Bandgap of two-dimensional materials: Thorough assessment of modern exchange-correlation functionals

First-principle investigation of structural, electronic, and phase stabilities in chalcopyrite semiconductors: insights from Meta-GGA functionals

We undertake a comprehensive first-principles investigation into the factors influencing the optoelectronic efficiencies of PIQIIIR2VIchalcopyrite semiconductors. The structural attributes, electronic properties, and phase stabilities are explored using various meta-GGA exchange-correlation (XC) functionals within the density functional framework. In particular, we assess the relative performance of these XC functionals in obtaining estimates of various relevant parameters. The structural parameteruin chalcopyrite semiconductors is a noteworthy aspect, as it is intrinsically tied to the extent of orbital hybridization between distinct atoms and thereby strongly influences the electronic properties. In general, the application of widely used GGA-PBE XC functional to these chalcopyrites results in unreliable predictions of band gaps and 'u' parameter due to delocalization errors that in turn arise due to the inclusion ofdandfcore electrons. While hybrid functionals offer remarkable accuracy through state-of-the-art methods, their main drawback lies in their computational expense and resource demands. Our findings strongly suggest that in comparison to GGA-PBE, the meta-GGA XC functionals perform quite well and provide results that closely align with experimental values. In particular, ther2SCAN andrMGGAC XC functionals are preferable and superior for investigating chalcopyrites and other solid-state systems. This preference is rooted in their excellent performance and substantially reduced computational costs compared to hybrid functionals.

Two-Dimensional Noble Metal Chalcogenides in the Frustrated Snub-Square Lattice

We study two-dimensional noble metal chalcogenides, with compositions {Cu, Ag, Au}2{S, Se, Te}, crystallizing in a snub-square lattice. This is a semiregular two-dimensional tesselation formed by triangles and squares that exhibits geometrical frustration. We use for comparison a square lattice, from which the snub-square tiling can be derived by a simple rotation of the squares. The monolayer snub-square chalcogenides are very close to thermodynamic stability, with the most stable system (Ag2Se) a mere 7 meV/atom above the convex hull of stability. All compounds studied in the square and snub-square lattice are semiconductors, with band gaps ranging from 0.1 to more than 2.5 eV. Excitonic effects are strong, with an exciton binding energy of around 0.3 eV. We propose the Cu (001) surface as a possible substrate to synthesize Cu2Se, although many other metal and semiconducting surfaces can be found with very good lattice matching.

Density functional applications of jellium with a local gap model correlation energy functional

We develop a realistic density functional approximation for the local gap, which is based on a semilocal indicator that shows good screening properties. The local band model has remarkable density scaling behaviors and works properly for the helium isoelectronic series for the atoms of the Periodic Table, as well as for the non-relativistic noble atom series (up to 2022 e-). Due to these desirable properties, we implement the local gap model in the jellium-with-gap correlation energy, developing the local-density-approximation-with-gap correlation functional (named LDAg) that correctly gives correlation energies of atoms comparable with the LDA ones but shows an improvement for ionization potential of atoms and molecules. Thus, LDAg seems to be an interesting and useful tool in density functional theory.

Statistical analysis of the performance of a variety of first-principles schemes for accurate prediction of binary semiconductor band gaps

Standard density functional theory (DFT) approximations tend to strongly underestimate band gaps, while the more accurate GW and hybrid functionals are much more computationally demanding and unsuitable for high-throughput screening. In this work, we have performed an extensive benchmark of several approximations with different computational complexity [G0W0@PBEsol, HSE06, PBEsol, modified Becke-Johnson potential (mBJ), DFT-1/2, and ACBN0] to evaluate and compare their performance in predicting the bandgap of semiconductors. The benchmark is based on 114 binary semiconductors of different compositions and crystal structures, for about half of which experimental band gaps are known. Surprisingly, we find that, compared with G0W0@PBEsol, which exhibits a noticeable underestimation of the band gaps by about 14%, the much computationally cheaper pseudohybrid ACBN0 functional shows a competitive performance in reproducing the experimental data. The mBJ functional also performs well relative to the experiment, even slightly better than G0W0@PBEsol in terms of mean absolute (percentage) error. The HSE06 and DFT-1/2 schemes perform overall worse than ACBN0 and mBJ schemes but much better than PBEsol. Comparing the calculated band gaps on the whole dataset (including the samples with no experimental bandgap), we find that HSE06 and mBJ have excellent agreement with respect to the reference G0W0@PBEsol band gaps. The linear and monotonic correlations between the selected theoretical schemes and experiment are analyzed in terms of the Pearson and Kendall rank coefficients. Our findings strongly suggest the ACBN0 and mBJ methods as very efficient replacements for the costly G0W0 scheme in high-throughput screening of the semiconductor band gaps.

Effect of vacancy defects on the electronic and mechanical properties of two-dimensional MoSi2N4

MoSi₂N₄ is a recently fabricated 2-dimensional indirect bandgap semiconductor material that has attracted interest in various fields due to its promising properties. A defect-based thorough and reliable investigation of its physical properties is indispensable in this regard to explore its industrial applications in the future. In this work, a comprehensive vacancy defect-based analysis of the electronic and mechanical characteristics of this material is conducted with varying defect percentages. We have analyzed the gradual change in electronic properties of MoSi₂N₄ by performing first-principles density functional theory-based investigation and presented a detailed analysis for point vacancies ranging from 0.297% to 14.29%, revealing the transition of this monolayer from the semiconductor to metal phase. The gradual change in mechanical properties due to the defect introduction has also been reported and analyzed, where the Young's modulus, Poisson ratio, elastic constant, etc. are calculated by the stress-strain method using Matrix Sets (OHESS). Further, we extend the investigation to the exploration of thermal and topological characteristics and report the triviality of the MoSi₂N₄ material as well as the effect on specific heat, entropy, and free energy with respect to temperature. We believe that the results presented in this study could assist the process of incorporating MoSi₂N₄ in future 2D electronics.

Efficient and improved prediction of the band offsets at semiconductorheterojunctions from meta-GGA density functionals: a benchmark study

Accurate theoretical prediction of the band offsets at interfaces of semiconductor heterostructures can of-ten be quite challenging. Although density functional theory has been reasonably successful to carry outsuch calculations and efficient and accurate semilocal functionals are desirable to reduce the computational cost. In general, the semilocal functionals based on the generalized gradient approximation (GGA) significantly underestimate the bulk band gaps. This, in turn, results in inaccurate estimates of the band offsets at the heterointerfaces. In this paper, we investigate the performance of several advanced meta-GGA functionals in the computational prediction of band offsets at semiconductor heterojunctions. In particular, we investigate the performance of r 2 SCAN (revised strongly-constrained and appropriately-normed functional), rMGGAC (revised semilocal functional based on cuspless hydrogen model and Pauli kinetic energy density functional), mTASK (modified Aschebrock and Kümmel meta-GGA functional), and LMBJ (local modified Becke-Johnson) exchange-correlation functionals. Our results strongly suggest that these meta-GGA functionals for supercell calculations perform quite well, especially, when compared to computationally more demanding GW calculations. We also present band offsets calculated using ionization potentials and electron affinities, as well as band alignment via the branch point energies. Overall, our study shows that the aforementioned meta-GGA functionals can be used within the DFT framework to estimate the band offsets in semiconductor heterostructures with predictive accuracy.

Solid-state performance of a meta-GGA screened hybrid density functional constructed from Pauli kinetic enhancement factor dependent semilocal exchange hole

The semilocal form of the exchange hole is highly useful in developing non-local range-separated hybrid density functionals for finite and extended systems. The way to construct the conventional exact exchange hole model is based on either the Taylor series expansion or the reverse engineering technique from the corresponding exchange energy functional. Although the latter technique is quite popular in context of generalized gradient approximation (GGA) functionals, the same for the meta-GGA functionals is not so much explored. Thus, in this study, we propose a reverse-engineered semilocal exchange hole of a meta-GGA functional, that depends only on the meta-GGA ingredient α (also known as the Pauli kinetic energy enhancement factor). The model is used subsequently to design the short-range-separated meta-GGA hybrid density functional. We show that the present method can be successfully applied for several challenging problems in the context of solids, especially for which the GGA based hybrid fails drastically. This assessment proves that the present functional is quite useful for materials sciences. Finally, we also use this method for several molecular test cases, where the results are also as comparative as its base semilocal functional.

Accurate band gaps from exchange potentials designed from a cuspless hydrogen density-based exchange hole model

The explicit forms of exchange-correlation (XC) potentials, which are not functional derivatives of any XC energy functional, are reasonably efficient in predicting the band gap of materials. The most successful example in this genre is the MBJ [F. Tran et al., Phys. Rev. Lett., 2009 102, 226401] exchange potential, which is based on the asymptotically correct Becke-Roussel (BR) exchange potential. We employ the cuspless hydrogen density and corresponding exchange hole to construct a BR like potential. The modified BR potential is again utilized in the framework of MBJ for band gap calculations. Also, we employ a Laplacian free model of the exchange hole in the framework of MBJ. These methods are analyzed by calculating band gaps of various test sets containing narrow, intermediate, and wide bandgap materials. Besides, we apply these potentials to eighteen ternary semiconductors with a chalcopyrite structure, exciting materials for photovoltaic applications. By comparing them with MBJ, we find that the band gaps obtained using the new potentials are not uniformly larger values than the MBJ potential in all cases. But, in many instances where MBJ overestimates the gap, the new potentials' band gaps are comparatively smaller and closer to the experimental ones. We also show that these potentials can correctly predict the band structure of three-dimensional topological insulators.

Improved electronic structure prediction of chalcopyrite semiconductors from a semilocal density functional based on Pauli kinetic energy enhancement factor

The correct treatment ofdelectrons is of prime importance in order to predict the electronic properties of the prototype chalcopyrite semiconductors. The effect ofdstates is linked with the anion displacement parameteru, which in turn influences the bandgap of these systems. Semilocal exchange-correlation functionals which yield good structural properties of semiconductors and insulators often fail to predict reasonableubecause of the underestimation of the bandgaps arising from the strong interplay betweendelectrons. In the present study, we show that the meta-generalized gradient approximation (meta-GGA) obtained from the cuspless hydrogen density (MGGAC) (2019Phys. Rev.B 100 155140) performs in an improved manner in apprehending the key features of the electronic properties of chalcopyrites, and its bandgaps are comparative to that obtained using state-of-art hybrid methods. Moreover, the present assessment also shows the importance of the Pauli kinetic energy enhancement factor,α= (τ-τ^W)/τ^unifin describing thedelectrons in chalcopyrites. The present study strongly suggests that the MGGAC functional within semilocal approximations can be a better and preferred choice to study the chalcopyrites and other solid-state systems due to its superior performance and significantly low computational cost.