo project consortium at CEA laboratories. The module is composed of 8 cells in series combining coating deposition techniques and laser patterning. The project has the objective to reach module cost below 0.40€/Wp (Watt peak).

Stability

One big challenge for perovskite solar cells (PSCs) is the aspect of short-term and long-term stability. The instability of PSCs is mainly related to environmental influence (moisture and oxygen), thermal stress and intrinsic stability of methylammonium-based perovskite, and formamidinium-based perovskite, heating under applied voltage, photo influence (ultraviolet light) (visible light) and mechanical fragility. Several studies about PSCs stability have been performed and some elements have been proven to be important to the PSCs stability. However, there is no standard "operational" stability protocol for PSCs. But a method to quantify the intrinsic chemical stability of hybrid halide perovskites has been recently proposed.

The water-solubility of the organic constituent of the absorber material make devices highly prone to rapid degradation in moist environments. The degradation which is caused by moisture can be reduced by optimizing the constituent materials, the architecture of the cell, the interfaces and the environment conditions during the fabrication steps. Encapsulating the perovskite absorber with a composite of carbon nanotubes and an inert polymer matrix can prevent the immediate degradation of the material by moist air at elevated temperatures. However, no long term studies and comprehensive encapsulation techniques have yet been demonstrated for perovskite solar cells. Devices with a mesoporous TiO2 layer sensitized with the perovskite absorber, are also UV-unstable, due to the interaction between photogenerated holes inside the TiO2 and oxygen radicals on the surface of TiO2.

The measured ultra low thermal conductivity of 0.5 W/(Km) at room temperature in CH3NH3PbI3 can prevent fast propagation of the light deposited heat, and keep the cell resistive on thermal stresses that can reduce its life time. The PbI2 residue in perovskite film has been experimentally demonstrated to have a negative effect on the long-term stability of devices. The stabilization problem is claimed to be solved by replacing the organic transport layer with a metal oxide layer, allowing the cell to retain 90% capacity after 60 days. Besides, the two instabilities issues can be solved by using multifunctional fluorinated photopolymer coatings that confer luminescent and easy-cleaning features on the front side of the devices, while concurrently forming a strongly hydrophobic barrier toward environmental moisture on the back contact side. The front coating can prevent the UV light of the whole incident solar spectrum from negatively interacting with the PSC stack by converting it into visible light, and the back layer can prevent water from permeation within the solar cell stack. The resulting devices demonstrated excellent stability in terms of power conversion efficiencies during a 180-day aging test in the lab and a real outdoor condition test for more than 3 months.

In July 2015, major hurdles were that the largest perovskite solar cell was only the size of a fingernail and that they degraded quickly in moist environments. However, researchers from EPFL published in June 2017, a work successfully demonstrating large scale perovskite solar modules with no observed degradation over one year (short circuit conditions). Now, together with other organizations, the research team aims to develop a fully printable perovskite solar cell with 22% efficiency and with 90% of performance after ageing tests.

Early in 2019, the longest stability test reported to date showed a steady power output during at least 4000 h of continuous operation at Maximum power point tracking (MPPT) under 1 sun illumination from a xenon lamp based solar simulator without UV light filtering. Remarkably, the light harvester used during the stability test is classical methylammonium (MA) based perovskite, MAPbI3, but devices are built up with neither organic based selective layer nor metal back contact. Under these conditions, only thermal stress was found to be the major factor contributing to the loss of operational stability in encapsulated devices.

The intrinsic fragility of the perovskite material requires extrinsic reinforcement to shield this crucial layer from mechanical stresses. Insertion of mechanically reinforcing scaffolds directly into the active layers of perovskite solar cells resulted in the compound solar cell formed exhibiting a 30-fold increase in fracture resistance, repositioning the fracture properties of perovskite solar cells into the same domain as conventional c-Si, CIGS and CdTe solar cells. Several approaches have been developed to improve perovskite solar cell stability. For instance, in 2021 researchers reported that the stability and long-term reliability of perovskite solar cells was improved with a new kind of "molecular glue".

Recycling

Another core problem in the development, production and use of perovskite solar cells is their recyclability. Designs and processes or protocols for efficient recycling would reduce negative environmental impacts, exploitation of critical materials, health impacts and energy requirements beyond what can be achieved with increases in device lifetime. In a review, scientists concluded that "recycle and recovery technologies of perovskite solar cells should be researched and developed proactively". Some aspects of recyclability and recycling-rates depend on the design of the disseminated products. Scientific research and development may not get facilitated to design for recyclability – instead most scientists mainly "look at performance" – "energy conversion efficiency and stability" and often "neglect designing for recycling".

Hysteretic current-voltage behavior

Another major challenge for perovskite solar cells is the observation that current-voltage scans yield ambiguous efficiency values. The power conversion efficiency of a solar cell is usually determined by characterizing its current-voltage (IV) behavior under simulated solar illumination. In contrast to other solar cells, however, it has been observed that the IV-curves of perovskite solar cells show a hysteretic behavior: depending on scanning conditions – such as scan direction, scan speed, light soaking, biasing – there is a discrepancy between the scan from forward-bias to short-circuit (FB-SC) and the scan from short-circuit to forward bias (SC-FB). Various causes have been proposed such as ion movement, polarization, ferroelectric effects, filling of trap states, however, the exact origin for the hysteretic behavior is yet to be determined. But it appears that determining the solar cell efficiency from IV-curves risks producing inflated values if the scanning parameters exceed the time-scale which the perovskite system requires in order to reach an electronic steady-state. Two possible solutions have been proposed: Unger et al. show that extremely slow voltage-scans allow the system to settle into steady-state conditions at every measurement point which thus eliminates any discrepancy between the FB-SC and the SC-FB scan.

Henry Snaith et al. have proposed 'stabilized power output' as a metric for the efficiency of a solar cell. This value is determined by holding the tested device at a constant voltage around the maximum power-point (where the product of voltage and photocurrent reaches its maximum value) and track the power-output until it reaches a constant value. Both methods have been demonstrated to yield lower efficiency values when compared to efficiencies determined by fast IV-scans. However, initial studies have been published that show that surface passivation of the perovskite absorber is an avenue with which efficiency values can be stabilized very close to fast-scan efficiencies. No obvious hysteresis of photocurrent was observed by changing the sweep rates or the direction in devices or the sweep rates. This indicates that the origin of hysteresis in photocurrent is more likely due to the trap formation in some non optimized films and device fabrication processes. The ultimate way to examine the efficiency of a solar cell device is to measure its power output at the load point. If there is large density of traps in the devices or photocurrent hysteresis for other reasons, the photocurrent would rise slowly upon turning on illumination This suggests that the interfaces might play a crucial role with regards to the hysteretic IV behavior since the major difference of the inverted architecture to the regular architectures is that an organic n-type contact is used instead of a metal oxide.

The observation of hysteretic current-voltage characteristics has thus far been largely underreported. Only a small fraction of publications acknowledge the hysteretic behavior of the described devices, even fewer articles show slow non-hysteretic IV curves or stabilized power outputs. Reported efficiencies, based on rapid IV-scans, have to be considered fairly unreliable and make it currently difficult to genuinely assess the progress of the field.

The ambiguity in determining the solar cell efficiency from current-voltage characteristics due to the observed hysteresis has also affected the certification process done by accredited laboratories such as NREL. The record efficiency of 20.1% for perovskite solar cells accepted as certified value by NREL in November 2014, has been classified as 'not stabilized'. To be able to compare results from different institution, it is necessary to agree on a reliable measurement protocol, as it has been proposed by  including the corresponding Matlab code which can be found at GitHub.

Perovskites for tandem applications

A perovskite cell combined with bottom cell such as Si or copper indium gallium selenide (CIGS) as a tandem design can suppress individual cell bottlenecks and take advantage of the complementary characteristics to enhance the efficiency. This type of cells have higher efficiency potential, and therefore attracted recently a large attention from academic researchers.

4-terminal tandems

Using a four terminal configuration in which the two sub-cells are electrically isolated, Bailie et al. obtained a 17% and 18.6% efficient tandem cell with mc-Si (η ~ 11%) and copper indium gallium selenide (CIGS, η ~ 17%) bottom cells, respectively. A 13.4% efficient tandem cell with a highly efficient a-Si:H/c-Si heterojunction bottom cell using the same configuration was obtained. The application of TCO-based transparent electrodes to perovskite cells allowed to fabricate near-infrared transparent devices with improved efficiency and lower parasitic absorption losses. The application of these cells in 4-terminal tandems allowed improved efficiencies up to 26.7% when using a silicon bottom cell and up to 23.9% with a CIGS bottom cell. In 2020, KAUST-University of Toronto teams reported 28.2% efficient four terminal perovskite/silicon tandems solar cells. To achieve this results, the team used Zr-doped In2O3 transparent electrodes on semitransparent perovskite top cells, which was previously introduced by Aydin et al., and improved the near infrared response of the silicon bottom cells by utilizing broadband transparent H-doped In2O3 electrodes. Also, the team enhanced the electron-diffusion length (up to 2.3 µm) thanks to Lewis base passivation via urea. The record efficiency for perovskite/silicon tandems currently stands at 28.2 %

2-terminal tandems

Mailoa et al. started the efficiency race for monolithic 2-terminal tandems using an homojunction c-Si bottom cell and demonstrate a 13.7% cell, largely limited by parasitic absorption losses. Then, Albrecht et al. developed a low-temperature processed perovskite cells using a SnO2 electron transport layer. This allowed the use of silicon heterojunction solar cells as bottom cell and tandem efficiencies up to 18.1%. Werner et al. then improved this performance replacing the SnO2 layer with PCBM and introducing a sequential hybrid deposition method for the perovskite absorber, leading to a tandem cell with 21.2% efficiency. Important parasitic absorption losses due to the use of Spiro-OMeTAD were still limiting the overall performance. An important change was demonstrated by Bush et al., who inverted the polarity of the top cell (n-i-p to p-i-n). They used a bilayer of SnO2 and zinc tin oxide (ZTO) processed by ALD to work as a sputtering buffer layer, which enables the following deposition of a transparent top indium tin oxide (ITO) electrode. This change helped to improve the environmental and thermal stability of the perovskite cell and was crucial to further improve the perovskite/silicon tandem performance to 23.6%.

In the continuity, using a p-i-n perovskite top cell, Sahli et al. demonstrated in June 2018 a fully textured monolithic tandem cell with 25.2% efficiency, independently certified by Fraunhofer ISE CalLab. This improved efficiency can largely be attributed to the massively reduced reflection losses (below 2% in the range 360 nm-1000 nm, excluding metallization) and reduced parasitic absorption losses, leading to certified short-circuit currents of 19.5 mA/cm2. Also in June 2018 the company Oxford Photovoltaics presented a cell with 27.3% efficiency. In March 2020, KAUST-University of Toronto teams reported tandem devices with spin-cast perovskite films on fully textured textured bottom cells with 25.7% in Science Magazine. In the present, the research teams show effort to utilize more solution-based scalable techniques on textured bottom cells. Accordingly blade-coated perovskite based tandems were reported by a collaborative team of University of North Carolina and Arizona State University. Following this, in August 2020 KAUST team demonstrated first slot-die coated perovskite based tandems, which was important step for accelerated processing of tandems. In September 2020, Aydin et al. showed the highest certified short-circuit currents of 19.8 mA/cm2 on fully textured silicon bottom cells. Also, Aydin et al. showed the first outdoor performance results for perovskite/silicon tandem solar cells, which was an important hurdle for the reliability tests of such devices. The record efficiency for perovskite/silicon tandems currently stands at 29.15% as of January 2020.

Theoretical modelling

There have been some efforts to predict the theoretical limits for these traditional tandem designs using a perovskite cell as top cell on a c-Si or a-Si/c-Si heterojunction bottom cell. To show that the output power can be even further enhanced, bifacial structures were studied as well. It was concluded that extra output power can be extracted from the bifacial structure as compared to a bifacial HIT cell when the albedo reflection takes on values between 10 and 40%, which are realistic. It has been pointed out that the so-called impact ionization process can take place in strongly correlated insulators such as some oxide perovskites, which can lead to multiple carrier generation. Also, Aydin et al. revealed that, the temperature should be considered while calculating the theoretical limits since these devices reaches the temperature of almost 60 °C under real operations. This case is special to perovskite/silicon tandems since the temperature dependence of both the silicon and perovskite bandgaps—which follow opposing trends—shifts the devices away from current matching for two-terminal tandems that are optimized at standard test conditions.

Up-scaling

In May 2016, IMEC and its partner Solliance announced a tandem structure with a semi-transparent perovskite cell stacked on top of a back-contacted silicon cell. A combined power conversion efficiency of 20.2% was claimed, with the potential to exceed 30%.

All-perovskite tandems

In 2016, the development of efficient low-bandgap (1.2 - 1.3eV) perovskite materials and the fabrication of efficient devices based on these enabled a new concept: all-perovskite tandem solar cells, where two perovskite compounds with different bandgaps are stacked on top of each other. The first two- and four-terminal devices with this architecture reported in the literature achieved efficiencies of 17% and 20.3%. All-perovskite tandem cells offer the prospect of being the first fully solution-processable architecture that has a clear route to exceeding not only the efficiencies of silicon, but also GaAs and other expensive III-V semiconductor solar cells.

In 2017, Dewei Zhao et al. fabricated low-bandgap (~1.25 eV) mixed Sn-Pb perovskite solar cells (PVSCs) with the thickness of 620 nm, which enables larger grains and higher crystallinity to extend the carrier lifetimes to more than 250 ns, reaching a maximum power conversion efficiency (PCE) of 17.6%. Furthermore, this low-bandgap PVSC reached an external quantum efficiency (EQE) of more than 70% in the wavelength range of 700–900 nm, the essential infrared spectral region where sunlight transmitted to bottom cell. They also combined the bottom cell with a ~1.58 eV bandgap perovskite top cell to create an all-perovskite tandem solar cell with four terminals, obtaining a steady-state PCE of 21.0%, suggesting the possibility of fabricating high-efficiency all-perovskite tandem solar cells.

A study in 2020 shows that all-perovskite tandems have much lower carbon footprints than silicon-pervoskite tandems.

Shockley–Queisser limit

From Wikipedia, the free encyclopedia
 
The Shockley–Queisser limit for the efficiency of a solar cell, without concentration of solar radiation. The curve is wiggly because of absorption bands in the atmosphere. In the original paper, the solar spectrum was approximated by a smooth curve, the 6000K blackbody spectrum. As a result, the efficiency graph was smooth and the values were slightly different.

In physics, the Shockley–Queisser limit (also known as the detailed balance limit, Shockley Queisser Efficiency Limit or SQ Limit, or in physical terms the radiative efficiency limit) is the maximum theoretical efficiency of a solar cell using a single p-n junction to collect power from the cell where the only loss mechanism is radiative recombination in the solar cell. It was first calculated by William Shockley and Hans-Joachim Queisser at Shockley Semiconductor in 1961, giving a maximum efficiency of 30% at 1.1 eV. This first calculation used the 6000K black-body spectrum as an approximation to the solar spectrum. Subsequent calculations have used measured global solar spectra (AM1.5G) and included a back surface mirror which increases the maximum efficiency to 33.7% for a solar cell with a bandgap of 1.34 eV. The limit is one of the most fundamental to solar energy production with photovoltaic cells, and is considered to be one of the most important contributions in the field.

The limit is that the maximum solar conversion efficiency is around 33.7% for a single p-n junction photovoltaic cell, assuming typical sunlight conditions (unconcentrated, AM 1.5 solar spectrum), and subject to other caveats and assumptions discussed below. This maximum occurs at a band gap of 1.34 eV. That is, of all the power contained in sunlight (about 1000 W/m2) falling on an ideal solar cell, only 33.7% of that could ever be turned into electricity (337 W/m2). The most popular solar cell material, silicon, has a less favorable band gap of 1.1 eV, resulting in a maximum efficiency of about 32%. Modern commercial mono-crystalline solar cells produce about 24% conversion efficiency, the losses due largely to practical concerns like reflection off the front of the cell and light blockage from the thin wires on the cell surface.

The Shockley–Queisser limit only applies to conventional solar cells with a single p-n junction; solar cells with multiple layers can (and do) outperform this limit, and so can solar thermal and certain other solar energy systems. In the extreme limit, for a multi-junction solar cell with an infinite number of layers, the corresponding limit is 68.7% for normal sunlight, or 86.8% using concentrated sunlight. (See Solar cell efficiency.)

Background

The Shockley–Queisser limit, zoomed in near the region of peak efficiency.

In a traditional solid-state semiconductor such as silicon, a solar cell is made from two doped crystals, one an n-type semiconductor, which has extra free electrons, and the other a p-type semiconductor, which is lacking free electrons, referred to as "holes." When initially placed in contact with each other, some of the electrons in the n-type portion will flow into the p-type to "fill in" the missing electrons. Eventually enough 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 on each side of the interface. In silicon, this transfer of electrons produces a potential barrier of about 0.6 V to 0.7 V.

When the material is placed in the sun, photons from the sunlight can be absorbed in the p-type side of the semiconductor, causing electrons in the valence band to be promoted in energy to the conduction band. This process is known as photoexcitation. As the name implies, electrons in the conduction band are free to move about the semiconductor. When a load is placed across the cell as a whole, these electrons will flow from the p-type side into the n-type side, lose energy while moving through the external circuit, and then go back into the p-type material where they can re-combine with the valence-band holes they left behind. In this way, sunlight creates an electric current.

The limit

The Shockley–Queisser limit is calculated by examining the amount of electrical energy that is extracted per photon of incoming sunlight. There are several considerations:

Blackbody radiation

Any material, that is not at absolute zero (0 Kelvin), emits electromagnetic radiation through the black-body radiation effect. In a cell at room temperature, this represents approximately 7% of all the energy falling on the cell.

Any energy lost in a cell is turned into heat, so any inefficiency in the cell increases the cell temperature when it is placed in sunlight. As the temperature of the cell increases, the outgoing radiation and heat loss through conduction and convection also increase, until an equilibrium is reached. In practice, this equilibrium is normally reached at temperatures as high as 360 Kelvin, and consequently, cells normally operate at lower efficiencies than their room-temperature rating. Module datasheets normally list this temperature dependency as TNOCT (NOCT - Nominal Operating Cell Temperature).

For a "blackbody" at normal temperatures, a very small part of this radiation (the number per unit time and per unit area given by Qc, "c" for "cell") is photons having energy greater than the band gap (wavelength less than about 1.1 microns for silicon), and part of these photons (Shockley and Queisser use the factor tc) are generated by recombination of electrons and holes, which decreases the amount of current that could be generated otherwise. This is a very small effect, but Shockley and Queisser assume that the total rate of recombination (see below) when the voltage across the cell is zero (short circuit or no light) is proportional to the blackbody radiation Qc. This rate of recombination plays a negative role in the efficiency. Shockley and Queisser calculate Qc to be 1700 photons per second per square centimetre for silicon at 300K.

Recombination

Black curve: The limit for open-circuit voltage in the Shockley–Queisser model (i.e., voltage at zero current). The red dotted line shows that this voltage is always below the bandgap. This voltage is limited by recombination.

Absorption of a photon creates an electron-hole pair, which could potentially contribute to the current. However, the reverse process must also be possible, according to the principle of detailed balance: an electron and a hole can meet and recombine, emitting a photon. This process reduces the efficiency of the cell. Other recombination processes may also exist (see "Other considerations" below), but this one is absolutely required.

In the Shockley–Queisser model, the recombination rate depends on the voltage across the cell but is the same whether or not there is light falling on the cell. A factor fc gives the ratio of recombination that produces radiation to total recombination, so the rate of recombination per unit area when V = 0 is 2tcQc/fc and thus depends on Qc, the flux of blackbody photons above the band-gap energy. The factor of 2 was included on the assumption that radiation emitted by the cell goes in both directions. (This is actually debatable if a reflective surface is used on the shady side.) When the voltage is non-zero, the concentrations of charge carriers (electrons and holes) change, and according to the authors the rate of recombination changes by a factor of exp(V/Vc), where Vc is the voltage equivalent of the temperature of the cell, or "thermal voltage", namely

(q being the charge of an electron). Thus the rate of recombination, in this model, is proportional to exp(V/Vc) times the blackbody radiation above the band-gap energy:

(This is actually an approximation, correct so long as the cell is thick enough to act as a black body, to the more accurate expression

The difference in maximum theoretical efficiency however is negligibly small, except for tiny bandgaps below 200meV.)

The rate of generation of electron-hole pairs not due to incoming sunlight stays the same, so recombination minus spontaneous generation is

where

(Shockley and Queisser take fc to be a constant, although they admit that it may itself depend on voltage.)

The rate of generation of electron-hole pairs due to sunlight is

where is the number of photons above the band-gap energy falling on the cell per unit area, and ts is the fraction of these that generate an electron-hole pair. This rate of generation is called Ish because it is the "short circuit" current (per unit area). When there is a load, then V will not be zero and we have a current equal to the rate of generation of pairs due to the sunlight minus the difference between recombination and spontaneous generation:

The open-circuit voltage is therefore given (assuming fc does not depend on voltage) by

The product of the short-circuit current Ish and the open-circuit voltage Voc Shockley and Queisser call the "nominal power". It is not actually possible to get this amount of power out of the cell, but we can get close (see "Impedance matching" below).

The ratio of the open-circuit voltage to the band-gap voltage Shockley and Queisser call V. Under open-circuit conditions, we have

Asymptotically, this gives

or

where Vs is the voltage equivalent of the temperature of the sun. As the ratio Vc/Vs goes to zero, the open-circuit voltage goes to the band-gap voltage, and as it goes to one, the open-circuit voltage goes to zero. This is why the efficiency falls if the cell heats up. In fact this expression represents the thermodynamic upper limit of the amount of work that can be obtained from a heat source at the temperature of the sun and a heat sink at the temperature of the cell.

Spectrum losses

Since the act of moving an electron from the valence band to the conduction band requires energy, only photons with more than that amount of energy will produce an electron-hole pair. In silicon the conduction band is about 1.1 eV away from the valence band, this corresponds to infrared light with a wavelength of about 1.1 microns. In other words, photons of red, yellow and blue light and some near-infrared will contribute to power production, whereas radio waves, microwaves, and most infrared photons will not. This places an immediate limit on the amount of energy that can be extracted from the sun. Of the 1,000 W/m2 in AM1.5 sunlight, about 19% of that has less than 1.1 eV of energy, and will not produce power in a silicon cell.

Another important contributor to losses is that any energy above and beyond the bandgap energy is lost. While blue light has roughly twice the energy of red light, that energy is not captured by devices with a single p-n junction. The electron is ejected with higher energy when struck by a blue photon, but it loses this extra energy as it travels toward the p-n junction (the energy is converted into heat). This accounts for about 33% of the incident sunlight, meaning that, for silicon, from spectrum losses alone there is a theoretical conversion efficiency limit of about 48%, ignoring all other factors.

There is a trade-off in the selection of a bandgap. If the band gap is large, not as many photons create pairs, whereas if the band gap is small, the electron-hole pairs do not contain as much energy.

Shockley and Queisser call the efficiency factor associated with spectrum losses u, for "ultimate efficiency function". Shockley and Queisser calculated that the best band gap for sunlight happens to be 1.1 eV, the value for silicon, and gives a u of 44%. They used blackbody radiation of 6000K for sunlight, and found that the optimum band gap would then have an energy of 2.2 kTs. (At that value, 22% of the blackbody radiation energy would be below the band gap.) Using a more accurate spectrum may give a slightly different optimum. A blackbody at 6000 K puts out 7348 W per square centimetre, so a value for u of 44% and a value of 5.73×1018 photons per joule (corresponding to a band gap of 1.09 V, the value used by Shockley and Queisser) gives Qs equal to 1.85×1022 photons per second per square centimetre.

Impedance matching

If the resistance of the load is too high, the current will be very low, while if the load resistance is too low, the voltage drop across it will be very low. There is an optimal load resistance that will draw the most power from the solar cell at a given illumination level. Shockley and Queisser call the ratio of power extracted to IshVoc the impedance matching factor, m. (It is also called the fill factor.) The optimum depends on the shape of the I versus V curve. For very low illumination, the curve is more or less a diagonal line, and m will be 1/4. But for high illumination, m approaches 1. Shockley and Queisser give a graph showing m as a function of the ratio zoc of the open-circuit voltage to the thermal voltage Vc. According to the authors, this ratio is well approximated by ln(fQs/Qc), where f is the combination of factors fsfωts/(2tc), in which fω is the solid angle of the sun divided by π. The maximum value of f without light concentration (with reflectors for example) is just fω/2, or 1.09×10−5, according to the authors. Using the above-mentioned values of Qs and Qc, this gives a ratio of open-circuit voltage to thermal voltage of 32.4 (Voc equal to 77% of the band gap). The authors derive the equation

which can be solved to find zm, the ratio of optimal voltage to thermal voltage. For a zoc of 32.4, we find zm equal to 29.0. One can then use the formula

to find the impedance matching factor. For a zoc of 32.4, this comes to 86.5%.

All together

Considering the spectrum losses alone, a solar cell has a peak theoretical efficiency of 48% (or 44% according to Shockley and Queisser – their "ultimate efficiency factor"). Thus the spectrum losses represent the vast majority of lost power. Including the effects of recombination and the I versus V curve, the efficiency is described by the following equation:

with

where u, v, and m are respectively the ultimate efficiency factor, the ratio of open-circuit voltage Vop to band-gap voltage Vg, and the impedance matching factor (all discussed above), and Vc is the thermal voltage, and Vs is the voltage equivalent of the temperature of the Sun. Letting ts be 1, and using the values mentioned above of 44%, 77%, and 86.5% for the three factors gives about 29% overall efficiency. Shockley and Queisser say 30% in their abstract, but do not give a detailed calculation. A more recent reference gives, for a single-junction cell, a theoretical peak performance of about 33.7%, or about 337 W/m2 in AM1.5.

When the amount of sunlight is increased using reflectors or lenses, the factor fω (and therefore f) will be higher. This raises both v and m. Shockley and Queisser include a graph showing the overall efficiency as a function of band gap for various values of f. For a value of 1, the graph shows a maximum efficiency of just over 40%, getting close to the ultimate efficiency (by their calculation) of 44%.

Other considerations

Shockley and Queisser's work considered the most basic physics only; there are a number of other factors that further reduce the theoretical power.

Limited mobility

When an electron is ejected through photoexcitation, the atom it was formerly bound to is left with a net positive charge. Under normal conditions, the atom will pull off an electron from a surrounding atom in order to neutralize itself. That atom will then attempt to remove an electron from another atom, and so forth, producing an ionization chain reaction that moves through the cell. Since these can be viewed as the motion of a positive charge, it is useful to refer to them as "holes", a sort of virtual positive electron.

Like electrons, holes move around the material, and will be attracted towards a source of electrons. Normally these are provided through an electrode on the back surface of the cell. Meanwhile, the conduction-band electrons are moving forward towards the electrodes on the front surface. For a variety of reasons, holes in silicon move much more slowly than electrons. This means that during the finite time while the electron is moving forward towards the p-n junction, it may meet a slowly moving hole left behind by a previous photoexcitation. When this occurs, the electron recombines at that atom, and the energy is lost (normally through the emission of a photon of that energy, but there are a variety of possible processes).

Recombination places an upper limit on the rate of production; past a certain rate there are so many holes in motion that new electrons will never make it to the p-n junction. In silicon this reduces the theoretical performance under normal operating conditions by another 10% over and above the thermal losses noted above. Materials with higher electron (or hole) mobility can improve on silicon's performance; gallium arsenide (GaAs) cells gain about 5% in real-world examples due to this effect alone. In brighter light, when it is concentrated by mirrors or lenses for example, this effect is magnified. Normal silicon cells quickly saturate, while GaAs continue to improve at concentrations as high as 1500 times.

Non-radiative recombination

Recombination between electrons and holes is detrimental in a solar cell, so designers try to minimize it. However, radiative recombination—when an electron and hole recombine to create a photon that exits the cell into the air—is inevitable, because it is the time-reversed process of light absorption. Therefore, the Shockley–Queisser calculation takes radiative recombination into account; but it assumes (optimistically) that there is no other source of recombination. More realistic limits, which are lower than the Shockley–Queisser limit, can be calculated by taking into account other causes of recombination. These include recombination at defects and grain boundaries.

In crystalline silicon, even if there are no crystalline defects, there is still Auger recombination, which occurs much more often than radiative recombination. By taking this into account, the theoretical efficiency of crystalline silicon solar cells was calculated to be 29.4%.

Frequency-dependent absorption

The Ozdemir-Barone method considers two additional factors in calculating the solar efficiency limit, namely, the frequency dependence of the absorption and reflectance in certain materials. According to Shockley-Quiesser limit, solar cell efficiency of semiconductors depend on the band gap of the material. Here, it is assumed that optical absorption starts above the band gap of the material. However, due to finite temperature, optical excitations are possible below the optical gap. We can clearly see this from the tail of the imaginary dielectric function below the optical gap depending on temperature. Since imaginary dielectric functions is, even though low, non-zero below the optical gap, there is absorption of light below the optical gap. For thick enough materials this can cause significant absorption. In the Shockley-Quiesser limit, 100% light absorption is assumed above the band gap of the material. However, there are two problems with this assumption. First, there can be absorbance below the band gap of the material at finite temperatures. Secondly, reflectance of the material is non-zero, therefore absorbance cannot be 100% above the band gap. These two problems are solved in Ozdemir-Barone method.

Exceeding the limit

Breakdown of the causes for the Shockley–Queisser limit. The black height is energy that can be extracted as useful electrical power (the Shockley–Queisser efficiency limit); the pink height is energy of below-bandgap photons; the green height is energy lost when hot photogenerated electrons and holes relax to the band edges; the blue height is energy lost in the tradeoff between low radiative recombination versus high operating voltage. Designs that exceed the Shockley–Queisser limit work by overcoming one or more of these three loss processes.

It is important to note that the analysis of Shockley and Queisser was based on the following assumptions:

  1. One electron–hole pair excited per incoming photon
  2. Thermal relaxation of the electron–hole pair energy in excess of the band gap
  3. Illumination with non-concentrated sunlight

None of these assumptions is necessarily true, and a number of different approaches have been used to significantly surpass the basic limit.

Multijunction cells

The most widely explored path to higher efficiency solar cells has been multijunction photovoltaic cells, also known as "tandem cells". These cells use multiple p-n junctions, each one tuned to a particular frequency of the spectrum. This reduces the problem discussed above, that a material with a single given bandgap cannot absorb sunlight below the bandgap, and cannot take full advantage of sunlight far above the bandgap. In the most common design, a high-bandgap solar cell sits on top, absorbing high-energy, shorter-wavelength light, and transmitting the rest. Beneath it is a lower-bandgap solar cell which absorbs some of the lower-energy, longer-wavelength light. There may be yet another cell beneath that one, with as many as four layers in total.

The calculation of the fundamental efficiency limits of these multijunction cells works in a fashion similar to those for single-junction cells, with the caveat that some of the light will be converted to other frequencies and re-emitted within the structure. Using methods similar to the original Shockley–Queisser analysis with these considerations in mind produces similar results; a two-layer cell can reach 42% efficiency, three-layer cells 49%, and a theoretical infinity-layer cell 68% in non-concentrated sunlight.

The majority of tandem cells that have been produced to date use three layers, tuned to blue (on top), yellow (middle) and red (bottom). These cells require the use of semiconductors that can be tuned to specific frequencies, which has led to most of them being made of gallium arsenide (GaAs) compounds, often germanium for red, GaAs for yellow, and GaInP2 for blue. They are very expensive to produce, using techniques similar to microprocessor construction but with "chip" sizes on the scale of several centimeters. In cases where outright performance is the only consideration, these cells have become common; they are widely used in satellite applications for instance, where the power-to-weight ratio overwhelms practically every other consideration. They also can be used in concentrated photovoltaic applications (see below), where a relatively small solar cell can serve a large area.

Tandem cells are not restricted to high-performance applications; they are also used to make moderate-efficiency photovoltaics out of cheap but low-efficiency materials. One example is amorphous silicon solar cells, where triple-junction tandem cells are commercially available from Uni-Solar and other companies.

Light concentration

Sunlight can be concentrated with lenses or mirrors to much higher intensity. The sunlight intensity is a parameter in the Shockley–Queisser calculation, and with more concentration, the theoretical efficiency limit increases somewhat. If, however, the intense light heats up the cell, which often occurs in practice, the theoretical efficiency limit may go down all things considered.

In practice, the choice of whether or not to use light concentration is based primarily on other factors besides the small change in solar cell efficiency. These factors include the relative cost per area of solar cells versus focusing optics like lenses or mirrors, the cost of sunlight-tracking systems, the proportion of light successfully focused onto the solar cell, and so on.

A wide variety of optical systems can be used to concentrate sunlight, including ordinary lenses and curved mirrors, fresnel lenses, arrays of small flat mirrors, and luminescent solar concentrators. Another proposal suggests spreading out an array of microscopic solar cells on a surface, and focusing light onto them via microlens arrays, while yet another proposal suggests designing a semiconductor nanowire array in such a way that light is concentrated in the nanowires.

Intermediate band photovoltaics

There has been some work on producing mid-energy states within single crystal structures. These cells would combine some of the advantages of the multi-junction cell with the simplicity of existing silicon designs. A detailed limit calculation for these cells with infinite bands suggests a maximum efficiency of 77.2% To date, no commercial cell using this technique has been produced.

Photon upconversion

As discussed above, photons with energy below the bandgap are wasted in ordinary single-junction solar cells. One way to reduce this waste is to use photon upconversion, i.e. incorporating into the module a molecule or material that can absorb two or more below-bandgap photons and then emit one above-bandgap photon. Another possibility is to use two-photon absorption, but this can only work at extremely high light concentration.

Thermal photon upconversion

Thermal upconversion is based on the absorption of photons with low energies in the upconverter, which heats up and re-emits photons with higher energies. The upconversion efficiency can be improved by controlling the optical density of states of the absorber and also by tuning the angularly-selective emission characteristics. For example, a planar thermal upconverting platform can have a front surface that absorbs low-energy photons incident within a narrow angular range, and a back surface that efficiently emits only high-energy photons. A hybrid thermophotovoltaic platform exploiting thermal upconversion was theoretically predicted to demonstrate maximum conversion efficiency of 73% under illumination by non-concentrated sunlight. A detailed analysis of non-ideal hybrid platforms that allows for up to 15% of absorption/re-emission losses yielded limiting efficiency value of 45% for Si PV cells.

Hot electron capture

One of the main loss mechanisms is due to the loss of excess carrier energy above the bandgap. It should be no surprise that there has been a considerable amount of research into ways to capture the energy of the carriers before they can lose it in the crystal structure. One system under investigation for this is quantum dots.

Multiple exciton generation

A related concept is to use semiconductors that generate more than one excited electron per absorbed photon, instead of a single electron at the band edge. Quantum dots have been extensively investigated for this effect, and they have been shown to work for solar-relevant wavelengths in prototype solar cells.

Another, more straightforward way to utilise multiple exciton generation is a process called singlet fission (or singlet exciton fission) by which a singlet exciton is converted into two triplet excitons of lower energy. This allows for higher theoretical efficiencies when coupled to a low bandgap semiconductor and quantum efficiencies exceeding 100% have been reported.

Also in materials where the (excited) electrons interact strongly with the remaining electrons such as Mott insulators multiple excitons can be generated.

Fluorescent downconversion/downshifting

Another possibility for increased efficiency is to convert the frequency of light down towards the bandgap energy with a fluorescent material. In particular, to exceed the Shockley–Queisser limit, it is necessary for the fluorescent material to convert a single high-energy photon into several lower-energy ones (quantum efficiency > 1). For example, one photon with more than double the bandgap energy can become two photons above the bandgap energy. In practice, however, this conversion process tends to be relatively inefficient. If a very efficient system were found, such a material could be painted on the front surface of an otherwise standard cell, boosting its efficiency for little cost. In contrast, considerable progress has been made in the exploration of fluorescent downshifting, which converts high-energy light (e. g., UV light) to low-energy light (e. g., red light) with a quantum efficiency smaller than 1. The cell may be more sensitive to these lower-energy photons. Dyes, rare-earth phosphors and quantum dots are actively investigated for fluorescent downshifting. For example, silicon quantum dots enabled downshifting has led to the efficiency enhancement of the state-of-the-art silicon solar cells.

Thermophotovoltaic downconversion

Thermophotovoltaic cells are similar to phosphorescent systems, but use a plate to act as the downconvertor. Solar energy falling on the plate, typically black-painted metal, is re-emitted as lower-energy IR, which can then be captured in an IR cell. This relies on a practical IR cell being available, but the theoretical conversion efficiency can be calculated. For a converter with a bandgap of 0.92 eV, efficiency is limited to 54% with a single-junction cell, and 85% for concentrated light shining on ideal components with no optical losses and only radiative recombination.

Cryogenics

From Wikipedia, the free encyclopedia https://en.wikipedia.org/wiki/Cryogenics...