title: Particle in a box

text: The probability density for finding a particle with a given momentum is derived from the wavefunction as formula_48. As with position, the probability density for finding the particle at a given momentum depends upon its state, and is given by


title: Particle in a box

text: where, again, formula_35. The expectation value for the momentum is then calculated to be zero, and the variance in the momentum is calculated to be:


title: Particle in a box

text: The uncertainties in position and momentum (formula_52 and formula_53) are defined as being equal to the square root of their respective variances, so that:


title: Particle in a box

text: This product increases with increasing "n", having a minimum value for "n"=1. The value of this product for "n"=1 is about equal to 0.568 formula_4 which obeys the Heisenberg uncertainty principle, which states that the product will be greater than or equal to formula_56


title: Particle in a box

text: Another measure of uncertainty in position is the information entropy of the probability distribution "H":


title: Particle in a box

text: Another measure of uncertainty in momentum is the information entropy of the probability distribution "H":


title: Particle in a box

text: where "γ" is Euler's constant. The quantum mechanical entropic uncertainty principle states that for formula_60


title: Particle in a box

text: The energy levels increase with formula_65, meaning that high energy levels are separated from each other by a greater amount than low energy levels are. The lowest possible energy for the particle (its "zero-point energy") is found in state 1, which is given by


title: Particle in a box

text: The particle, therefore, always has a positive energy. This contrasts with classical systems, where the particle can have zero energy by resting motionlessly. This can be explained in terms of the uncertainty principle, which states that the product of the uncertainties in the position and momentum of a particle is limited by


title: Particle in a box

text: It can be shown that the uncertainty in the position of the particle is proportional to the width of the box. Thus, the uncertainty in momentum is roughly inversely proportional to the width of the box. The kinetic energy of a particle is given by formula_68, and hence the minimum kinetic energy of the particle in a box is inversely proportional to the mass and the square of the well width, in qualitative agreement with the calculation above.


title: Particle in a box

text: If a particle is trapped in a two-dimensional box, it may freely move in the formula_69 and formula_70-directions, between barriers separated by lengths formula_71 and formula_72 respectively. For a centered box, the position wave function may be written including the length of the box as formula_73. Using a similar approach to that of the one-dimensional box, it can be shown that the wavefunctions and energies for a centered box are given respectively by


title: Particle in a box

text: The n-dimensional momentum wave functions may likewise be represented by formula_81 and the momentum wave function for an n-dimensional centered box is then:


title: Particle in a box

text: An interesting feature of the above solutions is that when two or more of the lengths are the same (e.g. formula_83), there are multiple wavefunctions corresponding to the same total energy. For example, the wavefunction with formula_84 has the same energy as the wavefunction with formula_85. This situation is called "degeneracy" and for the case where exactly two degenerate wavefunctions have the same energy that energy level is said to be "doubly degenerate". Degeneracy results from symmetry in the system. For the above case two of the lengths are equal so the system is symmetric with respect to a 90° rotation.


title: Particle in a box

text: The wavefunction for a quantum-mechanical particle in a box whose walls have arbitrary shape is given by the Helmholtz equation subject to the boundary condition that the wavefunction vanishes at the walls. These systems are studied in the field of quantum chaos for wall shapes whose corresponding dynamical billiard tables are non-integrable.


title: Particle in a box

text: Because of its mathematical simplicity, the particle in a box model is used to find approximate solutions for more complex physical systems in which a particle is trapped in a narrow region of low electric potential between two high potential barriers. These quantum well systems are particularly important in optoelectronics, and are used in devices such as the quantum well laser, the quantum well infrared photodetector and the quantum-confined Stark effect modulator. It is also used to model a lattice in the Kronig-Penney model and for a finite metal with the free electron approximation.


title: Particle in a box

text: Conjugated polyene systems can be modeled using particle in a box. The conjugated system of electrons can be modeled as a one dimensional box with length equal to the total bond distance from one terminus of the polyene to the other. In this case each pair of electrons in each π bond corresponds to their energy level. The energy difference between two energy levels, "n" and "n" is:


title: Particle in a box

text: The difference between the ground state energy, n, and the first excited state, n+1, corresponds to the energy required to excite the system. This energy has a specific wavelength, and therefore color of light, related by:


title: Particle in a box

text: A common example of this phenomenon is in β-carotene. β-carotene (CH) is a conjugated polyene with an orange color and a molecular length of approximately 3.8 nm (though its chain length is only approximately 2.4 nm). Due to β-carotene's high level of conjugation, electrons are dispersed throughout the length of the molecule, allowing one to model it as a one-dimensional particle in a box. β-carotene has 11 carbon-carbon double bonds in conjugation; each of those double bonds contains two π-electrons, therefore β-carotene has 22 π-electrons. With two electrons per energy level, β-carotene can be treated as a particle in a box at energy level "n"=11. Therefore, the minimum energy needed to excite an electron to the next energy level can be calculated, "n"=12, as follows (recalling that the mass of an electron is 9.109 × 10 kg):


title: Particle in a box

text: Using the previous relation of wavelength to energy, recalling both Planck's constant "h" and the speed of light "c":


title: Particle in a box

text: This indicates that β-carotene primarily absorbs light in the infrared spectrum, therefore it would appear white to a human eye. However the observed wavelength is 450 nm, indicating that the particle in a box is not a perfect model for this system.


title: Particle in a box

text: The particle in a box model can be applied to quantum well lasers, which are laser diodes consisting of one semiconductor “well” material sandwiched between two other semiconductor layers of different material . Because the layers of this sandwich are very thin (the middle layer is typically about 100 Å thick), quantum confinement effects can be observed. The idea that quantum effects could be harnessed to create better laser diodes originated in the 1970s. The quantum well laser was patented in 1976 by R. Dingle and C. H. Henry.


title: Particle in a box

text: Specifically, the quantum wells behavior can be represented by the particle in a finite well model. Two boundary conditions must be selected. The first is that the wave function must be continuous. Often, the second boundary condition is chosen to be the derivative of the wave function must be continuous across the boundary, but in the case of the quantum well the masses are different on either side of the boundary. Instead, the second boundary condition is chosen to conserve particle flux as formula_90, which is consistent with experiment. The solution to the finite well particle in a box must be solved numerically, resulting in wave functions that are sine functions inside the quantum well and exponentially decaying functions in the barriers. This quantization of the energy levels of the electrons allows a quantum well laser to emit light more efficiently than conventional semiconductor lasers.


title: Particle in a box

text: Due to their small size, quantum dots do not showcase the bulk properties of the specified semi-conductor but rather show quantised energy states. This effect is known as the quantum confinement and has led to numerous applications of quantum dots such as the quantum well laser.


title: Particle in a box

text: Researchers at Princeton University have recently built a quantum well laser which is no bigger than a grain of rice. The laser is powered by a single electron which passes through two quantum dots; a double quantum dot. The electron moves from a state of higher energy, to a state of lower energy whilst emitting photons in the microwave region. These photons bounce off mirrors to create a beam of light; the laser.


title: Particle in a box

text: The quantum well laser is heavily based on the interaction between light and electrons. This relationship is a key component in quantum mechanical theories which include the De Broglie Wavelength and Particle in a box. The double quantum dot allows scientists to gain full control over the movement of an electron which consequently results in the production of a laser beam.


title: Particle in a box

text: Quantum dots are extremely small semiconductors (on the scale of nanometers). They display quantum confinement in that the electrons cannot escape the “dot”, thus allowing particle-in-a-box approximations to be used. Their behavior can be described by three-dimensional particle-in-a-box energy quantization equations.


title: Particle in a box

text: The energy gap of a quantum dot is the energy gap between its valence and conduction bands. This energy gap formula_91 is equal to the gap of the bulk material formula_92 plus the energy equation derived particle-in-a-box, which gives the energy for electrons and holes. This can be seen in the following equation, where formula_93 and formula_94 are the effective masses of the electron and hole, formula_95 is radius of the dot, and formula_96 is Planck's constant:


title: Particle in a box

text: Hence, the energy gap of the quantum dot is inversely proportional to the square of the “length of the box,” i.e. the radius of the quantum dot.


title: Particle in a box

text: Manipulation of the band gap allows for the absorption and emission of specific wavelengths of light, as energy is inversely proportional to wavelength. The smaller the quantum dot, the larger the band gap and thus the shorter the wavelength absorbed.


title: Particle in a box

text: Different semiconducting materials are used to synthesize quantum dots of different sizes and therefore emit different wavelengths of light. Materials that normally emit light in the visible region are often used and their sizes are fine-tuned so that certain colors are emitted. Typical substances used to synthesize quantum dots are cadmium (Cd) and selenium (Se). For example, when the electrons of two nanometer CdSe quantum dots relax after excitation, blue light is emitted. Similarly, red light is emitted in four nanometer CdSe quantum dots.


title: Particle in a box

text: Quantum dots have a variety of functions including but not limited to fluorescent dyes, transistors, LEDs, solar cells, and medical imaging via optical probes.


title: Particle in a box

text: One function of quantum dots is their use in lymph node mapping, which is feasible due to their unique ability to emit light in the near infrared (NIR) region. Lymph node mapping allows surgeons to track if and where cancerous cells exist.


title: Particle in a box

text: Quantum dots are useful for these functions due to their emission of brighter light, excitation by a wide variety of wavelengths, and higher resistance to light than other substances.


title: Particle in a box

text: A more general model is the particle in a box with a period potential model: The box's interior has a periodic potential, and the box contains periods of a positive integer number in each dimension. A periodic potential becomes a constant potential, and a Bloch wave becomes a plane wave when the period(s) involved goes zero. The periodic potential is more general than the constant potential; the Bloch wave is more general than the plane wave.


title: Particle in a box

text: The problem can be considered quantum confinement of Bloch waves, more general than the quantum confinement of plane waves discussed in previous sections. The new theory found that, in one-dimensional cases, the problem can be analytically solved. Moreover, in many essential and simple multi-dimensional cases, the problem can be analytically solved based on relevant mathematical theorems with the help of reasonings of physics intuitions. In the following, we only briefly describe some essential conclusions. Readers interested in mathematical reasonings and more relevant details are referred to original publications.


title: Particle in a box

text: length formula_98 with two ends at formula_99 and formula_100 (formula_101: potential period, formula_102: a positive integer).


title: Particle in a box

text: We are mainly interested in cases where the bulk energy bands have a band gap between two consecutive energy bands.


title: Particle in a box

text: The new theory found that "two different types of states exist in such a box with a periodic potential".


title: Particle in a box

text: For each bulk energy band, there are formula_103 states in the finite crystal whose energies and properties


title: Particle in a box

text: depend on formula_102 but not formula_99 and map the energy band exactly. These states are the stationary Bloch states;


title: Particle in a box

text: "There is always one and only one state for each band gap, whose energy and properties depend on formula_99 but not formula_102."


title: Particle in a box

text: "The very existence of such formula_99-dependent states is the fundamental distinction of the quantum confinement of the Bloch waves".


title: Particle in a box

text: The Schrödinger equation with a multi-dimensional periodic potential is a partial differential equation; the mathematics is more difficult. However, many fundamental understandings can also be obtained.


title: Particle in a box

text: between formula_110 and formula_111 ( formula_112: the period, formula_113: the positive integer indicating the box size in the formula_109 direction)


title: Particle in a box

text: The formula_113-dependent states are stationary Bloch states. The energy of the formula_110-dependent state


title: Particle in a box

text: "Again, the very existence of such formula_110-dependent states is a fundamental distinction of the quantum confinement of multi-dimensional Bloch waves."


title: Particle in a box

text: For example, in some simplest cases in a simple box of a rectangular cuboid shape having formula_124 periods separately in three


title: Particle in a box

text: perpendicular dimensions, for each bulk energy band, there are (formula_125) (formula_126) (formula_127) bulk-like states,


title: Particle in a box

text: The properties and energy of the vertex-like state depend on three formula_110, but neither one formula_113;


title: Particle in a box

text: The properties and energy of each edge-like state depend on two formula_110 and the other formula_113, but neither one of the corresponding two formula_113 nor the other formula_110;


title: Particle in a box

text: The properties and energy of each surface-like state depend on two formula_113 and the other formula_110, but neither one of the corresponding two formula_149 nor the other formula_150;


title: Particle in a box

text: The properties and energy of each bulk-like state depend on three formula_113, but neither one formula_110.


title: Particle in a box

text: The probability density does not go to zero at the nodes if relativistic effects are taken to account via Dirac equation.


title: The Firebird

text: The Firebird (; ) is a ballet and orchestral concert work by the Russian composer Igor Stravinsky. It was written for the 1910 Paris season of Sergei Diaghilev's Ballets Russes company; the original choreography was by Michel Fokine, who collaborated with Alexandre Benois on a scenario based on the Russian fairy tales of the Firebird and the blessing and curse it possesses for its owner. It was first performed at the Opéra de Paris on 25 June 1910 and was an immediate success, catapulting Stravinsky to international fame. Although designed as a work for the stage, with specific passages accompanying characters and action, the music achieved equal if not greater recognition as a concert piece.


title: The Firebird

text: Stravinsky was a young, virtually unknown composer when Diaghilev recruited him to create works for the Ballets Russes; "L'Oiseau de feu" was the first such major project. The success of the ballet was the start of Stravinsky's partnership with Diaghilev, which would subsequently produce further ballet productions until 1928, including the acclaimed "Petrushka" (1911), "The Rite of Spring" (1913), and "Apollon Musagète" (1928).


title: The Firebird

text: Igor Stravinsky was the son of Fyodor Stravinsky, the principal bass at the Imperial Mariinsky Theatre in Saint Petersburg, and Anna (née Kholodovskaya), a competent amateur singer and pianist from an old established Russian family. Fyodor's association with many of the leading figures in Russian music, including Rimsky-Korsakov, Borodin and Mussorgsky, meant that Igor grew up in an intensely musical home. In 1901, Stravinsky began to study law at Saint Petersburg Imperial University, while taking private lessons in harmony and counterpoint. Sensing talent in the young composer's early efforts, Rimsky-Korsakov took Stravinsky under his private tutelage. By the time of his mentor's death in 1908, Stravinsky had produced several works, among them a Piano Sonata in F-sharp minor, a Symphony in E-flat, and a short orchestral piece titled "Feu d'artifice" ("Fireworks").


title: The Firebird

text: In 1909, Stravinsky's "Scherzo fantastique" and "Feu d'artifice" were premiered in Saint Petersburg. Among those in the audience was the impresario Sergei Diaghilev, who was about to debut his Ballets Russes in Paris. Diaghilev's intention was to present new works in a distinctively 20th-century style, and he was looking for fresh compositional talent. Impressed by Stravinsky, he commissioned from him orchestrations of Chopin's music for the ballet "Les Sylphides".


title: The Firebird

text: Alexandre Benois recalled that in 1908 he had suggested to Diaghilev the production of a Russian nationalist ballet, an idea all the more attractive given both the newly awakened French passion for Russian dance and the expense of staging opera. The idea of mixing the mythical Firebird with the unrelated Russian tale of Koschei the Deathless possibly came from a popular child's verse by Yakov Polonsky, "A Winter's Journey" ("Zimniy put", 1844), which includes the lines:


title: The Firebird

text: Benois collaborated with the choreographer Michel Fokine, drawing from several books of Russian fairy tales including the collection of Alexander Afanasyev, to concoct a story involving the Firebird and the evil magician Koschei. The scenery was designed by Aleksandr Golovin and the costumes by Léon Bakst.


title: The Firebird

text: Diaghilev first approached the Russian composer Anatoly Lyadov in September 1909 to write the music. There is no evidence that he ever accepted the commission, despite the anecdote that he was slow to start composing the work. Nikolai Tcherepnin composed some music for the ballet (which he later used in his "The Enchanted Kingdom"), but withdrew from the project without explanation after completing only one scene. After deciding against using Alexander Glazunov and Nikolay Sokolov, Diaghilev finally chose the 28-year-old Stravinsky, who had already begun sketching the music in anticipation of the commission.


title: The Firebird

text: Stravinsky would later remark about working with Fokine that it meant "nothing more than to say that we studied the libretto together, episode by episode, until I knew the exact measurements required of the music." Several ideas from works by Rimsky-Korsakov were used in "The Firebird". Koschei's "Infernal Dance" borrows the highly chromatic scale Rimsky-Korsakov created for the character Chernobog in his opera "Mlada", while the Khorovod uses the same folk tune from his "Sinfonietta", Op. 31. The piano score was completed on 21 March 1910 and was fully orchestrated by May, although not before work was briefly interrupted by another Diaghilev commission: an orchestration of Grieg's "Kobold", Op. 71, no. 3 for a charity ball dance featuring Vasily Nijinsky.


title: The Firebird

text: Soon thereafter, Diaghilev began to organize private previews of "The Firebird" for the press. French critic Robert Brussel, who attended one of these events, wrote in 1930:


title: The Firebird

text: The composer, young, slim, and uncommunicative, with vague meditative eyes, and lips set firm in an energetic looking face, was at the piano. But the moment he began to play, the modest and dimly lit dwelling glowed with a dazzling radiance. By the end of the first scene, I was conquered: by the last, I was lost in admiration. The manuscript on the music-rest, scored over with fine pencillings, revealed a masterpiece.


title: The Firebird

text: "The Firebird" was premiered by the Ballets Russes at the Palais Garnier in Paris on 25 June 1910, conducted by Gabriel Pierné. Even before the first performance, the company sensed a huge success in the making; and every performance of the ballet in that first production, as Tamara Karsavina recalled, met a "crescendo" of success. "Mark him well," Diaghilev said of Stravinsky, "he is a man on the eve of celebrity."


title: The Firebird

text: Critics praised the ballet for its integration of decor, choreography and music. "The old-gold vermiculation of the fantastic back-cloth seems to have been invented to a formula identical with that of the shimmering web of the orchestra," wrote Henri Ghéon in "Nouvelle revue française", who called the ballet "the most exquisite marvel of equilibrium" and added that Stravinsky was a "delicious musician." Michel-Dimitri Calvocoressi hailed the young composer as the legitimate heir to The Mighty Handful. The ballet’s success also secured Stravinsky's position as Diaghilev's star composer, and there were immediate talks of a sequel, leading to the composition of "Petrushka" and "The Rite of Spring". In Russia, however, reaction was mixed. While Stravinsky's friend Andrey Rimsky-Korsakov spoke approvingly of it, the press mostly took a dim view of the music, with one critic denouncing what he considered its "horrifying poverty of melodic invention." A fellow Rimsky-Korsakov pupil, Jāzeps Vītols, wrote that "Stravinsky, it seems, has forgotten the concept of pleasure in sound... [His] dissonances unfortunately quickly become wearying, because there are no ideas hidden behind them."


title: The Firebird

text: Sergei Bertensson recalled Sergei Rachmaninoff saying of the music: "Great God! What a work of genius this is! This is true Russia!" Another colleague, Claude Debussy, who later became an admirer took a more sober view of the score: "What do you expect? One has to start somewhere." Richard Strauss told the composer in private conversation that he had made a "mistake" in beginning the piece "pianissimo" instead of astonishing the public with a "sudden crash." Shortly thereafter he summed up to the press his experience of hearing "The Firebird" for the first time by saying, "it's always interesting to hear one's imitators."


title: The Firebird

text: The "Firebird" has been restaged by many choreographers, including George Balanchine and Jerome Robbins (co-choreographers), Graeme Murphy, Alexei Ratmansky, and Yuri Possokhov.


title: The Firebird

text: The ballet was revived in 1934 by Colonel Wassily de Basil's company, the Ballets Russes de Monte-Carlo, in a production staged in London, using the original decor and costumes from Diaghilev's company. The company subsequently performed the ballet in Australia, during the 1936–37 tour.


title: The Firebird

text: The work was staged by George Balanchine for the New York City Ballet in 1949 with Maria Tallchief as the Firebird, with scenery and costumes by Marc Chagall, and was kept in the repertory until 1965. The ballet was restaged by George Balanchine and Jerome Robbins in 1970 for the New York City Ballet with elaborated scenery by Chagall, and with new costumes by Karinska based on Chagall's for the 1972 Stravinsky Festival that introduced Gelsey Kirkland as the Firebird.


title: The Firebird

text: In 1970 Maurice Béjart staged his own version in which the ballet's protagonist was a young man who rose from the ranks of the revolutionists and became their leader. The lead role was danced by Michel Denard.


title: The Firebird

text: The Mariinsky Ballet performed the original choreography at Covent Garden in August 2011, as part of their Fokine retrospective.


title: The Firebird

text: The National Ballet of Canada created a version of the "Firebird" for television, occasionally rebroadcast, in which special effects were used to make it appear that the Firebird is in flight.


title: The Firebird

text: On 29 March 2012, the American Ballet Theatre premiered the ballet with choreography by Alexei Ratmansky at the Segerstrom Center for the Arts in Costa Mesa, California, starring Misty Copeland.


title: The Firebird

text: The Royal Ballet staged 6 performances of the ballet at the Royal Opera House in London in June 2019, with Yasmine Naghdi performing the role of the Firebird.


title: The Firebird

text: The ballet centers on the journey of its hero, Prince Ivan. While hunting in the forest, he strays into the magical realm of the evil Koschei the Immortal, whose immortality is preserved by keeping his soul in a magic egg hidden in a casket. Ivan chases and captures the Firebird and is about to kill her; she begs for her life, and he spares her. As a token of thanks, she offers him an enchanted feather that he can use to summon her should he be in dire need.


title: The Firebird

text: Prince Ivan then meets thirteen princesses who are under the spell of Koschei and falls in love with one of them, Tsarevna. The next day, Ivan confronts the magician and eventually they begin quarrelling. When Koschei sends his minions after Ivan, he summons the Firebird. She intervenes, bewitching the monsters and making them dance an elaborate, energetic dance (the "Infernal Dance").


title: The Firebird

text: Exhausted, the creatures and Koschei then fall into a deep sleep. While they sleep, the Firebird directs Ivan to a tree stump where the casket with the egg containing Koschei's soul is hidden. Ivan destroys the egg, and with the spell broken and Koschei dead, the magical creatures that Koschei held captive are freed and the palace disappears. All of the "real" beings, including the princesses, awaken and with one final hint of the Firebird's music (though in Fokine's choreography she makes no appearance in that final scene on-stage), celebrate their victory.


title: The Firebird

text: Shortly after the completion of The Firebird, Stravinsky wrote a piano solo reduction of the whole ballet. Furthermore, besides the complete 50-minute ballet score of 1909–10, Stravinsky arranged three suites for concert performance which date from 1911, 1919, and 1945. The following is a description of most other derivative compositions from The Firebird:


title: The Firebird

text: "Instrumentation": essentially as per the original ballet. The score was printed from the same plates, with only the new endings for the movements being newly engraved.


title: The Firebird

text: "Instrumentation": 2 flutes (2nd also piccolo); 2 oboes (2nd also English horn for one measure); 2 clarinets; 2 bassoons; 4 horns; 2 trumpets; 3 trombones; tuba; timpani; bass drum; cymbals; triangle; xylophone; harp; piano (also opt. celesta); strings.


title: The Firebird

text: This suite was created in Switzerland for conductor Ernest Ansermet. When it was originally published, the score contained many mistakes, which were only fixed in 1985.


title: The Firebird

text: "Instrumentation": 2 Flutes (2nd also Piccolo); 2 Oboes; 2 Clarinets; 2 Bassoons; 4 Horns; 2 Trumpets; 3 Trombones; Tuba; Timpani; Bass Drum; Snare Drum; Tambourine; Cymbals; Triangle; Xylophone; Harp; Piano; Strings.


title: The Firebird

text: In 1945, shortly before he acquired American citizenship, Stravinsky was contacted by Leeds Music with a proposal to revise the orchestration of his first three ballets in order to recopyright them in the United States. The composer agreed, setting aside work on the finale of his Symphony in Three Movements. He proceeded to fashion a new suite based on the 1919 version, adding to it and reorchestrating several minutes of the pantomimes from the original score.


title: The Firebird

text: Pianist Guido Agosti also made a short reduction of three fragments from the ballet, specifically the three main numbers at the end. Dedicated to the memory of Ferruccio Busoni, the reduction process started in Forte dei Marmi, in Italy, in August 1928, and finished in Berlin in October 1928. The three-movement suite was written for solo piano. The movement list is as follows:


title: The Firebird

text: This suite is notable for its difficulty and has been played and recorded by many renowned pianists, such as Martin Jones and Daniil Trifonov.


title: The Firebird

text: Excerpts from "The Firebird" were used in Bruno Bozzetto's 1976 animated film "Allegro Non Troppo" and in Walt Disney's animated film "Fantasia 2000".


title: The Firebird

text: Saviour Pirotta and Catherine Hyde's picture book, "Firebird", is based on the original stories that inspired the ballet, and was published in 2010 to celebrate the ballet's centenary.


title: The Firebird

text: The influence of "The Firebird" has been felt beyond classical music. Stravinsky was an important influence on Frank Zappa, who used the melody from the "Berceuse" in his 1967 album "Absolutely Free", in the "Amnesia Vivace" section of the "Duke of Prunes" suite (along with a melody from "The Rite of Spring"). Prog rock band Yes has regularly used the ballet's finale as their "walk-on" music for concerts since 1971. Jazz musician and arranger Don Sebesky featured a mash-up of the piece, with the jazz fusion composition "Birds of Fire" by John McLaughlin, on his 1973 album "Giant Box". During the 1980s and 1990s, the chord which opens the "Infernal Dance" became a widely used orchestra hit sample in music, specifically within new jack swing.


title: Perovskite solar cell

text: A perovskite solar cell (PSC) is a type of solar cell that 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 cesium lead halide, are cheap to produce and simple to manufacture.


title: Perovskite solar cell

text: Solar-cell efficiencies of laboratory-scale devices using these materials have increased from 3.8% in 2009 to 25.7% in 2021 in single-junction architectures, and, in silicon-based tandem cells, to 29.8%, exceeding the maximum efficiency achieved in single-junction silicon solar cells. Perovskite solar cells have therefore been the fastest-advancing solar technology . 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.


title: Perovskite solar cell

text: 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 ability to create low cost, high efficiency, thin, lightweight, and flexible solar modules. Perovskite solar cells have found use in powering prototypes of low-power wireless electronics for ambient-powered Internet of things applications, and may help mitigate climate change.


title: Perovskite solar cell

text: Perovskite cells also possess many optoelectrical properties that benefit their use in solar cells. For example, the exciton binding energy is small. This allows electron holes and electrons to be easily separated upon the absorption of a Photon. Moreover, the long diffusion distance of the charge carrier and the high diffusivity - the rate of diffusion - allow the charge carriers to travel long distances within the perovskite solar cell, which improves the chance of it to be absorbed and converted to power. Lastly, perovskite cells are characterized by wide Absorption ranges and high absorption coefficients, which further increase the power efficiency of the solar cell by increasing the range of photon energies that are absorbed


title: Perovskite solar cell

text: The name "perovskite solar cell" is derived from the ABX crystal structure of the absorber materials, referred to as perovskite structure, where A and B are cations and X is an anion. A cations with radii between 1.60 Å and 2.50 Å have been found to form perovskite structures. The most commonly studied perovskite absorber is methylammonium lead trihalide (CHNHPbX, where X is a halogen ion such as iodide, bromide, or chloride), which has an optical bandgap between ~1.55 and 2.3 eV, depending on halide content. Formamidinium lead trihalide (HNCHNHPbX) has also shown promise, with bandgaps between 1.48 and 2.2 eV. Its 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 CsSnI as a p-type hole transport layer and absorber. A common concern is the inclusion of lead as a component of perovskite materials; solar cells composed from tin-based perovskite absorbers such as CHNHSnI have also been reported, though with lower power-conversion efficiencies.


title: Perovskite solar cell

text: 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.


title: Perovskite solar cell

text: and "u" is the ultimate efficiency factor, and "v" is the ratio of open circuit voltage "V" to band-gap voltage "V", and "m" is the impedance matching factor, and "V" is the thermal voltage, and "V" is the voltage equivalent of the temperature of the Sun.


title: Perovskite solar cell

text: 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.


title: Perovskite solar cell

text: 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. The 1.3 eV bandgap energy has been successfully achieved with the hybrid cell, which has a tunable bandgap energy (E) from 1.24 – 1.41 eV


title: Perovskite solar cell

text: 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 synthesise lattice-matched and crystalline solar cells with more than one junction is very expensive, making it a less than ideal candidate for widespread use.


title: Perovskite solar cell

text: Perovskite semiconductors offer an option that has the potential to rival the efficiency of multi-junction solar cells but can be synthesised under more common conditions at a greatly reduced cost. Rivalling 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 multi-junction perovskite solar cells, in addition to being available for cost-effective synthesis, also maintain high PCE under varying weather extremes – making them utilizable worldwide.


title: Perovskite solar cell

text: 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.


title: Perovskite solar cell

text: The highest performing perovskites solar cells suffer from chemical instability. The organic components such as methylammonium or formamidinium are the basis of the weakness. Encapsulation to prevent this decay is expensive. Fully inorganic perovskites could miminize these problems. Fully inorganic perovskites have PCE over 17%.  These high performing fully inorganic perovskite cells are created using CsPbI, which has a band gap similar to that of high performing OIHPs (~1.7 eV), as well as excellent optoelectrical properties. Although chemically stable, these perovskite materials face significant issues with phase stability that prevent its broad industrial application. In high efficiency CsPbI, for example, the photoactive black α-phase is prone to transform into the inactive yellow δ-phase seriously inhibiting the performance, especially when exposed to moisture. The challenge of stabilizing the photoactive black α-phase of inorganic perovskite materials has been tackled in a variety of strategies, including octahedral anchoring and secondary crystal growth.


title: Perovskite solar cell

text: 2D perovskites are characterized by improved stability and excitonic confinement properties compared with 3D perovskites, while maintaining the charge transport properties of 3D perovskite materials. Furthermore, the 2D hybrid organic-inorganic perovskite (HOIP) structure also eases the steric restrictions on the “B” cations, as outlined by the Goldschmidt’s tolerance factor in 3D HOIPs, providing a much larger compositional space to engineer new materials with tailored properties.


title: Perovskite solar cell

text: HOIPs follow the same ABX stoichiometry as their 3D counterparts. In this case, B is a metal cation, X is halogen anions (Cl, Br, I) and A represents an organic molecular cation. The A-site cations are caged in a BX corner-sharing octahedra network via the hydrogen bond of N-H-X between the ammonium group from the A-site cation and the halogen from octahedra. As the length of the 2D organic ion increases, the spacing between the corner sharing octahedra does as well, forming a 2D or quasi-2D structure. The organic and inorganic layers are held together by van der waals forces. A formula of RABX is used to characterize the 2D and quasi 2D structures. Here, R is the large organic cation space that separates the inorganic layers and “n” refers to the number of organic units between inorganic layers.


title: Perovskite solar cell

text: To achieve mechanically durable devices, a top priority is to understand the inherent mechanical properties of the materials. Like other 2D materials, mechanical properties are analyzed using computational methods and are verified using experiments.


title: Perovskite solar cell

text: Nanoindentation is a common technique to measure mechanical properties of 2D materials. Nanoindentation results in 2D HOIP reveal anisotropy in the Young’s modulus along different plane directions (100, 001, and 110). Gao et al. showed single-crystal (CHCHNH)PbCl had mid-range anisotropy in these directions because of corner sharing inherent to the crystal structure. The strongest direction was the [100] direction which is perpendicular to the inorganic layers. Generally, across many 2D HOIPs, there is a dominant correlation between increased Pb-X (very common cation) bond strength and Young’s moduli. Similarly, another nanoindentation study found that changing the A ion from organic CHNH to inorganic Cs has negligible effects on the Young’s modulus, whereas the Pb–X strength has the dominating effect. Due to the increased mechanical stability of the inorganic layers, nanoindentation finds that 2D HOIP structures with thicker and more densely packed inorganic layers have increased Young’s moduli and increased stability.


title: Perovskite solar cell

text: A study by Tu et al. performed mechanical properties testing on a simple lead iodide system to investigate the role of the number and the length of subunits (organic layer) on the out of plane Young’s modulus utilizing nanoindentation. This study found that 2D HOIPs are softer than 3D counterparts due to a shift from covalent/ionic bonding to van der waals bonding. Furthermore, increasing the number of subunits “n” from (1-5) increases the Young’s modulus and hardness until reaching 3D standard values. The length of the organic chain decreases and plateau’s the Young’s modulus. These factors can be tailored when designing perovskites solar cells for unique applications.


title: Perovskite solar cell

text: 2D HOIP are also susceptible to the negative poisson’s ratio phenomena, in which a material contracts laterally with stretched and expands laterally when compressed. This phenomena is observed commonly in 2D materials and the Poisson's ratio can be modulated by changing the “X” halide in the 2D HOIP chemistry. Halides with weaker electronegativity form weaker bonds with the “B” cation resulting in increased (in magnitude) negative poisson ratio. This leaver allows for tunable flexibility of 2D HOIPs and applications of microelectromechanical and nanoelectronics devices.


title: Perovskite solar cell

text: 3D perovskite cells have shown poor environmental stability and will decompose under water,light and heat. To stabilize them, researchers such as Krishna et al. have investigated developing lower dimension perovskites such as 2D cells. These cells are characterized by alternating organic and inorganic layers also known as Ruddelson-Popper (RP) phases. These cells are more stable to environmental conditions due to the large cation sizes which disrupt ionic motion. Oragnic moiety are also present in the cell, which provide its hydrophobic character. However, 2D perovskite cells have shown inferior optoelectrical properties such as wider bandgaps and larger exciton binding energy. These factors reduce the overall efficiency. As a result, researchers are looking to strike a balance between the improved efficiency of 3D cells and improved stability of 2D cells by mixing 2D perovskite cells with traditional 3D Pervoskite cells.


title: Perovskite solar cell

text: An example of such compound is a RP structure of phenylethylammonium(PEA) and methylammonium(MA) cations. The composition of this compound first fabricated by Karunadasa et al. is (PEA)(MA)[PbI]. In its crystal structure, the 3D perovskite layers are separated by the PEA chains such that a layered structure is formed. The researchers displayed a decent power conversion efficiency of 4.57% and improved environmental stability. To follow up on this research, Quan et al. investigated the stability of said compound and concluded that the intercolation of PEA molecules between the perovskite layers introduced Van-Der-Waals interactions which increase the formation energy of the 3D perovskite, increasing its stability.


title: Perovskite solar cell

text: Solar cells based on transition metal oxide perovskites and heterostructures thereof such as LaVO/SrTiO have been studied.


title: Perovskite solar cell

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


title: Perovskite solar cell

text: Perovskite quantum dot solar cell technology may extend cell durability, which remains a critical limitation.


title: Perovskite solar cell

text: 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 CsSnI double perovskite, have been investigated.


title: Perovskite solar cell

text: 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.


title: Perovskite solar cell

text: 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 CHNHPbI, CHNHPbBr, and CsSnI.


title: Perovskite solar cell

text: 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.


title: Perovskite solar cell

text: 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."


title: Perovskite solar cell

text: 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.


title: Perovskite solar cell

text: Pb halide perovskites can be fabricated from a PbI precursor, or non-PbI precursors, such as PbCl, Pb(Ac), and Pb(SCN), giving films different properties.


title: Perovskite solar cell

text: In 2015, a new approach for forming the PbI nanostructure and the use of high CHNHI 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 PbI is formed by incorporating small amounts of rationally chosen additives into the PbI precursor solutions, which significantly facilitate the conversion of perovskite without any PbI residue. On the other hand, through employing a relatively high CHNHI concentration, a firmly crystallized and uniform CHNHPbI film is formed. Furthermore, this is an inexpensive approach.


title: Perovskite solar cell

text: 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.


title: Perovskite solar cell

text: 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 ("See also" Stability).


title: Perovskite solar cell

text: 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.


title: Perovskite solar cell

text: 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.


title: Perovskite solar cell

text: 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 TiO, SnO and ZnO. Currently, to make TiO 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 TiO layer in large area. Same methods also apply to SnO deposition.


title: Perovskite solar cell

text: As for hole transport layer (HTL), instead of commonly used PEDOT:PSS, NiO 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.


title: Perovskite solar cell

text: 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.


title: Perovskite solar cell

text: Toxicity issues associated with the lead 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, "K", of 10 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 "K"=4.4×10 which significantly increases their potential bioavailability and hazard for human health, as confirmed by recent toxicological studies. Although the 50% lethal dose of lead [LD(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 25 mm 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. Recently, Hong Zhang et al. reported a universal co-solvent dilution strategy to significantly reduce the toxic lead waste production, the usage of perovskite materials as well as the fabrication cost by 70%, which also delivers PCEs of over 24% and 18.45% in labotorary cells and modules, respectively.


title: Perovskite solar cell

text: 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.


title: Perovskite solar cell

text: 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 Sn to Sn, 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 CsSnGeI 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.


title: Perovskite solar cell

text: Apart from the Tin and Germanium based perovskites, there has also been research on the viability of double-perovskites with the formula of AMMX. 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 CsSbI and CsBiI, 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.


title: Perovskite solar cell

text: 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.


title: Perovskite solar cell

text: 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, Pb lead is effectively adsorbed and bonded onto the surface of CERs, even in the presence of competing divalent ions such as Mg and Ca that might also occupy binding sites on the CER surface.


title: Perovskite solar cell

text: 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 Ca 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%.


title: Perovskite solar cell

text: A co-solvent dilution strategy has been reported to obtain high-quality perovskite films with very low concentration precursor solutions. This strategy substantially reduces the quantity of expensive raw materials in the perovskite precursor ink and reduces the toxic waste production by spin coating through two key routes: minimizing precursor loss during the processing of perovskite films and enhancing the lifetime and shelf-life of the inks by suppressing aggregation of precursor colloids. A PCE of over 24% for laboratory PSCs could be achieved with a co-solvent dilution to a level as low as 0.5 M. In addition, scalability of the co-solvent dilution strategy is tested via fabrication of perovskite solar modules (PSMs) with different sizes using industrial spin coating. The modules fabricated by co-solvent dilution strategy show higher PCEs and far better uniformity and reproducibility than modules prepared with conventional perovskite inks, whilst using a fraction of the precursor. Importantly, more than 70% toxic waste/solvent, perovskite raw material, and fabrication cost are projected to be reduced for module fabrication compared to the same modules made using conventional inks by industrial spin coating, and in doing so make spin coating a sustainable technique for medium scale manufacturing, for instance, for standalone modules or Si wafer-scale integration. This work shows that through judicious selection of a greener co-solvent, we can significantly reduce the usage and waste of toxic solvents and perovskite raw materials, while also simplifying fabrication and cutting costs of PSCs.


title: Perovskite solar cell

text: An important characteristic of the most commonly used perovskite system, the methylammonium lead halides, is a bandgap controllable by the halide content.


title: Perovskite solar cell

text: 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.


title: Perovskite solar cell

text: 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.


title: Perovskite solar cell

text: 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/m, 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%.


title: Perovskite solar cell

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


title: Perovskite solar cell

text: 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.


title: Perovskite solar cell

text: 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.


title: Perovskite solar cell

text: 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 TiO – 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.


title: Perovskite solar cell

text: 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.


title: Perovskite solar cell

text: 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.


title: Perovskite solar cell

text: "The Perovskite Database" is a database and analysis tool of perovskite solar cells research data which systematically integrates over 15,000 publications, in particular device-data about "over 42,400" perovskite devices. Authors described the FAIR open database site – which as of January 2022 requires signing up to access the data and uses software that is partly open source but not marked as having a free software license on GitHub – as a participative "Wikipedia for perovskite solar cell research". It allows data to be filtered and displayed according to various criteria such as material compositions or component type and could thereby support the development of optimal architecture designs (including the used materials).


title: Perovskite solar cell

text: High-throughput screening of mixtures and contact layers is one development mechanism that has been used to develop relatively stable perovskite solar cells.


title: Perovskite solar cell

text: 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.


title: Perovskite solar cell

text: 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 TiO as electron-collector. Moreover, because a liquid corrosive electrolyte was used, the cell was only stable for a few minutes. Nam-Gyu Park et al. improved upon this in 2011, using the same dye-sensitized concept, achieving 6.5% PCE.


title: Perovskite solar cell

text: 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 TiO layer in order to transport electrons.


title: Perovskite solar cell

text: They showed that efficiencies of almost 10% were achievable using the 'sensitized' TiO architecture with the solid-state hole transporter, but higher efficiencies, above 10%, were attained by replacing it with an inert scaffold.


title: Perovskite solar cell

text: Further experiments in replacing the mesoporous TiO with AlO resulted in increased open-circuit voltage and a relative improvement in efficiency of 3–5% more than those with TiO scaffolds.


title: Perovskite solar cell

text: 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.


title: Perovskite solar cell

text: 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.


title: Perovskite solar cell

text: 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.


title: Perovskite solar cell

text: 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%.


title: Perovskite solar cell

text: Continuing the trend, a new record of efficiency for a single-junction perovskite solar cell efficiency was set each year since 2015, with the most frequent record-breakers coming from KRICT and UNIST. The latest record-holders are researchers from UNIST who achieved 25.7% efficiency. There are also efforts focused on reducing energy cost, including the Apolo project consortium at CEA laboratories which aims to bring the module cost below €0.40/Wp (Watt peak).


title: Perovskite solar cell

text: At least since 2016, the records for perovskite-silicon tandem solar cells have consistently remained higher than the ones for single-junction cells. Since 2018 the records were interchangeably broken by Oxford Photovoltaics and researchers from Helmholtz-Zentrum Berlin. In 2021, the latter achieved the best efficiency so far: 29.8%.


title: Perovskite solar cell

text: One big challenge for perovskite solar cells (PSCs) is the aspect of short-term and long-term stability. The traditional silicon-wafer solar cell in a power plant can last 20–25 years, setting that timeframe as the standard for solar cell stability. PSCs have great difficulty lasting that long [196]. 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.


title: Perovskite solar cell

text: 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 TiO layer sensitized with the perovskite absorber, are also UV-unstable, due to the interaction between photogenerated holes inside the TiO and oxygen radicals on the surface of TiO.


title: Perovskite solar cell

text: The measured ultra low thermal conductivity of 0.5 W/(Km) at room temperature in CHNHPbI can prevent fast propagation of the light deposited heat, and keep the cell resistive on thermal stresses that can reduce its life time. The PbI 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.


title: Perovskite solar cell

text: 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.


title: Perovskite solar cell

text: In 2017, Henry Snaith et al. achieved an efficiency of 17.5% ± 1.3% 2D-3D heterostructure butylammonium-cesium-formamidinium lead halide perovskite which can maintain 80% of its efficiency after 1000 hours in air and 4000 hours when encapsulated. The 2D Ruddlesden-Popper layers in the structure of BA(FACs)Pb(IBr) 2D-3D perovskites are believed to be able to increase crystallinity of perovskite and thus reduce defects which are responsible for non-radiative recombination. Later in 2021, Yang et al published on phenylformamidinium-enabled 2D Ruddlesden-Popper perovskite with improved stability. They achieved efficiency of 14.78% using 4-chloro-phenylformamidinium (CPFA) as spacer cation in 2D CPFAMAPbn(ICl)vperovskite film, which can maintain 80% of its efficiency over 2000 hours of storage under ambient condition, compared to 3D MAPbI, which can only sustain 45% of efficiency. It is believed that the Ruddlesden-Popper perovskite can have better stability as a solar cells used as solar cells, but with lower power conversion efficiency.


title: Perovskite solar cell

text: 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, MAPbI, 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.


title: Perovskite solar cell

text: 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,


title: Perovskite solar cell

text: in 2021 researchers reported that the stability and long-term reliability of perovskite solar cells was improved with a new kind of "molecular glue".


title: Perovskite solar cell

text: As of 2021, the existing stability tests for solar panels and solar cell systems are designed solely for those containing silicon wafers. As such, these tests, produced by the International Electrotechnical Commission (IEC), have been re-evaluated for their lack of suitability. At the International Summit on Organic PV Stability (ISOS), stability checks for in-lab development of all solar cells were created, but these were not adopted by the IEC. These tests are not pass/fail criteria, rather they evaluate the various causes of solar cell stability issues to root out the problems. They are grouped into five categories: dark storage testing, outdoor testing, light soaking testing, thermal cycling testing, and light-humidity-thermal cycling testing. In these tests, the PCE and J-V data graphs of the PSCs were calculated among varying physical conditions to determine the various causes of PSC degradation.


title: Perovskite solar cell

text: Overall, these ISOS tests helped determine the causes of PSC degradation, which were found to include extended exposure to visible and UV light, environmental contamination, high temperatures, and electrical biases. After 200 temperature cycles, the 2020 PSCs still retained 90% of their power, indicating that they are capable of short-term stability. Now, what remains to be researched is long-term stability, and what material advances could be applied to boost these 200 temperature cycles (days) to 20–25 years.


title: Perovskite solar cell

text: Another core problem in the development, production and use of perovskite solar cells is their recyclability. Perovskite recycling is an absolute necessity due to the presence of lead in perovskites. The use of this element means that simply disposing of perovskite solar cells into landfills would be a major health hazard due to lead runoff and toxicity to both bodies of water and human health [195]. 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.<ref name="10.1038/s41893-021-00737-z"></ref><ref name="10.1039/D0TA07495K"></ref> In a review, scientists concluded that "recycle and recovery technologies of perovskite solar cells should be researched and developed proactively".<ref name="10.1016/j.mattod.2020.11.024"></ref> 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".


title: Perovskite solar cell

text: In 2021, many solar cells implemented in the year 2000 are nearing their end-of-life stage. As such, research into perovskite recycling is crucial. One tricky component of perovskites to recycle is lead. Currently, producing 1 GW of energy using the most efficient perovskite solar cell would result in 3.5 tons of lead waste. The main strategy used right now to mitigate lead contamination is in-operation of the solar cell. Lead absorbing P,P’-di(2-ethylhexyl)methanediphosphonic acid and sulfonic acid cation-exchange resin are used to prevent lead leaking from any damages the solar panels may incur during use 195.


title: Perovskite solar cell

text: Research is ongoing to discover means to reduce lead's impact beyond simply lead leakage prevention. Carboxylic acid cation-exchange resin has been found to adsorb lead ions via ion-exchange with hydrogen, and these ions can be easily released via recrystallization from adding sodium iodide to the aqueous solution. This process was found to be low-cost compared to other existing lead recycling techniques, and could theoretically be implemented commercially.


title: Perovskite solar cell

text: Recently, since the efficiency of the best perovskite solar-cell reached 25.5%, comparable to the best PV cells made of single-crystal silicon, it is optimistic for the perovskite PV cells to be commercial in the future. Therefore, the recycling of the lead and transparent conductors are essential for the development of perovskite PV cells since the former reduces harmful environmental impact and the latter reduces costs. The organic solvent such as dimethylformamide (DMF) is used in the research to dissolve Pb and separate ITO/glass, then the carboxylic acid cation-exchange resin, in this research WAC-gel is used because of best performance, is utilized to absorb Pb ions in the DMF and release it in a form of Pb(NO). By adding NaI into the solution, PbI can precipitate and be recycled. The recycled materials properties are analyzed in that both PbI and ITO/glass have the same performance as the new ones do, and the recycling efficiency reached 99.2%. Moreover, the cost analysis shows that solar modules based on recycling cost around $12 per square meter, whereas those based on new materials cost around $24.8 per square meter. Therefore, it is beneficial to recycle the perovskite PV cells from both environmental and economical perspectives.


title: Perovskite solar cell

text: Another major challenge for perovskite solar cells is the observation that current-voltage scans yield ambiguous efficiency values.


title: Perovskite solar cell

text: 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.


title: Perovskite solar cell

text: 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.


title: Perovskite solar cell

text: 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.


title: Perovskite solar cell

text: 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.


title: Perovskite solar cell

text: 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.


title: Perovskite solar cell

text: 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.


title: Perovskite solar cell

text: As of 2021, the recorded peak power conversion efficiency has been found to be 25.6% efficiency. This was done using a formamidinium lead iodide metal-halide perovskite. Anions were pumped into existing highly efficient perovskites, and functioned to fill in gaps caused by trapped holes in the PV cell. Furthermore, this cell was found to be stable up to 450 hours, which is considered long-term stability. Finally, this device served to prove that anions other than iodine and bromine ions are capable of being bombarded into gaps in PV cells, breaking a trend that was evidently hindering prior research [198].


title: Perovskite solar cell

text: 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.


title: Perovskite solar cell

text: 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 InO 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 InO 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%


title: Perovskite solar cell

text: 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 SnO 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 SnO 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 SnO 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%.


title: Perovskite solar cell

text: 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/cm. 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/cm 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. In December 2021, KAUST team updated the champion PCE to 28.2% (certified).


title: Perovskite solar cell

text: 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.


title: Perovskite solar cell

text: 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


title: Perovskite solar cell

text: 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.


title: Perovskite solar cell

text: To investigate possible all-tandem perovskite candidates in an efficient and economical way, simulation software has been implemented. Shankar et al. published a paper in 2022 detailing their use of the Solar Cell Capacitance Simulator – One Dimensional software. This software allows the user to vary device parameters and properties to optimize performance. Results from this simulation research have exhibited efficiencies as high as 30% for a band gap of 1.4 eV, which resulted from increasing the external quantum efficiency to 95% via doping the transport layer. Shankar et al simulated an efficiency of 32.3% by altering the material and thickness of the electron transport and hole transport layers. This simulated efficiency represents a 37% increase in simulated work so far and was obtained upon optimization of work done by Zhao et al. in two-terminal all-perovskite tandem solar cells.


title: Perovskite solar cell

text: 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%.


title: Perovskite solar cell

text: 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%. In addition, making formamidinium cesium lead iodide bromide perovskite into four-terminal tandem cells could achieve efficiency ranging from 19.8% to 25.2%, depending on the parameters of the measurements. 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.


title: Perovskite solar cell

text: 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.


title: Perovskite solar cell

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