Supercell Geometry Research Articles

Lithium doping effect on structural, electronic and optical properties of KCaF3 fluoroperovskite: DFT insights using GGA-PBE

In order to evaluate the effects of Lithium (Li) doping on the various properties of KCaF3, we present first-principles calculations built on density functional theory (DFT) and employing approximation GGA-PBE. The compound possesses a 2 × 2 × 1 supercell and cubic geometry with space group pm3m. By putting the TDOS and PDOS concepts into practice, the effects of Li-doping on electronic structure and, consequently, optical characteristics have been investigated and evaluated in detail. With the formation of new states in band structure, the substitution of the Lithium (Li) atom for the Calcium (Ca) atom drastically adjusts the electronic band structure. The indirect bandgap of pure KCaF3 was measured to be 5.37 eV. The band gap was slightly shrunk as a result of changes in Li concentration. This causes the indirect band gap of KCaF3 to change to the direct band gap for Li-doped KCaF3. A strong interaction between the Li atom and the atoms around it is seen and the density of states for Li-doped KCaF3 relocates at slightly lower energies. Additionally, there is a noticeable change in the partial density of states of KCaF3 near the conduction band bottom, leading us to believe that Li-doping has an impact on the electronic band structure. Investigations into the optical characteristics of doped and undoped KCaF3 and correlations with its electrical structure are made. The massive difference in optical characteristics and band gap (i.e., indirect to direct) caused by Li-doping makes this substance a desirable candidate for optoelectronic materials.

Predictions on Structural and Electronic Properties to Synthesize Bismuth-Carbon Compounds in Different Periodicities.

This work was carried out to explore the compounds of bismuth with carbon using density functional theory (DFT)-based computations. The structures of the compounds BiC, BiC2, BiC3, Bi2C3, BiC5, and Bi2C5 were predicted at a generalized gradient approximation (GGA-PBE) level of theory. The calculations were carried out on the structures in unit cell and supercell geometries in slab and bulk periodicities. The structural and electronic properties of the mentioned compounds were investigated in detail. The calculations of the structures revealed lattice constants of the compounds for cubic unit cell as 212.2 pm for BiC, 176.9 pm for BiC2, 240.5 pm for BiC3, 232.4 pm for Bi2C3, and 354.5 pm for Bi2C5. The compounds BiC, BiC2, BiC3, BiC5, and Bi2C5 were found to be metallic, whereas Bi2C3 exhibited semiconducting character with a band gap of 0.305 eV. This work provides an initial framework for preparing new 2D materials from BixCy.

Design of ZnO with Reduced Direct Bandgap using First-principles Calculation: Electronic, Band Structure, and Optical Properties

In the current work, lattice parameters, band structure, and optical characteristics of neat and doped ZnO are studied by utilizing ultrasoft pseudopotentials (USP) and generalized gradient approximation (GGA) with the support of Firstprinciples calculation (FPC) derived from density functional theory (DFT). The measurements had been performed in the supercell geometry that had been optimized. To discover the lattice parameters, electronic band structure, and optical characteristics of V-doped ZnO, the FPC based on DFT has been applied in CASTEP. The calculated lattice parameters are agree with observed experimental data. The volume of the doped system grows as the content of Vdoping in it increases. Pure and doped ZnO were investigated for band structure and energy bandgaps using the Monkhorst-Pack scheme’s k-point sampling techniques in the high symmetry direction of the Brillouin zone (G-A-H-K-G-M-L-H). In the presence of high V content, the bandgap energy decreases from 3.331 to 2.055 eV. From the band E-K diagram (V.B and C.B), PDOS and DOS diagrams insight into the electronic structure of the atom and the amount to which each energy band contributes to a specific atomic orbital were specified. The bandgaps were manipulated so that they narrowed, resulting in a redshift of the absorption spectrum in the IR region. The imaginary and real parts of the extinction coefficient, refractive index, and dielectric function have all increased at lower photon energies.

Electronic structure and magnetic properties of bulk and (001) surfaces of [formula omitted]-Fe4C from first principles

We report first principles investigation of the electronic structure and magnetic properties of bulk γ′-Fe4C and its (001) surfaces within density functional theory. The bulk equilibrium lattice parameter (a0 = 3.81Å ) and bulk modulus (B0=141.2 GPa) were determined by first relaxing the cell volume while keeping the atoms located at their ideal positions. The corresponding magnetic moments were found to be 3.10 μB and 1.77 μB on the two inequivalent iron sites. The magnetic exchange parameters between the magnetic spin moments were computed as functions of inter-atomic distances up to four times the lattice parameter, from which the mean-field estimates of the Curie temperature were obtained. Effects of disorder, due in one case to substitution of carbon atoms by nitrogen atoms, and in an other to a small concentration of vacancies on the iron sites, on the Curie temperature were also investigated within the coherent potential approximation. We found that disorder has a dramatic effect on the transition temperature, especially in the second case. The electronic structure and magnetic profile of the γ′-Fe4C (001) surface with Fe2C termination was studied in the supercell geometry. Substantial surface relaxations were found to occur, but they do not induce significant changes in the magnetic moments when compared to those of the unrelaxed surface. No notable charge transfers were found either in the bulk or at the surface.

Theoretical Investigations of Electronic and Optical Properties of Vanadium Doped Wurtzite Zinc Oxide from First Principle Calculation Method

In this study lattice parameters, band structure, and optical characteristics of pure and V-doped ZnO are examined by employing (USP) and (GGA) with the assistance of First-principles calculation (FPC) derived from (DFT). The measurements are performed in the supercell geometry that were optimized. GGA+U, the geometrical structures of all models, are utilized to compute the amount of energy after optimizing all parameters in the models. The volume of the doped system grows as the content of the dopant V is increased. Pure and V-doped ZnO are investigated for band structure and energy bandgaps using the Monkhorst–Pack scheme's k-point sampling techniques in the Brillouin zone (G-A-H-K-G-M-L-H). In the presence of high V content, the bandgap energy decreases from 3.331 to 2.043 eV as seen by the band diagram. PDOS diagram was utilized to get the insight of the electronic structure of the atoms and the amount to which all energy bands contribute to a particular orbit of the atoms. As the V content grew, so did the PDOS for all of the states. The manipulation of bandgaps was carried out in a way that narrowing the bandgaps occurs, resulting in a redshift of the absorption spectrum in the IR region. At lower photon energies, the imaginary and real parts dielectric functions have increased. The effectiveness of V atoms on transmissivity especially in the low energy region of the V-doped ZnO perovskite has been verified compared to the other theoretical results.

Unified ab initio description of Fröhlich electron-phonon interactions in two-dimensional and three-dimensional materials

\textit{Ab initio} calculations of electron-phonon interactions including the polar Fr\"ohlich coupling have advanced considerably in recent years. The Fr\"ohlich electron-phonon matrix element is by now well understood in the case of bulk three-dimensional (3D) materials. In the case of two-dimensional (2D) materials, the standard procedure to include Fr\"ohlich coupling is to employ Coulomb truncation, so as to eliminate artificial interactions between periodic images of the 2D layer. While these techniques are well established, the transition of the Fr\"ohlich coupling from three to two dimensions has not been investigated. Furthermore, it remains unclear what error one makes when describing 2D systems using the standard bulk formalism in a periodic supercell geometry. Here, we generalize previous work on the \textit{ab initio} Fr\"ohlich electron-phonon matrix element in bulk materials by investigating the electrostatic potential of atomic dipoles in a periodic supercell consisting of a 2D material and a continuum dielectric slab. We obtain a unified expression for the matrix element, which reduces to the existing formulas for 3D and 2D systems when the interlayer separation tends to zero or infinity, respectively. This new expression enables an accurate description of the Fr\"ohlich matrix element in 2D systems without resorting to Coulomb truncation. We validate our approach by direct \textit{ab initio} density-functional perturbation theory calculations for monolayer BN and MoS$_2$, and we provide a simple expression for the 2D Fr\"ohlich matrix element that can be used in model Hamiltonian approaches. The formalism outlined in this work may find applications in calculations of polarons, quasiparticle renormalization, transport coefficients, and superconductivity, in 2D and quasi-2D materials.

Tailoring interfacial properties in CaVO3 thin films and heterostructures with SrTiO3 and LaAlO3 : A DFT+DMFT study

In this paper we use density functional theory combined with dynamical mean-field theory (DFT+DMFT) to study interface effects between thin films of the correlated metal CaVO$_3$ and the two typical substrate materials SrTiO$_3$ and LaAlO$_3$. We find that the CaVO$_3$/SrTiO$_3$ interface has only a marginal influence on the CaVO$_3$ thin film, with the dominant effect being the (bulklike) epitaxial strain imposed by the large lattice mismatch, rendering the CaVO$_3$ film insulating due to the enhanced orbital polarization related to the strong level splitting between the t$_{\mathrm{2g}}$ orbitals. In contrast, at the polar CaVO$_3$/LaAlO$_3$ interface, the presence of the interface can have a huge effect on the thin film properties, depending both on the specific interface termination as well as the specific boundary conditions imposed by the multilayer geometry. We compare three different approaches to model the interface between the correlated metal CaVO$_3$ and the band insulator LaAlO$_3$, which all impose a different set of (electrostatic) boundary conditions on the electronic structure. The spectral properties obtained from our calculations reveal a strong influence of the supercell geometry, ranging from bulklike to highly doped and structurally distorted phases, indicating a potential tunability of the interfacial properties via multilayer engineering.

Pentacene and tetracene molecules and films on H/Si(111): level alignment from hybrid density functional theory

The electronic properties of hybrid organic–inorganic semiconductor interfaces depend strongly on the alignment of the electronic carrier levels in the organic/inorganic components. In the present work, we address this energy level alignment from first principles theory for two paradigmatic organic–inorganic semiconductor interfaces, the singlet fission materials tetracene and pentacene on H/Si(111), using all-electron density functional theory calculations with a hybrid exchange–correlation functional. For isolated tetracene on H/Si(111), a type I-like heterojunction (lowest-energy electron and hole states on Si) is found. For isolated pentacene, the molecular and semiconductor valence band edges are degenerate. For monolayer films, we show how to construct supercell geometries with up to 1192 atoms, which minimize the strain between the inorganic surface and an organic monolayer film. Based on these models, we predict the formation of type II heterojunctions (electron states on Si, hole-like states on the organic species) for both acenes, indicating that charge separation at the interface between the organic and inorganic components is favored. The paper discusses the steps needed to find appropriate low-energy interface geometries for weakly bonded organic molecules and films on inorganic substrates from first principles, a necessary prerequisite for any computational level alignment prediction.

Combined Molecular Dynamics and DFT Simulation Study of the Molecular and Polymer Properties of a Catechol-Based Cyclic Oligomer of Polyether Ether Ketone.

The geometrical, energetic, noncovalent, and material properties of a catechol-based cyclic oligomer of Polyether Ether Ketone (PEEK) called o-PEEK were investigated using Molecular Dynamics (MD) and Density Functional Theory (DFT) simulations. The DFT (and MD) calculation performed with the PBEsol functional (and COMPASS II force field) gave a density of 1.39 (and 1.36) gcm−3 and a volume of 2744.5 (and 2808.5) cm3 for o-PEEK and are comparable with the corresponding experimental values of 1.328 gcm−3 and 2884.6 cm3, respectively. The absolute values of the glass transition temperature (Tg) MD simulated using the unit-cell and 2 × 2 × 2 supercell geometries of the o-PEEK system were 424.4 and 428.6 K, respectively. Although these values slightly differ from each other, both are close to the experiment (Tg = 418.2 K). The results of the (charge) density gradient analysis suggest that the supramolecular assembly between the o-PEEK oligomers in the experimentally observed infinite semi-crystal is driven by a wide range of noncovalent interactions. While the individual local interactions between the oligomers were recognized to be weak-to-medium in strength and are theoretically difficult to quantify, the B97-D3/cc-pVTZ level stabilization energy responsible for the formation of each of the five binary complex configurations extracted from the PBEsol relaxed 2 × 2 × 2 supercell geometry of the o-PEEK system was calculated to vary between –3.5 and –33.0 kcal mol−1.

Structural, electronic, vibrational, and elastic properties of graphene/ MoS2 bilayer heterostructures

Graphene/MoS$_2$ van der Waals (vdW) heterostructures have promising technological applications due to their unique properties and functionalities. Many experimental and theoretical research groups across the globe have made outstanding contributions to benchmark the properties of graphene/MoS$_2$ heterostructures. Even though some research groups have already made an attempt to model the graphene/MoS$_2$ heterostructures using {\it first-principles} calculations, there exists several discrepancies in the results from different theoretical research groups and the experimental findings. In the present work, we revisit this problem by first principles approach and address the existing discrepancies about the interlayer spacing between graphene and MoS$_2$ monolayers in graphene/MoS$_2$ heterostructures, and the location of Dirac points near Fermi-level. We find that the Tkatchenko--Scheffler method efficiently evaluates the long-range vdW interactions and accurately predicts interlayer spacing between graphene and MoS$_2$ sheets. We further investigate the electronic, mechanical and vibrational properties of the optimized graphene/MoS$_2$ heterostructures created using 5$\times$5/4$\times$4 and 4$\times$4/3$\times$3 supercell geometries having different magnitudes of lattice mismatch. The effect of the varying interlayer spacing on the electronic properties of heterostructures is discussed. Our phonon calculations reveal that the interlayer shear and breathing phonon modes, which are very sensitive to the weak vdW interactions, play vital role in describing the thermal properties of the studied systems. The thermodynamic and elastic properties of heterostructures are further discussed. A comparison between our results and the results reported from other research groups is presented.

Effects of short-range electron-electron interactions in doped graphene

We study theoretically the effects of short-range electron-electron interactions on the electronic structure of graphene, in the presence of single substitutional impurities. Our computational approach is based on the $\pi$ orbital tight-binding approximation for graphene, with the electron-electron interactions treated self-consistently at the level of the mean-field Hubbard model. We compare explicitly non-interacting and interacting cases with varying interaction strength and impurity potential strength. We focus in particular on the interaction-induced modifications in the local density of states around the impurity, which is a quantity that can be directly probed by scanning tunneling spectroscopy of doped graphene. We find that the resonant character of the impurity states near the Fermi level is enhanced by the interactions. Furthermore, the size of the energy gap, which opens at high-symmetry points of the Brillouin zone of the supercell upon doping, is significantly affected by the interactions. The details of this effect depend subtly on the supercell geometry. We use a perturbative model to explain these features and find quantitative agreement with numerical results.

Design of plasmonic backcontact nanogratings for broadband and polarization-insensitive absorption enhancement in thin-film solar cell

We discuss the rules for designing nanostructured plasmonic backcontact of thin-film crystalline silicon solar cells using two-dimensional finite-difference time-domain (2D-FDTD) method. A novel efficient quasi-periodic plasmonic nanograting is designed. Numerical calculations demonstrate that broadband and polarization-insensitive absorption enhancement is achieved by the proposed structure which is based on a supercell geometry containing N subcells in each of which there is one Ag nanowire deposited on the backcontact of the solar cell. The proposed structure offers the possibility of controlling the number and location of photonic and plasmonic modes and outperforms the periodic plasmonic nanogratings which only utilize plasmonic resonances. We start by tuning the plasmonic mode of one subcell and then construct the supercell based on the final design of the subcell. Our findings show that with a proper choice of key parameters of the nanograting, several photonic and plasmonic modes can be excited across the entire spectral region where crystalline silicon (c-Si) is absorbing. The absorption enhancement is significant, particularly in the long wavelength region where c-Si is weakly absorbing.

Nano-Scale Corrugations in Graphene: A Density Functional Theory Study of Structure, Electronic Properties and Hydrogenation

Graphene rippled at the nanoscale level is gathering attention for advanced applications, especially in the field of nanoelectronics and hydrogen storage. Convexity enhanced reactivity toward H was demonstrated on naturally corrugated graphene grown by Si evaporation on SiC, which makes this system a platform for fundamental studies on the effects of rippling. In this work, we report a density functional theory study on a model system specifically designed to mimic graphene on SiC. We first study the supercell geometry and configuration that better reproduce the corrugated monolayer. The relatively low computational cost of this model system allows a systematic study of the dependence of stability, structure, and electronic properties of graphene subject to different levels of stretching and corrugation. The most representative structure is then progressively hydrogenated, imitating the exposure to atomic hydrogen, and stability, structural and electronic properties are evaluated as a function of hydrogen...

Identifying the nuclei of nanoscale lithium colloids in LiF crystals

Various spatial and charge configurations of precolloidal centers in lithium fluoride crystals are explored. Theoretical investigations are based on density functional theory and pseudopotential and supercell geometry. Band gap structure is analyzed from the energy distribution of the electronic density of states.

Absorption and Losses in One-Dimensional Photonic-Crystal-Based Absorbers Incorporating Graphene

We investigate the linear response of single and multiple graphene sheets embedded in quarter-wave one-dimensional photonic crystals (PhCs) in terms of absorption and losses. In particular, we show that it is possible to achieve near-perfect narrowband absorption when a single monolayer graphene is sandwiched between two PhC mirrors with optimized pair numbers. The simulations reveal that the resonant wavelength and the total absorption frequency may be tuned by tilting the angle of incidence of the impinging source. We also show that the losses, related to the dielectric materials constituting the one-dimensional PhC, can degrade the optical performance of the device. Conversely, by arranging the same dielectric slabs in a different order (supercell), it is possible to achieve a broadband absorption that is almost constant over a wide range of angle of incidence. In this configuration, the absorption and the bandwidth can be tuned by varying the supercell geometry. These features make these devices attractive for different applications ranging from tunable and saturable absorbers for short-pulse lasers to graphene-based photodetectors.

Finite-size supercell correction scheme for charged defects in one-dimensional systems

We propose a finite-size correction scheme for the formation energy of charged defects and impurities in one-dimensional systems within density functional theory. The energy correction in a supercell geometry is obtained by solving the Poisson equation in a continuum model which is described by an anisotropic permittivity tensor, with the defect charge distribution derived from first-principles calculations. We implement our scheme to study impurities and dangling bonds in silicon nanowires and demonstrate that the formation energy of charged defects rapidly converges with the supercell size.

Optically active metasurface with non-chiral plasmonic nanoantennas.

We design, fabricate, and experimentally demonstrate an optically active metasurface of λ/50 thickness that rotates linearly polarized light by 45° over a broadband wavelength range in the near IR region. The rotation is achieved through the use of a planar array of plasmonic nanoantennas, which generates a fixed phase-shift between the left circular polarized and right circular polarized components of the incident light. Our approach is built on a new supercell metasurface design methodology: by judiciously designing the location and orientation of individual antennas in the structural supercells, we achieve an effective chiral metasurface through a collective operation of nonchiral antennas. This approach simplifies the overall structure when compared to designs with chiral antennas and also enables a chiral effect which quantitatively depends solely on the supercell geometry. This allows for greater tolerance against fabrication and temperature effects.

Exact exchange plane-wave-pseudopotential calculations for slabs.

The exact exchange of density functional theory is applied to both free-standing graphene and a Si(111) slab, using the plane-wave pseudopotential (PWPP) approach and a periodic repetition of the supercell containing the slab. It is shown that (i) PWPP calculations with exact exchange for slabs in supercell geometry are basically feasible, (ii) the width of the vacuum required for a decoupling of the slabs is only moderately larger than in the case of the local-density approximation, and (iii) the resulting exchange potential vx shows an extended region, both far outside the surface of the slab and far from the middle of the vacuum region between the slabs, in which vx behaves as -e(2)/z, provided the width of the vacuum is chosen sufficiently large. This last result is corroborated by an analytical analysis of periodically repeated jellium slabs. The intermediate -e(2)/z behavior of vx can be used for an absolute normalization of vx and the total Kohn-Sham potential, which, in turn, allows the determination of the work function.

Long-range interactions between substitutional nitrogen dopants in graphene: Electronic properties calculations

Being a true two-dimensional crystal, graphene has special properties. In particular, a point-like defect in graphene may have effects in the long range. This peculiarity questions the validity of using a supercell geometry in an attempt to explore the properties of an isolated defect. Still, this approach is often used in ab-initio electronic structure calculations, for instance. How does this approach converge with the size of the supercell is generally not tackled for the obvious reason of keeping the computational load to an affordable level. The present paper addresses the problem of substitutional nitrogen doping of graphene. DFT calculations have been performed for 9x9 and 10x10 supercells. Although these calculations correspond to N concentrations that differ by about 10%, the local densities of states on and around the defects are found to depend significantly on the supercell size. Fitting the DFT results by a tight-binding Hamiltonian makes it possible to explore the effects of a random distribution of the substitutional N atoms, in the case of finite concentrations, and to approach the case of an isolated impurity when the concentration vanishes. The tight-binding Hamiltonian is used to calculate the STM image of graphene around an isolated N atom. STM images are also calculated for graphene doped with 0.5 % concentration of nitrogen. The results are discussed in the light of recent experimental data and the conclusions of the calculations are extended to other point defects in graphene.

Engineering gratings for light trapping in photovoltaics: The supercell concept

The question of the optimal surface structure for light trapping is widely debated in thin-film solar cell research. Here we propose a generic design approach that can tailor the strength of the diffraction orders of a periodic structure. Our approach is based on a supercell geometry that is able to suppress the low orders that do not couple into the quasiguided modes of the thin film. We demonstrate the concept theoretically and experimentally, showing that the supercell outperforms conventional gratings.