Predicted Band Gap Research Articles

Machine Learning Aided Design of Polymer with Targeted Band Gap Based on DFT Computation

Polymer band gap is one of the most important properties associated with electric conductivity. In this work, the machine learning model called support vector regression (SVR) was developed to predict the polymer band gap, where the training data of the polymer band gap were obtained from DFT computation while the descriptors were generated from Dragon. After feature selection with the maximum relevance minimum redundancy, the SVR model using 16 key features as inputs gave the optimal performance for predicting polymer band gaps. The determination coefficient (R2) of the SVR model between the DFT computations and SVR predictions of polymer band gaps reached as high as 0.824 for the leave-one-out cross-validation and 0.925 for the independent test. Besides, the 16 key features were explored through correlation analysis and sensitivity analysis. The available model can be used to screen out the polymers with targeted band gaps before experiments, which is very helpful for rapid design of new polymers.

Effect of lattice polarisability in optical properties of methylammonium lead iodide by modified Becke-Johnson functionals and Bethe-Salpeter equation

In this work, we used a non-local functional proposed by Tran-Blaha (TB09) with an inclusion of spin-orbit coupling (SOC) in band structure determinations of cubic methylammonium lead iodide (MAPI). We found that the predicted band gap of 1.67 eV is in a good agreement with the experimentally reported values. Moreover, we incorporated TB09 and SOC into the random phase approximation (RPA), and also the Bethe-Salpeter equation (BSE) in order to calculate the dielectric function and the optical response. The BSE calculation significantly features the electron-hole interaction and excitons. However, there are some significant discrepancies between the calculated and the measured dielectric function, which could be explained by the inclusion of the lattice polarisability of MAPI.

DFT study on some polythiophenes containing benzo[d]thiazole and benzo[d]oxazole: structure and band gap

ABSTRACT The content of this paper focuses/shed light on the effects of X (X = S in P1 and X = O in P2) in C11H7NSX and R (R = H in P3, R = OCH3 in P4, and R = Cl in P5) in C18H9ON2S2-R on structural features and band gaps of the polythiophenes containing benzo[d]thiazole and benzo[d]oxazole by the Density Function Theory (DFT) method/calculation. The structural features including the electronic structure lattice constant (a), shape, total energy (Etot) per cell, and link length (r), are measured via band gap (Eg) prediction with the package of country density (PDOS) and total country density (DOS) of material studio software. The results obtained showed that the link angle and the link length between atoms were not changed significantly while the Etot was decreased from Etot = – 1904 eV (in P1) to Etot = – 2548 eV (in P2) when replacing O with S; and the Etot of P3 was decreased from Etot = – 3348 eV (in P3) when replacing OCH3, Cl on H of P3 corresponding to Etot = – 3575 eV (P4), – 4264 eV (P5). Similarly, when replacing O in P1 with – S to form P2, the Eg of P1 was dropped from Eg = 0.621 eV to Eg = 0.239 eV for P2. The Eg of P3, P4, and P5 is Eg = 0.006 eV, 0.064 eV, and 0.0645 eV, respectively. When a benzo[d]thiazole was added in P1 (changing into P3), the Eg was extremely strongly decreased, nearly 100 times (from Eg = 0.621 eV to Eg = 0.006 eV). The obtained results serve as a basis for future experimental work and used to fabricate smart electronic device.

Prediction of band gap for 2D hybrid organic–inorganic perovskites by using machine learning through molecular graphics descriptors

Molecular graphics descriptors are used to predict the band gap of 2D perovskites.

Learning properties of ordered and disordered materials from multi-fidelity data.

Predicting the properties of a material from the arrangement of its atoms is a fundamental goal in materials science. While machine learning has emerged in recent years as a new paradigm to provide rapid predictions of materials properties, their practical utility is limited by the scarcity of high-fidelity data. Here, we develop multi-fidelity graph networks as a universal approach to achieve accurate predictions of materials properties with small data sizes. As a proof of concept, we show that the inclusion of low-fidelity Perdew-Burke-Ernzerhof band gaps greatly enhances the resolution of latent structural features in materials graphs, leading to a 22-45% decrease in the mean absolute errors of experimental band gap predictions. We further demonstrate that learned elemental embeddings in materials graph networks provide a natural approach to model disorder in materials, addressing a fundamental gap in the computational prediction of materials properties.

Improved band gaps and structural properties from Wannier–Fermi–Löwdin self-interaction corrections for periodic systems

The accurate prediction of band gaps and structural properties in periodic systems continues to be one of the central goals of electronic structure theory. However, band gaps obtained from popular exchange–correlation (XC) functionals (such as LDA and PBE) are severely underestimated partly due to the spurious self-interaction error (SIE) inherent to these functionals. In this work, we present a new formulation and implementation of Wannier function-derived Fermi–Löwdin (WFL) orbitals for correcting the SIE in periodic systems. Since our approach utilizes a variational minimization of the self-interaction energy with respect to the Wannier charge centers (WCC), it is computationally more efficient than the HSE hybrid functional and other self-interaction corrections that require a large number of transformation matrix elements. Calculations on several (17 in total) prototypical molecular solids, semiconductors, and wide-bandgap materials show that our WFL self-interaction correction approach gives better band gaps and bulk moduli compared to semilocal functionals, largely due to the partial removal of self-interaction errors.

Density Functional Theory and Experimental Determination of Band Gaps and Lattice Parameters in Kesterite Cu2ZnSn(SxSe1–x)4

The structures and band gaps of copper-zinc-tin selenosulfides (CZTSSe) are investigated for a range of anion compositions through experimental analysis and complementary first-principles simulations. The band gap was found to be extremely sensitive to the Sn-anion bond length, with an almost linear correlation with the average Sn-anion bond length in the mixed anion phase Cu2ZnSn(SxSe1-x)4. Therefore, an accurate prediction of band gaps using first-principles methods requires the accurate reproduction of the experimental bond lengths. This is challenging for many widely used approaches that are suitable for large supercells. The HSE06 functional was found to predict the structure and band gap in good agreement with the experiment but is computationally expensive for large supercells. It was shown that a geometry optimization with the MS2 meta-GGA functional followed by a single point calculation of electronic properties using HSE06 is a reasonable compromise for modeling larger supercells that are often unavoidable in the study of point and extended defects.

First-principles calculations of structural, electronic, and optical properties of double perovskites Cs2Sn1-B I6 (B = Si, Ge; x = 0, 0.25, 0.50, 0.75, 1)

• The effect of Si/Ge doping on the material properties of Cs 2 SnI 6 is studied. • The structural stability of Cs 2 SnI 6 is reduced by doping Si or Ge. • Cs 2 SnI 6 shows strong optical absorption coefficient in the visible light region. In this study, the structural stability, electronic and optical properties of all-inorganic mixed-metal double perovskites Cs 2 Sn 1- x B x I 6 (B = Si, Ge; x = 0, 0.25, 0.50, 0.75, 1) have been explored by using first-principles calculations. Our calculated results show that Cs 2 SnI 6 shows excellent stability, while Cs 2 SiI 6 and Cs 2 GeI 6 are unstable. Moreover, the structural stability of Cs 2 SnI 6 is reduced by doping Si or Ge. The predicted band gaps of the Cs 2 Sn 1- x Si x I 6 systems are in the range of 1.1–1.3 eV. The band gaps of the Cs 2 Sn 1- x Ge x I 6 systems decrease gradually with the increasing concentration of Ge doping. Cs 2 SnI 6 exhibits the highest optical absorption coefficient in the visible light region among the Cs 2 Sn 1- x Si x I 6 systems. The Cs 2 Sn 1- x Ge x I 6 systems show stronger absorption coefficients in the range of 500–1000 nm compared to the pure Cs 2 SnI 6 perovskite. Based on our calculated results, Cs 2 SnI 6 is expected to become the most promising candidate material for perovskite solar cells.

Systematic theoretical study of carbon nanotubes rolled from a two-dimensional tetrahex-carbon nanosheet

A recently proposed two-dimensional (2D) carbon allotrope, tetrahex-carbon composed of tetragonal and hexagonal rings in a buckled plane, draws scientific research interests due to its remarkable mechanical and electronic properties, including ultrahigh strength, negative Poisson's ratio, finite direct band gap, and high carrier mobility. In this work, a series of carbon nanotubes rolled from this new 2D tetrahex-C nanosheet with various size and chirality are studied through first-principles density-functional theory calculations. The tube diameter is in the range of 4.5--18 \AA{}. It is found that the smallest thermodynamically stable nanotubes have the diameter of 4.5 \AA{} for zigzag tetrahex-C nanotubes (z-TH-CNTs) and 6.0 \AA{} for armchair tetrahex-C nanotubes (a-TH-CNTs). The z-TH-CNTs are energetically more favorable than the a-TH-CNTs given similar size. The single-wall nanotubes have a particular wall thickness which shrinks with the decrease of tube size. It is also found that all explored nanotubes show semiconducting behavior and HSE predicted band gaps can be effectively tuned in the range of 1.84--2.69 eV with size and chirality. Large curvature in small z-TH-CNTs alters the band structures, resulting in a significantly reduced effective mass of electron thus indicating potentially enhanced carrier mobility. Work function of the tubes can be manipulated within the range of 5.25--5.43 eV dependent on the tube size and chirality. These remarkable structural and electronic properties in the tetrahex-C nanotubes may have potential applications in nanoelectronics.

Tuplewise Material Representation Based Machine Learning for Accurate Band Gap Prediction.

The open-access material databases allowed us to approach scientific questions from a completely new perspective with machine learning methods. Here, on the basis of open-access databases, we focus on the classical band gap problem for predicting accurately the band gap of a crystalline compound using a machine learning approach with newly developed tuplewise graph neural networks (TGNN), which is devised to automatically generate input representation of crystal structures in tuple types and to exploit crystal-level properties as one of the input features. Our method brings about a highly accurate prediction of the band gaps at hybrid functionals and GW approximation levels for multiple material data sets without heavy computational cost. Furthermore, to demonstrate the applicability of our prediction model, we provide a data set of GW band gaps for 45835 materials predicted by TGNN posing higher accuracy than standard density functional theory calculations.

The effects of cation and halide anion on the electronic and optical properties of Ti-based double perovskite: A first-principles calculations

In recent years, all-inorganic lead-free double perovskites as promising photovoltaic materials have received great attention. In this study, we have investigated the stability, electronic and optical properties of the pure and mixed halide Ti-based double perovskites. The calculated lattice parameters of the pure Ti-based double perovskites agree well with the available experimental values. These Ti-based double perovskites show good stability based on the calculations of their formation energies. The predicted band gaps of Cs2TiX6 (X = Cl, Br, I) within the GGA + U framework are in good agreement with their experimental values. Moreover, we find that the band gap increases slightly when inorganic cation changes from K to Rb and Cs in A2TiCl6. The electronic and optical properties can be tuned by changing the concentration of doping Cl. Cs2TiI2Cl4 has a suitable direct band gap with 1.60 eV, which is considered as an ideal candidate material for single-junction solar cells. Our study shows that the mixed halide Ti-based double perovskites can become nontoxic and environmentally stable materials with excellent optoelectronic properties for applications in perovskite solar cells.

First-principles study of two-dimensional ferroelectrics using self-consistent Hubbard parameters

The discovery of two-dimensional (2D) materials possessing switchable spontaneous polarization with atomic thickness opens up exciting opportunities to realize ultrathin, high-density electronic devices with potential applications ranging from memories and sensors to photocatalysis and solar cells. First-principles methods based on density functional theory (DFT) have facilitated the discovery and design of 2D ferroelectrics (FEs). However, DFT calculations employing local and semilocal exchange-correlation functionals failed to predict accurately the band gaps for this family of low-dimensional materials. Here, we present a DFT+$U$+$V$ study on 2D FEs represented by single-layer $\alpha$-In$_2$Se$_3$ and its homologous III$_2$-VI$_3$ compounds with both out-of-plane and in-plane polarization, using Hubbard parameters computed from first-principles. We find that ACBN0, a pseudo-hybrid density functional that allows self-consistent determination of $U$ parameters, improves the prediction of band gaps for all investigated 2D FEs with a computational cost much lower than the hybrid density functional. The inter-site Coulomb interaction $V$ becomes critical for accurate descriptions of the electronic structures of van der Waals heterostructures such as bilayer In$_2$Se$_3$ and In$_2$Se$_3$/InTe. Pertinent to the study of FE-based catalysis, we find that the application of self-consistent $U$ corrections can strongly affect the adsorption energies of open-shell molecules on the polar surfaces of 2D FEs.

Density-functional theory methods for electronic band structure properties of materials

Electronic band structure of a material plays a dominant role for its application in photoelectronic energy conversion. The development of highly accurate and efficient first-principles approaches to electronic band structure of materials has been a long-standing challenge in computational materials science. Density-functional theory (DFT) in local density approximation (LDA) or generalized gradient approximation (GGA), currently “the standard model” for first-principles computational materials science, suffers from the so-called band gap problem, i.e ., systematic underestimation of band gaps of insulating systems. There have been active developments in the field of DFT that aim at improving the description of the band gap prediction. In this work, an overview is given on the conceptual foundation for theoretical treatment of electronic band structure in the DFT framework. A systematic review is presented on various approaches that have been recently developed to overcome the DFT band problem. Some personal perspectives are also presented regarding remaining issues and possible solutions to them in the future. In addition, a concise review is also presented on the recent developments in the field of GW -based quasi-particle theoretical approaches to electronic band structure of materials.

The effect of divalent europium doping on stability and electronic properties of CH3NH3PbI3: a theoretical investigation

In the present study, we have investigated the effect of Eu2+ doping on the stability and electronic properties of MAPbI3 based on first-principles calculations. Our calculated results indicate that Eu doping is a good strategy to improve the structural stability of MAPbI3. The predicted band gaps for the Eu-doped MAPbI3 are in the range of 1.5–2.8 eV. A direct-to-indirect band gap transition is observed for the Eu-doped perovskite systems. MAPb0.75Eu0.25I3 and MAPb0.50Eu0.50I3 are potential candidate materials for applications in single-junction solar cells, and the content of the toxic element Pb can be further reduced to a certain extent.

Extracting Knowledge from DFT: Experimental Band Gap Predictions Through Ensemble Learning

Many of the machine learning-based approaches for materials property predictions use low-cost computational data. The motivation for machine learning models is based on the orders of magnitude speedup compared to DFT calculations or experimental characterization. High-quality experimental materials data would be ideal for training these models; unfortunately, experimental data are typically costly to obtain. As a result, experimental databases are often smaller and less cohesive. Using band gap, we demonstrate how an ensemble learning approach allows us to efficiently model experimental data by combining models trained on otherwise disparate computational and experimental data. This approach demonstrates how disparate data sources can be incorporated into the modeling of sparsely represented experimental data. In the case of band gap prediction, we reduce the root mean squared error by over 9%.

Exchange-correlation functionals for band gaps of solids: benchmark, reparametrization and machine learning

We conducted a large-scale density-functional theory study on the influence of the exchange-correlation functional in the calculation of electronic band gaps of solids. First, we use the large materials data set that we have recently proposed to benchmark 21 different functionals, with a particular focus on approximations of the meta-generalized-gradient family. Combining these data with the results for 12 functionals in our previous work, we can analyze in detail the characteristics of each approximation and identify its strong and/or weak points. Beside confirming that mBJ, HLE16 and HSE06 are the most accurate functionals for band gap calculations, we reveal several other interesting functionals, chief among which are the local Slater potential approximation, the GGA AK13LDA, and the meta-GGAs HLE17 and TASK. We also compare the computational efficiency of these different approximations. Relying on these data, we investigate the potential for improvement of a promising subset of functionals by varying their internal parameters. The identified optimal parameters yield a family of functionals fitted for the calculation of band gaps. Finally, we demonstrate how to train machine learning models for accurate band gap prediction, using as input structural and composition data, as well as approximate band gaps obtained from density-functional theory.

Band gap reconstruction at the interface between black phosphorus and a gold electrode

We experimentally investigate charge transport through the interface between a gold electrode and a black phosphorus single crystal. The experimental $dI/dV(V)$ curves are characterized by well developed zero-bias conductance peak and two strongly different branches. We find that two branches of asymmetric $dI/dV(V)$ curves correspond to different band gap limits, which is consistent with the theoretically predicted band gap reconstruction at the surface of black phosphorus under electric field. This conclusion is confirmed by experimental comparison with the symmetric curves for narrow-gap (WTe$_2$) and wide-gap (GaSe) metal-semiconductor structures. In addition, we demonstrate p-type dopants redistribution at high bias voltages of different sign, which opens a way to use the interface structures with black phosphorus in resistive memory applications.

Importance of structural deformation features in the prediction of hybrid perovskite bandgaps

Given the surging growth of artificial-intelligence-inspired computational methods in materials science, experimental laboratories around the globe have become open to adopting data-driven approaches for materials discovery. The field witnesses emerging machine-learning models trained over databases, of which data are collected from high-throughput experimentation or first-principles calculation. Here, we address the impediment of constructing a highly accurate predictor for perovskite bandgap when the inorganic network undergoes the deformation. The predictor is trained on a dataset of first-principles calculations of pure and mixed-cation hybrid perovskites. We investigate the impact of the inclusion/exclusion of structural deformation features by training the model carefully. A high level of accuracy could be achieved with a scrupulous investigation of the input features. Our analysis emphasizes how important the feature selection is for the construction of the predictive model as we challenge the robustness of our machine learning predictor in a lab validation setup.

Fundamental band gap and alignment of two-dimensional semiconductors explored by machine learning**This work is dedicated to Michelle Mucheng Zhu. Project supported by the National Key R&D Program of China (Grant No. 2017YFA0206301).

Two-dimensional (2D) semiconductors isoelectronic to phosphorene have been drawing much attention recently due to their promising applications for next-generation (opt)electronics. This family of 2D materials contains more than 400 members, including (a) elemental group-V materials, (b) binary III–VII and IV–VI compounds, (c) ternary III–VI–VII and IV–V–VII compounds, making materials design with targeted functionality unprecedentedly rich and extremely challenging. To shed light on rational functionality design with this family of materials, we systemically explore their fundamental band gaps and alignments using hybrid density functional theory (DFT) in combination with machine learning. First, calculations are performed using both the Perdew–Burke–Ernzerhof exchange–correlation functional within the general-gradient-density approximation (GGA-PBE) and Heyd–Scuseria–Ernzerhof hybrid functional (HSE) as a reference. We find this family of materials share similar crystalline structures, but possess largely distributed band-gap values ranging approximately from 0 eV to 8 eV. Then, we apply machine learning methods, including linear regression (LR), random forest regression (RFR), and support vector machine regression (SVR), to build models for the prediction of electronic properties. Among these models, SVR is found to have the best performance, yielding the root mean square error (RMSE) less than 0.15 eV for the predicted band gaps, valence-band maximums (VBMs), and conduction-band minimums (CBMs) when both PBE results and elemental information are used as features. Thus, we demonstrate that the machine learning models are universally suitable for screening 2D isoelectronic systems with targeted functionality, and especially valuable for the design of alloys and heterogeneous systems.

The effect of hydrostatic pressure on melt-castable energetic materials bis-oxadiazole-bis-methylene dinitrate: A density functional theory study

Using density functional theory calculations, the structural and electronic properties of the melt-castable energetic materials of bis-oxadiazole-bis-methylene dinitrate (BODN) were studied. The calculated lattice parameters, molecular geometry and band gap by the semi-empirical dispersion (Grimme) corrected generalized gradient approximation functional of Perdew-Burke-Ernzerhof (GGA-PBE-G06) are in good agreement with experimental and theoretical results. Also, the pressure effect on BODN was studied in this work. It is found that although the calculated lattice parameters a, b and c are all decreased monotonically with pressure up to 25 GPa, the b-axis is the easiest compressible. The compression behaviors of geometry were investigated, and found the bond C1–N1 and C3–O2 respective in the oxadiazole and alkyl nitric ester groups were more compressible than the others. The molecular interactions were examined by the Hirshfeld surface and 2D-fingerprint analysis. Moreover, the predicted band gap under high-pressure conditions was discussed as well.