Application In Solar Cell Devices Research Articles

Structural, electronic, optical, and thermoelectric features of Rb2XSbX’6 (X= Ag, Cu; X’= Cl, Br): Ab-initio calculations

This study investigates the electronic, optical, and thermoelectric properties of lead-free double halide perovskite materials, Rb2XSbX'6, through first-principles calculations employing Density Functional Theory (DFT) and the Wien2k code, complemented by Boltzmann transport theory. By substituting X with Ag or Cu and X’ with Cl or Br in Rb2XSbX’6, we uncover interesting properties. Rb2AgSbBr6, Rb2AgSbCl6, Rb2CuSbCl6, and Rb2CuSbBr6 exhibit low indirect band gaps of 1.18 eV, 2.17 eV, 1.22 eV, and 0.87 eV, respectively, alongside high absorption in the visible region. The studied compounds sustained a high level of structural and thermodynamic stability, which was confirmed by their high bulk modulus and negative formation energy. Furthermore, extensive values were observed for the figure of merit in the thermoelectric study. Given the strong agreement with previous research, these findings position the investigated materials as promising candidates for visible-light solar cell device applications.

DFT and TD-DFT Investigations for the Limitations of Lengthening the Polyene Bridge between N,N-dimethylanilino Donor and Dicyanovinyl Acceptor Molecules as a D-π-A Dye-Sensitized Solar Cell.

One useful technique for increasing the efficiency of organic dye-sensitized solar cells (DSSCs) is to extend the π-conjugated bridges between the donor (D) and the acceptor (A) units. The present study used the DFT and TD-DFT techniques to investigate the effect of lengthening the polyene bridge between the donor N, N-dimethyl-anilino and the acceptor dicyanovinyl. The results of the calculated key properties were not all in line with expectations. Planar structure was associated with increasing the π-conjugation linker, implying efficient electron transfer from the donor to the acceptor. A smaller energy gap, greater oscillator strength values, and red-shifted electronic absorption were also observed when the number of polyene units was increased. However, some results indicated that the potential of the stated dyes to operate as effective dye-sensitized solar cells is limited when the polyene bridge is extended. Increasing the polyene units causes the HOMO level to rise until it exceeds the redox potential of the electrolyte, which delays regeneration and impedes the electron transport cycle from being completed. As the number of conjugated units increases, the terminal lobes of HOMO and LUMO continue to shrink, which affects the ease of intramolecular charge transfer within the dyes. Smaller polyene chain lengths yielded the most favorable results when evaluating the efficiency of electron injection and regeneration. This means that the charge transfer mechanism between the conduction band of the semiconductor and the electrolyte is not improved by extending the polyene bridge. The open circuit voltage (VOC) was reduced from 1.23 to 0.70 V. Similarly, the excited-state duration (τ) decreased from 1.71 to 1.23 ns as the number of polyene units increased from n = 1 to n = 10. These findings are incompatible with the power conversion efficiency requirements of DSSCs. Therefore, the elongation of the polyene bridge in such D-π-A configurations rules out its application in solar cell devices.

Photovoltaic energy conversion in multiferroic perovskite absorber-based devices via experiment and theoretical calculations

Initially, La and Ti-doped BiFeO3 (BLFTO) was prepared through the solid-state method, and the formation of perovskite structure was confirmed through powder X-ray diffraction (XRD) analysis. SEM-EDX analysis confirms the merging of grains for the increasing concentration of Ti ion doping and the presence of all elements in the samples. The bandgap tuning in BLFTO (2.05 eV–2.11 eV) was analyzed through UV–vis spectroscopy and confirming the change in bandgap for Ti-doped BLFO samples. The observed energy bandgap range of the doped BFO absorber suggested its potential applications in solar cell devices. Therefore, we have designed lead-free FTO/TiO2/absorber/Spiro-OMeTAD/Au heterostructure device and achieved a power conversion efficiency (PCE) of ∼5.61% with an open-circuit voltage (VOC) of ∼0.91 V, fill factor (FF) of 55.55%, and current density (JSC) of 10.87 mA/cm2 for lead-free doped Bi0.80La0.20Fe1−xTixO3 (x = 0.0) based perovskite solar cells with proper optimization of thickness of absorber and operating temperature.

Fabrication, electrical performance analysis and photovoltaic characterization of β-H2Pc/p-Si heterojunction for solar cell device applications

The aim of this study was to explore the potential of nanocrystalline β-metal-free phthalocyanine (β-H2Pc) in optoelectronics, particularly for the creation of a β-H2Pc/p-Si heterojunction. With a focus on photovoltaic performance, the present work aimed to assess its thermal stability, crystalline structure, optical characteristics, electrical behavior, and applicability in optoelectronic applications. We successfully fabricated a β-H2Pc/p-Si heterojunction at room temperature using a conventional high-vacuum thermal evaporation method, offering a practical approach for integrating these materials into electronic devices. Thermal gravimetric Assessment (TGA) confirmed β-H2Pc’s remarkable thermal stability up to 470 °C, which holds significant promise for high-temperature applications. Transmission Electron Microscopy (TEM) revealed the nanocrystalline nature of the deposited β-H2Pc, which is crucial for the structural integrity of advanced electronic devices. The absorption coefficient spectrum exhibited distinct absorption bands attributed to π–π* excitations, with electronic transitions identified and characterized by a 1.51 eV onset band gap and a 2.74 eV fundamental optical energy gap, highlighting its potential in optoelectronic applications. The current–voltage characteristics of the β-H2Pc/p-Si heterojunction displayed a diode-like behavior at various temperatures, with excellent rectifying properties. Photovoltaic behavior under illumination showed a power conversion efficiency of 1.1%, emphasizing its promise for renewable energy applications and future optoelectronic devices.

Lead-free perovskites InSnX3 (X = Cl, Br, I) for solar cell applications: a DFT study on the mechanical, optoelectronic, and thermoelectric properties

This study aims to explore for the first time the mechanical, electronic, optical and thermoelectric properties of cubic lead-free perovskites InSnBr3 and InSnI3 to investigate their potential applications in solar cell devices. Additionally, the previously examined InSnCl3 perovskite is also included. The properties of the perovskites were determined using first-principles calculation based on the well-known Density Functional Theory (DFT) with the Generalized Gradient Approximation (GGA) functional implemented in the Quantum Espresso package. One of the most important findings was that the bandgaps of the compounds decrease and undergo an indirect-to-direct bandgap transition when Cl is replaced by Br and I. This indicates that InSnBr3 and InSnI3 perovskites are more suitable for solar cell applications. The bandgap energies for InSnCl3, InSnBr3, and InSnI3 perovskites are 0.59 eV (R→X), 0.44 eV (R→R), and 0.24 eV (R→R), respectively. The improved band gaps using the HSE06 functional are 2.35 eV, 2.13 eV, and 2.01 eV for the respective perovskites. The materials were found to possess chemical, mechanical, and thermodynamic stability as well as ductile behaviour. Furthermore, the materials exhibit remarkable optical properties, including high absorption coefficients and relatively small reflectivity. The calculated thermoelectric properties indicated high electrical conductivity and reasonable figure of merit values, making them promising candidates for the application in thermoelectric devices.

Investigation of optoelectronic & thermoelectric features of ZnCrX2 (X = S Se Te) chalcopyrite semiconductor using mBJ potential

In the present investigation, we have examined the structural, optoelectronic and thermoelectric properties of the compound ZnCrX2 (X = S, Se, Te) using the full potential linearized augmented plane wave (FP-LAPW) method with the generalized gradient approximation (GGA-PBEsol) and the modified Becke–Johnson (mBJ) implemented on Wien2k code. By calculating the electronic structure, we observed that the indirect band gap was 1.76 eV, 1.68 eV, and 1.59 eV, for these selected compounds and the type of chemical bonding was ionic between Zn-X and Cr-X. For the three ternary chalcopyrites their optical properties including optical conductivity, complex dielectric functions, complex refractive index, reflectivity, energy loss, and absorption coefficient were examined. The calculated optical conductivity indicates that the studied compounds are suitable for optoelectronic applications as they have good absorbance and less energy loss in the low energy range of the electromagnetic spectrum. For ZnCrTe2, the maximum reflectivity was in the low energy range (0.48 or 48% at 9 eV). The BoltzTrap code was executed for the calculation of the thermoelectric properties and thermal efficiency of the compounds investigated, depending upon the Seebeck coefficient, thermal conductivity and electrical conductivity. The high value of the figure of merit and the Seebeck coefficient (260 uV/k) defines the high efficiency of the materials studied. Hence, the studied chalcopyrite compounds offer applications in solar cell devices and p-type semiconducting nature predictive in transport investigations.

Design of an eco-friendly perovskite Au/NiO/FASnI3/ZnO0.25S0.75/FTO, device structure for solar cell applications using SCAPS-1D

Formamidinium Tin Iodide (FASnI3) based perovskite solar cells (PSC) have captured the interest of scientific community because of wide bandgap and good thermal stability, but limited power conversion efficiency (PCE) restricts their extensive adaptation. Here, we present the design of a FASnI3 active layer-based PSC with Nickel oxide (NiO) as Hole Transport Layer (HTL) & Zinc Oxy-Sulphide (ZnO0.25S0.75) as the Electron Transport Layer (ETL). The proposed Au/NiO/FASnI3/ZnO0.25S0.75/FTO, device structure is investigated using SCAPS-1D solar cell capacitance simulator. The performance parameters of proposed solar cells device structure are investigated with variations in active layer (FASnI3) thickness, defect density & doping concentration; and variations of NiO HTL & ZnO0.25S0.75 ETL thickness, electron affinity & doping concentration to obtain higher performance. Moreover, the influence of series & shunt resistance, and temperature on the performance parameters of proposed solar cell device structure is inspected. The proposed Au/NiO/FASnI3/ZnO0.25S0.75/FTO, device structure revealed excellent solar cell performance parameters such as low short-circuit current density (Jsc) of ∼28.35 mA/cm2, high Fill Factor (FF) of ∼89.64%, reasonable open-circuit voltage (Voc) of ∼1.2419 V, & admirable PCE of ∼31.57%, suitable for lead-free and eco-friendly solar cell device applications.

Antimony Doping of CsBi3I10 for Tailoring the Film Morphology and Defects toward Efficient Lead-Free Thin-Film Solar Cells

The CsBi3I10 (CBI) semiconductor as a light absorber emerges as a promising alternative to lead-based perovskites owing to its low toxicity, good stability, and satisfying physical properties. However, CBI exhibits an uncontrollable crystallization process, poor film morphology, high defect density, and short carrier lifetime, which lead to inferior optoelectronic properties, limiting its practical application in solar cell devices. Here, the Sb doping strategy is successfully developed for CBI films by a one-step antisolvent-free fabrication method. It is found that Sb incorporation in binary CsBi3–xSbxI10 can modulate the crystallization kinetics and optimize the film quality. As a result, polycrystalline films with high density and few pinholes are obtained to enable the enhancement of light absorbance, reduction of defects, suppression of nonradiative recombination, and increase of surface hydrophobicity. The solar cells based on the CsBi2.7Sb0.3I10 film show a remarkably improved power conversion efficiency of 0.82% compared to that of pristine CBI (0.22%), which is among the highest reported efficiencies for CBI-based thin-film solar cells. Moreover, unencapsulated devices based on Sb-doped CBI exhibit outstanding environmental stability and moisture tolerance. This work not only offers insights into understanding the binary Bi-based materials but also provides a new way to fabricate efficient and stable Bi-based solar cells.

Systematic study of optoelectronic and thermoelectric properties of new lead-free halide double perovskites A2KGaI6(A = Cs, Rb) for solar cell applications via ab-initio calculations

The variant perovskites are considered novel materials for studying solar cells and other electro-optic applications. Born’s stability criteria confirm the mechanical stability, while Poisson coefficient (ν > 0.26) and Pugh ratio (B0/G > 1.75) certify the ductile nature of the compounds by investigating elastic properties. For Cs2KGaI6 and Rb2KGaI6, the computed bandgap is direct 1.81 eV and 1.85 eV, respectively, in terms of exploring the band structures. Their band gaps may capture electromagnetic waves in the visible spectrum, excelling themfor solar cell devices. The optical properties have been studied against photon energy (eV) with maximum transition and absorption in the visible region. BoltzTrap code is employed for the thermoelectric properties executed by electrical conductivity, thermal conductivity, power factor, and figure of merit (ZT), which shows a slight variation in the temperature. Hence, the considered lead-free double perovskite compounds offer applications in solar cell devices and p-type semiconducting behavior predictive in transport investigations.

Ge incorporation in kesterite thin films by solution processing route: An in-depth study of structural and optoelectronic properties

Herein, we report a promising solution-processing method for the controlled incorporation of germanium (Ge) into Cu2ZnSnS4 (CZTS) films using a nontoxic molecular ink. The effect of Ge concentration on structural, optical, electrical and electronic properties of the films were systematically investigated. The successful Ge alloying in CZTS was confirmed by XRD analysis and exploring the sensitivity of Raman scattering. The as-synthesized Cu2ZnSn1-xGexS4 (CZTGS; x = 0, 0.1, 0.15, 0.2 and 0.25) films exhibit strong absorption in the visible region with the gradual increment in the band gap energy from 1.46 to 1.61 eV by increasing x from 0 to 0.25. A decrease in Urbach energy at higher [Ge]/[Sn + Ge] ratio supports the reduction of overall disorder into the system. The information about the correct oxidation states of the constituent elements and optimal chemical composition of the CZTGS films was obtained from X-ray photoelectron spectroscopy (XPS). The decrease in SnII/SnIV signal ratio with the increase in Ge further supports the suppression of deep-trap SnZn antisite defects. The XPS valence band spectra reveal that the position of valence band maximum ascended from 0.09 to 0.15 eV with increasing Ge content in the films. Several relevant optical constants were determined of the CZTGS films which are important for applications in solar cell devices as well as for simulation purpose.

Structural, Electronic and Optical Properties of 6H-SiC and 3C-SiC with the Application in Solar Cell Devices

6H-SiC and 3C-SiC structural, electronic and optical properties have been calculated by applying the principles of density functional theory based on the plane wave pseudo-potential. This method is implanted in Wien2k Software. Structural parameters are calculated at the level of Perdew Burke and Ernzerhof (PBE) parameterized generalized gradient approximation (GGA). The obtained results given in Table I were compared to the experimental data in relation with the lattice constant hexagonal ration c/a and the band gap value parameters of 6H-SiC and 3C-SiC, there was a very accurate concordance. The superior gap value and the good absorption coefficient drives us to realize a p+nn+ solar cell device using SILVACO Software. The 3C-SiC material resulted in a considerable performance for photovoltaic applications.

Systemically study of optoelectronic and transport properties of chalcopyrite HgAl2X4 (X= S, Se) compounds for solar cell device applications

This article investigated the structure, optoelectronic characteristics, and transport properties of the Hg-based chalcopyrite HgAl2X4 (X = S, Se) using DFT. To calculate the optimized lattice constant, we applied Perdew-Burke-Ernzerhof’s generalized-gradient-approximation (PBEsol-GGA) and found calculated lattice constant of both chalcopyrites is reasonable compared to experimental values. In addition, modified Becke and Johnson (mBJ) potential were used to investigate the optoelectronic properties. Studied HgAl2S4 and HgAl2Se4 chalcopyrite compounds have a direct bandgap of 3.20 eV and an indirect bandgap of 2.60 eV, respectively. Projectile and total density of states were computed to check the maximum contribution of chalcopyrite HgAl2X4 (X = S, Se). HgAl2S4 and HgAl2Se4 chalcopyrite have a substantial optical absorption near 3.5 eV and 3.9 eV making them interesting for hetero-junction solar cell. Furthermore, based on measured results of large thermal properties, we discovered that the structures are thermally and mechanically robust in a cubic structure. Finally, the BoltzTrap code is used to study the figure of merit (ZT), power factor, Seebeck coefficient, and electrical and thermal conductivity of transport characteristics.

Electronic and thermoelectric properties of group IV–VI van der Waals heterostructures

Stacking of two-dimensional materials, in the form of heterostructures, is recently considered as a promising candidate for thermoelectric devices application because it can combine the advantages of the individual 2D materials. The structural, electronic, and thermoelectric properties of group IV–VI [AB/XY (A = Ge, B = O, S, Se, Te, X = C, Sn, Si, Sn, and Y = Se, S)] van der Waals heterostructures are investigated by using first principles calculations. Binding energies and thermal stability showed that all heterobilayers are energetically and thermally stable. Calculated electronic band structure confirmed that IV–VI [AB/XY (A = Ge, B = O, S, Se, Te, X = C, Sn, Si, Sn, and Y = Se, S)] van der Waals heterostructures have indirect with type-II band alignment, which is crucial for separation of photogenerated carriers in solar cell device applications. Transport coefficients including Seebeck coefficient, electrical conductivity and power factor versus chemical potential are calculated by using Boltzmann transport theory which is implemented in BoltzTrap code. Among these heterobilayers, GeO/CSe has considerably large power factor at 800 K, making it more promising for good thermoelectric purposes. These findings pave the way for designing future electronic and thermoelectric devices.

Opto-electronic, and thermoelectric properties of chalcopyrite compounds HgGa2X4(X = S, Se) for solar cell applications

The ab-initio method has been applied to explore the chalcopyrite compounds HgGa2X4 (X = S, Se) structural, optoelectronics, and thermoelectric characteristics. We attained the optimized parameters of lattice constant by employing Perdew–Burke–Ernzerhof generalized gradient approximation (PBEsol-GGA) and computed the values are approximately equal to experimental values. To calculate accurate bandgap values of both compounds, we used Trans along with Bhala reformed Becke and Johnson (TB-mBJ). Remarkably, both HgGa2X4 (X = S, Se) compounds yield a direct bandgap nature, having calculated values 2.80 eV and 2.30 eV, respectively, which are accurately comparable to experimental values. It also observed that the strong optical absorption is below 3.0 eV, which made both compounds favorable for solar cell device applications. In last, we make a detailed investigation of thermoelectric characteristics in terms of electric and thermal conductivity, power factor, and figure of merit (ZT) with the help of the BoltzTrap code. To check the material’s thermal stability, we accomplished the thermal parameters against temperatures.

Retraction notice to “Structural, electronic, optical, elastic and thermal properties of CdSnP2 with the application in solar cell devices” [Superlattice. Microst. 85 (2015) 859–871

Retraction notice to “Structural, electronic, optical, elastic and thermal properties of CdSnP2 with the application in solar cell devices” [Superlattice. Microst. 85 (2015) 859–871

Clariant significantly increased profitability in 3Q 2021 on the back of double-digit sales growth: 3Q 2021 - particularly strong, double-digit sales growth facilitates significant profitability improvement

Molybdenum disulfide (MoS2) is a layered material with promising photo-electroactive properties with possible application in solar cell devices. In this work, exfoliated MoS2 (E-MoS2) was produced using a chemical intercalation and exfoliation process. After an exhaustive characterization of the material, two different solar cell arrays were studied for the photoanode using the synthetized exfoliated MoS2, as sensitizer and thin film. Normalized incident photon-to-current conversion efficiency and electrochemical impedance spectra were generated to further understand the photocurrent and electron transition behavior in the dye sensitized solar cell array. An increase in normalized incident photon-to-current conversion efficiency (IPCE) for E-MoS2/TiO2 hybrids and layered films was observed when compared to TiO2. The results provide evidence of device enhancement after using exfoliated MoS2 by increasing photocurrent efficiencies and lowering charge transfer resistance.

Ternary composite based on MoSe2-rGO/ polyaniline as an efficient counter electrode catalyst for dye sensitized solar cells

The closely stacked layer in molybdenum diselenide (MoSe2) and low rate of charge transfer limits its application in solar cell devices. Here, in-situ polymerization of aniline was carried out on MoSe2/r-GO nanocomposites to achieve an enhanced electronically conductive system with a homogenously dispersed phase for its active role as a counter electrode electrocatalyst in dye sensitized solar cell (DSSC). Physicochemical studies such as Raman and XRD confirmed the formation of a hybrid system. The hybrid showed up a buffered surface area of 41.892 m2/g as estimated by the BET study. The uniformly dispersed phase was observed in the SEM morphology. Nyquist plots provided Rct ≈ 38Ω revealing the low charge transfer resistance offered by the hybrid, improving the charge transfer phenomenon on its surface. The cyclic voltammograms showed nearly symmetrical oxidation-reduction peaks indicating the excellent reversibility of the charge transfer cycle. Additionally, solar cell characterization results pursued that the fabricated hybrid system can be a potential alternative as a counter electrode electrocatalyst in DSSC.

Grain size control of perovskite films based on β-alanine self-assembled monolayers surface treatment

The grain size of the perovskite layer can be tuned by the surface treatment of Ultraviolet ozone (UVO) with β-alanine self-assembled molecular films (SAMs) on the Nickel oxide (NiOx) substrate. The UVO treatment had been used to control the hydroxy (-OH) end-group on NiOx substrate and the condensation reaction of β-alanine SAMs, in which the end-group of the amino group (-NH2) correlates with the nucleation of the perovskite layer. The difference of surface end-group with/without the UVO treatment on the NiOx substrate was revealed by the shift of the oxidation peak of the SAMs layer in the cyclic voltammetry and the electrochemical impedance spectroscopy. It is found that the wettability of NiOx substrate was enhanced by the SAMs treatment time due to the increment of -NH2 end-group and the UVO treatment. Larger grain size of the perovskite layer was achieved on the NiOx substrate with SAMs 15 minutes treatment. Moreover, the optical absorbance of perovskite films in the short wavelength range was enhanced by the assembling time of SAMs. This study provides a method to control the surface morphology of the perovskite active layer in its solar cell device applications.

Enhanced Optical Properties of FeS2 Using Ni@Cu Doping and Characterization of the Structural and Chemical Compositions for Solar Cell Applications

Transition metals doped FeS2 thin films are promising materials for optoelectronics, energy saving and storage applications. This is a first time report on the simultaneously Ni@Cu doped Fe1 – xMxS2 (M = Ni@Cu = 0, 2, 5, 10, and 20 at %) thin films fabricated by a simple chemical spray pyrolysis technique. In this paper we investigate the impact of doping on the structural, chemical states, optical properties and band gap nature by different characterization techniques. The SEM results show that surface morphology and granular grain size changes with the increment of Ni@Cu content which are coherent with the XRD results. The EDX and XPS measurements exhibit that the films are composed of Fe, S, Ni, and Cu elements whilst the films were slightly oxidized due to processing in the atmospheric conditions. Spectroscopy ellipsometry (SE) analysis demonstrates that the indirect band gap gradually increased from 1.38 eV (FeS2) to 1.64 eV (Ni@Cu = 10 at %) while at higher doping the band gap was decreased to 1.53 could be due to incomplete doping. So, the band gap of FeS2 can be tuned in between 1.38 and 1.64 eV by simultaneous Ni@Cu doping could be a suitable candidate for absorber application in solar cell devices. The other optical constants (dielectric constants, refractive index and extinction coefficient) explicitly carried out using SE measurement. Interestingly, progressing the absorption nature and bang gap in the visible region disclose a significant impact on the optical properties for optoelectronics applications.

Influence of substrate temperature on physical properties of MnSbInS4 thin films prepared by a simplified spray pyrolysis technique for photovoltaic applications

MnSbInS 4 multi-component semiconductor thin films are prepared by chemical spray pyrolysis on glass substrates at various substrate temperatures ranging from 250-400 °C with a constant spray time (5mins). The structural, morphological, optical and electrical properties of the thin films are investigated through different techniques such as X-ray diffraction (XRD), electron diffraction spectroscopy (EDS), UV-Vis absorption spectroscopy and four probe method. The X-ray spectra reveal that the MnSbInS 4 films are polycrystalline in nature with a cubic spinel structure having (220) plane as the preferred orientation. The energy dispersive analysis by X-ray (EDS) studies confirm the presence of Mn, In, Sb and S in the film grown at a substrate temperature of 250 °C. Optical measurements allow us to determine the absorption coefficient which is as high as (1.22 x 10 5 cm -1 ) at 250 ºC indicating that MnSbInS 4 compound has an absorbing property favorable for applications in solar cell devices. It is interesting to note that the structural homogeneity and crystallinity of the films is improved due to the decrease in absorption coefficient (α) and extinction coefficient (k) with an increase of substrate temperature. The observations from photoluminescence measurements reveal that the photoemission is mainly due to the donar-acceptor pair transitions. Moreover, from the electrical studies, it is observed that the electrical resistivity (ρ ) is strongly affected by substrate temperature and the lowest resistivity (ρ = 4.77 x 10 3 Ω m ) is obtained for the film grown at 400 ºC. Stylus profilometer was used to measure the film thickness and the values range between 768 nm (250 °C) to 617 nm (400 °C). This indicates that, as the substrate temperature increases, the thickness of the film decreases. Other important parameters like micro-strain (ε) and dislocation density (δ) which are commonly used to describe the structural analysis are also presented.