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While ferroelectric hafnia ($\mathrm{HfO_2}$) has become a technically important material for microelectronics, the physical origin of its ferroelectricity remains poorly understood. The tetragonal $P4_2/nmc$ phase is commonly assigned as its paraelectric mother phase but has no soft mode at the Brillouin zone center. In this work, we propose that the paraelectric-ferroelectric transition in hafnia-like $Pca2_1$ ferroelectric family can be described by a $Pcca$-$Pca2_1$ transition, where the $Pcca$ mother phase will evolve into either the $Pca2_1$ ferroelectric phase or the centrosymmetric $P2_1/c$ monoclinic phase, depending on the strain conditions. The $Pcca$ phase is directly linked to both phases in the context of continuous phase transition. Hafnia is regarded as a special case of this family, in that it has accidental atomic degeneracy because all anions are oxygen. The theory is also correlated to the seven-coordination theory that explains the ferroelectricity in hafnia from a chemical perspective. In addition, the strain conditions to promote the ferroelectric phase in hafnia are discussed., Comment: 12 pages, 4 figures

Two-dimensional materials-based field-effect transistors (2DM-FETs) exhibit both ambipolar and unipolar transport types. To physically and compactly cover both cases, we put forward a quasi-Fermi-level phase space (QFLPS) approach to model the ambipolar effect in our previous work. This work aims to further improve the QFLPS model's numerical aspect so that the model can be implanted into the standard circuit simulator. We first rigorously derive the integral-free formula for the drain-source current to achieve this goal. It is more friendly to computation than the integral form. Besides, it explicitly gives the correlation terms between the electron and hole components. Secondly, to work out the boundary values required by the new expressions, we develop a fast evaluation algorithm for the surface electrostatic potential based on the zero-temperature limit property of the 2DM-FET system. By calibrating the model with the realistic device data of black phosphorus (BP) and monolayer molybdenum disulfide (ML-MoS2) FETs, the completed algorithm is tested against practical cases. The results show a typical superiority to the benchmark algorithm by two orders of magnitude in time consumption can be achieved while keeping a high accuracy with 7 to 9 significant digits., Comment: 17 pages, 9 figures

$\mathrm{HfO_2}$-based dielectrics are promising for nanoscale ferroelectric applications, and the most favorable material within the family is Zr-substituted hafnia, i.e., $\mathrm{Hf_{1-x}Zr_xO_2}$ (HZO). The extent of Zr substitution can be great, and x is commonly set to 0.5. However, the band gap of $\mathrm{ZrO_2}$ is lower than $\mathrm{HfO_2}$, thus it is uncertain how the Zr content should influence the electronic band structure of HZO. A reduced band gap is detrimental to the cycling endurance as charge injection and dielectric breakdown would become easier. Another issue is regarding the comparison on the band gaps between $\mathrm{HfO_2}$/$\mathrm{ZrO_2}$ superlattices and HZO solid-state solutions. In this work we systematically investigated the electronic structures of $\mathrm{HfO_2}$, $\mathrm{ZrO_2}$ and HZO using self-energy corrected density functional theory. In particular, the conduction band minimum of $Pca2_1$-$\mathrm{HfO_2}$ is found to lie at an ordinary k-point on the Brillouin zone border, not related to any interlines between high-symmetry k-points. Moreover, the rule of HZO band gap variation with respect to x has been extracted. The physical mechanisms for the exponential reduction regime and linear decay regime have been revealed. The band gaps of $\mathrm{HfO_2}$/$\mathrm{ZrO_2}$ ferroelectric superlattices are investigated in a systematic manner, and the reason why the superlattice could possess a band gap lower than that of $\mathrm{ZrO_2}$ is revealed through comprehensive analysis., Comment: 23 pages, 9 figures

DFT-1/2 is an efficient band gap rectification method for density functional theory (DFT) under local density approximation (LDA) or generalized gradient approximation. It was suggested that non-self-consistent DFT-1/2 should be used for highly ionic insulators like LiF, while self-consistent DFT-1/2 should still be used for other compounds. Nevertheless, there is no quantitative criterion prescribed for which implementation should work for an arbitrary insulator, which leads to severe ambiguity in this method. In this work we analyze the impact of self-consistency in DFT-1/2 and shell DFT-1/2 calculations in insulators or semiconductors with ionic bonds, covalent bonds and intermediate cases, and show that self-consistency is required even for highly ionic insulators for globally better electronic structure details. The self-energy correction renders electrons more localized around the anions in self-consistent LDA-1/2. The well-known delocalization error of LDA is rectified, but with strong overcorrection due to the presence of additional self-energy potential. However, in non-self-consistent LDA-1/2 calculations, the electron wavefunctions indicate that such localization is much more severe and beyond a reasonable range, because the strong Coulomb repulsion is not counted in the Hamiltonian. Another common drawback of non-self-consistent LDA-1/2 lies in that the ionicity of the bonding gets substantially enhanced, and the band gap can be enormously high in mixed ionic-covalent compounds like $\mathrm{TiO_2}$. The impact of LDA-1/2-induced stress is also discussed comprehensively., Comment: 31 pages, 16 figures

The wake-up phenomenon widely exists in hafnia-based ferroelectric capacitors, which causes device parameter variation over time. Crystallization at higher temperatures have been reported to be effective in eliminating wake-up, but high temperature may yield the monoclinic phase or generate high concentration oxygen vacancies. In this work, a unidirectional annealing method is proposed for the crystallization of $\mathrm{Hf_{0.5}Zr_{0.5}O_2}$ (HZO) superlattice ferroelectrics, which involves heating from the $\mathrm{Pt/ZrO_2}$ interface side. Nanoscale $\mathrm{ZrO_2}$ is selected to resist the formation of monoclinic phase, and the chemically inert Pt electrode can avoid the continuous generation of oxygen vacancies during annealing. It is demonstrated that $\mathrm{600^oC}$ annealing only leads to a moderate content of monoclinic phase in HZO, and the TiN/HZO/Pt capacitor exhibits wake-up free nature and a $2P_\mathrm{r}$ value of 27.4 $\mu\mathrm{C/cm^2}$. On the other hand, heating from the $\mathrm{TiN/HfO_2}$ side, or using $\mathrm{500^oC}$ annealing temperature, both yield ferroelectric devices that require a wake-up process. The special configuration of $\mathrm{Pt/ZrO_2}$ is verified by comparative studies with several other superlattice structures and HZO solid-state solutions. It is discovered that heating from the $\mathrm{Pt/HfO_2}$ side at $\mathrm{600^oC}$ leads to high leakage current and a memristor behavior. The mechanisms of ferroelectric phase stabilization and memristor formation have been discussed. The unidirectional heating method can also be useful for other hafnia-based ferroelectric devices., Comment: 16 pages, 7 figures

The highly non-linear switching behavior of hafnia memristor actually hinders its wide application in neuromorphic computing. Theoretical understanding into its switching mechanism has been focused on the processes of conductive filament generation and rupture, but possible phase transition and crystallization around the region of conductive filaments (CFs) due to the variation of O content have been paid less attention to. In this paper, HfO$\mathrm{_x}$ structural models covering the full stoichiometries from Hf to HfO$\mathrm{_2}$ were established, and the crystal structure evolution during the reduction process of hafnia was obtained through first-principles calculation. The electronic structures and O vacancy migration characteristics of these structures were analyzed. A criterion was prescribed to predict the mode of abrupt binary switching or gradual conductance modulation according to the structure evolution of the CFs. In particular, factors that influence the merging of tiny conductive channels into strong filaments are intensively discussed, including the anisotropy of O vacancy migration and the size effect. The feasibility of Mg doping to achieve robust gradual switching is discussed., Comment: 33 pages, 18 figures

The Kohn-Sham gaps of density functional theory (DFT) obtained in terms of local density approximation (LDA) or generalized gradient approximation (GGA) cannot be directly linked to the fundamental gaps of semiconductors, but in engineering there is a strong demand to match them through certain rectification methods. Shell DFT-1/2 (shDFT-1/2), as a variant of DFT-1/2, is a potential candidate to yield much improved band gaps for covalent semiconductors, but its accuracy depends on the LDA/GGA ground state, including optimized lattice parameters, basic Kohn-Sham gap before self-energy correction and the amount of self-energy correction that is specific to the exchange-correlation (XC) functional. In this work, we test the LDA/GGA as well as shDFT-1/2 results of six technically important covalent semiconductors Si, Ge, GaN, GaP, GaAs and GaSb, with an additional ionic insulator LiF for comparison. The impact of XC flavor (LDA, PBEsol, PBE and RPBE), either directly on the gap value, or indirectly through the optimized lattice constant, is examined comprehensively. Moreover, we test the impact of XC flavor on LDA/GGA and shDFT-1/2 gaps under the condition of fixed experimental lattice constants. In-depth analysis reveals the rule of reaching the best accuracy in calculating the electronic band structures of typical covalent semiconductors. Relevant parameters like lattice constant, self-consistency in shDFT-1/2 runs, as well as the exchange enhancement factor of GGA, are discussed in details., Comment: 23 pages, 10 figures

Ferroelectricity observed in thin film $\mathrm{HfO_2}$, either doped with Si, Al, etc. or in the $\mathrm{Hf_{0.5}Zr_{0.5}O_2}$ form, has gained great technical significance. However, the soft mode theory faces a difficulty in explaining the origin of such ferroelectricity. In this work, we propose that the 7 cation coordination number of $\mathrm{HfO_2/ZrO_2}$ lies at the heart of this ferroelectricity, which stems from the proper ionic radii of Hf/Zr compared with O. Among the numerous compounds with non-centrosymmetric nature, e.g., $mm2$ point group, $\mathrm{HfO_2}$ and $\mathrm{ZrO_2}$ are special in that they are close to the border of 7 and 8 cation coordination, such that the 8-coordination tetragonal intermediate phase could greatly reduce the switching barrier. Other 7-coordination candidates, including $\mathrm{SrI_2}$, TaON, YSBr and YOF are also studied in comparison to $\mathrm{HfO_2}$/$\mathrm{ZrO_2}$, and six switching paths are analyzed in detail for the $Pca2_1$ phase. A rule of preferred switching path in terms of ionic radii ratio and coordination number has been established. We also show the possible route from ferroelectric $Pca2_1$ phase to monoclinic $P2_1/c$ phase in $\mathrm{HfO_2}$, which is relevant to the fatigue phenomenon., Comment: 14 pages, 4 figures

Searching for novel two-dimensional (2D) materials is highly desired in the field of nanoelectronics. We here propose a new 2D crystal barium tri-arsenide ($\mathrm{BaAs_3}$) with a series of encouraging functionalities. Being kinetically and thermally stable, the monolayer and bilayer forms of $\mathrm{BaAs_3}$ possess narrow indirect band gaps of 0.87 eV and 0.40 eV, respectively, with high hole mobilities on the order of ~$\mathrm{10^3\ cm^{2}\,V^{-1}\,s^{-1}}$. The electronic properties of 2D $\mathrm{BaAs_3}$ can be manipulated by controlling the layer thickness. The favorable cleavage energy reveals that layered $\mathrm{BaAs_3}$ can be produced as a freestanding 2D material. Furthermore, by introducing vacancy defects monolayer $\mathrm{BaAs_3}$ can be transformed from a semiconductor to a metal. 2D $\mathrm{BaAs_3}$ may find promising applications in nanoelectronic devices., Comment: 22 pages, 4 figures; Supporting Information contains 10 pages and 12 figures

We suggest a tetragonal $I4_1/amd$ phase ($\eta$-phase) as the ground state of $\mathrm{Ta_2O_5}$ at zero temperature, which is a high symmetry version of the triclinic $\gamma$-phase $\mathrm{Ta_2O_5}$ predicted by Yang and Kawazoe. Our calculation shows that $\gamma$-phase $\mathrm{Ta_2O_5}$ will automatically be transformed into the $\eta$-phase during structural relaxation. Phonon dispersion confirms that the $\eta$-phase is dynamically stable, while the high temperature $\alpha$-phase $\mathrm{Ta_2O_5}$, which also has the $I4_1/amd$ symmetry, is unstable at zero temperature. A thorough energy comparison of the $\beta_{AL}$, $\delta$, $\lambda$, $\mathrm{B}$, $\mathrm{L_{SR}}$, $\beta_R$, $Pm$, $Cmmm$, $\gamma$, $\eta$ and $\alpha$ phases of $\mathrm{Ta_2O_5}$ is carried out. The GGA-1/2 method is applied in calculating the electronic structure of various phases, where the $\eta$-phase demonstrates a 4.24 eV indirect band gap, close to experimental value. The high symmetry tetragonal phase together with computationally efficient GGA-1/2 method greatly facilitate the $ab\ initio$ simulation of $\mathrm{Ta_2O_5}$-based devices. As an example, we have explicitly shown the Ohmic contact nature between metal Ta and $\mathrm{Ta_2O_5}$ by calculating an interface model of $b.c.c.$ Ta and $\eta$-$\mathrm{Ta_2O_5}$, using GGA-1/2., Comment: 27 pages, 8 figures

Searching for materials with single atom-thin as well as planar structure, like graphene and borophene, is one of the most attractive themes in two dimensional materials. Herein, using density functional theory calculations, we have proposed a series of single layer planar penta-transition metal phosphide and arsenide, i.e. TM$\mathrm{_2}$X$\mathrm{_4}$ (TM= Ni, Pd and Pt; X=P, As). According to the calculated phonon dispersion relation and elastic constants, as well as ab initio molecular dynamics simulation results, monolayers of planar penta-TM$\mathrm{_2}$X$\mathrm{_4}$ are dynamically, mechanically, and thermally stable. In addition, the band structures calculated with the screened HSE06 hybrid functional including spin-orbit coupling show that these monolayers are direct-gap semiconductors with sizeable band gaps ranging from 0.14 eV to 0.69 eV. Besides, the optical properties in these monolayers are further investigated, where strong in-plane optical absorption with wide spectral range has been revealed. Our results indicate that planar penta-TM$\mathrm{_2}$X$\mathrm{_4}$ monolayers are interesting narrow gap semiconductors with excellent optical properties, and may find potential applications in photoelectronics., Comment: 6 figures, with Supporting Information

Highly-efficient water splitting based on solar energy is one of the most attractive research focuses in the energy field. Searching for more candidate photocatalysts that can work under visible-light irradiation are highly demanded. Herein, using first principle calculations based on density functional theory, we predict that the two dimensional silicon chalcogenides, i.e. SiX (X=S, Se, Te) monolayers, as semiconductors with 2.43 eV~3.00 eV band gaps, exhibit favorable band edge positions for photocatalytic water splitting. The optical adsorption spectra demonstrate that the SiX monolayers have pronounced optical absorption in the visible light region. Moreover, the band gaps and band edge positions of silicon chalcogenides monolayers can be tuned by applying biaxial strain or increasing the number of layers, in order to better fit the redox potentials of water. The combined novel electronic, high carrier mobility, and optical properties render the two dimensional SiX a promising photocatalyst for water splitting., Comment: 5 figures, 2 tables

Two-dimensional materials with a proper band gap and high carrier mobility are urgently desired in the field of nanoelectronics. We propose a novel two-dimensional crystal monolayer $\mathrm{TlP_5}$, which is dynamically and thermodynamically stable and possesses a direct band gap of 2.02 eV with high carrier mobilities (13960 $\mathrm{cm^2\ V^{-1}s^{-1}}$ for electrons and 7560 $\mathrm{cm^2\ V^{-1}s^{-1}}$ for holes), comparable to that of phosphorene. The band gap value and band characteristics of monolayer $\mathrm{TlP_5}$ can be adjusted by biaxial and uniaxial strains, and excellent optical absorption over the visible-light range is predicted. These properties, especially for the balanced high mobilities for not only the electrons but also the holes, render monolayer $\mathrm{TlP_5}$ an exciting functional material for future nanoelectronics and optoelectronic applications., Comment: 5 figures, 1 table

The LDA-1/2 method for self-energy correction is a powerful tool for calculating accurate band structures of semiconductors, while keeping the computational load as low as standard LDA. Nevertheless, controversies remain regarding the arbitrariness of choice between (1/2)e and (1/4)e charge stripping from the atoms in group IV semiconductors, the incorrect direct band gap predicted for Ge, and inaccurate band structures for III-V semiconductors. Here we propose an improved method named shell-LDA-1/2 (shLDA-1/2 for short), which is based on a shell-like trimming function for the self-energy potential. With the new approach, we obtained accurate band structures for group IV, and for III-V and II-VI compound semiconductors. In particular, we reproduced the complete band structure of Ge in good agreement with experimental data. Moreover, we have defined clear rules for choosing when (1/2)e or (1/4)e charge ought to be stripped in covalent semiconductors, and for identifying materials for which shLDA-1/2 is expected to fail., Comment: 15 pages, 4 figures, 1 table

The LDA-1/2 method expands Slater's half occupation technique to infinite solid state materials by introducing a self-energy potential centered at the anions to cancel the energy associated with electron-hole self-interaction. To avoid an infinite summation of long-ranged self-energy potentials they must be trimmed at a variationally-defined cutoff radius. The method has been successful in predicting accurate band gaps for a large number of elementary and binary semiconductors. Nevertheless, there has been some confusion regarding carbon and silicon, both in the cubic diamond structure, which require different ionizations of the valence charge, 1/2 for carbon and 1/4 for silicon respectively, to yield band gaps in agreement with experimental data. We here analyze the spatial distribution of the valence electrons of these two materials to conclude that in silicon and in carbon LDA-1/4 and LDA-1/2, respectively, must be adopted for the proper cancellation of the self-energies. Such analysis should be applied to other covalent semiconductors in order to decide which ionization to adopt for the proper correction of the self-energy., Comment: 8 pages, 4 figures

Using first-principles evolutionary simulations, we have systematically investigated phase stability in the Hf-O system at pressure up to 120 GPa. New compounds Hf5O2, Hf3O2, HfO and HfO3 are discovered to be thermodynamically stable at certain pressure ranges and a new stable high-pressure phase is found for Hf2O with space group Pnnm and anti-CaCl2-type structure. Both P62m-HfO and P4m2-Hf2O3 show semimetallic character. Pnnm-HfO3 shows interesting structure, simultaneously containing oxide O2- and peroxide [O-O]2- anions. Remarkably, it is P62m-HfO rather than OII-HfO2 that exhibits the highest mechanical characteristics among Hf-O compounds. Pnnm-Hf2O, Imm2-Hf5O2, P31m-Hf2O and P4m2-Hf2O3 phases also show superior mechanical properties, these phases can be quenched to ambient pressure and their properties can be exploited.

A tetragonal phase is predicted for Hf2O3 and Zr2O3 using density functional theory. Starting from atomic and unit cell relaxations of substoichiometric monoclinic HfO2 and ZrO2, such tetragonal structures are only reached at zero temperature by introducing the oxygen vacancy pair with the lowest formation energy. The tetragonal Hf2O3 and Zr2O3 structures belong to space group P-4m2 and are more stable than their corundum structure counterparts. These phases are semi-metallic, as confirmed through further G0W0 calculations. The carrier concentrations are estimated to be 1.77E21 cm^{-3} for both electrons and holes in tetragonal Hf2O3, and 1.75E21 cm^{-3} for both electrons and holes in tetragonal Zr2O3. The tetragonal Hf2O3 phase is probably related to the low resistivity state of hafnia-based resistive random access memory (RRAM).