Hybrid functionals based on a screened Coulomb potential
23 Apr 2003-Journal of Chemical Physics (American Institute of Physics)-Vol. 118, Iss: 18, pp 8207-8215
TL;DR: In this paper, a new hybrid density functional based on a screened Coulomb potential for the exchange interaction is proposed, which enables fast and accurate hybrid calculations, even of usually difficult metallic systems.
Abstract: Hybrid density functionals are very successful in describing a wide range of molecular properties accurately. In large molecules and solids, however, calculating the exact (Hartree–Fock) exchange is computationally expensive, especially for systems with metallic characteristics. In the present work, we develop a new hybrid density functional based on a screened Coulomb potential for the exchange interaction which circumvents this bottleneck. The results obtained for structural and thermodynamic properties of molecules are comparable in quality to the most widely used hybrid functionals. In addition, we present results of periodic boundary condition calculations for both semiconducting and metallic single wall carbon nanotubes. Using a screened Coulomb potential for Hartree–Fock exchange enables fast and accurate hybrid calculations, even of usually difficult metallic systems. The high accuracy of the new screened Coulomb potential hybrid, combined with its computational advantages, makes it widely applicable to large molecules and periodic systems.
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TL;DR: In this article, a few-layer black phosphorus crystals with thickness down to a few nanometres are used to construct field effect transistors for nanoelectronic devices. But the performance of these materials is limited.
Abstract: Two-dimensional crystals have emerged as a class of materials that may impact future electronic technologies. Experimentally identifying and characterizing new functional two-dimensional materials is challenging, but also potentially rewarding. Here, we fabricate field-effect transistors based on few-layer black phosphorus crystals with thickness down to a few nanometres. Reliable transistor performance is achieved at room temperature in samples thinner than 7.5 nm, with drain current modulation on the order of 10(5) and well-developed current saturation in the I-V characteristics. The charge-carrier mobility is found to be thickness-dependent, with the highest values up to ∼ 1,000 cm(2) V(-1) s(-1) obtained for a thickness of ∼ 10 nm. Our results demonstrate the potential of black phosphorus thin crystals as a new two-dimensional material for applications in nanoelectronic devices.
6,924 citations
TL;DR: In this paper, the 2D counterpart of layered black phosphorus, which is called phosphorene, is introduced as an unexplored p-type semiconducting material and the authors find that the band gap is direct, depends on the number of layers and the in-layer strain, and significantly larger than the bulk value of 0.31-0.36 eV.
Abstract: We introduce the 2D counterpart of layered black phosphorus, which we call phosphorene, as an unexplored p-type semiconducting material. Same as graphene and MoS2, single-layer phosphorene is flexible and can be mechanically exfoliated. We find phosphorene to be stable and, unlike graphene, to have an inherent, direct, and appreciable band gap. Our ab initio calculations indicate that the band gap is direct, depends on the number of layers and the in-layer strain, and is significantly larger than the bulk value of 0.31–0.36 eV. The observed photoluminescence peak of single-layer phosphorene in the visible optical range confirms that the band gap is larger than that of the bulk system. Our transport studies indicate a hole mobility that reflects the structural anisotropy of phosphorene and complements n-type MoS2. At room temperature, our few-layer phosphorene field-effect transistors with 1.0 μm channel length display a high on-current of 194 mA/mm, a high hole field-effect mobility of 286 cm2/V·s, and an...
5,233 citations
Ohio State University1, North Carolina State University2, Stanford University3, Pennsylvania State University4, Columbia University5, Northwestern University6, University of Texas at Austin7, University of Notre Dame8, Cornell University9, University of California, Berkeley10, Case Western Reserve University11
TL;DR: The properties and advantages of single-, few-, and many-layer 2D materials in field-effect transistors, spin- and valley-tronics, thermoelectrics, and topological insulators, among many other applications are highlighted.
Abstract: Graphene’s success has shown that it is possible to create stable, single and few-atom-thick layers of van der Waals materials, and also that these materials can exhibit fascinating and technologically useful properties. Here we review the state-of-the-art of 2D materials beyond graphene. Initially, we will outline the different chemical classes of 2D materials and discuss the various strategies to prepare single-layer, few-layer, and multilayer assembly materials in solution, on substrates, and on the wafer scale. Additionally, we present an experimental guide for identifying and characterizing single-layer-thick materials, as well as outlining emerging techniques that yield both local and global information. We describe the differences that occur in the electronic structure between the bulk and the single layer and discuss various methods of tuning their electronic properties by manipulating the surface. Finally, we highlight the properties and advantages of single-, few-, and many-layer 2D materials in...
4,123 citations
TL;DR: In this article, a few-layer phosphorene has been introduced as a 2D p-type material for electronic applications, which has an inherent, direct and appreciable band gap that depends on the number of layers.
Abstract: Preceding the current interest in layered materials for electronic applications, research in the 1960's found that black phosphorus combines high carrier mobility with a fundamental band gap. We introduce its counterpart, dubbed few-layer phosphorene, as a new 2D p-type material. Same as graphene and MoS2, phosphorene is flexible and can be mechanically exfoliated. We find phosphorene to be stable and, unlike graphene, to have an inherent, direct and appreciable band-gap that depends on the number of layers. Our transport studies indicate a carrier mobility that reflects its structural anisotropy and is superior to MoS2. At room temperature, our phosphorene field-effect transistors with 1.0 um channel length display a high on-current of 194 mA/mm, a high hole field-effect mobility of 286 cm2/Vs, and an on/off ratio up to 1E4. We demonstrate the possibility of phosphorene integration by constructing the first 2D CMOS inverter of phosphorene PMOS and MoS2 NMOS transistors.
3,846 citations
TL;DR: A detailed theoretical investigation of the atomic and electronic structure of few-layer black phosphorus (BP) is presented to predict its electrical and optical properties, finding that the mobilities are hole-dominated, rather high and highly anisotropic.
Abstract: Two-dimensional crystals are emerging materials for nanoelectronics. Development of the field requires candidate systems with both a high carrier mobility and, in contrast to graphene, a sufficiently large electronic bandgap. Here we present a detailed theoretical investigation of the atomic and electronic structure of few-layer black phosphorus (BP) to predict its electrical and optical properties. This system has a direct bandgap, tunable from 1.51 eV for a monolayer to 0.59 eV for a five-layer sample. We predict that the mobilities are hole-dominated, rather high and highly anisotropic. The monolayer is exceptional in having an extremely high hole mobility (of order 10,000 cm(2) V(-1) s(-1)) and anomalous elastic properties which reverse the anisotropy. Light absorption spectra indicate linear dichroism between perpendicular in-plane directions, which allows optical determination of the crystalline orientation and optical activation of the anisotropic transport properties. These results make few-layer BP a promising candidate for future electronics.
3,622 citations
Cites background or methods from "Hybrid functionals based on a scree..."
...Mobilities μx_1D and μy_1D were calculated using Supplementary Equation (2)....
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...Mobilities µx_1D and µy_1D were calculated using Supplementary Equation (2)....
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...(2) for BP ribbons of 10nm in width, which is a reasonable value for experimental fabrication....
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...2 x_1D x_1D 1/2 * 3/2 2 B e 1x 2 ( ) ( ) e C k T m E (2)...
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References
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TL;DR: A simple derivation of a simple GGA is presented, in which all parameters (other than those in LSD) are fundamental constants, and only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked.
Abstract: Generalized gradient approximations (GGA’s) for the exchange-correlation energy improve upon the local spin density (LSD) description of atoms, molecules, and solids. We present a simple derivation of a simple GGA, in which all parameters (other than those in LSD) are fundamental constants. Only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked. Improvements over PW91 include an accurate description of the linear response of the uniform electron gas, correct behavior under uniform scaling, and a smoother potential. [S0031-9007(96)01479-2] PACS numbers: 71.15.Mb, 71.45.Gm Kohn-Sham density functional theory [1,2] is widely used for self-consistent-field electronic structure calculations of the ground-state properties of atoms, molecules, and solids. In this theory, only the exchange-correlation energy EXC › EX 1 EC as a functional of the electron spin densities n"srd and n#srd must be approximated. The most popular functionals have a form appropriate for slowly varying densities: the local spin density (LSD) approximation Z d 3 rn e unif
146,533 citations
TL;DR: In this article, a semi-empirical exchange correlation functional with local spin density, gradient, and exact exchange terms was proposed. But this functional performed significantly better than previous functionals with gradient corrections only, and fits experimental atomization energies with an impressively small average absolute deviation of 2.4 kcal/mol.
Abstract: Despite the remarkable thermochemical accuracy of Kohn–Sham density‐functional theories with gradient corrections for exchange‐correlation [see, for example, A. D. Becke, J. Chem. Phys. 96, 2155 (1992)], we believe that further improvements are unlikely unless exact‐exchange information is considered. Arguments to support this view are presented, and a semiempirical exchange‐correlation functional containing local‐spin‐density, gradient, and exact‐exchange terms is tested on 56 atomization energies, 42 ionization potentials, 8 proton affinities, and 10 total atomic energies of first‐ and second‐row systems. This functional performs significantly better than previous functionals with gradient corrections only, and fits experimental atomization energies with an impressively small average absolute deviation of 2.4 kcal/mol.
87,732 citations
TL;DR: In this paper, an analysis of the performances of a parameter free density functional model (PBE0) obtained combining the so-called PBE generalized gradient functional with a predefined amount of exact exchange is presented.
Abstract: We present an analysis of the performances of a parameter free density functional model (PBE0) obtained combining the so called PBE generalized gradient functional with a predefined amount of exact exchange. The results obtained for structural, thermodynamic, kinetic and spectroscopic (magnetic, infrared and electronic) properties are satisfactory and not far from those delivered by the most reliable functionals including heavy parameterization. The way in which the functional is derived and the lack of empirical parameters fitted to specific properties make the PBE0 model a widely applicable method for both quantum chemistry and condensed matter physics.
13,411 citations
TL;DR: An algorithm is presented for the rapid evaluation of the potential and force fields in systems involving large numbers of particles whose interactions are Coulombic or gravitational in nature, making it considerably more practical for large-scale problems encountered in plasma physics, fluid dynamics, molecular dynamics, and celestial mechanics.
5,003 citations