Density Functional Theory Band Gap Research Articles

Unveiling the Electronic Structure of SnS for Photocatalytic Applications: A DFT Approach†

AbstractPhotocatalytic materials are of great scientific interest due to their potential applications in sustainable energy sources. Band gap and optical absorption of the materials are two core characteristics for photocatalysis that eventually depend on electronic structure. In order to accurately compute (predict) the electronic‐scale properties of a crystalline solid using first principles calculations, which might be costly to measure experimentally, large‐scale atomic level calculation frameworks have been made possible through the use of density functional theory (DFT). We have used DFT with many body perturbation theory (MBPT) by solving the bethe‐salpeter equation (BSE) to priorly predict the properties of bulk tin sulfide (SnS) as it meets the necessary requirements for photocatalytic applications. We fixed the DFT band gap underestimation by including the Hubbard parameter (U) and used projector augmented wave pseudo‐potentials with generalized‐gradient approximation (GGA) to calculate the electronic and optical properties of SnS. Optical properties were computed using independent particle approximation (IPA) and BSE with DFT+U wave functions. Our theoretical results align with experimental data for this material, demonstrating the potential for further research in validating experimental results with theoretical approximations and empirical relations.

Theory of magnetic 3d transition metal dopants in gallium nitride

Using first-principles density functional theory (DFT) methods and size-converged supercell models, we analyze the electronic and atomic structure of magnetic $3d$ transition metal dopants in cubic gallium nitride (c-GaN). All stable defect charge states for Fermi levels across the full experimental gap are computed using a method that correctly resolves the boundary condition problem (without a jellium approximation) and eliminates finite-size errors. The resulting computed defect levels are not impacted by the DFT band-gap problem, they span a width consistent with the experimental gap rather than being limited to the single-particle DFT gap. All defects with electronically degenerate (half-metal) ${T}_{d}$ ground states are found to have significant distortions, relaxing to ${D}_{2d}$ structures driven by the Jahn-Teller instability. This leads to insulating ground states for all substitutional $3d$ dopants, refuting claims in the literature that $+U$ or hybrid functional methods are required to avoid artificial half-metal results. Interpreting the ${d}^{n}$ atomic occupations within a crystal-field model and exchange splittings, we identify a systematic trend across the $3d$ transition metal series. Approaches to estimate excited-state energies as observed in photoluminescence from defect centers are assessed, ranging from a Koopmans-type single-particle energy interpretation to relaxed total energy differences in fully self-consistent DFT. The single-particle interpretations are found to be qualitatively predictive and the calculations are consistent with the limited available experimental data across the $3d$ dopant series. These results provide a baseline understanding to guide future studies and a conceptual framework within which to interpret new results.

Syntheses, DFT studies and comparatively photovoltaic applications of some pyrene-imine hybrid derivatives

In this study, (E)-N-phenyl-1(pyren-1yl)methanimine (3) and a isomeric mixture of 5ZZ and 5EE (1,4-phenylenebis(1-(pyren-1-yl)methanimine) were synthesized by condensation of pyrene-1-carbaldehyde (1) with aniline (2) or benzene-1,4-diamine (4) The synthesized compounds were characterized using NMR, UV–vis, IR and HRMS spectroscopic techniques.Utilizing the density functional theory (DFT) and a basis set of B3LYP/6-311G(2d,2p), theoretical computations were done. The computed values were applied to simulated spectra of compounds 3 and the isomeric mixtures 5EE, and 5ZZ demonstrating good agreement with observed spectra. In various solvents, the UV–vis spectra of compounds 3, 5EE, and 5ZZ were recorded in areas 200–500 nm, and function density theory (DFT) and time-dependent density functional theory (TD-DFT) algorithms were used to determine if they can serve as metal-free organic dyes in the use of dye-sensitized solar cells (DSSCs). The charge separation distance (Δr) between an electron and the hole it corresponds to was investigated in addition to the degree of electron-hole overlap (Λ) because transition density matrices (TDM) give information about how each electron departs from its corresponding hole during excitations, resulting in charge transfer (CT). To obtain more insight into the characteristics of complexes, the Mulliken population approach, density of states (TDOS), natural population analysis (NPA), molecular electrostatic potential (MEP), condensed Fukui function, and relative nucleophilicity indices derived from orbital charge calculation results (NPA) were used. In addition, the photovoltaic properties of these compounds were studied comparatively. DFT band gap for 3 was 2.493, 5EE was 2.050, and 5ZZ was 2.071 eV. Furthermore, the power conversion efficiency (PCE) values for compound 3 and the isomeric mixture of compound 5 are calculated as 2.31%, and 2.82%, respectively. The results obtained can provide a useful reference for the development of organic compounds containing pyrene units in more efficient organic-based compounds for photovoltaic applications.

Impact of coordination ability of the selected anions on tuning the structure of Hg(II) complexes constructed from a neutral dithione ligand: Iodine uptake and DFT theoretical studies

In view to examine the role of coordination potential of the selected anions on architect of complexes, HgL2](ClO4)2 (C1) and [HgL2](PF6)2 (C2) were synthesized with a HgS4 core structure by a flexible sulfur donor (1,1-bis(3-methyl-4-imidazoline-2-thione)methane ligand(L). The C1 was crystalized via a branched tube method in MeOH/H2O as a solvent. They have been characterized by the FT-IR, elemental analysis, X-ray powder diffraction (PXRD), density functional theory (DFT) calculations, and considered for the iodine adsorption experiments. Although MOFs and CPS were extensively being studied, but mono and binuclear complexes were rarely used as an adsorbent for removal of the iodine. Additionally, to probe the impact of anions on the structure of complexes, and iodine uptake properties, C1 and C2 were compared with the published dimeric ones [Hg2L2Cl4](C3) and [Hg2L2Br4](C4) with a HgX2S2 core structure. All complexes showed a good performance in removal of iodine from the pollutants. This was supported by a sharp decrease in the intensity of a band at 523 nm nominated to the π*g(p) (HOMO) → σ*u(p) (LUMO) transitions in the free I2 molecule. The iodine capture performance of the monomeric complexes is substantially different with the dimeric ones. C1and C2 remove more than 99% of iodine molecules in the solution within 2 h, whereas C3 and C4 need 24 h to achieve the equilibrium point. The DFT studies and band gap calculations confirmed a charge transfer transition from each of the complexes to the σ*u(p) (LUMO) of the adsorbed iodine molecules with a lower energy relative to the free I2 band gap. Nonlinear optical responses (NLO) and charge transfer properties of the C1-C4 complexes were inspected by the DFT calculations.

Bandgap Correction and Spin-Orbit Coupling Induced Absorption Spectra of Dimethylammonium Lead Iodide for Solar Cell Absorber

The search for stable and highly efficient solar cell absorbers has revealed interesting materials; however, the ideal solar cell absorber is yet to be discovered. This research aims to explore the potentials of dimethylammonium lead iodide (CH3NH2CH3PbI3) as an efficient solar cell absorber. (CH3NH2CH3PbI3) was modeled from the ideal organic–inorganic perovskite cubic crystal structure and optimized to its ground state. Considering the spin-orbit coupling (SOC) effects on heavy metals, the electronic band structure and bandgaps were calculated using the density functional theory (DFT). In contrast, bandgap correction was achieved by using the GW quasiparticle methods of the many-body perturbation theory. The optical absorption spectra were calculated from the real and imaginary dielectric tensors, which are determined by solving the Bethe–Salpeter equations of the many-body perturbation theory. Spin-orbit coupling induces band splitting and bandgap reduction in both DFT and GW methods, while the GW method improves the DFT bandgap. We report a DFT band gap of 1.55 eV, while the effect of spin-orbit coupling reduces the bandgap to 0.50 eV. Similarly, the self-consistent GW quasiparticle method recorded a bandgap of 2.27 eV, while the effect of spin-orbit coupling on the self-consistent GW quasiparticle method reported a bandgap of 1.20 eV. The projected density of states result reveals that the (CH3NH2CH3PbI3) does not participate in bands around the gap, with the iodine (I) p orbital and the lead (Pb) p orbital showing most prominence in the valence band and the conduction band. The absorption coefficient reaches 106 in the ultraviolet, visible, and near-infrared regions, which is higher than the absorption coefficient of CH3NH3PbI3. The spectroscopic limited maximum efficiency predicts a high maximum efficiency of about 62% at room temperature and an absorber thickness of about 10–1 to 102 μm, suggesting that (CH3NH2CH3PbI3) has an outstanding prospect as a solar cell absorber.

DFT study of undoped and As-doped Si nanowires approaching the bulk limit

The electronic properties of pure and As-doped Si nanowires (NWs) with radii up to 9.53 nm are studied using large scale density functional theory (DFT) calculations. We show that, for the undoped NWs, the DFT bandgap reduces with increasing diameter and converges to its bulk value, a trend in agreement with experimental data. Moreover, we show that the atoms closest to the surface of the nanowire (NW) contribute less to the states near the band edges, when compared with atoms close to the centre; this is shown to be due to differences in Si–Si atomic distances, as well as surface passivation effects. When considering As-doped Si NWs we show that dopant placement within the NW plays an important role in deciding electronic properties. We show that a low velocity band is introduced by As doping, in the gap, but close to the conduction band edge. The curvature of this low velocity band depends on the dopant location, with the curvature reducing when the dopant is placed closer to the center. We also show that asymmetry of dopant location with the NW leads to splitting of the valence band edge.

Study of the linear and nonlinear response properties of the zinc-blende AlP, GaP and their AlxGa1-xP ternary alloys using first principle calculations

The structural, electronic, thermodynamic, vibrational, elastic, linear and nonlinear optical properties of AlxGa1-xP ternary alloys are studied using plane-wave pseudopotential method based on the density functional theory. The alchemical mixing method is used to construct an alloy by mixing the pseudopotentials in an appropriate way. The local density approximation is used for the exchange and correlation potentials calculations using the ABINIT code. The Born effective charges, phonon frequencies, longitudinal-transvers optical splitting and thermal properties are calculated using density functional perturbation theory. By applying the many-body effects within the Bethe-Salpeter approach using the Tam-Dancoff approximation, the frequency-dependent macroscopic dielectric function is calculated. The nonlinear dielectric (electronic) susceptibility, the electro-optic tensor and the Raman tensor are investigated in the framework of density functional perturbation theory using the 2n+1 theorem. Moreover, due to density functional theory band gap problem, the band-gap correction is performed within the one-shot GW approximation of many-body perturbation theory. The calculated results of AlP and GaP compounds are in acceptable agreement with available theoretical and experimental results, so the present study on the AlxGa1-xP alloys would be helpful for future experimental and theoretical investigations.

First principle characterization of structural, electronic, mechanical, thermodynamic, linear and nonlinear optical properties of zinc blende InAs, InSb and their InAsxSb1-x ternary alloys

The structural and electronic properties of InAsxSb1-x ternary alloys are studied using plane-wave pseudopotential method based on the density functional theory. The Born effective charge, elastic constants, phonon dispersion curves, linear and nonlinear optical properties of these compounds are calculated using density functional perturbation theory. Based on the calculated phonon frequency, the specific heat at constant volume and entropy are obtained within the harmonic approximation. Moreover, due to the density functional theory band gap problem, the band gap correction is performed within the one-shot GW approximations. The distinguished role of In 4d states on the electronic energy band gap and nonlinear properties of these alloys are extensively explored by the comparison between the calculated results of Hartwigsen-Goedecker-Hutter and Trouiller-Martins-type pseudopotentials. The calculated results show that InAsxSb1-x alloys are mechanically stable and can be a good candidate for high-performance nonlinear optical material. The calculated results of InAs and InSb compounds are in acceptable agreement with available theoretical and experimental results, so the calculated results of InAsxSb1-x alloys will be helpful for future experimental and theoretical investigations.

Anhydrous proline crystals: Structural optimization, optoelectronic properties, effective masses and Frenkel exciton energy

The anhydrous orthorhombic l-proline crystal P212121 (Z=4) was studied using density functional theory (DFT) calculations to obtain its structural, electronic and optical properties. Optical absorption measurements were carried out as well, and the resulting absorption spectrum was compared with theoretical results. It is shown that pure LDA and GGA functionals fail to obtain lattice parameters close to experiment, being required the inclusion of a dispersion correction scheme to achieve good results. A complex electronic structure with eight very close indirect band gaps starting at 4.87 eV with a 12 meV energy range is hinted by the simulations. Applying the Δ-sol scheme to correct the DFT band gap, a theoretical gap estimate of 5.50 eV was obtained, which is very close to the experimental value of 5.54 eV extracted from the optical absorption experimental data. Calculated effective masses of electrons and holes in anhydrous proline are very anisotropic and large, as well as the complex dielectric function and the optical absorption. This is likely due to the way proline molecules inside the crystal form permanent electron dipoles interacting through hydrogen bonds and van der Waals forces. Furthermore, the Frenkel exciton binding energy in proline was experimentally and theoretically found to be about 1.3 eV.

Single layers and multilayers of GaN and AlN in square-octagon structure: Stability, electronic properties, and functionalization

Further to planar single-layer hexagonal structures, GaN and AlN can also form free-standing, single-layer structures constructed from squares and octagons. We performed an extensive analysis of dynamical and thermal stability of these structures in terms of ab initio finite-temperature molecular dynamics and phonon calculations together with the analysis of Raman and infrared active modes. These single-layer square-octagon structures of GaN and AlN display directional mechanical properties and have wide, indirect fundamental band gaps, which are smaller than their hexagonal counterparts. These density functional theory band gaps, however, increase and become wider upon correction. Under uniaxial and biaxial tensile strain, the fundamental band gaps decrease and can be closed. The electronic and magnetic properties of these single-layer structures can be modified by adsorption of various adatoms, or by creating neutral cation-anion vacancies. The single-layer structures attain magnetic moment by selected adatoms and neutral vacancies. In particular, localized gap states are strongly dependent on the type of vacancy. The energetics, binding, and resulting electronic structure of bilayer, trilayer, and three-dimensional (3D) layered structures constructed by stacking the single layers are affected by vertical chemical bonds between adjacent layers. In addition to van der Waals interaction, these weak vertical bonds induce buckling in planar geometry and enhance their binding, leading to the formation of stable 3D layered structures. In this respect, these multilayers are intermediate between van der Waals solids and wurtzite crystals, offering a wide range of tunability.

Wannier Koopman method calculations of the band gaps of alkali halides

Correcting the band structure within the density functional theory (DFT) formalism is a long term goal for its development. Recently, we have proposed a Wannier Koopman method (WKM) to correct the DFT bandgap using the Kohn-Sham equation. Previous tests show that WKM works well for common semiconductors. Here, we test its accuracy in terms of predicting the bandgap of extreme ionic crystals: alkali halides. We found that the WKM can accurately reproduce the alkali halide bandgaps with accuracy in par with the GW method. On the other hand, the hybrid functional with common parameters, which work well for common semiconductors, significantly underestimate the alkali halides.

Tuning the Schottky Barrier at the Graphene/MoS2 Interface by Electron Doping: Density Functional Theory and Many-Body Calculations

Using ab initio calculations we investigate the energy level alignment at the graphene/MoS2 heterostructure and the use of electron doping as a strategy to lower the Schottky barrier and achieve a low-resistance Ohmic contact. For the neutral heterostructure, density functional theory (DFT) with a generalized gradient approximation predicts a Schottky barrier height of 0.18 eV, whereas the G0W0 method increases this value to 0.60 eV. While the DFT band gap of MoS2 does not change when the heterostructure is formed, the G0W0 gap is reduced by 0.30 eV as a result of the enhanced screening by the graphene layer. In contrast to the case of metal substrates, where the band alignment is governed by Pauli repulsion-induced interface dipoles, the graphene/MoS2 heterostructure shows only a negligible interface dipole. As a consequence, the band alignment at the neutral heterostructure is not changed when the two layers are brought into contact. We systematically follow the band alignment as a function of doping co...

Doping effect from Ag and Sb in KBiO3 photocatalyst: first principles study

The direct band gap of cubic KBiO3 with space group Pn-3 calculated from the standard density functional theory (DFT) within the Perdew–Burke–Ernzerhof functional is ∼0·54 eV and obviously underestimated in comparison with the experimental value of 2·1 eV. Using the Heyd–Scuseria–Ernzerhof hybrid functional, the band gap can be corrected to ∼1·77 eV. Further, first principles calculations on Ag/Sb doped KBiO3 indicate that a flexible band gap can be obtained by adjusting the amount of Ag and Sb doping in KBiO3. In particular, K0·667Ag0·333Bi0·5Sb0·5O3 has a DFT band gap of 0·61 eV and larger dispersion at the bottom of the conduction band with smaller effective electron masses, which would lead to an enhancement in photocatalytic activity in comparison with pure KBiO3.

Modeling charged defects inside density functional theory band gaps

Density functional theory (DFT) has emerged as an important tool to probe microscopic behavior in materials. The fundamental band gap defines the energy scale for charge transition energy levels of point defects in ionic and covalent materials. The eigenvalue gap between occupied and unoccupied states in conventional DFT, the Kohn–Sham gap, is often half or less of the experimental band gap, seemingly precluding quantitative studies of charged defects. Applying explicit and rigorous control of charge boundary conditions in supercells, we find that calculations of defect energy levels derived from total energy differences give accurate predictions of charge transition energy levels in Si and GaAs, unhampered by a band gap problem. The GaAs system provides a good theoretical laboratory for investigating band gap effects in defect level calculations: depending on the functional and pseudopotential, the Kohn–Sham gap can be as large as 1.1eV or as small as 0.1eV. We find that the effective defect band gap, the computed range in defect levels, is mostly insensitive to the Kohn–Sham gap, demonstrating it is often possible to use conventional DFT for quantitative studies of defect chemistry governing interesting materials behavior in semiconductors and oxides despite a band gap problem.

Importance of the correct Fermi energy on the calculation of defect formation energies in semiconductors

Density functional theory (DFT) is a major theoretical tool for the study of defects in semiconductors. However, the results suffer from the often too-small DFT band gap. The calculation of defect formation energy (ΔH) using more sophisticated DFT+GW and hybrid functional methods, however, suggest qualitatively different conclusions about the nature of the DFT error. Here we show that these discrepancies originate from large differences in the representation of the Fermi energy of bulk for the different methods and that they can be largely brought into agreement by correcting the DFT ionization energy.

Electronic structure and band gap of zinc spinel oxides beyond LDA: ZnAl2O4, ZnGa2O4 and ZnIn2O4

We examine the electronic structure of the family of ternary zinc spinel oxides ZnX2O4 (X=Al, Ga and In). The band gap of ZnAl2O4 calculated using density functional theory (DFT) is 4.25 eV and is overestimated compared with the experimental value of 3.8–3.9 eV. The DFT band gap of ZnGa2O4 is 2.82 eV and is underestimated compared with the experimental value of 4.4–5.0 eV. Since DFT typically underestimates the band gap in the oxide system, the experimental measurements for ZnAl2O4 probably require a correction. We use two first-principles techniques capable of describing accurately the excited states of semiconductors, namely the GW approximation and the modified Becke–Johnson (MBJ) potential approximation, to calculate the band gap of ZnX2O4. The GW and MBJ band gaps are in good agreement with each other. In the case of ZnAl2O4, the predicted band gap values are >6 eV, i.e. ∼2 eV larger than the only reported experimental value. We expect future experimental work to confirm our results. Our calculations of the electron effective masses and the second band gap indicate that these compounds are very good candidates to act as transparent conducting host materials.

Three-dimensional extended Hückel theory-nonequilibrium Green’s function spin polarized transport model for Fe/MgO/Fe heterostructures

Although the theory of tunnel magnetoresistance (TMR) in Fe/MgO/Fe heterostructures is well known, there is a discrepancy between the values predicted by ab initio calculations with a band gap of 5.2 eV and the ones predicted by other methods, e.g., empirical tight-binding with a band gap of 7.6 eV. To our knowledge, no one has yet used the same theory to explore the reasons behind this discrepancy. In this work, we report a three-dimensional atomistic nonequilibrium Green’s function transport model with two set of transferable extended Hückel theory parameters for MgO; one with the experimental band gap of 7.8 eV and the other with the local density approximation of the density functional theory band gap of 5.2 eV. To capture the symmetry filtering property of MgO, we parameterize using the k-resolved orbital projected density of states as the benchmark. We show that the band gap has a significant effect on the barrier width dependence and the bias dependence of the transport quantities. By using the experimental band gap, the TMR is much smaller than the one observed with a band gap of 5.2 eV.

First Principles Predictions of Intrinsic Defects in Aluminum Arsenide, AlAs

ABSTRACTThe structures, energies, and energy levels of a comprehensive set of simple intrinsic point defects in aluminum arsenide are predicted using density functional theory (DFT). The calculations incorporate explicit and rigorous treatment of charged supercell boundary conditions. The predicted defect energy levels, computed as total energy differences, do not suffer from the DFT band gap problem, spanning the experimental gap despite the Kohn-Sham eigenvalue gap being much smaller than experiment. Defects in AlAs exhibit a surprising complexity—with a greater range of charge states, bistabilities, and multiple negative-U systems—that would be impossible to resolve with experiment alone. The simulation results can be used to populate defect physics models in III-V semiconductor device simulations with reliable quantities in those cases where experimental data is lacking, as in AlAs.

Band structures and native defects of ammonia borane

Band structures and native defects in molecular solid ammonia borane (AB) are investigated by using first-principles calculations based on the density-functional theory (DFT). The native defects include ${\text{NH}}_{3}$ and ${\text{BH}}_{3}$ antisites, interstitials, and vacancies in the various charge states. Despite that the AB crystal is an insulator with a DFT band gap larger than 6 eV, some of the charge-neutral native defects can be abundant, especially at the ${\text{NH}}_{3}$-rich growth conditions, due to their exceptionally low formation energies. This is in sharp contrast to defects in semiconductors for which the formation energies of charge-neutral defects are usually high and correspondingly the concentrations of those defects are low.

First-principles study of native point defects in crystalline indium gallium zinc oxide

Materials in In–Ga–Zn–O system are promising candidates for channel layers of high-performance thin-film transistors (TFTs). We investigated the atomic arrangements and the electronic structures of crystalline InGaZnO4 containing point defects such as oxygen vacancy (VO), interstitial hydrogen (Hi), and interstitial oxygen (Oi) by density functional theory (DFT) using a plane-wave pseudopotential method. The calculations for the atomic structure relaxation suggest that Hi bonds to a lattice oxygen (OO), and Oi occupies a split interstitial site [Oi(split)] forming a chemical bond with OO which is similar to O2 molecule, or Oi occupies an octahedral interstitial site [Oi(oct)]. The electronic structure calculations reveal that VO forms fully occupied states around the middle of the DFT band gap, while Hi does not form a defect level in the band gap but raises the Fermi level above the conduction band minimum. Oi(split) forms fully occupied states above the valence band maximum of the defect-free model (VBM0), while Oi(oct) forms both occupied and unoccupied states above the VBM0. It is thus suggested that VO and Oi(split) are electrically inactive for electrons but work as hole traps, Hi acts as a donor, and Oi(oct) is electrically active, trapping both electrons and holes. These observations imply that VO and Oi(split) do not but Hi and Oi(oct) influence electrical properties of the n-channel TFTs based on the In–Ga–Zn–O semiconductor materials.