Photoconversion efficiency of quantum-well solar cells for the optimum doping level of a base

written by chinedu j. ekerue Photoconversion efficiency of quantum-well solar cells for the optimum doping level of a base Abstract. Analytical expressions for the maximum obtainable photoconversion efficiency of quantum-well solar cells (QWSCs) under AM0 conditions are given. The modeling of the photoconversion efficiency of QWSCs under AM1.5 conditions using the SimWindows program is fulfilled. It is shown that the photoconversion efficiency of QWSCs with the A3B5 p-i-n structure is rather low because of a low photovoltage value. To improve this situation, the base region should be doped heavily enough. Light concentration makes it possible to realize high photoconversion efficiencies for A3B5 quantum-well p-i-n structures with a low background level of the base region doping. Their values are comparable to the photoconversion efficiencies for solar cells (SCs) with rather high base region doping levels. 1. Introduction The question of the availability of quantum-well solar cells (QWSCs) is highly attended last years. Many researches cover features of QWSCs, and there are the special sections on such questions at European and world solar energy conferences for last nine years. By efforts of scientists headed by Prof. K.W.J. Barnham at the Imperial College in London, the laboratory patterns of A3B5 QWSCs with high efficiency comparable with the record value in conventional SCs have been obtained [1–3]. However, up to now, all efforts have been concerned with the analysis and the fabrication of QWSCs with p-i-n structures and a low doping of the base region. There was no comparative analysis of the photoconversion efficiency for QWSCs and conventional SCs. In this work, we present the results of a theoretical analysis of the efficiency of photoconversion at the optimum doping of the base region. The present paper consists of three sections. Analytical expressions for the maximum obtainable photoconversion efficiency of QWSCs at AM0 conditions are obtained in the first section. The maximum obtainable photoconversion efficiency of QWSCs as a function of the quantum well bandgap for GaAs, AlGaAs, and Si as the barrier material is calculated using these expressions. The calculations have been carried out for both concentrated and non-concentrated illuminations. The modeling of the photoconversion efficiency of QWSCs at a non-concentrated illumination under AM1.5 conditions is fulfilled using the SimWindows program [4, 5] in the second section. GaAs is considered as the barrier material with InGaAs quantum wells. It is shown that the photoconversion efficiency of QWSCs can considerably exceed the conventional efficiency of SCs under two conditions: 1) the quantum well carrier lifetime exceeds the barrier carrier lifetime; 2) the doping level of the base region does not exceed 1017 cm−3. However, the maximum photoconversion efficiency is achieved in conventional SCs with doping levels higher than 1017 cm−3. In the third section, it is shown that concentrated illumination allows one to achieve the high photoconversion efficiency in quantum well p-i-n structures with the low base region doping. This efficiency is comparable with the efficiency of SCs with highly doped base region. Then we present a detailed description of the obtained results. CHAPTER TWO photoconversion is a photoactivatable fluorescent protein naturally originated from a stony coral, Trachyphyllia geoffroyi. It was named Kaede, meaning "maple leaf" in Japanese. With the irradiation of ultraviolet light (350–400 nm), Kaede undergoes irreversible photoconversion from green fluorescence to red fluorescence. It is a homotetrameric protein with the size of 116 kDa. The tetrameric structure was deduced as its primary structure is only 28 kDa. This tetramerization possibly makes Kaede have a low tendency to form aggregates when fused to other proteins. The property of photoconverted fluorescence Kaede protein was serendipitously discovered and first reported by Ando et al. in Proceedings of the United States National Academy of Sciences.[1] An aliquot of Kaede protein was discovered to emit red fluorescence after being left on the bench and exposed to sunlight. Subsequent verification revealed that Kaede, which is originally green fluorescent, after exposure to UV light is photoconverted, becoming red fluorescent. It was then named Kaede. Properties The property of photoconversion in Kaede is contributed by the tripeptide, His62-Tyr63-Gly64, that acts as a green chromophore that can be converted to red.[2] Once Kaede is synthesized, a chromophore, 4-(p-hydroxybenzylidene)-5-imidazolinone, derived from the tripeptide mediates green fluorescence in Kaede. When exposed to UV, Kaede protein undergoes un conventional cleavage between the amide nitrogen and the α carbon (Cα) at His62 via a formal β-elimination reaction. Followed by the formation of a double bond between His62-Cα and –Cβ, the π-conjugation is extended to the imidazole ring of His62. A new chromophore, 2-[(1E)-2-(5-imidazolyl)ethenyl]-4-(p-hydroxybenzylidene)-5-imidazolinone, is formed with the red-emitting property. The cleavage of the tripeptide was analysed by SDS-PAGE analysis. Unconverted green Kaede shows one band at 28 kDa, where two bands at 18 kDa and 10 kDa are observed for converted red Kaede, indicating that the cleavage is crucial for the photoconversion. A shifting of the absorption and emission spectrum in Kaede is caused by the cleavage of the tripeptide. Before the photoconversion, Kaede displays a major absorption wavelength maximum at 508 nm, accompanied with a slight shoulder at 475 nm. When it is excited at 480 nm, green fluorescence is emitted with a peak of 518 nm. When Kaede is irradiated with UV or violet light, the major absorption peak shifts to 572 nm. When excited at 540 nm, Kaede showed an emission maximum at 582 nm with a shoulder at 627 nm and the 518-nm peak. Red fluorescence is emitted after this photoconversion. The photoconversion in Kaede is irreversible. Exposure in dark or illumination at 570 nm cannot restore its original green fluorescence. A reduced fluorescence is observed in red, photoconverted Kaede when it is intensively exposed to 405 nm light, followed by partial recover after several minutes. Applications As all other fluorescent proteins, Kaede can be the regional optical markers for gene expression and protein labeling for the study of cell behaviors.[3] One of the most useful applications is the visualization of neurons. Delineation of an individual neuron is difficult due to the long and thin processes which entangle with other neurons. Even when cultured neurons are labeled with fluorescent proteins, they are still difficult to identify individually because of the dense package. In the past, such visualization could be done conventionally by filling neurons with Lucifer yellow or sulforhodamine, which is a laborious technique.[1] After the discovery of Kaede protein, it was found to be useful in delineating individual neurons. The neurons are transfected by Kaede protein cDNA, and are UV irradiated. The red, photoconverted Kaede protein has free diffusibility in the cell except for the nucleus, and spreads over the entire cell including dendrites and axon. This technique help disentangle the complex networks established in a dense culture. Besides, by labeling neurons with different colors by UV irradiating with different duration times, contact sites between the red and green neurons of interest are allowed to be visualized. The ability of visualization of individual cells is also a powerful tool to identify the precise morphology and migratory behaviors of individual cells within living cortical slices. By Kaede protein, a particular pair of daughter cells in neighboring Kaede-positive cells in the ventricular zone of mouse brain slices can be followed. The cell-cell borders of daughter cells are visualized and the position and distance between two or more cells can be described. As the change in the fluorescent colour is induced by UV light, marking of cells and subcellular structures is efficient even when only a partial photoconversion is induced. Advantages as an optical marker Due to the special property of photo-switchable fluorescence, Kaede protein possesses several advantages as an optical cell marker. After the photoconversion, the photoconverted Kaede protein emits bright and stable red fluorescence. This fluorescence can last for months without anaerobic conditions. As this red state of Kaede is bright and stable compared to the green state, and because the unconverted green Kaede emits very low intensity of red fluorescence, the red signals provides contrast.[1] Besides, before the photoconversion, Kaede emits bright green fluorescence which enables the visualization of the localization of the non-photoacivated protein. This is superior to other fluorescent proteins such as PA-GFP and KFP1, which only show low fluorescence before photoactivation. In addition, as both green and red fluorescence of Kaede are excited by blue light at 480 nm for observation, this light will not induce photoconversion. Therefore, illumination lights for observation and photoconversion can be separated completely. Limitations In spite of the usefulness in cell tracking and cell visualization of Kaede, there are some limitations. Although Kaede will shift to red upon the exposure of UV or violet light and display a 2,000-fold increase in red-to-green fluorescence ratio, using both the red and green fluorescence bands can cause problems in multilabel experiments. The tetramerization of Kaede may disturb the localization and trafficking of fusion proteins. This limits the usefulness of Kaede as a fusion protein tag. Ecological significance The photoconversion property of Kaede does not only contribute to the application on protein labeling and cell tracking, it is also responsible for the vast variation in the colour of stony corals, Trachyphyllia geoffroyi. Under sunlight, due to the photoconversion of Kaede, the tentacles and disks will turn red. As green fluorescent Kaede is synthesized continuously, these corals appear green again as more unconverted Kaede is created. By the different proportion of photoconverted and unconverted Kaede, great diversity of colour is found in corals. Increasing photoconversion efficiency of DSSC "Dye sensitized solar cell (DSSC) has gained much research interest in recent years for its positive characteristics in contributing to renewable energy generator" said Dr. Gamolwan Tumcharern a researcher at NanoSens Lab at NANOTEC. "The ability to synthesize hybridized material of titanate nanoparticles and CNT using hydrothermal process has greatly increased the photoconversion efficiency of DSSC". Because DSSC could potentially be made of low-cost materials, and does not require elaborate apparatus to manufacture, this cell is technically attractive as a renewable energy generator. Likewise, manufacturing DSSC can be significantly less expensive than older solid-state cell designs. It can also be engineered into flexible sheets and is mechanically robust, requiring no protection from minor events like hail or tree strikes. For this reason, the ability to increase the efficiency of photoconversion is of most interest to the energy sector. A ‘quantum well’ is a potential well that confines particles to two dimensions that are otherwise free to move in three dimensions. Both electrons and holes can be confined in semiconductor quantum wells. The effect is to increase the gain and efficiency of the solid state device such as lasers in CD or DVD players, infrared imaging, and more recently, solar cells. Quantum dot solar cell Spin-cast quantum dot solar cell built by the Sargent Group at the University of Toronto. The metal disks on the front surface are the electrical connections to the layers below. A quantum dot solar cell is a solar cell design that uses quantum dots as the absorbing photovoltaic material. It attempts to replace bulk materials such as silicon, copper indium gallium selenide (CIGS) or CdTe. Quantum dots have bandgaps that are tunable across a wide range of energy levels by changing the dots' size. In bulk materials the bandgap is fixed by the choice of material(s). This property makes quantum dots attractive for multi-junction solar cells, where a variety of materials are used to improve efficiency by harvesting multiple portions of the solar spectrum. Solar cell concepts In a conventional solar cell, light is absorbed by a semiconductor, producing an electron-hole (e-h) pair; the pair may be bound and is referred to as an exciton. This pair is separated by an internal electric field (present in p-n junctions or Schottky diodes) and the resulting flow of electrons and holes creates electric current. The internal electric field is created by doping one part of semiconductor interface with atoms that act as electron donors (n-type doping) and another with electron acceptors (p-type doping) that results in a p-n junction. Generation of an e-h pair requires that the photons have energy exceeding the bandgap of the material. Effectively, photons with energies lower than the bandgap do not get absorbed, while those that are higher can quickly (within about 10−13 s) thermalize to the band edges, reducing output. The former limitation reduces current, while the thermalization reduces the voltage. As a result, semiconductor cells suffer a trade-off between voltage and current (which can be in part alleviated by using multiple junction implementations). The detailed balance calculation shows that this efficiency can not exceed 31% if one uses a single material for a solar cell. Numerical analysis shows that the 31% efficiency is achieved with a bandgap of 1.3-1.4 eV, corresponding to light in the near infrared spectrum. This band gap is close to that of silicon (1.1 eV), one of the many reasons that it dominates the market. However, silicon's efficiency is limited to about 29%. It is possible to improve on a single-junction cell by vertically stacking cells with different bandgaps – termed a "tandem" or "multi-junction" approach. The same analysis shows that a two layer cell should have one layer tuned to 1.64 eV and the other to 0.94 eV, providing a theoretical performance of 44%. A three-layer cell should be tuned to 1.83, 1.16 and 0.71 eV, with an efficiency of 48%. An "infinity-layer" cell would have a theoretical efficiency of 86%, with other thermodynamic loss mechanisms accounting for the rest. Traditional (crystalline) silicon preparation methods do not lend themselves to this approach due to lack of bandgap tunability. Thin-films of amorphous silicon, which due to a relaxed requirement in crystal momentum preservation can achieve direct bandgaps and intermixing of carbon, can tune the bandgap, but other issues have prevented these from matching the performance of traditional cells.[5] Most tandem-cell structures are based on higher performance semiconductors, notably indium gallium arsenide (InGaAs). Three-layer InGaAs/GaAs/InGaP cells (bandgaps 1.89/1.42/0.94 eV) hold the efficiency record of 42.3% for experimental examples. Quantum dots Quantum dots are semiconducting particles that have been reduced below the size of the Exciton Bohr radius and due to quantum mechanics considerations, the electron energies that can exist within them become finite, much alike energies in an atom. Quantum dots have been referred to as "artificial atoms". These energy levels are tuneable by changing their size, which in turn defines the bandgap. The dots can be grown over a range of sizes, allowing them to express a variety of bandgaps without changing the underlying material or construction techniques. In typical wet chemistry preparations, the tuning is accomplished by varying the synthesis duration or temperature. The ability to tune the bandgap makes quantum dots desirable for solar cells. Single junction implementations using lead sulfide (PbS) CQDs have bandgaps that can be tuned into the far infrared, frequencies that are typically difficult to achieve with traditional. Half of the solar energy reaching the Earth is in the infrared, most in the near infrared region. A quantum dot solar cell makes infrared energy as accessible as any other. Moreover, CQDs offer easy synthesis and preparation. While suspended in a colloidal liquid form they can be easily handled throughout production, with a fumehood as the most complex equipment needed. CQDs are typically synthesized in small batches, but can be mass-produced. The dots can be distributed on a substrate by spin coating, either by hand or in an automated process. Large-scale production could use spray-on or roll-printing systems, dramatically reducing module construction costs. Production Early examples used costly molecular beam epitaxy processes, but less expensive fabrication methods were later developed. These use wet chemistry (colloidal quantum dots – CQDs) and subsequent solution processing. Concentrated nanoparticle solutions are stabilized by long hydrocarbon ligands that keep the nanocrystals suspended in solution. To create a solid, these solutions are cast down and the long stabilizing ligands are replaced with short-chain crosslinkers. Chemically engineering the nanocrystal surface can better passivate the nanocrystals and reduce detrimental trap states that would curtail device performance by means of carrier recombination. This approach produces an efficiency of 7.0%. A more recent study uses different ligands for different functions by tuning their relative band alignment to improve the performance to 8.6%. The cells were solution-processed in air at room-temperature and exhibited air-stability for more than 150 days without encapsulation. In 2014 the use of iodide as a ligand that does not bond to oxygen was introduced. This maintains stable n- and p-type layers, boosting the absorption efficiency, which produced power conversion efficiency up to 8%. The idea of using quantum dots as a path to high efficiency was first noted by Burnham and Duggan in 1990. At the time, the science of quantum dots, or "wells" as they were known, was in its infancy and early examples were just becoming available. Using quantum dots as an alternative to molecular dyes was considered from the earliest days of DSSC research. The ability to tune the bandgap allowed the designer to select a wider variety of materials for other portions of the cell. Collaborating groups from the University of Toronto and École Polytechnique Fédérale de Lausanne developed a design based on a rear electrode directly in contact with a film of quantum dots, eliminating the electrolyte and forming a depleted heterojunction. These cells reached 7.0% efficiency, better than the best solid-state DSSC devices, but below those based on liquid electrolytes. Model and main results Energy d of QWSCs: dp, db, and dn are the thicknesses of the p+, base, and n+ regions, respectively. the blackbody spectrum at a temperature of 5800 K. One electron-hole pair generation by every photon in the interband absorption range was assumed. Light reflection and contact grid shadowing were neglected. We took the photocurrent collection coefficient to be 1. The recombination in the base region consisting of the bulk recombination in barriers, recombination in quantum wells, and “surface” recombination on the barrier − quantum well interfaces was taken into consideration. Recombination velocities are Vr and S, respectively. Quantum wells are assumed to be located outside the screening area. The concentration Δp of excess electron-hole pairs in the base region is determined as Δp = JSC / qVeff, (1) where Veff = Vr + S; JSC is the surface short-circuit current density, and q is the electron charge. The open circuit voltage VOC = (kT / q)[ln(Δp / p0) + ln(1 + Δp / n0)], (2) where k is the Boltzmann constant, T is the absolute temperature, and p0 and n0 are, respectively, the concentrations of majority and minority current carriers. The short-circuit current density JSC is a function of the barrier material bandgap Egb, quantum wells bandgap Egq, and the effective times of recombination τeff and quantum well carrier escape τesc : [ ( ) ( )] . ( ) eff esc eff τ + τ τ+ −= +SC gq SC gb SC SC gb J E J E J J E (3) We have calculated the limiting photoconversion efficiency of QWSCs under AM0 conditions by using relations (1)-(3). We set τeff = db /Veff , where db is the base region thickness, and take τesc =W 2πm / kT exp(Ea / kT) [6] (W is the quantum well width, m is the effective mass of a quantum well carrier, and Ea ≈ (Eb − Eg) / 2 is the activation energy). The band structure of a QWSC is demonstrated in corresponds to a low doping of the base region and the Δp < n0 condition. In this case, a strong electric field acts in the base region in the maximum power takeoff mode. In this case, there is no electric field in the base region in the maximum power takeoff mode. When Δp < n0, the open-circuit voltage VOC ≈ (kT / q)ln(Δpn0 / ni 2), where ni is the intrinsic carrier concentration of a barrier material, and ni logarithmically depends on the doping level of the base region. The greater is n0, the greater is VOC . In the case of a high excitation level when Δp > n0, the open-circuit voltage VOC ≈ (2kT / q)ln(Δp / ni), and it does not depend on the doping of the base region. The non-equilibrium carrier lifetime in direct band semiconductors is low enough, so the Δp << n0 criterion is satisfied under AM0 and AM1.5 conditions. High excitation levels in such semiconductors can be reached under concentrated illumination. Therefore, the QWSCs with direct band semiconductor p-i-n structures and with a low doped base region have low photovoltage and photoconversion efficiency relative to those in structures with a highly doped base region. There is another situation in Si SCs, where a high excitation level can be realized under AM0 or AM1.5 condition. Thereby, the photovoltage and the photoconversion efficiency of Si p-i-n structures are high enough and cannot be increased by a higher doping of the base region, the limiting photoconversion efficiency of QWSCs with p-i-n structure versus the quantum well material bandgap Egq for AM0 (Fig. 2a) and at the light concentration M = 400 (M is the degree of concentration of the illumination). The barrier material is GaAs. the photoconversion efficiency of SCs with p-i-n structure versus the quantum well material bandgap Egq for AM0, the barrier material being Al0.35Ga0.65As5. The curves are built for various Veff. The background doping level is 1015 cm−3. Efficiencies in these figures are compared with the limiting photoconversion efficiency of conventional SCs at a base region doping level of 1017 cm−3. 3 Limiting photoconversion efficiency of GaAs QWSCs versus the quantum well bandgap under AM0 conditions (2a) and at the light concentration М = 400 (2b). di = 0.5 μm, n0 =1015 cm−3, Veff = 3•104 cm/s (1), 105 (2), and 106 (3). However, in a more realistic case for Veff ≈ 105 cm/s, the photoconversion efficiency is 29 % at AM0 and 35 % under light concentration. These values do not differ strongly from the corresponding values for conventional SCs (26 − 27 % under AM0 conditions and 31 % under light concentration). With the further increase in Veff, the limiting photoconversion efficiency of QWSCs becomes less than the limiting photoconversion efficiency of conventional SCs. First of all, it covers GaAs-InGaAs and Si-GeSi structures with high percentages of In and Ge. We tried to take into account the fact that Veff increases, as Egq decreases. So, by taking Veff = V0[1 + a(ΔE / Ex)m], where ΔE = Eg − Egq, V0 = 10 cm/s, and a, Ex, and m are variable parameters, we had a maximum of the limiting photoconversion efficiency of Si QWSCs versus Egq, and this maximum was a little higher than the maximum for conventional SCs. Dependences in Fig. 4 are illustrative. Generally, there are many possible choices of Veff as a function of ΔE. The point is that these dependences illustrate the possibility of the decrease in the open circuit voltage stronger than the increase in the short circuit current with increase in ΔE. The results of numerical modeling of the photoconversion efficiency of GaAs-InGaAs QWSCs by using the SimWindows program are described in what follows. We should like to mention the unavoidable factors decreasing the photoconversion efficiency which were taken into account in the modeling. First of all, it is the bulk recombination that consists of the Shockley-Reed recombination, radiative recombination, and Auger recombination. We assumed the front and rear surface recombination velocities to be 103 cm/s, what is quite a low value for direct band A3B5 semiconductors. The thickness dp of the heavily doped p+-region was varied and assumed to be 1 μm, which corresponds to the photoconversion efficiency optimum taking into account the series resistance of the p+-region and the recombination. The thickness dn of the n+-region was also 1 μm. The doping level of the p+- and n+-regions was 7•1018 cm−3. Calculations were carried out for 50 InGaAs quantum wells of 9 nm in width separated by 6-nm-wide barriers symmetrically disposed relative to the base region center. The base region thickness db was also varied, and its mean value is assumed to be 1.15 μm. Losses of 12 % due to reflection and contact grid shadowing were assumed. In the modeling of QWSCs under concentrated sunlight, GaAs and InGaAs were used as materials for barriers and quantum wells, respectively. The computational parameters were identical to those in the case without light concentration. CHAPTER THREE 3. Conclusions 1. The photoconversion efficiency of A3B5 p-i-n QWSCs is quite low because of a low photovoltage. The base region should be doped strongly enough to increase this efficiency. However, the photoconversion efficiency of QWSCs at a high doping (> 3•1017 cm−3) of the base region is proved to be less than that of conventional SCs. 2. Light concentration enables one to get a considerable increase in the photoconversion efficiency of A3B5 p-i-n QWSCs, by making it comparable to that of SCs with the highly doped base region. 3. Most effective QWSCs have a constant-sign electric field localized in narrow areas near the boundaries of the base region. There is no strong electric field in the area of quantum wells, and this situation is shown in Fig. 1b. 4. The difference in the photoconversion efficiencies of QWSCs and conventional A3B5 SCs at the same doping of the base region is small and does not exceed 5 % for parameters used in this computation (see Fig. 5). References 1. J.P. Connolly, I.M. Ballard, K.W.J. Barnham, et al., Efficiency limits of quantum well solar cells // Proc. 19th European Photovoltaic Solar Energy Conference (Paris, France, 2004), p. 355. 2. T.N.D. Tibbits, I.M. Ballard, K.W.J. Barnham, et al., Strain-balanced multi-quantum well solar cells tandem structures – first experimental results // Proc. 19th European Photovoltaic Solar Energy Conference (Paris, France, 2004), p. 3715. 3. M.C. Lynch, I.M. Ballard, A. Bessière, M. Hoyes, D.C. Johnson, P.N. Stavrinou1, T.N.D. Tibbits, I. Tongue, K.W.J. Barnham, et al., Strain balanced quantum well solar cells for high concentration applications // Proc. 20th European Photovoltaic Solar Energy Conference (Barcelona, Spain, 2005), p. 523. 4. D.W. Winston, Physical simulation of optoelectronic semiconductor devices // Ph. D. Dissertation, University of Colorado, 1996. 5. D.W. Winston //www-os.colorado.edu/SimWindows/ simwin.html. 6. M.A. Green, K. Emery, D.L. King, S. Igary, W. Warta // Progr. Photovolt.: Res. Appl. 10, p. 355 (2002). 7. A. Alemu, L. Williams, L. Bhusal, A. 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