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Concretely, a completed appearance model represents both (in-plane) shape and texture using the linked linear models x= x¯+ Qxc g= g¯+ Qgc where x is a vector containing the annotation point coordinates, x¯ is the mean shape vector, g is a vector containing the grayscale pixel intensities in the mean shape reference frame, g¯ is the mean grayscale intensity vector, the columns of Qx and Qg are the ordered eigenvectors that span the variance in shape and texture across the images, and c is the vector of appearance model parameters. We refer to each eigenvector as a mode of shape and texture variation. These modes linearly map the compact parameter vector c to the shape and texture vectors x and g.
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The appearance model allows new images with different shapes and textures to be generated by selecting new values for the parameters in c. Each image can then be compactly encoded by a vector of parameters,c, obtained by fitting a parameter vector c that synthesizes an image as close as possible to the original .
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A total sample of 400 older adults (ages 70–79) was selected from the longitudinal Health, Aging and Body Composition (Health ABC) study [30–32]. Two sets of 100 cases (participants who died during the first six years of follow-up) and 100 BMI-, sex-, and age-matched controls were selected. One set was used for model calibration and the other was used for validation. Selection was stratified by sex and race (black and white). The Health ABC study was initiated in 1997 by the National Institute on Aging to examine the impact of changes in body composition and health conditions on age-related physiologic and functional status. At baseline, each participant received numerous clinical evaluations including whole body DXA scans acquired using Hologic QDR 4500A systems (Hologic, Inc., Bedford, MA) and software version 9.03, located at two study sites. Validity of fan-beam dual-energy X-ray absorptiometry for measuring fat-free mass and leg muscle mass has been previously reported .
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Statistical appearance models were trained on the calibration dataset and validated on the validation dataset. We investigated the bivariate association of the SAM parameter vectors to continuous variables of BMI and age using general linear regression models (proc GLM), and categorical variables of mortality status, sex, and race using logistic regression (proc LOGISTIC). Stepwise selection for the most significant SAM parameters, i.e. the number the explained 95% of the variance, were used to select parameters at a significance of p ≤ 0.05 to estimate each outcome variable. All statistical analysis was done using SAS software, version 9.2 (SAS Institute, Inc., Cary, NC). This study and all included analyses were approved by Health ABC and the UCSF Committee on Human Research.
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Fig 1(a) shows the 82 points used to describe the outline of the body and some key landmarks on the skeleton. Fig 1(b) shows the associated triangulation scheme used to warp the image to a reference frame. Fig 1(c) shows the 52-point subset that excludes the points associated with the lower arms and legs. Fig 1(d) shows the associated triangles to the 52 points. Wherever possible, the triangles in the 52-point annotation are unchanged from the 82-point annotation. This demonstrates how our algorithm can select how the image is warped by manually defining the triangle relationships.
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Table 1 shows the relevant demographic and anthropometric markers for the sample participants included in this study. Fig 2 shows the mean image of the 200 calibration participants with progressively more sophisticated registration: (a) translating the images so that the centres of gravity coincide, (b) applying an affine transformation so that the bounding boxes coincide, and (c) using the full piece-wise affine transformation from triangulated mesh. The final registration has corrected for a range of body positions and shapes to bring all the pixels into approximate correspondence, allowing analysis of equivalent structures to be done easily. The images are displayed using the histogram equalised R-images. The models are built from 200 examples and their reflections (400 samples in total).
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We found that 23 shape modes explained 95% of the shape variance defined by our markers. The first 6 shape modes are shown in Fig 3. Furthermore, after registering all images to the average shape, we found that 261 texture modes explained 95% of the variance in X-ray attenuation (represented as greyscale.) Six texture modes are shown in Fig 4. Fig 5 shows the combination of the shape and texture variances to form the full statistical appearance model. The first 237 SAM modes explained 95% of the combined shape and texture appearance. The model is capable of synthesizing both in-plane shape changes and intensity changes, and shows the main correlations between the two.
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For each mode, the -/+ 3 standard deviation (left and right respectively) images are shown. 23 modes were required to explain 95% of shape variance. At a high level, we see that body height is captured in Mode 1, width in Mode 5, and android/gynoid shape variation in Mode 2. Note that several modes capture variation in subject pose.
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For each mode, the -/+ 3 standard deviation (left and right respectively) images are shown. 261 modes explained 99% of the variance. Since this model captures only texture information, all images have the same shape, but differing grayscale intensity indicating different distributions of tissues throughout the regions of the body.
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Several examples are given of how different appearance models can be created from different texture information found in the DXA images. Fig 5 shows the first 6 modes of the R-value images where white represents higher density. Fig 6 shows the first 8 modes of an appearance model of shape and body thickness, using a 52-point annotation excluding the forelimbs. Fig 7 shows a combined appearance model of shape, thickness, and leanness, where thickness is encoded as green and leanness is encoded as red in an RGB image. Linear scaling was applied to ensure the data range was in 0 to 255 range. The blue channel was not used.
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Bivariate correlation coefficients between demographic and anthropometric variables and shape modes are found in Table 2. Of these variables, we found that only height predicted sex (AUC = 0.95). Body thickness and leanness, however, was more strongly predictive of sex—the final logistic model includes three shape modes (Table 3) and achieved AUC = 0.99. No combination of the following anthropometric or demographic variables (of sex, BMI, height, weight, sagittal diameter, nor abdominal circumference) predicted race even though this may not be universally true in all datasets. However, body thickness and leanness was a strong predictor of race—the final logistic model includes six shape modes (Table 3) and achieved AUC = 0.91. Visualizations of sex and race models are shown in Fig 8. Using a statistical appearance model of body thickness on the calibration dataset, we found that a logistic model with three SAM parameters predicted mortality with AUC = 0.66. Example images of low- and high-risk body appearances are shown in Fig 9. Note that the primary differences between the low and high risk were the apparent lung volume and waist shape. The mortality model had an AUC = 0.62 when applied to the validation dataset. Regression equations for sex, race, and mortality are provided in Table 3.
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There were 3 appearance modes used in the sex model that achieved an AUROC of 0.99. There were 6 appearance modes used in the Race model that achieved an AUROC of 0.91. These models show that statistical appearance of body shape, thickness, and leanness accurately identifies sex and race differences in the sample population.
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We have developed methods to describe and analyze the rich regional body shape and composition information captured in whole-body DXA images. We applied statistical appearance modeling techniques to body thickness and leanness images derived from raw DXA attenuation data. The resulting SAM principal components describing holistic body shape were shown to be highly predictive of race and sex, indicating that this technique is capable of distinguishing the unique shape characteristics of each group. Importantly, appearance modes of body thickness were predictive of mortality status. Inspection of the body shape differences captured by the appearance model (Fig 9) reveals interesting features such as apparent lung volume that differ by mortality status. These results suggest that this technique could be used to elucidate body shape and composition phenotypes that may be strongly associated with health status, provide new metrics for risk assessment in individuals, and reveal body features worthy of further research.
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Previous work in this area was performed by Wilson in his PhD dissertation . Wilson created whole body principal component models that used only rigid affine-aligned thickness images. This work did not include piecewise registration, or other image types. The preliminary models had a blurry appearance, similar to Fig 2(b), due to the lack of precise registration. Nonetheless, Wilson was still able to show strong correlations to patient demographic variables. Later, Wilson showed that body shape was related to mortality using trunk to leg volume ratios from DXA images . In his fully adjusted models for mortality, he demonstrated strong AUC values of 0.83. Besides the representation of body shape, the Wilson study design differed from our design in population (Wilson: NHANES 1999–2004, ages 20 to 85 years; Health ABC: 75 years at baseline) and adjustments (Wilson: Age, gender, race, BMI, waist circumference, activity level, poverty index; Health ABC: none). Further future evaluations are planned in the NHANES population Wilson used to directly compare the SAM methods directly to simple measures like trunk to leg volume ratio.
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Shape and appearance modeling has been applied to proximal femur DXA scans with success [22, 36, 37]. Goodyear et al. showed that the combination of shape and appearance models with bone density produced the best AUC = 0.65 compared to any single measure for predicting hip fracture risk. To our knowledge, this is the first application of SAM techniques to whole body DXA images. The models for sex, race, and mortality risk derived herein demonstrate the potential of this approach to provide novel and significant image features from standard DXA data.
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This study had notable strengths. First, there was a similar number of men and women, and black and white participants. This is important because the models derived are equally weighted by sex and ethnicity. Second, because of our case and control design, we were able to increase the signal present in the model for mortality over what would be expected in a prospective study of the same number of participants. However, this study had some limitations. First, the DXA data was acquired on one make of DXA system (Hologic). Our statistical appearance models would not be applicable to other makes without further validation. Additionally, the study population was limited to a narrow age range. A more complete analysis of body shape and appearance in a broader, representative sample of adults is warranted to ensure generalizability. Another issue was the limited data available for training the constrained local model for automatic annotation of the DXA images. All images required some degree of manual annotation point adjustment where the automated placement algorithm did not accurately detect body landmarks. Given sufficient high-quality training data, though, the automated CLM technique has been shown to achieve very good accuracy . We expect that a large training dataset of DXA images across a wide range of body shapes and compositions would yield a precise and accurate active appearance model for fully-automated annotation.
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Detailed models of the body shape and tissue distribution offer significantly more information than standard DXA analyses. This study demonstrates a method for describing holistic body shape, thickness, and leanness that reveals unique features by sex, race, and also predicts mortality risk. Further study is warranted to investigate body shape associations to other outcome variables of interest, across different populations. As this technique utilizes standard whole body DXA image data, it is readily applicable to several existing study databases of DXA scans. In addition, supervised methods of feature selection beyond principal component analysis may yield more sensitive and specific predictors for clinical outcomes.
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Perovskite-based solar cells employing metal halide perovskites as absorber materials belong to one of the most promising photovoltaic technologies for next-generation solar cells. This is illustrated by the remarkable increase in the power conversion efficiency (PCE) from 3.8% in 2009 to now over 22% within a few years [2–4]. This outstanding performance is based on the exceptional properties of metal halide perovskites exhibiting high charge carrier mobilities, a balanced electron and hole transport, high absorption coefficients, direct and tunable band gaps , and long carrier diffusion lengths [6–8].
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Another important advantage is that they can be prepared via a variety of different processing technologies, i.e. solution and vacuum-based techniques, and especially the facile low-temperature solution processability makes metal halide perovskite semiconductors that interesting [9–15]. Based on these assets, metal halide perovskites can already be regarded as a potential low-cost alternative to silicon-based photovoltaics.
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The most extensively studied and also most efficient perovskite absorber materials are based on semiconducting (hybrid) lead halide perovskites adopting an ABX3 structure, where A is a monovalent organic cation (e.g. methylammonium (CH3NH3 +, MA+), formamidinium (CH(NH2)2+, FA+) or an inorganic cation (e.g. K+, Rb+, Cs+), B is a divalent Pb2+ metal cation and the X-site of the perovskite structure is occupied by halide counterions (X = Cl−, Br−, I−). The properties of lead perovskites can be tuned by changing A-site or X-site ions and also mixed ion approaches turned out to be beneficial for the performance of the perovskites in photovoltaic devices.
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Current limitations impeding the commercialization of lead-based halide perovskite solar cells are (1) the toxicity, bioavailability, and probable carcinogenicity of lead and lead halides, (2) the water solubility of lead that might contaminate water supplies, and (3) the chemical instability under ambient conditions, especially in the presence of air, humidity, and/or light [16–19].
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These shortcomings are currently tackled by huge research efforts and progress could already be made in these fields. The stability of perovskite solar cells could be improved very recently by the partly exchange of the CH3NH3 + cation with CH(NH2)2+ and Cs+ ions in the triple cation approach or by the addition of Rb+ as A-site cation . These changes in the composition of the perovskite led to stable solar cells, which only lost 5% of their initial PCE within a 500-h test under illumination and maximum power point tracking .
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Therefore, many research groups took up the challenge to substitute lead with other elements to find new non-toxic and environmentally benign perovskite materials suitable as efficient solar cell absorbers [25, 26]. Because of the fact that the perovskite crystal structure can be found in many compounds, many different material combinations are possible. However, due to these manifold possibilities, a huge number of materials needs to be screened. Table 1 shows an overview of the efficiencies of the currently best alternative lead-free halide perovskite materials and based on these PCE values, it is obvious that they currently cannot compete with lead-based materials, as today, the highest efficiencies for lead-free materials are about 6.4% for tin-based perovskites .Table 1Dimensionality, optical band gap, and power conversion efficiencies (PCEs) of the currently most promising lead-free perovskite absorber materials for photovoltaic applicationsPerovskiteDimensionalityBand gap/eVPCE/%ReferencesCH3NH3SnI3 3D1.236.4CH3NH3GeI3 3D2.00.20(CH3(CH2)3NH3)2CuBr4 2D1.760.63Rb3Sb2I9 2D2.10.66Cs3Bi2I9 0D dimer2.21.09
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This review will focus on the class of lead-free metal halide perovskites for photovoltaic applications. It involves the results from experimental studies on lead-free metal halide perovskites and discusses insights from theoretical work for potential candidates to replace lead via both homo- and heterovalent substitution. Furthermore, we give a brief overview on lead-free metal chalcogenide perovskites, which also exhibit interesting properties for solar cell applications.
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Perovskites are crystalline materials with an ABX3 structure similar to CaTiO3. Depending on the nature of the anionic species (X), oxide (O2−) and non-oxide perovskites such as chalcogenide (S2−, Se2−, Te2−) and halide (Cl−, Br−, I−) metal perovskites are distinguished. Moreover, molecular anions such as HCOO− , BF4 − [38, 39], PF6 − , or SCN− were successfully incorporated as counterion.
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Perovskite-based solar cells are primarily prepared in two device architectures, one has been adopted from dye-sensitized solar cells using mainly mesoporous TiO2 as electron transport material and Spiro-OMeTAD (2,2′,7,7′-tetrakis[N,N-di(4-methoxyphenyl)amino]-9,9′-spirobifluorene) as hole transport material. The other one is derived from organic solar cells where PEDOT:PSS (poly(3,4-ethylenedioxythiophene)-poly(styrenesulfonate)) and PCBM (-phenyl-C61-butyric acid methyl ester) are applied as hole and electron transport layer, respectively. Details to these device architectures and their influences on the performance of perovskite solar cells are described in recent reviews [28–32].
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Currently, many research projects are initiated to identify further possible lead-free perovskite absorber materials and to incorporate them into tailored device architectures, giving rise to significant advancements in PCE of lead-free perovskite solar cells in the near future.
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In metal halide perovskites, the A-site is occupied by a monovalent organic (e.g. CH3NH3 +, CH(NH2)2+ (NH2)3C+) or inorganic (e.g. K+, Rb+, Cs+) cation, the B-site by a divalent metal cation and the X-site by a halide counterion (Cl−, Br−, I−). Depending on the nature of the ions within the perovskite structure, hybrid organic–inorganic or purely inorganic metal halide perovskites are distinguished. A range of different divalent metal cations such as Pb2+, Sn2+, Ge2+, Mg2+, Ca2+, Sr2+, Ba2+, Cu2+, Fe2+, Pd2+, and Eu2+ have already been investigated as B-site cation.
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The ABX3-type perovskite structure consists of corner-sharing BX6 octahedra to form a three-dimensional network, whereby the A-site cations occupy the 12-fold coordinated (cuboctahedral) voids to maintain charge neutrality (Fig. 1). Alternatively, the perovskite structure can be described by a cubic close packed AX3 sublattice with divalent B-site cations within the sixfold coordinated (octahedral) cavities .Fig. 1Crystal structure of ABX3-type metal halide perovskites
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The formability of metal halide perovskites depends on various requirements: (1) charge neutrality between cations and anions, i.e. N(A) + N(B) = 3 N(X), whereby N represents the valence of the respective A, B, or X ions ; (2) the stability of the BX6 octahedra, which can be predicted by the octahedral factor µ; (3) the ionic radii of A, B, and X need to meet the requirements for the Goldschmidt tolerance factor t .
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The octahedral factor µ, which is the ratio of the radii of the B-site cation (r B) and the halide counterion (r X), can be used to estimate the stability of the BX6 octahedra (Eq. 1) [41, 44]. The incorporation of the B-site cation is limited by ionic size restrictions defined by the X6 octahedron. For µ values between 0.442 and 0.895, metal halide perovskites have been found to be stable .
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The Goldschmidt tolerance factor concept was recently adapted for the family of hybrid organic–inorganic metal halide perovskite materials taking organic molecular cations such as CH3NH3 + into consideration [33, 47–50]. Moreover, these replacement rules are a viable tool to explain the concept of homovalent (isovalent) and heterovalent (aliovalent) substitution in metal halide perovskites. Therefore, the Goldschmidt replacement rules have attracted considerable attention recently to predict novel lead-free perovskite compounds for photovoltaic applications based on the ionic radii of the involved ions (see Table 2 for the radii of commonly used ions). Thereby, it is an essential concept that allows predictions for potential replacement candidates not only on the B-site but also on the other ion positions in the perovskite structure. The viability of this approach is shown by Kieslich et al., who theoretically studied divalent metal cations for homovalent substitution of lead in the perovskite structure to form hybrid metal halide perovskites via tolerance factor calculations . Around 600 hypothetical perovskites were predicted as potential candidates that have not been reported yet including alkaline-earth metal- and lanthanide-based materials . In addition, the tolerance factor concept was used to predict novel metal halide perovskites in various other investigations [41, 47–49].Table 2Effective ionic radii of organic molecular cations and Shannon ionic radii of inorganic cations as well as effective ionic radii of various anions [28, 48, 50, 51, 52]Cation AEffective radius r A,eff/pmReferencesCation BEffective radius r B,eff/pmReferencesAnion XEffective radius r X,eff/pmReferencesAmmonium, [NH4]+ 146Pb2+ 119Fluoride, F− 129Hydroxylammonium, [NH3OH]+ 216Sn2+ 110Chloride, Cl− 181Methylammonium, [CH3NH3]+ 217Sn4+ 69Bromide, Br− 196Hydrazinium, [NH3NH2]+ 217Ge2+ 73Iodide, I− 220Azetidinium, [(CH2)3NH2]+ 250Mg2+ 72Formate, HCOO− 136Formamidinium, [CH(NH2)2]+ 253Ca2+ 100Imidazolium, [C3N2H5]+ 258Sr2+ 118Dimethylammonium, [(CH3)2NH2]+ 272Ba2+ 135Ethylammonium, [(CH3CH2)NH3]+ 274Cu2+ 73Guanidinium, [(NH2)3C]+ 278Fe2+ 78Tetramethylammonium, [(CH3)4N]+ 292Pd2+ 86Thiazolium, [C3H4NS]+ 320Eu2+ 1173-Pyrrolinium, [NC4H8]+ 272Tm2+ 103Tropylium, [C7H7]+ 333Yb2+ 102Piperazinium, [C4H12N2]2+ 322Tl+ 150Dabconium, [C6H14N2]2+ 339Au+ 137K+ 164Au3+ 85Rb+ 172Sb3+ 76Cs+ 188Bi3+ 103Te4+ 97La3+ 103Ce3+ 101Pr3+ 99Nd3+ 98Sm3+ 96Eu3+ 95Gd3+ 94Dy3+ 91Er3+ 89Tm3+ 88Lu3+ 86Pu3+ 100Am3+ 98Bk3+ 96Shannon ionic radii of metal cations consider the respective coordination sphere of the metal, i.e. sixfold (octahedral) coordination for alkali metals (K+, Rb+, Cs+) or 12-fold (cuboctahedral) coordination for the other ones
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Beyond the stability range of the Goldschmidt tolerance factor, perovskite-like derivatives with lower dimensionality can be found. For example, two-dimensional layered perovskites isostructural to Ruddlesden–Popper phases (e.g. (CH3NH3)2CuClxBr4−x ) are obtained by introducing large (interlayer) A-site cations (Fig. 2). However, for lower dimensional variants such as one-dimensional chain-like (e.g. HDABiI5, with HDA = 1,6-hexanediammonium ([H3NC6H12NH3]2+) ) or zero-dimensional structures (e.g. (CH3NH3)3Sb2I9 ), the Goldschmidt tolerance factor concept cannot be assessed in the same way since the aforementioned ionic size restrictions are gradually lifted .Fig. 2Schematic representation of the stacking of inorganic octahedral layers (n) in the 〈100〉-oriented two-dimensional perovskite structure. A three-dimensional perovskite is formed, when n is ∞. Reprinted with permission from . Copyright (2001) Royal Society of Chemistry
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The Goldschmidt tolerance factor t is calculated according to Eq. (1) using the ionic radii of the involved A, B, and X ions (r A, r B, and r X) [41, 43, 44]. It can be used to evaluate which mismatches in size of the A, B, and X ions are tolerated to form perovskite-like structures:1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu = \frac{{ r_{B} }}{{r_{X} }}\quad\quad t = \frac{{(r_{A} + r_{X} )}}{{\sqrt {2 } \left( {r_{B} + r_{X} } \right)}}.$$\end{document}μ=rBrXt=(rA+rX)2rB+rX.
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Based on these ionic size restrictions for the involved cations and anions, a stability and formability range for ABX3 perovskite-like structures can be derived for which the tolerance factor was empirically found to be 0.8 ≤ t ≤ 1.0 . A tolerance factor of 1.0, for example, indicates the formation of an ideal ABX3-type perovskite with a cubic crystal structure (e.g. SrTiO3 ). If the values for the tolerance factor are between 1.0 and 0.9, perovskites with a cubic crystal structure are formed predominantly. If the tolerance factor is lower (t = 0.80–0.89), distorted perovskite structures with orthorhombic, tetragonal, or rhombohedral crystal structures are more likely to be formed. If t < 0.8, the A cation is too small for the formation of a perovskite structure and, therefore, alternative structures such as the ilmenite-type FeTiO3 are formed instead. If t > 1.0, the A cation is too large for the formation of a perovskite structure. Hexagonal structures are introduced instead comprising layers of face-sharing octahedra [41, 47, 48].
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Schematic representation of the stacking of inorganic octahedral layers (n) in the 〈100〉-oriented two-dimensional perovskite structure. A three-dimensional perovskite is formed, when n is ∞. Reprinted with permission from . Copyright (2001) Royal Society of Chemistry
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A substitution of lead with nontoxic and environmentally benign elements forming lead-free metal halide perovskites can be generally achieved via two approaches:homovalent substitution of lead with isovalent cations such as group-14 elements (Ge, Sn), alkaline-earth metals (Mg, Ca, Sr, Ba), transitions metals (Mn, Fe, Ni, Pd, Cu, Cd), and lanthanides (Eu, Tm, Yb),heterovalent substitution with aliovalent metal cations such as transition metals (Au), main group elements (Tl, Sb, Bi, Te), lanthanides (La, Ce, Pr, Nd, Sm, Eu, Gd, Dy, Er, Tm, Lu), and actinides (Pu, Am, Bk). Since charge neutrality cannot be obtained with these ions in an ABX3 structure, a direct substitution is not possible in this case. However, a successful replacement of the divalent lead cation can be accomplished via a mixed-valence approach, i.e. an equal proportion of mono- and trivalent metal cations to give an overall divalent state in average to balance the total charge and valence , as reported for thallium [58, 59] and gold halide perovskites [60–62]. In addition, double halide perovskites (A2BIBIIX6), which are based on the mixture of different mono- and trivalent metal cations, are a further approach towards heterovalent substitution [16, 63, 64]. Another possible avenue is based on the mixture of higher valent metal cations and vacancies to accommodate the total charge neutrality, which is accompanied by a considerable change in structure leading to A3B2X9-type perovskites (B = Sb, Bi) [35, 36, 55, 57, 65, 66]. However, these substitution approaches cannot be predicted via Goldschmidt replacement rules.
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| 28.17 |
heterovalent substitution with aliovalent metal cations such as transition metals (Au), main group elements (Tl, Sb, Bi, Te), lanthanides (La, Ce, Pr, Nd, Sm, Eu, Gd, Dy, Er, Tm, Lu), and actinides (Pu, Am, Bk). Since charge neutrality cannot be obtained with these ions in an ABX3 structure, a direct substitution is not possible in this case. However, a successful replacement of the divalent lead cation can be accomplished via a mixed-valence approach, i.e. an equal proportion of mono- and trivalent metal cations to give an overall divalent state in average to balance the total charge and valence , as reported for thallium [58, 59] and gold halide perovskites [60–62]. In addition, double halide perovskites (A2BIBIIX6), which are based on the mixture of different mono- and trivalent metal cations, are a further approach towards heterovalent substitution [16, 63, 64]. Another possible avenue is based on the mixture of higher valent metal cations and vacancies to accommodate the total charge neutrality, which is accompanied by a considerable change in structure leading to A3B2X9-type perovskites (B = Sb, Bi) [35, 36, 55, 57, 65, 66]. However, these substitution approaches cannot be predicted via Goldschmidt replacement rules.
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Homovalent and heterovalent substitution approaches lead to a wide range of lead-free metal halide perovskite semiconductors based on various elements in the periodic table (see Fig. 3), which are discussed in the following chapters.Fig. 3Lead replacement candidates in perovskite-type compounds from the periodic table of elements with the focus on homovalent substitution with group-14 elements (Ge, Sn), alkaline-earth metals (Mg, Ca, Sr, Ba), transition metals (Cu, Fe, Pd), lanthanides and actinides (Eu, Tm, Yb), heterovalent substitution with Tl, Au, Sb, Bi, and Te, and metal chalcogenide perovskites (Ti, Zf, Hf)
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The group-14 elements tin and germanium are the first logical candidates for the homovalent substitution of lead [27, 33, 68], as Sn2+ and Ge2+ have a similar electronic configuration as Pb2+. While tin and germanium halide perovskites have also good optoelectronic properties, both Sn2+ and Ge2+ ions possess a drawback compared to Pb2+ because they can be easily oxidized to the oxidation state +4 , which has its origin in the reduced inert pair effect and is even more pronounced for Ge2+ than for Sn2+.
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Sn2+ metal cations are the most obvious substitute for Pb2+ in the perovskite structure because of the similar s2 valence electronic configuration to Pb2+ and the similar ionic radius (Pb2+: 119 pm, Sn2+: 110 pm ), which makes it possible to form a perovskite with a basic formula ASnX3 (X = halide) in analogy to lead compounds. Even though tin is often presented as non-toxic alternative to lead, the toxicity of tin-based perovskites can be argued as well .
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| 29.34 |
Lead replacement candidates in perovskite-type compounds from the periodic table of elements with the focus on homovalent substitution with group-14 elements (Ge, Sn), alkaline-earth metals (Mg, Ca, Sr, Ba), transition metals (Cu, Fe, Pd), lanthanides and actinides (Eu, Tm, Yb), heterovalent substitution with Tl, Au, Sb, Bi, and Te, and metal chalcogenide perovskites (Ti, Zf, Hf)
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A wide range of elements with a stable oxidation state of +2 are in principle suitable for homovalent substitution of lead in the perovskite structure. In particular, group-14 elements (Ge2+, Sn2+) but also alkaline-earth metals (Be2+, Mg2+, Ca2+, Sr2+, Ba2+), transition metals (V2+, Mn2+, Fe2+, Co2+, Ni2+, Pd2+, Pt2+, Cu2+, Zn2+, Cd2+, Hg2+), lanthanides (Eu2+, Tm2+, Yb2+), and p-block elements (Ga2+, In2+) can be considered for alternative lead-free perovskites [49, 50, 67]. However, some of these candidates have to be excluded due to their limited ability to form perovskites, or are not well suited for photovoltaic applications because of too high band gaps (Be, Ca, Sr, Ba), their toxicity (Cd, Hg), radioactivity, or their instability of the +2 oxidation state. As a consequence, based on the aforementioned considerations and computational screening of homovalent substitution of lead in the cesium and methylammonium metal halide perovskite, the most promising candidates are Sn2+, Ge2+, Mg2+, V2+, Mn2+, Ni2+, Zn2+, and Co2+ [49, 67].
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| 27.42 |
The most studied tin halide perovskites are CH3NH3SnI3 and CH(NH2)2SnI3. In addition, in analogy to the lead halide perovskites, the structural properties of the tin-based perovskites, i.e. dimensionality and connectivity of the perovskite lattice [69, 70], can be greatly affected by the size and functionality of the A-site cation as well as by the used halide. Small monovalent A-site cations (e.g. CH3NH3 +, CH(NH2)2+, Cs+) lead to the formation of three-dimensional structures, whereas larger ones (e.g. cyclobutylammonium, tropylium) cause a reduced dimensionality such as two-dimensional layered, one-dimensional chain-like, or zero-dimensional structures [69, 71, 72]. These compositional and structural changes affect the optical and electronic properties as well.
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| 28.55 |
The first study on an entirely lead-free tin halide perovskite semiconductor used as absorber material, namely methylammonium tin iodide (CH3NH3SnI3), was reported by Noel et al. . The solar cells yielding PCE values over 6% were prepared in the device architecture glass/FTO/c-TiO2/mp-TiO2/CH3NH3SnI3/Spiro-OMeTAD/Au (FTO: fluorine-doped tin oxide, c: compact, mp: mesoporous). A scanning electron microscopy (SEM) image of the cross section of the corresponding device is shown in Fig. 4a. Using mesoporous TiO2 has been beneficial due to the shorter charge carrier diffusion lengths of the tin halide perovskite compared to the lead-based analogue. Because of the challenging stability of tin halide perovskites, solar cell preparation had to be performed entirely in inert atmosphere starting from highly pure precursor materials. It is also remarkable that an open-circuit voltage (V OC) of 0.88 V was obtained using an absorber material which has a relatively low band gap of 1.23 eV. The obtained short-circuit current density (J SC) was 16.8 mA cm−2 and the fill factor (FF) was 42% (Fig. 4b).Fig. 4 a Cross-sectional SEM image of a CH3NH3SnI3-based perovskite solar cell in meso-structured configuration. b J–V curves of tin- (CH3NH3SnI3) and lead-based (CH3NH3PbI3−xClx) perovskite solar cells under illuminated and dark conditions. Adapted with permission from . Copyright (2014) Royal Society of Chemistry
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| 29.9 |
a Cross-sectional SEM image of a CH3NH3SnI3-based perovskite solar cell in meso-structured configuration. b J–V curves of tin- (CH3NH3SnI3) and lead-based (CH3NH3PbI3−xClx) perovskite solar cells under illuminated and dark conditions. Adapted with permission from . Copyright (2014) Royal Society of Chemistry
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| 33.5 |
By substituting the I− counterion with other halides, a range of different tin halide perovskite analogues CH3NH3SnX3 (X = Cl, Br) is accessible with calculated band gaps in the range of 1.7–3.0 eV . CH3NH3SnBr3, for example, with an optical band gap of ca. 2.2 eV can be processed via vapor deposition-based methods using SnBr2 and CH3NH3Br as starting compounds . Jung et al. reported PCE values of 0.35% (co-evaporation) and 1.12% (sequential deposition) for planar perovskite solar cells with CH3NH3SnBr3 as absorber material . The optical band gap can be further fine-tuned via the halide ratio using a mixed halide approach. By variation of the I:Br ratio, the optical band gap can be engineered between 1.3 eV (CH3NH3SnI3) and 2.15 eV (CH3NH3SnBr3) . Based on this approach, Hao et al. reported a mixed iodide–bromide tin perovskite semiconductor (CH3NH3SnIBr2) with an optical band gap of 1.75 eV yielding a PCE of 5.73% in meso-structured perovskite solar cells . Figure 5a shows the absorption properties of the mixed halide tin perovskites and Fig. 5b the corresponding energy levels of the compounds, which reveal almost no change in the valence band position and an upward shift of the conduction band position when increasing the bromide content. The J–V curves are presented in Fig. 5c showing the correlation of decreasing J SC and increasing V OC when the band gap of the respective perovskite material becomes wider.Fig. 5 a Absorption properties, b energy level diagram and c J–V curves of CH3NH3Sn(I,Br)3-based perovskite solar cells. Adapted with permission from . Copyright (2014) Macmillan Publishers Limited
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| 28.27 |
CsSnBr3 possesses a direct band gap of 1.75 eV and solar cells with efficiencies of up to 2.1% have been reported using this material as absorber layer . However, CsSnBr3-based solar cells currently suffer from a low V OC (up to 420 mV) stemming most likely from a mismatch of the energy levels of the materials (TiO2, CsSnBr3, Spiro-OMeTAD) used in these devices, which gives space for further optimization by investigating better suited ETLs and HTLs. Mixed chloride/bromide cesium tin halide perovskites reveal PCE values of up to 3.2% as well as a good thermal and device stability [91, 92].
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study
| 29.55 |
Because of its good p-type conductivity under Sn-poor conditions , CsSnI3 can be used as solution-processable HTL in solid-state dye-sensitized solar cells. By SnF2-doping forming CsSnI2.95F0.05, a PCE of 8.51% (using the dye N719 as sensitizer) could be obtained [82, 94]. This report considers the perovskite layer as HTL; however, based on the presented spectral response measurements of the solar cells, it seems that also the perovskite itself contributes to the overall PCE, and thus these solar cells should be seen more as mixed dye-sensitized/perovskite solar cells.
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| 27.6 |
By introducing the CH(NH2)2+ ion into tin iodide perovskites forming CH(NH2)2SnI3, the band gap is widened to 1.41 eV. CH(NH2)2SnI3 has, in contrast to CH(NH2)2PbI3, only one thermally accessible phase, which is stable up to 200 °C. By adding SnF2, which increases the stability of Sn2+, a PCE of 2.1% could be obtained [76, 77]. Further optimization using the SnF2–pyrazine complex causing a more homogeneous distribution of SnF2 in the perovskite led to PCE values of 4.8% and recently the efficiency of this material could be further increased to 6.22% . In this latter study, PEDOT:PSS and fullerene (C60) have been used as hole transport layer (HTL) and electron transport layer (ETL) in contrast to the both aforementioned reports, in which Spiro-OMeTAD and TiO2 have been used. Moreover, this study points out that similar to the lead-based perovskites solvent treatment during spin coating is crucial for the performance of tin-based perovskite solar cells and diethyl ether dripping was found to give the best results in terms of PCE and reproducibility. In a further study, mixed iodide/bromide CH(NH2)2Sn-halide perovskites led to a PCE of 1.72% using MoO3 as hole transport material .
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| 28.83 |
Introducing Cs+ as cation leads to CsSnI3, which is thermally even more stable than CH(NH2)2SnI3 and melts at 451 °C [81, 82]. Two polymorphs are existing at room temperature: B-γ-CsSnI3, a black orthorhombic phase, suitable for solar cell applications [81, 83, 84], and a yellow Y-CsSnI3 phase with a one-dimensional double-chain structure [83, 85, 86]. B-γ-CsSnI3 has a direct band gap of 1.3 eV and by preparing it via an alternating deposition of SnCl2 and CsI layers followed by a thermal treatment at 175 °C, solar cells with a PCE of 0.9% could be obtained in a glass/ITO/CsSnI3/Au/Ti device structure (ITO: indium tin oxide) . By a controlled grain-coarsening of CsSnI3 films based on heat treatment and using a planar device architecture (NiOx as HTL, PCBM as ETL) solar cells with a PCE of 3.31% have been reported by Wang et al. . The addition of 20% SnF2 to CsSnI3 was found to positively influence the solar cell performance in meso-structured perovskite solar cells and a PCE of 2.02% was reached . The addition of SnF2 lowers the background charge carrier density by neutralizing traps [89, 90].
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| 29.56 |
Even though encouraging stability data have already been reported, the main drawback of tin halide perovskites is still the chemical instability of the divalent metal cation, which is due to the oxidation of Sn2+ to Sn4+ in ambient conditions . As a consequence, the oxidation of Sn2+ to the chemically more stable Sn4+ analogue impedes the charge neutrality of the perovskite and causes the degradation of the perovskite by formation of oxides/hydroxides of tin, and furthermore Sn4+ leads to hole doping of the material [27, 95]. To avoid oxidation, inert processing and rigorous encapsulation of the tin-based perovskite devices are necessary.
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| 27.34 |
To overcome this oxidation stability issue, double perovskite semiconductors with a basic formula A2SnX6 (A = Cs, C7H7, X = halide) have been introduced [69, 96–99]. The double perovskite structure is built up from face-centered nearly isolated SnX6 octahedra, in which the cuboctahedral voids are occupied by A-site cations . In this structure, tin has the more stable oxidation state +4 resulting in improved air and moisture stability and processability [69, 96–99]. Due to enhanced air stability and promising photovoltaic properties , tin-based double perovskite semiconductors (e.g. Cs2SnI6) have recently been considered as absorber material in perovskite solar cells yielding PCE values of almost 1% . Alternatively, double perovskites were discussed as hole transport materials (Cs2SnI6 , Cs2SnI3Br3 ) in solid-state dye-sensitized solar cells using classical dyes as absorbers leading to PCE values up to 7.8% .
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| 27.44 |
Furthermore, optoelectronically active cations like the tropylium (C7H7 +) ion have been investigated as A-site cation in tin halide perovskites. (C7H7)2SnI6 appears as a deep black solid, and crystallizes in a monoclinic crystal system containing isolated tin(IV)-iodide octahedra .
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| 32.4 |
A summary of structural and optical data of tin halide perovskites and their performance as absorber material in photovoltaic devices is given in Table 3.Table 3Structural and optical data of tin halide perovskites and the highest obtained PCEs (if applied in photovoltaic devices)PerovskiteSim./exp.Crystal system (space group)DimensionalityBand gap/eVPCE/%ReferencesCH3NH3SnBr3 Exp.Pseudocubic (P4mm)3D2.15–2.24.27[74, 75]CH3NH3SnIBr2 Exp.Pseudocubic (P4mm)3D1.755.73CH3NH3SnI2BrExp.Pseudocubic (P4mm)3D1.565.48[73, 75]CH3NH3SnI3 Exp.Pseudocubic (P4mm)3D1.27–1.355.23[75, 102, 103]Tetragonal (P4mm)1.21–1.356.4[27, 71]CH(NH2)2SnI2BrExp.Orthorhombic (–)3D1.681.72CH(NH2)2SnI3 Exp.Orthorhombic (Amm2)3D1.4–1.416.22[71, 76, 78, 79](C7H7)2SnI6 Exp.Monoclinic (–)0D1.2–CsSnCl3 Exp.Monoclinic (–)3D2.8–CsSnBrCl2 Exp.Monoclinic (–)3D2.1–CsSnBr2ClExp.Cubic (–)3D1.9–CsSnBr3 Exp.Cubic (–)3D1.75–1.82.1[90, 91, 104, 105]CsSnIBr2 Exp.Cubic (–)3D1.63–1.653.2[91, 92, 104]CsSnI2BrExp.Cubic (–)3D1.37–1.411.67[91, 104]CsSnI3 Exp.Orthorhombic (–)3D1.27–1.313.31[82, 88, 89, 91, 104]CsSnI2.95F0.05 Exp.Orthorhombic (Pnma)3D1.38.51a Cs2SnCl6 Exp.Cubic (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Fm\bar{3}m$$\end{document}Fm3¯m m)3D3.90.07a Cs2SnBr6 Exp.Cubic (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Fm\bar{3}m$$\end{document}Fm3¯m m)3D2.70.04a Cs2SnI6 Exp.Cubic (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Fm\bar{3}m$$\end{document}Fm3¯m m)3D1.26–1.620.86, 7.8a [97–99, 106]Cs2SnI3Br3 Exp.Cubic (Fm \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\bar{3}$$\end{document}3¯ m)3D1.433.63a aPerovskite was used as HTL in a dye-sensitized solar cell
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clinical case
| 29.1 |
Germanium halide perovskites, however, have rarely been investigated experimentally, which is presumably due to the chemical instability upon oxidation of the divalent Ge2+ cation [33, 68]. Due to the reduced inert electron pair effect, this oxidation stability issue is even more prominent in germanium-based perovskites than in tin-based ones.
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| 32.2 |
Stoumpos et al. thoroughly investigated the structural, electronic and optical properties of germanium halide perovskites with the basic formula AGeI3 incorporating Cs+ and different organic A-site cations . Depending on the A-site cation, different structures can be formed. Small cations such as Cs+, CH3NH3 + or CH(NH2)2+ ions form three-dimensional perovskite frameworks based on GeI6 4− corner-sharing octahedra . Bigger A-site cations (e.g. guanidinium, trimethylammonium) lead to distortions of the crystal structure and one-dimensional chain-like hexagonal perovskite structures (CsCdBr3-type) consisting of GeI6 4− face-sharing octahedra are formed [33, 68]. Using the n-butylammonium ion as A-site cation, the orthorhombic perovskite (C4H9NH3)2GeI4 is formed exhibiting a two-dimensional structure in which perovskite sheets consisting of corner-sharing GeI6 octahedra are separated by bilayers of n-butylammonium cations .
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| 30.25 |
Another potential candidate for the substitution of lead in the perovskite structure is the group-14 metalloid germanium. In comparison to Pb2+, the divalent germanium cation (Ge2+) is in the same oxidation state but exhibits a lower electronegativity, a more covalent character and an ionic radius (73 pm) lower than Pb2+ (119 pm) [51, 52]. Nevertheless, Goldschmidt tolerance factor calculations support the formation of germanium halide perovskites, as shown for CH3NH3GeX3 (X = Cl, Br, I) compounds with tolerance factor values of 1.005 (CH3NH3GeCl3), 0.988 (CH3NH3GeBr3), and 0.965 (CH3NH3GeI3), which coincide with t values reported for the ideal perovskite structure (0.97 < t < 1.03) [107, 108].
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| 30.47 |
Theoretical considerations using density functional theory (DFT) methods show that germanium halide perovskites have high absorption coefficients as well as similar absorption spectra and carrier transport properties as the lead analogues [33, 42, 107, 109]. First-principle calculations of CsGeX3 (X = Cl, Br, I) perovskites show that the band gaps depend on the halide ion, i.e. CsGeCl3 (3.67 eV) > CsGeBr3 (2.32 eV) > CsGeI3 (1.53 eV) , see also Table 4. Moreover, mixed halide germanium perovskites such as Cs2GeCl2I4, Cs2GeBr2I4, and Cs2GeI2Br4 were predicted to be promising direct band gap semiconductors . Sun et al. extended the theoretical investigations to hybrid germanium halide perovskites, namely to CH3NH3GeX3 (X = Cl, Br, I) compounds . The calculated band gaps based on PBE (Perdew–Burke–Ernzerhof) functionals were found to show a similar trend as for the cesium-based compounds, i.e. CH3NH3GeCl3 (3.76 eV) > CH3NH3GeBr3 (2.81 eV) > CH3NH3GeI3 (1.61 eV) and the band gaps of the iodide-based compounds are similar to the lead analogues CsPbI3 (1.73 eV) and CH3NH3PbI3 (1.57 eV) .Table 4Structural and optical data of germanium halide perovskites and the obtained PCEs (if used as absorber material in photovoltaic devices)PerovskiteSim./exp.Crystal system (space group)DimensionalityBand gap/eVPCE/%ReferencesRbGeCl3·x H2OExp.Monoclinic (P21/m)3D3.84–RbGeBr3 Exp.Trigonal (R3m)3D2.74–(RbxCs1−x)GeBr3 Exp.Trigonal (R3m)3D2.4 (x = 0.25)–2.4 (x = 0.5)2.4 (x = 0.75)CsGeCl3 Exp.Trigonal (R3m)3D3.4–3.67–CsGeBr3 Exp.Trigonal (R3m)3D2.32–2.4–CsGe(BrxCl1−x)3 Exp.Trigonal (R3m)3D2.65 (x = 0.25)–2.5 (x = 0.5)2.47 (x = 0.75)CsGeI3 Sim./exp.Trigonal (R3m)3D1.53–1.630.11[33, 42, 68, 108, 116, 117]CH3NH3GeCl3 Sim.Trigonal3D3.74–3.76–[107, 117]CH3NH3GeBr3 Sim.Trigonal3D2.76–2.81–[107, 117]CH3NH3GeI3 Exp.Trigonal (R3m)3D1.9–2.00.20[33, 68, 117]CH(NH2)2GeI3 Exp.Trigonal (R3m)3D2.2–2.35–[33, 68, 117]MFOGeI3 Exp.Monoclinic (P21)3D2.5–[68, 117]GUAGeI3 Exp.Monoclinic (P21/c)3D2.7–[68, 117]TMAGeI3 Exp.Hexagonal (P63)3D2.8–IPAGeI3 Exp.Tetragonal (I \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\bar{4}$$\end{document}4¯2d)3D2.7– MFO acetamidinium, GUA guanidinium, TMA trimethylammonium, IPA isopropylammonium
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clinical case
| 30.33 |
The A-site cation of the perovskite structure is particularly important for band gap engineering [33, 68]. For AGeI3 with a three-dimensional structure, the band gap was found to systematically increase when replacing the small Cs+ cation (1.6 eV) with larger ones such as CH3NH3 + (1.9 eV), CH(NH2)2+ (2.2 eV), or acetamidinium (2.5 eV) . Substitution with even bulkier organic cations does not only reduce the dimensionality of the perovskite framework but also further increases the band gap, e.g. trimethylammonium (2.8 eV), guanidinium (2.7 eV), and isopropylammonium (2.7 eV) . Moreover, three-dimensional perovskites are materials with a direct band gap, while one-dimensional compounds exhibit indirect band gaps .
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| 29.16 |
CsGeI3 and CH3NH3GeI3 have already been implemented as absorber materials in meso-structured perovskite solar cells yielding PCE values of 0.11 and 0.20%, respectively (Fig. 6) . This moderate performance might be due to the oxidation of Ge2+ to Ge4+ already occurring during the fabrication of the solar cell and the limited V OC, in particular of the CsGeI3 (74 mV), was suggested to originate from the defect chemistry in this material .Fig. 6 a UV–Vis absorption data of CsSnI3, CsGeI3, CH3NH3GeI3, and CH(NH2)2GeI3 and b J–V curves of CsGeI3- and CH3NH3GeI3-based solar cells. Adapted with permission from . Copyright (2015) Royal Society of Chemistry
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study
| 31.16 |
In a patent by Huang et al., a PCE of approximately 3% in a meso-structured perovskite solar cell architecture is claimed, however, with limited experimental data . This value is still much lower compared to the theoretically possible PCE values of 27.9% predicted by Qian et al. and further effort has to be made to improve the efficiency of germanium-based perovskites to competitive values . Nonetheless, germanium halide perovskites are promising low-temperature solution-processable semiconductors for photovoltaic applications and the full potential of this material is by far not exploited yet.
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| 29.12 |
Alkaline-earth metals such as magnesium, calcium, strontium, and barium can be potential homovalent substitutes due to ionic radii suitable to form perovskite structures, a high abundance in the Earth’s crust, non-toxicity, and stable +2 oxidation states similar to Pb2+ [47, 118]. Alkaline-earth metal halide perovskites with a basic formula ABX3 (B = Mg, Ca, Sr; X = Cl, Br, I) employing inorganic A-site cations (e.g. K+, Cs+) have been studied extensively with regard to their photoluminescence properties resulting from doping with rare earth metal cations such as Eu2+, Yb2+, or Tm2+ [119–123]. Until now, only a few research studies have been focused on alkaline-earth-metal-based halide perovskites for photovoltaic applications, which is due to the high calculated band gaps and extreme sensitivity towards humidity .
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| 28.78 |
Strontium is a fairly nontoxic, relatively inexpensive, highly abundant alkaline-earth metal with an ionic radius (Sr2+: 118 pm) very similar to lead (Pb2+: 119 pm), which makes strontium a suitable candidate for homovalent substitution of lead in the perovskite without affecting the crystal structure [51, 124].
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| 27.7 |
The current research in the field of strontium halide perovskites for optoelectronic applications is mainly focusing on CH3NH3SrI3 [118, 124]. DFT calculations of Jacobsson et al. and Pazoki et al. predict the formation of a stable CH3NH3SrI3 perovskite material despite the electronegativity difference between lead (2.33) and strontium (0.95) [118, 124, 125]. This lower electronegativity of strontium together with the missing d-orbitals in the valence of Sr2+ are responsible for a significantly higher band gap of 3.6 eV (CH3NH3SrI3) compared to the lead analogue (1.66 eV) [118, 124] and thus limit a possible application as absorber material in solar cells. In addition, the higher electronegativity difference between metal and halogen leads to more pronounced ionic interactions of the metal–halogen bond in strontium perovskites [118, 124]. CH3NH3SrI3 can be prepared following a one-step solution-based processing route from CH3NH3I and SrI2. Alternatively, vapor phase or layer-by-layer deposition methods are suggested as preparation pathways . CH3NH3SrI3 exhibits a poor stability under ambient conditions due to its hygroscopic nature. Alternatively, Pazoki et al. suggested a potential application as charge-selective contact material .
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| 30.28 |
According to simulations by Filip et al. and Choudhary et al., Mg2+ can replace lead in the perovskite structure forming magnesium halide perovskites with low effective masses, reasonable absorption coefficients, and direct band gaps tunable within the visible range of the electromagnetic spectrum depending on the size of the A-site cation [49, 67]. In case of AMgI3 perovskites, the band gap was predicted to be tunable using different A-site cations with calculated band gaps of 0.9 eV (CH(NH2)2MgI3), 1.5 eV (CH3NH3MgI3), and 1.7 eV (CsMgI3) . Theoretical calculations predicted magnesium halide perovskites to be stable despite the smaller ionic radius of Mg2+ (72 pm) compared to Pb2+ (119 pm) [49, 51]. Suta et al. synthesized Eu2+-doped CsMgI3, which crystallizes in a CsNiCl3 structure (a distorted perovskite structure) comprising face-sharing MgI6 4− octahedra which feature linear chains along the c-axis and 12-fold coordinated Cs+ ions in the anti-cuboctahedral positions . To our knowledge, magnesium halide perovskites have not been implemented as absorber materials in solar cells yet, which might be due to the sensitivity towards humidity .
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| 29.39 |
Uribe et al. synthesized CH3NH3CaI3 and CH3NH3CaI3−xClx with pseudocubic structure via a low-temperature solution-based route from CH3NH3I mixed with CaI2 or CaCl2 as precursors . The optical band gap of CH3NH3CaI3 was determined to be 3.78 eV matching quite well with the calculated band gap of 3.4 eV . Due to the high band gap, the low mobility and the instability in moist atmosphere, calcium halide perovskites are not very suitable for photovoltaic applications but might be possible candidates for charge-selective contacts [47, 118].
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other
| 29.08 |
The stable Ba2+ metal cation exhibits a slightly larger ionic radius (135 pm) compared to Pb2+ (119 pm) . Applying the Goldschmidt replacement rules, CH3NH3BaI3 has a tolerance factor t of 0.797, which is similar to the lead halide perovskite analogue CH3NH3PbI3 (t = 0.83) . Consequently, CH3NH3BaI3 is expected to have a similar crystal structure as CH3NH3PbI3. DFT calculations predicted CH3NH3BaI3 to form stable perovskite materials with an estimated band gap of 3.3 eV . In comparison to CH3NH3PbI3 (1.57 eV), the high band gap is caused by the low work function (2.7 eV) and low electronegativity (0.88) of barium [118, 125, 127].
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| 29.73 |
The structural and optical data of alkaline-earth metal halide perovskites are summarized in Table 5.Table 5Structural and optical data of alkaline-earth metal halide perovskitesPerovskiteSim./exp.Crystal system (space group)Band gap/eVReferencesCH3NH3MgI3 Sim.Tetragonal1.5CH(NH2)2MgI3 Sim.Trigonal (P3m1)0.9CsMgI3 Sim.Orthorhombic1.7CH3NH3CaI3 Sim./exp.Tetragonal/pseudo-orthorhombic2.95, 3.78[47, 118]CH3NH3CaI3−xClx Exp.––CH3NH3SrI3 Sim./exp.Tetragonal3.6 eVCH3NH3BaI3 Sim.Tetragonal3.3 eVDimensionality and PCE values have not been reported for these materials
|
clinical case
| 27.66 |
Considerable interest in the field of transition metal halide perovskites arises from the rich chemistry and relatively high abundance of transition metals . The multiple oxidation states of transition metals, however, might cause problems with regard to chemical stability . In addition, the small ionic radii of transition metal cations such as Cu2+ (73 pm), Fe2+ (78 pm), or Pd2+ (86 pm) sterically hinder the formation of three-dimensional structures, which leads to lower dimensional layered configurations isostructural to Ruddlesden–Popper perovskites (e.g. K2NiF4) [51, 128] such as (CH3NH3)2CuClxBr4−x (CH3NH3)2FeCl4 , or (CH3NH3)2PdCl4 .
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other
| 28.48 |
Transition metal halide perovskites were studied extensively in the last decades, in particular with regard to the magnetic properties and phase transitions resulting from the lower dimensional structures. Various transition metals such as vanadium, manganese, iron, cobalt, nickel, palladium, copper, zinc, cadmium, and mercury have been predicted as promising replacement candidates for lead in the perovskite structure [34, 49, 128]. Various alternative lead-free transition metal halide perovskite materials have been reported [131, 132]. CsNiX3 (X = Cl, Br, I), for example, was synthesized via a hydrothermal method to obtain a nickel-based perovskite with a BaNiO3 structure consisting of face-sharing NiX6 octahedra which are separated by CsX12 cuboctahedra . CsNiCl3 and CsNiBr3, in particular, were predicted to exhibit low electronic band gaps and dispersive band edges making these two compounds attractive for photovoltaics . This hydrothermal synthesis method is also suggested to be extendable to cobalt and iron perovskites . Layered perovskite structures of bis-(alkylammonium) metal(II) tetrahalide (CnH2n+1NH3)2MX4 and (α,ω-)polymethylene diammonium metal(II) tetrahalide NH3(CH2)mNH3MX4 (M = Cd, Cu, Fe, Mn, Pd and X = Cl, Br) were investigated by Arend et al. . Mercury and cadmium halide perovskites have the same inherent problems of high toxicity as lead-based materials. Despite the toxicity issue of cadmium-based compounds, a hybrid cadmium halide perovskite ((3-pyrrolinium)(CdCl3)) with an above-room-temperature ferroelectric behavior and an anomalous photovoltaic effect has been reported recently . The potential of this material for photovoltaic applications is supported by the extraordinary high V OC of 32 V of a 1-mm bulky crystal . A more detailed view on transition metal halide perovskites based on copper, iron and palladium is given in the following chapters.
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study
| 27.73 |
A further way to stabilize the layered structure is the use of organic diammonium cations (NH3 +-R-NH3 +, R = alkyl, aryl) in (NH3-R-NH3)CuX4 compounds . Diammonium-based layered structures feature hydrogen bonding interactions of both functional ammonium groups to halogen atoms of the inorganic sheets resulting in an “eclipsed” arrangement of the layers, which are separated by a single organic layer instead of a double or bilayer (Fig. 7, right) . The distance between adjacent inorganic layers can be influenced by the length of the organic spacer R, which eventually affects the compound's dimensionality and physical properties . Examples are (ethylenediammonium)CuBr4 and [NH3(CH2)nNH3]CuX (n = 2–5, X = Cl4, Cl2Br2) .
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other
| 29.95 |
Two-dimensional copper halide perovskites have been investigated with regard to their structural and magnetic properties (e.g. [C2H5NH3]2CuCl4 , 3-ammoniumpyridinium tetrachlorocuprate(II) , 3-ammoniumpyridinium tetrabromocuprate(II) , bis(morpholinium) tetrachlorocuprate(II) ), UV light-induced photochromic behavior (e.g. (C4H9NH3)2CuCl4 ), as intercalation-type cathode material in Li-ion batteries (e.g. (EDBE)[CuCl4] with EDBE = 2,2′-(ethylenedioxy) bis(ethylammonium) ), and as solution-processable absorber in perovskite solar cells [34, 53]. Cui et al. implemented two-dimensional layered copper perovskites (p-F-C6H5C2H4NH3)2CuBr4 and (CH3(CH2)3NH3)2CuBr4) as absorber materials in meso-structured perovskite solar cells and obtained PCE values of 0.51 and 0.63%, respectively (Fig. 8) . Both materials were prepared via a low-temperature, solution-based method from CuBr2 and the corresponding ammonium bromide compound, i.e. n-butylammonium bromide or 4-fluorophenethylammonium bromide, in aqueous hydrobromic acid and exhibited optical band gaps of 1.74 and 1.76 eV, respectively .Fig. 8 a J–V curves under illuminated and dark conditions and b IPCE (incident photon-to-electron conversion efficiency) spectra of copper halide perovskite-based solar cells using (p-F-C6H5C2H4NH3)2CuBr4 (P1) and (CH3(CH2)3NH3)2CuBr4) (P2) as absorber materials. Adapted with permission from . Copyright (2015) Elsevier
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other
| 28.98 |
Copper is a non-toxic, low-cost earth abundant transition metal. The divalent Cu2+ cation is of particular interest for the incorporation into the perovskite structure as replacement for Pb2+ because of its ambient stability and the high absorption coefficient in the visible region [53, 134]. Cu2+ has a 3d9 4s0 (t2g6 eg3) electronic configuration different to the group-14 main group metal cations of Sn2+ and Pb2+, i.e. lone pair electrons, which has a considerable effect on the electronic band structure [28, 53, 134].
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study
| 27.78 |
Due to the smaller ionic radius of Cu2+ (73 pm) compared to Pb2+ (119 pm) or Sn2+ (110 pm), the formation of three-dimensional structures is sterically hindered, and thus hybrid copper halide perovskites form two-dimensional layered structures, which are isostructural to Ruddlesden–Popper phase compounds [51, 53, 128, 135]. These hybrid perovskites have the general formula (R-NH3)2CuX4 incorporating monovalent ammonium cations (R = alkyl, aryl) and halide counterions . The two-dimensional structures form inorganic layers of corner-sharing BX6 octahedra separated by monolayers of organoammonium cations on either side of the metal halide sheets, which are accommodated within the voids of the inorganic framework [34, 135–138]. The layered structure is stabilized by hydrogen bonding interactions (N–H···X) between the ammonium groups and the halogen atoms and by van der Waals interactions between the interdigitating organic moieties [135, 139]. Each successive inorganic perovskite sheet is shifted to give a “staggered” configuration of the layers (Fig. 7, left) . Examples are (CH3(CH2)3NH3)2CuBr4 and (p-F-C6H5C2H4NH3)2CuBr4 .Fig. 7Schematic representation of 〈100〉-oriented perovskites with organic monoammonium ((R-NH3)2MX4, left) and diammonium ((NH3-R-NH3)MX4, right) cations. Reprinted with permission from . Copyright (2001) Royal Society of Chemistry
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| 29.98 |
a J–V curves under illuminated and dark conditions and b IPCE (incident photon-to-electron conversion efficiency) spectra of copper halide perovskite-based solar cells using (p-F-C6H5C2H4NH3)2CuBr4 (P1) and (CH3(CH2)3NH3)2CuBr4) (P2) as absorber materials. Adapted with permission from . Copyright (2015) Elsevier
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clinical case
| 29.33 |
Cortecchia et al. reported on two-dimensional copper halide perovskites with the general formula (CH3NH3)2CuClxBr4−x with a varying Br:Cl ratio . Ligand-to-metal charge transfer transitions and Cu d–d transitions influence the absorption properties of this material . In addition, the optical band gap was found to be tunable via the Br:Cl ratio within the visible to near-infrared range with a bathochromic shift for higher bromide content: (CH3NH3)2CuCl4 (2.48 eV), (CH3NH3)2CuCl2Br2 (2.12 eV), (CH3NH3)2CuClBr3 (1.90 eV), and (CH3NH3)2CuCl0.5Br3.5 (1.80 eV) . The as-prepared (CH3NH3)2CuClxBr4−x perovskites were investigated in solar cells using thick (5 µm) mesoporous TiO2 scaffolds giving PCE values of 0.0017% ((CH3NH3)2CuCl0.5Br3.5) and 0.017% ((CH3NH3)2CuCl2Br2) . However, the photovoltaic performance of layered copper halide perovskites in general is limited by various factors including low absorption coefficients, the high effective mass of holes and the intrinsic low conductivity of two-dimensional perovskite structures [34, 53].
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| 27.98 |
The choice of the halide counterion plays a key role not only in the engineering of the band gap but is also essential with regard to the material’s stability, film formation properties and photovoltaic performance. Bromide is responsible for the partial reduction of Cu2+ to Cu+ in the perovskite framework, which is accompanied by the formation of anion vacancies. These crystallographic defects act as electron traps and limit the photovoltaic performance since an additional charge recombination pathway is introduced . This is supported by Cortecchia et al. who found a pronounced photoluminescence with higher bromine contents resulting from the in situ formation of Cu+ ions and the corresponding charge carrier recombination at the charge traps . Chloride was found to be essential for the material’s stability against the copper reduction and to improve the crystallization of the perovskite accompanied by a hypsochromic shift of the optical band gap .
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| 27.98 |
The presence of the Jahn–Teller active Cu2+ metal cation introduces an additional flexibility into the inorganic framework, which also affects hydrogen bonding interactions . This is based on the Jahn–Teller distortion of the CuX6 octahedra leading to an elongation of two equatorial Cu–X bonds within the octahedral coordination. As a consequence, the layered perovskite adopts an antiferrodistortive structure in which adjacent Cu2+ ions are linked via one short (normal) and one Jahn–Teller elongated (semicoordinate) bond via a bridging halide ion . The normal bond length is relatively constant, whereas the semicoordinate bond is considerably elastic, allowing the inorganic layers to adopt a more flexible structure, which enables the interaction with larger organic ammonium cations to be incorporated into the two-dimensional structure [53, 137]. Other layered perovskite analogues with Jahn–Teller active metal cations such as Cr2+ show similar structural distortions and ferromagnetic behavior (e.g. (C6H5CH2NH3)2CrBr4) . The substitution of Cu2+ or Cr2+ with other divalent metal cations which do not show a Jahn–Teller effect (e.g. Mn2+, Fe2+, Cd2+) causes a rather rigid inorganic framework of the perovskite materials, which exhibit antiferromagnetic behavior [28, 137].
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| 30.2 |
Beside limitations of charge transport properties based on two-dimensional structures and inappropriate band gaps for solar cells, a drawback of iron halide perovskites are the multiple oxidation states of iron that limit the material’s stability towards oxidation, i.e. oxidation of Fe2+ to Fe3+ similar to tin- and germanium-based perovskites . Thus, iron halide perovskites have not been used as absorber material for photovoltaic applications yet.
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| 27.73 |
Only a few studies on palladium-based perovskites have been reported so far [44, 146, 147]. Most of the investigated palladium halide perovskites exhibit the general formula A2PdX4, where A is an organic aliphatic or aromatic ammonium cation (RNH3 +) such as CH3NH3 + and n-octylammonium , and X is a halide . These materials form two-dimensional layered structures consisting of an alternating stack of organic and inorganic layers .
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| 29.95 |
The smaller ionic radius of the divalent Fe2+ metal cation (78 pm) compared to Pb2+ (119 pm) sterically hinders the formation of three-dimensional structures . Two-dimensional layered structures isostructural to Ruddlesden–Popper perovskites are formed instead .
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| 28.78 |
Several two-dimensional iron halide perovskites with a general formula A2FeX4 have been studied, where A is an organic aliphatic or aromatic ammonium cation and X is a halide counterion [129, 143]. The layered perovskites are made up of alternating stacks of organic (alkyl, aryl) ammonium and inorganic metal–halogen sheets of corner-sharing FeX6 octahedra . Even though various hybrid iron halide perovskites such as (RNH3)2FeCl4 (R = CH3, C2H5, C3H7, C6H5CH2), (CH3NH3)2FeCl2Br2, (CH3NH3)2FeCl4, and (CH3NH3)2FeCl3Br have been investigated with regard to their magnetic properties, only a few studies pay attention to the electrical and optical properties [129, 143–145].
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| 30.38 |
Although (CH3NH3)2PdCl4 is expected to form a three-dimensional structure according to the Goldschmidt tolerance factor concept (t = 0.956, which is clearly within the range for three-dimensional perovskites (0.813–1.107) ), Huang et al. found a two-dimensional layered structure . (CH3NH3)2PdCl4, which was prepared via a low-temperature solution-based method using CH3NH3Cl and PdCl2 under ambient conditions, exhibits interesting properties for optoelectronic applications with a direct optical band gap of 2.22 eV and shows an absorption coefficient of about 104 cm−1 . X-ray diffraction and UV–Vis measurements confirm the improved ambient stability of the material compared to lead- and tin-based perovskites. The authors suggest the substitution of chloride with heavier halides such as bromide or iodide to lower the band gap. Together with the increased oxidation stability and promising optical properties, this could be a promising example of a palladium halide perovskites for optoelectronic applications.
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| 30.25 |
Cheng et al. synthesized (C8H17NH3)2PdCl4 using n-octylammonium chloride and PdCl2, which exhibits a similar two-dimensional layered structure as the methyl-ammonium analogue . The inorganic layers consist of a PdCl4 2− network and are sandwiched by organic n-octylammonium cations. This perovskite material was used as template for preparing self-assembled, ultrathin palladium nanosheets .
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| 33.28 |
In addition, rigid layered structures with high crystallinity can be prepared using PdCl2 and propylammonium-functionalized silsesquioxane under ambient conditions. The hybrid palladium halide perovskite material exhibits two-dimensional structures consisting of corner-sharing PdCl4 2− octahedra and organic interlayers of alkylammonium functional silsesquioxane with a cage-like structure . The material showed excitonic absorption/emission properties similar to other layered lead-based perovskites (PbCl4 2−). In addition, the silsesquioxane produces a microporous scaffold between the inorganic metal halide layers that can be filled with molecules. Similar approaches are reported for copper, lead, and manganese forming hybrid silsesquioxane–metal halide perovskites with porous structures .
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| 28.17 |
Table 6 gives an overview about structural and optical data of transition metal and europium halide perovskites and their performance as absorber material in solar cells.Table 6Structural and optical data of transition metal and europium halide perovskites and the obtained PCEs (if applied in photovoltaic devices)PerovskiteSim./exp.Crystal system (space group)DimensionalityBand gap/eVPCE/%References(p-F-C6H5C2H4NH3)2CuBr4 Exp.–2D1.740.51(CH3(CH2)3NH3)2CuBr4 Exp.–2D1.760.63(CH3NH3)2CuCl4 Exp.Monoclinic (P121/a1)2D2.48–(CH3NH3)2CuCl2Br2 Exp.Orthorhombic (Acam)2D2.120.017(CH3NH3)2CuClBr3 Exp.Orthorhombic (Acam)2D1.90–(CH3NH3)2CuCl0.5Br3.5 Exp.Orthorhombic (Acam)2D1.800.0017(CH3NH3)2FeCl4 Exp.Orthorhombic (Pccn) <335 K2D––[129, 143, 144]Tetragonal (I4/mmm) >335 K – (C2H5NH3)2FeCl4 Exp.–2D––(C3H7NH3)2FeCl4 Exp.–2D––(C6H5CH2NH3)2FeCl4 Exp.–2D––(CH3NH3)2FeCl2Br2 Exp.–2D––(CH3NH3)2FeCl3BrExp.–2D––(CH3NH3)2PdCl4 Exp.–2D2.22–(C8H17NH3)2PdCl4 Exp.–2D––CH3NH3EuI3 Exp.–3D––(C4H9NH3)2EuI4 Exp.–2D––[148, 149]
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| 39.1 |
Rare earth metal ions have been used as substituent for Pb2+ giving rise towards lanthanide and actinide halide perovskites [148, 149]. Liang and Mitzi investigated a novel class of luminescent europium halide perovskites: CH3NH3EuI3 is a three-dimensional ABX3-type perovskite with a tetragonally distorted structure of BX6 corner-connected octahedra, which can be synthesized via a diffusion-based solid-state synthesis route from CH3NH3I and EuI2 . (C4H9NH3)2EuI4 is a two-dimensional A2BX4-type perovskite adopting a layered structure of corner-sharing BX6 octahedra sandwiched by organic butylammonium cations on both sides of the metal halide sheets . The material was made by a low-temperature (ca. 140–160 °C) solid-state reaction of C4H9NH2·HI and EuI2 . Solution-based synthesis routes are limited by the oxidation instability of Eu2+, and by the strong tendency of Eu2+ to bind solvent molecules, thereby impeding the perovskite formation. However, both structure types are characterized by a sixfold Eu(II) coordination, i.e. EuI6 octahedra. The authors expect both families of compounds to be interesting materials for hybrid optoelectronic devices such as light-emitting diodes (see also Table 6).
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| 30 |
In addition, rare earth metal ions are commonly used as dopants in ABX3-type perovskites. In particular, alkaline-earth metal halide perovskites of the family CsBX3 (B = Mg, Ca, Sr; X = Cl, Br, I) have been investigated with regard to their optical properties (e.g. photoluminescence) due to doping with rare earth metal ions such as Eu2+ [119–121], Tm2+ , and Yb2+ . In case of CsBI3:Eu2+ and CsBBr3:Eu2+ (B = Mg, Ca, Sr), divalent Eu2+ metal cations occupy the sixfold, octahedrally coordinated alkaline-earth metal sites of the host compound [120, 121]. For thulium- and ytterbium-doped perovskites, the situation is quite similar [122, 123]. The applicability of these luminescent materials, for example in optoelectronic devices, is, however, limited because of the sensitivity towards moisture . Nevertheless, lanthanide-based perovskites are expected to have interesting optical properties and, therefore, might be potential candidates for novel absorber materials for photovoltaics .
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| 27.2 |
In addition, lanthanides (e.g. La3+, Ce3+, Pr3+, Nd3+, Sm3+, Eu3+, Gd3+, Dy3+, Er3+, Tm3+, Lu3+) and actinides (e.g. Pu3+, Am3+, Bk3+) have been employed in quaternary halide double perovskites [63, 150], but till now no studies on their photovoltaic properties have been reported.
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other
| 27.95 |
Heterovalent substitution is a second viable approach towards alternative lead-free perovskite materials. It is based on the replacement of the divalent lead cation with a cation in a different valence state, e.g. a mono-, tri- or tetravalent cation. Due to the different valence state, no straightforward substitution with heterovalent cations is possible. Therefore, two different procedures for heterovalent replacement can be distinguished: The first method, the mixed-valence approach, is based on a mixture of an equal number of mono- and trivalent cations to give an average overall valence state of +2 as present in Pb2+. Examples for perovskites following the mixed-valence approach are thallium [58, 59] and gold [60–62] halide perovskites. The second method is based on the heterovalent substitution of the divalent Pb2+ with trivalent cations such as Sb3+ and Bi3+ [35, 36, 55, 65, 66]. However, this is accompanied with a considerable change in the structure from ABX3-type to A3B2X9-type perovskites to maintain charge neutrality.
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study
| 28.17 |
Enormous progress in the development of novel lead-free perovskite semiconductors might arise from the heterovalent substitution approach since further non-divalent cations become amenable. In the next section, we give a general view on the structural diversity of heterovalently substituted metal halide perovskites ranging from zero-dimensional to three-dimensional systems, highlight remarkably interesting optoelectronic properties and discuss the recent progress in the field of photovoltaic applications of this class of semiconductors.
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| 30.69 |
Thallium is a p-block metal with a Tl+ cation isoelectronic to Pb2+ (6s2 6p0 electronic configuration). The monovalent Tl+ cation, however, cannot substitute the divalent Pb2+ metal cation directly in ABX3-type perovskites because of the violation of the charge neutrality between cationic and anionic species. Nevertheless, the incorporation of thallium into the perovskite structure is possible via the mixed-valence approach using Tl+ (6s2) and Tl3+ (6s0) . An example for such a mixed-valent thallium halide perovskite is \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{CsTl}}_{0.5}^{ + } {\text{Tl}}_{0.5}^{3 + } {\text{X}}_{ 3}$$\end{document}CsTl0.5+Tl0.53+X3 (X = F, Cl), where the mono- and trivalent thallium cations are accommodated in a charge-ordered perovskite structure . This class of thallium halide perovskites was investigated in terms of superconductive behavior by Retuerto et al. and Yin et al. [58, 59]. With regard to the optical properties, the optical band gap of CsTlCl3 was experimentally determined to be approximately 2.5 eV .
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| 33.44 |
A further interpretation of the mixed-valence approach involves the incorporation of two different metal cations in a different valence state. An example thereof is the mixed thallium–bismuth halide perovskite CH3NH3Tl0.5Bi0.5I3, where Pb2+ metal cation units of the lead-based analogue CH3NH3PbI3 are replaced with Tl+/Bi3+ heterovalent ionic pairs . Giorgi et al. theoretically investigated this lead-free hybrid perovskite with regard to its structural and electronic properties via DFT analysis and calculated a direct band gap of 1.68 eV . According to these calculations, CH3NH3Tl0.5Bi0.5I3 is predicted to be a potential alternative solar cell material. However, despite these quite promising considerations and optical properties (Table 7), thallium-based compounds are presumably no alternative to lead-based perovskites in terms of photovoltaic applications due to the inherent toxicity of thallium.Table 7Structural and optical data of thallium and gold halide perovskitesPerovskiteSim./exp.Crystal system(space group)DimensionalityBand gap/eVReferencesCsTlF3 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$({\text{CsTl}}_{0.5}^{ + } {\text{Tl}}_{0.5}^{3 + } {\text{F}}_{ 3} )$$\end{document}(CsTl0.5+Tl0.53+F3) Exp.Cubic(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Fm\bar{3}$$\end{document}Fm3¯ m)3D–[58, 59]CsTlCl3 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$({\text{CsTl}}_{0.5}^{ + } {\text{Tl}}_{0.5}^{3 + } {\text{F}}_{ 3} {\text{Cl}}_{ 3} )$$\end{document}(CsTl0.5+Tl0.53+F3Cl3) Exp.Tetragonal (I4/m)Cubic (Fm \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\bar{3}$$\end{document}3¯ m)3Dca. 2.5[58, 59]CH3NH3Tl0.5Bi0.5I3 Sim.Tetragonal–1.68Cs2AuIAuIIICl6 Exp.Tetragonal (I4/mmm)3D2.04[60, 152]Cs2AuIAuIIIBr6 Exp.Tetragonal (I4/mmm)3D1.60[152, 153]Cs2AuIAuIIII6 Exp.Tetragonal (I4/mmm)3D1.31[61, 152, 153][NH3(CH2)7NH3]2[(AuII2)(AuIIII4)(I3)2]Exp.Triclinic (P \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\bar{1}$$\end{document}1¯)2D0.95[NH3(CH2)8NH3]2[(AuII2)(AuIIII4)(I3)2]Exp.Monoclinic (C2/m)2D1.14These materials have not been implemented in photovoltaic devices so far
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clinical case
| 27.81 |
Gold halide perovskites are similar to thallium-based analogues amenable via the mixed-valence approach. Consequently, gold has to be present in a mixture of monovalent Au+ (5d10, t2g6 eg4) and trivalent Au3+ (5d8, t2g6 eg2) metal cations to form ABX3-type perovskite structures , like in the case of Cs2AuIAuIIIX6 (X = Cl, Br, I) compounds [60, 61, 152, 153]. Additionally, hybrid gold halide perovskites have been investigated such as [NH3(CH2)7NH3]2[(AuII2)(AuIIII4)(I3)2] and [NH3(CH2)8NH3]2[(AuII2)(AuIIII4)(I3)2] .
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| 29.12 |
Mixed-valent gold halide perovskites such as Cs2AuIAuIIIX6 were predominantly investigated in terms of superconductivity . Further research studies mainly focus on the structural characterization as well as on the electronic and optical behavior [60–62, 152, 153]. With regard to the optical properties, the choice of the halide counterion plays an essential role for band gap engineering in mixed-valent systems such as Cs2AuIAuIIIX6 (X = Cl, Br, I). By substitution of chlorine with bromine or iodine, the optical band gap can be shifted to lower values. Liu et al. determined the optical band gaps of the corresponding perovskites via optical reflectivity measurements to be 2.04 eV (X = Cl), 1.60 eV (X = Br), and 1.31 eV (X = I) . Cs2AuIAuIIII6, in particular, is a promising absorber material for photovoltaic applications due to the almost ideal band gap according to the Shockley–Queisser limit, and the three-dimensional distorted ABX3-type perovskite structure similar to lead-based analogues . To the best of our knowledge, however, this class of materials was not characterized with regard to its photovoltaic performance so far.
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other
| 30.94 |
Castro-Castro et al. investigated the optical properties of two-dimensional layered hybrid gold halide perovskites including [NH3(CH2)7NH3]2[(AuII2)(AuIIII4)(I3)2] and [NH3(CH2)8NH3]2[(AuII2)(AuIIII4)(I3)2], and determined band gaps of 0.95 and 1.14 eV, respectively , which are lower than in the three-dimensional Cs2AuIAuIIII6 perovskite (1.31 eV). These unusual low band gaps—lower dimensional perovskites usually exhibit higher band gaps —can be explained by additionally induced electronic interactions between the [AuII2]− and [AuIIII4]− units and I3 − ions, which are absent in Cs2AuIAuIIII6 .
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other
| 31.5 |
Due to the presence of mono- and trivalent metal cations, two different coordination spheres are present in mixed-valent gold halide perovskites, i.e. linear (twofold) and square-planar (fourfold) coordination of Au+ and Au3+, respectively. In the case of Cs2AuIAuIIIX6 (X = Cl, Br, I), the crystal structure is derived from a distorted ABX3-type perovskite consisting of BX2 (linear [AuIX2]− unit) and BX4 (square-planar [AuIIIX4]− unit) building blocks [60, 61, 152–154]. The BX2 and BX4 units arrange alternately to accomplish the nominal octahedral coordination in the perovskite structure. While linearly coordinated [AuIX2]− units are completed by neighboring [AuIIIX4]− units via four coplanar halide ions forming compressed octahedra, square-planar coordinated [AuIIIX4]− units are completed by apical [AuIX2]− units via two halide ions forming elongated octahedra. The resulting distorted three-dimensional perovskite network can, therefore, be expressed as Cs2[AuIX2][AuIIIX4] [61, 62, 153].
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other
| 29.6 |
The hybrid mixed-valent gold halide perovskites [NH3-R-NH3]2[(AuII2)(AuIIII4)(I3)2] (R = heptyl, octyl) feature inorganic metal halide sheets of corner-sharing octahedra which are separated by organic diammonium cations (e.g. (NH3(CH2)7NH3)2+) and (NH3(CH2)8NH3)2+) to give a layered two-dimensional structure. The nominal octahedral coordination of the AuI center within the [AuII2]− units is accomplished by neighboring [AuIIII4]− units via four coplanar halide ions forming compressed octahedra, while [AuIIII4]− units are completed by two asymmetric triiodide ions (I3 −) in apical position forming elongated nominal octahedra . The distorted nominal AuI6 octahedra are corner connected to give a layered structure separated by organic interlayers.
|
other
| 30.3 |
Antimony halide perovskites are a potential alternative to lead-based perovskite semiconductors for photovoltaic applications to address the chemical stability and the toxicity issue . The trivalent Sb3+ metal cation (1) is isoelectronic to Sn2+ (4d10 5s2) and has a similar s2 valence electronic configuration as Pb2+ (5s2 lone pair), (2) has a comparable electronegativity (Sb: 2.05, Sn: 1.96, Pb: 2.33) but (3) a significant smaller ionic radius (76 pm) compared to the divalent Sn2+ (110 pm) and Pb2+ (119 pm) metal cations [35, 51, 125, 156].
|
study
| 27.34 |
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