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While ceramic materials are widely used in our society, their understanding of the plasticity is not fully understood. MgO is one of the prototypical ceramics, extensively investigated experimentally and theoretically. However, there is still controversy over whether edge or screw dislocations glide more easily. In this study, we directly model the atomic structures of the dislocation cores in MgO based on the first-principles calculations and estimate the Peierls stresses. Our results reveal that the screw dislocation on the primary slip system exhibits a smaller Peierls stress than the edge dislocation. The tendency is not consistent with metals, but rather with TiN, suggesting a characteristic inherent to rock-salt type materials.

Performing highly accurate computational methods ­ specifically, a combination of direct atomic modeling and first-principles calculations ­ to estimate the Peierls stresses of MgO.

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The demand for increasingly fine detail in optical lithography for semiconductors necessitates the use of lower-wavelength lithographic light. This drives the need for lenses in optical lithography steppers made of vacuum ultraviolet-transparent (VUV-transparent) materials. In this work, the density functional theory (DFT) study of potassium magnesium fluoride KMgF3 is presented. Total energy was calculated with correlation functional generalized gradient approximation (GGA). The ground state quantities such as bulk modulus and lattice parameters have been evaluated. The material's cubic structure is scrutinized under various stress levels (0-100 GPa), revealing that KMgF3 starts to deform at 128 GPa. The C11, C12, and C44 independent elastic constants were used to analyze the structural stability of the KMgF3. The densities of states and electronic band structures have also been computed. According to electronic calculations, when stress is applied to KMgF3, the band gap increases for all values of stress (0-100 GPa). Mechanical parameters, including elastic constants and ratios, indicate the material's remarkable ductility and stability. Phonon density of states and thermal characteristics exhibit shifts and variations with increasing stress, providing insights into the material's behaviour below its melting point. The thermodynamic properties of KMgF3, such as enthalpy, free energy, entropy, heat capacity, and Debye temperatures at various temperatures ranging from 0 K to 1000 K, have also been examined to explore their basic properties. These findings contribute to a comprehensive understanding of KMgF3, opening avenues for its application in advanced technologies, particularly in the realms of semiconductors and optoelectronics.

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Constructing van der Waals (vdW) heterostructures is a prospective approach that is essential for developing a new generation of functional two-dimensional (2D) materials and designing new conceptual nanodevices. Using density-functional theory combined with a nonequilibrium Green's function approach allows for the theoretical and systematic exploration of the electronic structure, transport properties, and sensitivity of organic small molecules adsorbed on 2D C3B/graphene (Gra) and C3N/Gra vdW heterojunctions. Calculations show the metallic properties of C3B/Gra and C3N/Gra after the formation of heterojunctions. Interestingly, the heterojunctions C3B/Gra (C3N/Gra) for the adsorption of small organic molecules (C2H2, C2H4, CH3OH, CH4, and HCHO) at the C3B (C3N) side are sensitive to the chemisorption of C2H2 and C2H4. Similarly, the Gra/C3B is chemisorbed for both C2H2 and C2H4 when adsorbed on Gra side, while it is only chemisorbed for C2H2 in Gra/C3N. Interestingly, all heterojunctions on different sides are physisorbed for CH3OH, CH4, and HCHO. Furthermore, the calculated I-V curves demonstrate that the devices based on the adsorption of C2H2 and C2H4 at each side of the heterojunction have remarkable anisotropy, in with the current being considerably greater in the zigzag direction than in the armchair direction. More specifically, with C2H2 adsorbed on the Gra side, the sensitivity along the armchair direction is up to 85.0% for Gra/C3B and close to 100% for Gra/C3N. This study reveals that C3B/Gra (C3N/Gra) heterojunctions with high selectivity, high anisotropy, and excellent sensitivity are highly prospective 2D materials for applications, which further contributes new insights into the development of future electronic nanodevices.

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The exploration of novel two-dimensional (2D) materials with a direct band gap and high mobility has attracted huge attention due to their potential application in electronic and optoelectronic devices. Here, we propose a feasible way to construct multiatomic monolayer Ca2A2Z5 (A = Al and Ga and Z = S, Se, and Te) by first-principles calculations. Our results indicated that the energies of α1-phase Ca2A2Z5 are slightly lower than those of experimentally synthesized α3-phase-like Ca2A2Z5 monolayers with excellent structural stability. Moreover, the α1- and α3-phase Ca2A2Z5 monolayers possess not only direct band gaps but also high electron mobilities (up to ∼103 cm2 V-1 s-1), demonstrating an intriguing range of visible light absorption. Importantly, α1- and α3-phase Ca2Ga2Se5 monolayers are good donor materials, and the corresponding Ca2Ga2Se5/ZrSe2 type-II heterostructures exhibit desirable power conversion efficiencies of 22.4% and 22.9%, respectively. Our findings provide a feasible way to explore new 2D materials and offer several Ca2A2Z5 candidate monolayers for the application of high-performance solar cells.

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In recent years, the study of magnetic topological materials, with their variety of exotic physics, has significantly flourished. In this work, we predict the interplay of magnetism and topology in the non-centrosymmetric ternary manganese compound MnIn$_2$Te$_4$ under external hydrostatic pressure, using first-principles calculations and symmetry analyses. At ambient pressure, the ground state of the system is an antiferromagnetic insulator. With the application of a small hydrostatic pressure ($\sim$0.50 GPa), it undergoes a magnetic transition, and the ferromagnetic state becomes energetically favorable. At $\sim$2.92 GPa, the ferromagnetic system undergoes a transition into a Weyl semimetallic phase, which hosts multiple Weyl points in the bulk. The presence of non-trivial Weyl points have been verified by Wilson bands computations and the presence of characteristic surface Fermi arcs. Remarkably, we discover that the number of Weyl points in this system can be controlled by pressure and that these manifest in an anomalous Hall conductivity (AHC). In addition to proposing a new candidate magnetic topological material, our work demonstrates that pressure can be an effective way to induce and control topological phases, as well as AHC, in magnetic materials. These properties may allow our proposed material to be used as a novel pressure-controlled Hall switch.

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This article explores changes in the structural, electronic, elastic, and optical properties of the novel cubic Sr3BCl3 (B = As, Sb) with increasing pressure. This research aims to decrease the electronic band gap of Sr3BCl3 (B = As, Sb) by applying pressure, with the objective of enhancing the optical properties and evaluating the potential of these compounds for use in optoelectronic applications. It has been revealed that both the lattice parameter and cell volume exhibit a declining pattern as pressure increases. At ambient pressure, analysis of the band structure revealed that both Sr3AsCl3 and Sr3SbCl3 are direct band gap semiconductors. With increasing pressure up to 25 GPa the electronic band gap of Sr3AsCl3 (Sr3SbCl3) reduces from 1.70 (1.72) eV to 0.35 (0.10) eV. However, applying hydrostatic pressure enables the attainment of optimal bandgaps for Sr3AsCl3 and Sr3SbCl3, offering theoretical backing for the adjustment of Sr3BCl3 (B = As, Sb) perovskite's bandgaps. The electron and hole effective masses in this perovskite exhibit a gradual decrease as pressure rises from 0 to 25 GPa, promoting the conductivity of both electrons and holes. The elastic properties are calculated using the Thermo-PW tool, revealing that they are anisotropic, ductile, mechanically stable, and resistant to plastic deformation. Importantly, these mechanical properties of both compounds are significantly enhanced under pressure. Optical properties, including the absorption and extinction coefficients, dielectric function, refractive index, reflectivity, and loss function, were calculated within the 0-20 eV range under different pressure conditions. The calculated optical properties highlight the versatility and suitability of Sr3AsCl3 and Sr3SbCl3 perovskites for pressure-tunable optoelectronic devices.

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CONTEXT: The adsorptions of gas (CO, CO2, NH3) by metal (Au, Ag, Cu)-doped single layer WS2 are studied by density functional theory. The doping of metal atoms makes WS2 behave as n-type semiconductors. The final adsorption sites for CO, CO2, and NH3 are close to the atomic sites of the doped metal. The adsorptions of CO and NH3 gases on Cu/WS2, Ag/WS2, and Au/WS2 are dominated by chemisorption. The doped metal atoms enhance the hybridization of the substrate with the gas molecular orbitals, which contributes to the charge transfer and enhances the adsorption of the gas with the material surface. The adsorptions of CO and NH3 on Cu/WS2 and Ag/WS2 allow favorable desorption in a short time after heating. The single-layer Cu/WS2 is proved to have the potential to be used as a reliable recyclable sensor for CO. This work provides a theoretical basis for developing high-performance WS2-based gas sensors. METHODS: In this paper, the adsorption energy, electronic structure, charge transfer, and recovery time of CO, CO2, and NH3 in the doped system have been investigated based on the CASTEP code of density functional theory. The exchange correlation function used is the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA). The TS (Tkatchenko-Scheffler) dispersion correction method was used to involve the effects of van der Waals interaction on the adsorption energies for all adsorption system. The ultrasoft pseudopotentials are chosen and the plane-wave cut-off energies are set to 500 eV. The k-point mesh generated by the Monkhorst package scheme is used to perform the numerical integration of the Brillouin zone and 5 × 5 × 1 k-point grid is used. The tolerances of total energy convergence, maximum ionic force, ionic displacement, and stress component are 1.0 × 10-5 eV/atom, 0.03 eV/Å, 0.001 Å, and 0.05 GPa, respectively.

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Hydrogen and hydride materials have long been considered promising materials for high-temperature superconductivity. However, the extreme pressures required for the metallization of hydrogen-based superconductors limit their applications. Here, a series of high-temperature perovskite hydrides is designed that can be stable within 10 GPa. The research covered 182 ternary systems and ultimately determined that eight new compounds are stable within 20 GPa, of which five exhibited superconducting transition temperatures exceeding 120 K within 10 GPa, including KGaH3 (146 K at 10 GPa), RbInH3 (130 K at 6 GPa), CsInH3 (153 K at 9 GPa), RbTlH3 (170 K at 4 GPa) and CsTlH3 (163 K at 7 GPa). Excitingly, KGaH3 and RbGaH3 are thermodynamically stable at 50 GPa. Among these perovskite hydrides, alkali metals are responsible for providing a fixed amount of charge and supporting alloy framework composed of hydrogen and IIIA group elements to maintain stable crystal structure, while the cubic hydrogen alloy framework formed by IIIA group elements and hydrogen is crucial for high-temperature superconductivity. This work will inspire further experimental exploration and take an important step in the exploration of low-pressure stable high-temperature superconductors.

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Lithium difluoro(oxalate) borate (LiDFOB) contributes actively to cathode-electrolyte interface (CEI) formation, particularly safeguarding high-voltage cathode materials. However, LiNixCozMnyO2-based batteries benefit from the LiDFOB and its derived CEI only with appropriate electrolyte design while a comprehensive understanding of the underlying interfacial mechanisms remains limited, which makes the rational design challenging. By performing ab initio calculations, the CEI evolution on the LiNi0.8Co0.1Mn0.1O2 has been investigated. The findings demonstrate that LiDFOB readily adheres to the cathode via semidissociative configuration, which elevates the Li deintercalation voltage and remains stable in solvent. Electrochemical processes are responsible for the subsequent cleavage of B-F and B-O bonds, while the B-F bond cleavage leading to LiF formation is dominant in the presence of adequate Li+ with a substantial Li intercalation energy. Thus, impregnation is established as an effective method to regulate the conversion channel for efficient CEI formation, which not only safeguards the cathode's structure but also counters electrolyte decomposition. Consequently, in comparison to utilizing LiDFOB as an electrolyte additive, employing LiDFOB impregnation in the NCM811/Li cell yields significantly improved cycling stability for over 2000 h.

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Magnetizing the surface states of topological insulators without damaging their topological features is a crucial step for realizing the quantum anomalous Hall (QAH) effect and remains a challenging task. The TI-ferromagnetic material interface system was constructed and studied by the density functional theory (DFT). A two-dimensional magnetic semiconductor CrWI6 has been proven to effectively magnetize topological surface states (TSSs) via the magnetic proximity effect. The non-trivial phase was identified in the Bi2Se3 (BS) films with six quantum layers (QL) within the CrWI6/BS/CrWI6 heterostructure. BS thin films exhibit the generation of spin splitting near the TSSs, and a band gap of approximately 2.9 meV is observed at the Γ in the Brillouin zone; by adjusting the interface distance of the heterostructure, we increased the non-trivial band gap to 7.9 meV, indicating that applying external pressure is conducive to realizing the QAH effect. Furthermore, the topological non-triviality of CrWI6/6QL-BS/CrWI6 is confirmed by the nonzero Chern number. This study furnishes a valuable guideline for the implementation of the QAH effect at elevated temperatures within heterostructures comprising two-dimensional (2D) magnetic monolayers (MLs) and topological insulators.

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To meet the demands for high-temperature performance and lightweight materials in aerospace engineering, the Au-Ni solder is often utilized for joining dissimilar materials, such as Ti3Al-based alloys and Ni-based high-temperature alloys. However, the interaction between Ti and Ni can lead to the formation of brittle phases, like Ti2Ni, TiNi, and TiNi3, which diminish the mechanical properties of the joint and increase the risk of crack formation during the welding process. Cu doping has been shown to enhance the mechanical properties and high-temperature stability of the Au-Ni brazed joint's central area. Due to the difficulty in accurately controlling the solid solution content of Cu in the Au-Ni alloy, along with the high cost of Au, traditional experimental trial-and-error methods are insufficient for the development of Au-based solders. In this study, first principles calculations based on density functional theory were employed to analyze the effect of Cu content on the stability of the Au-2.0Ni-xCu (x = 0, 0.25, 0.5, 0.75, 1.0, 1.25 wt%) alloy phase structure. The thermal properties of the alloy were determined using Gibbs software fitting. The results indicate that the Au-2.0Ni-0.25Cu alloy exhibits the highest plastic toughness (B/G = 5.601, ν = 0.416, Cauchy pressure = 73.676 GPa) and a hardness of 1.17 GPa, which is 80% higher than that of Au-2.0Ni. This alloy balances excellent strength and plastic toughness, meeting the mechanical performance requirements of brazed joints. The constant pressure specific heat capacity (Cp) of the Au-2.0Ni-xCu alloy is higher than that of Au-2.0Ni and increases with Cu content. At 1000 K, the Cp of the Au-2.0Ni-0.25Cu alloy is 35.606 J·mol-1·K-1, which is 5.88% higher than that of Au-2.0Ni. The higher Cp contributes to enhanced high-temperature stability. Moreover, the linear expansion coefficient (CTE) of the Au-2.0Ni-0.25Cu alloy at 1000 K is 8.76 × 10-5·K-1, only 0.68% higher than Au-2.0Ni. The lower CTE helps to reduce the risk of solder damage caused by thermal stress. Therefore, the Au-2.0Ni-0.25Cu alloy is more suitable for brazing applications in high-temperature environments due to its excellent mechanical properties and thermal stability. This study provides a theoretical basis for the performance optimization and engineering application of the Au-2.0Ni-xCu alloy as a gold-based solder.

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Rechargeable lithium-sulfur (Li-S) batteries have been considered as a potential energy storage system due to their high theoretical specific energy. However, their practical commercial application has been hindered by unresolved key issues. One promising approach to overcoming these challenges is the development of anchoring materials with exceptional performance. In this work, we conducted detailed evaluations of twelve types of MA2Z4 (M = Ti, Zr, or Hf; A = Si or Ge; and Z = P or As) monolayers as potential Li-S battery electrodes through first-principles calculations. Our results indicate that these monolayers can effectively immobilize Li2Sn species, preventing them from dissolving into the electrolyte and preserving intact Li2Sn conformations. The high electrical conductivity of these monolayers can be perfectly retained after S8/L2Sn clusters adsorption. Furthermore, the MA2P4 monolayers demonstrate superior catalytic performance for the sulfur reduction reaction (SRR) compared to the MA2As4 counterparts, whereas the MA2As4 monolayers exhibit lower decomposition energy barriers. Our current work indicates that these MA2Z4 monolayers hold significant promise as electrode materials for Li-S batteries.

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Scandium-doped aluminum nitride with a wurtzite structure has emerged as a promising ferroelectric material due to its exceptional physical and chemical properties and its compatibility with existing processing techniques. However, its high coercive voltage presents a substantial challenge for its potential applications. To effectively reduce this high coercive voltage, it is crucial to comprehensively understand the factors governing polarization reversal processes. Unfortunately, a unified set of pivotal factors has not yet been identified. Herein, machine-learning regression models were developed to predict the uniform polarization reversal barrier (Eua) using data sets comprising 41 binary and 113 simple ternary wurtzite materials. Features were extracted based on elemental properties, crystal parameters, mechanical properties, and electronic properties. Calculation of Eua and partial feature extraction were performed using first-principles methods. The results revealed that the average cation-ion potential is the primary intrinsic factor influencing Eua. Additionally, the maximum value of the relative height ratio of cations to anions, cell parameter ratio, and average cation Mendeleev number were found to have secondary impacts. This study addresses gaps in the current understanding of Eua, by considering multiple influencing factors beyond a single material system. It contributes to the systematic evaluation of Eua in wurtzite materials, offering valuable insights not only into uniform polarization reversal processes but also as a reference for future research on more complex processes.

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Understanding the transition from nonplanar to planar clusters is crucial for the controllable synthesis of transition metal dichalcogenide (TMDC) monolayers. Using PtSe2 as a model, we investigate how the chemical environment influences the nucleation and growth stages of monolayer PtSe2 through structure searching and first-principles calculations. We established a comprehensive database of platinum selenide clusters (PtxSey, x = 1-10), analyzing 2095 unique clusters and identifying 191 stable isomers and 63 structures with the lowest formation energy on the convex hull. Our findings reveal a chemical environment-dependent phase transition from 3D structures to the planar T-phase of PtxSey clusters, representing an evolutionary route for PtSe2 growth. Clusters such as PtSe6, Pt2Se9, Pt3Se10, and Pt7Se10 in Pt-rich environments, as well as Pt2Se15 and Pt10Se32 in Se-rich environments, have been found to exhibit high stability. Additionally, the impact of varying chemical potentials of Pt and Se on the stability of these clusters is explored. PtSe4 and PtSe6 are found to be highly stable under most experimentally achievable chemical potential conditions and may serve as dominant precursors during PtSe2 growth. This work advances our understanding of the nucleation processes of PtSe2 and other T-phase TMDC materials.

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Regulating the spin states in transition-metal (TM)-based single-atom catalysts (SACs), such as the TM-Nx-C configurations, is crucial for improving the catalytic activity. However, the role of spin in single Ni atoms facilitating the electrochemical CO2 reduction reaction (CO2RR) has been largely overlooked. Using first-principles simulations, we investigated the electrocatalytic performance of Ni-N4-C SACs vertically stacked on the O-terminated MXene nanosheets for the CO2RR. The terminated O atoms on MXene axially interact with the Ni atom due to significant charge transfer between them. Unlike the pure Ni-N4 site, which lacks spin polarization, the newly formed Ni-N4O configuration breaks the spin degeneracy of Ni d orbitals, dramatically lifting the energy level of spin-down d orbitals relative to that of spin-up d orbitals. As a result, the d electrons of Ni in the two spin channels are rearranged, leading to large net spin moments of 1.4 µB. Compared to the Ni-N4 site, the partially filled minority-spin dz2 orbitals of Ni on Ni-N4O weaken the occupied d-π* orbitals between Ni and *COOH, significantly stabilizing the key intermediate. The detailed reaction mechanisms and energetics show that four MXenes, namely, Hf3C2, Zr3C2, Hf2C, and Zr2C, can induce a large spin on the Ni site, thereby improving catalytic activity for CO2 reduction to CO, with a lower onset potential of about -0.75 V vs SHE compared to pure Ni SACs (-1.17 V) according to the potential-constant model with an explicit solvent environment.

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Machine learning and data-driven methods have attracted a significant amount of attention for the acceleration of the design of molecules and materials. In this study, a material design protocol based on multimode modeling that combines literature modeling, numerical data collection, textual descriptor design, genetic modeling, experimental validation, first-principles calculation, and theoretical efficiency calculation is proposed, with a case study on designing compatible complex solvent molecules for a halide perovskite film, which is notorious for optoelectronic deactivation under hostile conditions, especially in water. In the multimode modeling design process, the textual descriptors play the central role and store rich literature scientific knowledge, which starts from the construction of a high-dimension literature model based on scientific articles and is realized by a genetic algorithm for materials predictions. The prediction is substantiated by follow-up experiments and first-principles calculations, leading to the successful identification of effective molecular combinations delivering an unprecedented large aqueous photocurrent (increasing by 3 orders of magnitude compared with that of CH3NH3PbI3) and remarkable aqueous stability (improving from 36% to 89% after immersion in water) under the hostile condition. This study provides a practical route via multimode modeling for accelerating the design of molecule-modified and solution-processed materials in a real scenario.

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Two-dimensional valleys and magnetism are rising areas with intriguing properties and practical uses in advanced information technology. By coupling valleys to collinear magnetism, valley degeneracy is lifted in a large number of magnetic valley materials to exploit the valley degree of freedom. Beyond collinear magnetism, new coupling modes between valley and magnetism are few but highly desirable. By tight-binding calculations of a breathing Kagome lattice, we demonstrate a tunable valley structure and valley-contrasting physical properties in noncollinear antiferromagnets. Distinct from collinear magnetism, noncollinear antiferromagnetic order enables valley splittings even without spin-orbit coupling. Both the canting and azimuthal angles of magnetic moments can be used as experimentally accessible knobs to tune valley splittings. Our first-principles calculations of the Fe3C6O6-silicene-Fe3C6O6 heterostructure also exhibit tunable valley splittings in noncollinear antiferromagnetism, agreeing with our tight-binding results. Our work paves avenues for designing novel magnetic valley materials and energy-efficient valleytronic devices based on noncollinear magnetism.

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Electron mobility in nitride semiconductors is limited by electron-phonon, defect, grain-boundary, and dislocation scatterings. Scandium nitride (ScN), an emerging rocksalt indirect bandgap semiconductor, exhibits varying electron mobilities depending on growth conditions. Since achieving high mobility is crucial for ScN's device applications, a microscopic understanding of different scattering mechanisms is extremely important. Utilizing the ab initio Boltzmann transport formalism and experimental measurements, here we show the hierarchy of various scattering processes in restricting the electron mobility of ScN. Calculations unveil that though Fröhlich interactions set an intrinsic upper bound for ScN's electron mobility of ∼524 cm2/V·s at room temperature, ionized-impurity and grain-boundary scatterings significantly reduce mobility. The experimental temperature dependence of mobilities is captured well considering both nitrogen-vacancy and oxygen-substitutional impurities with appropriate ratios, and room-temperature doping dependency agrees well with the empirical Caughey-Thomas model. Furthermore, we suggest modulation doping and polar-discontinuity doping to reduce ionized-impurity scattering in achieving a high-mobility ScN for device applications.

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Asymmetric doping of wide-gap semiconductors has long been a major challenge, hindering their wider applications. Despite numerous attempts to address this issue through engineering doping levels, the results were still inconclusive. In this work, we propose a quantum engineering strategy based on the state-of-the-art spin-polarized HSE06 hybrid functional method. The local band offset between the host and quantum structures can considerably compensate for the large carrier activation energy (Ea). We chose the system of the AlN host embedded by GaN quantum dots as an example to validate the feasibility of this strategy. The Ea of Si (n-type) and Be (p-type) dopants can be reduced from 222 and 404 meV to negative values and 2 meV, respectively. Therefore, electron and hole density can be increased to more than 1019 and 1020 cm-3, respectively. We also tested potential dopants (C and Ge for the n-type, Mg and Ca for the p-type), and the technique is equally effective. This mechanism can also be used to understand the experimental observations of the superlattice doping strategy. Overall, our study demonstrates that the quantum engineering strategy provides a potential solution to overcome the asymmetric doping problem for universal wide-gap semiconductors and supports a feasible pathway for more efficient devices in the future.

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To seek an earth-abundant and environmentally friendly absorber for thin-film solar cells, Cu3PSe4 is investigated by first-principles calculations and device simulations. We demonstrate that the compound has a suitable band gap width of 1.3 eV as well as a high sunlight absorption coefficient. However, drawbacks like small electron affinity, high hole concentration, large lattice mismatch with CdS, etc., are revealed, which may degrade the photovoltaic performance. To address those shortcomings, we propose (1) to optimize the carrier concentration by preparing the samples at low temperature and under a Cu-rich environment, (2) to replace the CdS buffer layer by a more suitable wide-gap semiconductor with smaller lattice mismatch, and (3) that the selected buffer layer should have small electron affinity in order to reduce the open-circuit voltage losses. After implementation of these optimization approaches, the device simulations demonstrate that the power conversion efficiency reaches 17.7% for a solar cell with the configuration Mo/Cu3PSe4/WS2/n-ZnO. The combination of first-principles calculations at the atomistic level and device simulations at the macroscopic level provides an appropriate approach to design ideal solar cells.