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Density functional modeling of structural and electronic properties of amorphous high temperature oxides
Abstract
Ab initio molecular dynamics modeling in the NPT ensemble is used to obtain amorphous states by melting SiO2, ZrO2 and HfO2 crystals. A wide range of melt stabilization temperatures are used. Two types of SiO2 amorphous states are obtained. For melt temperatures below 4500 K, a perfect silica glass is obtained without any point defects. For melt temperatures above 4500 K, silica point defects such as threefold coordinated oxygen atoms, edge-sharing SiO4-tetrahedra, and others together with a wide range of Si-O-Si rings including 3-, and 4-membered rings appear. When the temperature of the melt exceeds the ZrO2 and HfO2 crystal melting point by 100 – 400 K, a sharp drop in the density of amorphous states is observed, accompanied by a decrease in atomic coordination, but this does not lead to the formation of defect states in the depth of the band gap of hafnium and zirconium dioxides.
... At present, DFT methods are most widely used for such modeling [3,4]. A short review of modeling methods of amorphous silica, zirconia, and hafnia can be found in [5,6]. ...
... To understand reasons of such anomalous behavior, we applied a systematic approach for obtaining the amorphous states of hafnium dioxide doped with silicon dioxide by melting-quenching the corresponding crystals using QMD [5,6]. The melting-quenching procedure is carried out within the framework of the NPT ensemble, where N is the number of atoms, P is the pressure, and T is the temperature. ...
... The modeling is carried out using the VASP program (version vasp.5.4.4 compiled for GPU) [29] with popular PBE functionals, where the PBE abbreviation corresponds to names of authors of [30], and the projector-augmented wave (PAW) method [31]. The ENCUT parameter, which determines the size of the plane-wave basis, is 600.0 eV [6]. The supercell is large enough and sampling of the Brillouin zone is made with one point, since summing over eight irreducible k-points results in only a slight change in the energy and volume of the supercell. ...
This paper provides an atomistic exploration of amorphous composite ${{\rm HfO}_2} {\text{-}} {{\rm SiO}_2}$ H f O 2 - S i O 2 oxides to explain the experimentally observed anomalous behavior of the refractive index with increasing Si content. We use an approach to obtain amorphous states of high-temperature oxides by melting–quenching the initial ${{\rm HfO}_2}$ H f O 2 crystal containing various amounts of Si impurities. The calculations are carried out by quantum molecular dynamics. The coordination numbers of Hf, Si, and O atoms are studied at various doping levels. The change in the atomic structure of ${{\rm a{\text{-}}HfO}_2}$ a - H f O 2 depending on the doping level qualitatively explains the anomalous behavior of the refractive index.
... The modeling of amorphous states of SiO 2 , HfO 2, and ZrO 2 was performed in [209] using the DFT-based quantum molecular dynamics method. The amorphous states were obtained by melting SiO 2 , HfO 2, and ZrO 2 crystals in the NPT ensemble. ...
... The review of the quantum simulation of SiO 2 , HfO 2 and ZrO 2 film-forming oxides presented in the Introduction of the Ref. [209]. The conclusion from this review is that the structural characteristics of the amorphous phase of film-forming materials and their optical and electronic parameters significantly depend on the simulation method. ...
A review of the methods and results of atomistic modeling of the deposition of thin optical films and a calculation of their characteristics is presented. The simulation of various processes in a vacuum chamber, including target sputtering and the formation of film layers, is considered. Methods for calculating the structural, mechanical, optical, and electronic properties of thin optical films and film-forming materials are discussed. The application of these methods to studying the dependences of the characteristics of thin optical films on the main deposition parameters is considered. The simulation results are compared with experimental data.
... However, this is similar to the quench rates used to study amorphous oxides in other work, [130] where the results did not differ significantly when the quench rate was decreased to 0.1 Kp s −1 . Other studies [131] that investigate AIMD M&Q simulations for producing HfO 2 and ZrO 2 have used even higher quench rates (500 Kp s −1 ) and shorter melt equilibration times and found that the coordination number distributions are distinct from those produced in classical MD, which utilizes much lower quench rates and much longer equilibration times. The literature data therefore suggest that the high quenching rate of 100 Kp s −1 is at the limit of what can produce reasonable structures, as judged by the coordination number distributions and density. ...
Understanding defects in amorphous oxide films and heterostructures is vital to improving performance of microelectronic devices, thin‐film transistors, and electrocatalysis. However, to what extent the structure and properties of point defects in amorphous solids are similar to those in the crystalline phase are still debated. The validity of this analogy and the experimental and theoretical evidence of the effects of oxygen deficiency in amorphous oxide films are critically discussed. The authors start with the meaning and significance of defect models, such as “oxygen vacancy” in crystalline oxides, and then introduce experimental and computational methods used to study intrinsic defects in amorphous oxides and discuss their limitations and challenges. To test the validity of existing defect models, ab initio molecular dynamics is used with a non‐local density functional to model the structure and electronic properties of oxygen‐deficient amorphous alumina. Unlike some previous studies, the formation of deep defect states in the bandgap caused by the oxygen deficiency is found. Apart from atomistic structures analogous to crystal vacancies, the formation of more stable defect states characterized by the bond formation between under‐coordinated Al ions is shown. The limitations of such defect models and how they may be overcome in simulations are discussed.
... Amorphous silica has an average density of 2.39 g/cm 3 , which is in line with the findings of the experiments. 64 O atoms and 32 Si atoms make up the model [31,32]. ...
First-principles calculations were used to simulate the aggregation of the peroxy chain defect POL and the oxygen vacancy defect ODC(I). Defect aggregation’s electronic structure and optical properties were investigated. The two defects were most likely to accumulate on a 6-membered ring in ortho-position. When the two defects are aggregated, it is discovered that 0.75 ev absorption peaks appear in the near-infrared band, which may be brought on by the addition of oxygen vacancy defect ODC(I). We can draw the conclusion that the absorption peak of the aggregation defect of ODC(I) defect and POL is more prominent in the near infrared region and visible light area than ODC(I) defect and POL defect.
... However, the ability of QC-based force fields to work correctly with high-energy ions is not obvious, and the question of using such fields to simulate ion-assisted deposition requires a special separate study. In addition, the density functional modeling of SiO 2 was performed in our recent works [22,23]. It was concluded that at the moment classical methods are more suitable for simulating film deposition, since when using quantum methods, the sizes of simulation clusters are still too small. ...
A systematic study of the most significant parameters of the ion-assisted deposited silicon dioxide films is carried out using the classical molecular dynamics method. The energy of the deposited silicon and oxygen atoms corresponds to the thermal evaporation of the target; the energy of the assisting oxygen ions is 100 eV. It is found that an increase in the flow of assisting ions to approximately 10% of the flow of deposited atoms leads to an increase in density and refractive index by 0.5 g/cm3 and 0.1, respectively. A further increase in the flux of assisting ions slightly affects the film density and density profile. The concentration of point defects, which affect the optical properties of the films, and stressed structural rings with two or three silicon atoms noticeably decrease with an increase in the flux of assisting ions. The film growth rate somewhat decreases with an increase in the assisting ions flux. The dependence of the surface roughness on the assisting ions flux is investigated. The anisotropy of the deposited films, due to the difference in the directions of motion of the deposited atoms and assisting ions, is estimated using the effective medium approach.
CP2K is an open source electronic structure and molecular dynamics software package to perform atomistic simulations of solid-state, liquid, molecular, and biological systems. It is especially aimed at massively parallel and linear-scaling electronic structure methods and state-of-the-art ab initio molecular dynamics simulations. Excellent performance for electronic structure calculations is achieved using novel algorithms implemented for modern high-performance computing systems. This review revisits the main capabilities of CP2K to perform efficient and accurate electronic structure simulations. The emphasis is put on density functional theory and multiple post–Hartree–Fock methods using the Gaussian and plane wave approach and its augmented all-electron extension.
We report the growth of nanoscale hafnium dioxide (HfO2) and zirconium dioxide (ZrO2) thin films using remote plasma-enhanced atomic layer deposition (PE-ALD), and the fabrication of complementary metal-oxide semiconductor (CMOS) integrated circuits using the HfO2 and ZrO2 thin films as the gate oxide. Tetrakis (dimethylamino) hafnium (Hf[N(CH3)2]4) and tetrakis (dimethylamino) zirconium (IV) (Zr[N(CH3)2]4) were used as the precursors, while O2 gas was used as the reactive gas. The PE-ALD-grown HfO2 and ZrO2 thin films were analyzed using X-ray photoelectron spectroscopy (XPS), X-ray diffraction (XRD), and high-resolution transmission electron microscopy (HRTEM). The XPS measurements show that the ZrO2 film has the atomic concentrations of 34% Zr, 2% C, and 64% O while the HfO2 film has the atomic concentrations of 29% Hf, 11% C, and 60% O. The HRTEM and XRD measurements show both HfO2 and ZrO2 films have polycrystalline structures. n-channel and p-channel metal-oxide semiconductor field-effect transistors (nFETs and pFETs), CMOS inverters, and CMOS ring oscillators were fabricated to test the quality of the HfO2 and ZrO2 thin films as the gate oxide. Current-voltage (IV) curves, transfer characteristics, and oscillation waveforms were measured from the fabricated transistors, inverters, and oscillators, respectively. The experimental results measured from the HfO2 and ZrO2 thin films were compared.
Silica-based optical fibers, fiber-based devices and optical fiber sensors are today integrated in a variety of harsh environments associated with radiation constraints. Under irradiation, the macroscopic properties of the optical fibers are modified through three main basic mechanisms: the radiation induced attenuation, the radiation induced emission and the radiation induced refractive index change. Depending on the fiber profile of use, these phenomena differently contribute to the degradation of the fiber performances and then have to be either mitigated for radiation tolerant systems or exploited to design radiation detectors and dosimeters. Considering the strong impact of radiation on key applications such as data transfer or sensing in space, fusion and fission-related facilities or high energy physics facilities, since 1970′s numerous experimental and theoretical studies have been conducted to identify the microscopic origins of these changes. The observed degradation can be explained through the generation by ionization or displacement damages of point defects in the differently doped amorphous glass (SiO 2 ) of the fiber's core and cladding layers. Indeed, the fiber chemical composition (dopants/concentrations) and elaboration processes play an important role. Consequently, identifying the nature, the properties and the generation and bleaching mechanisms of these point defects is mandatory in order to imagine ways to control the fiber radiation behaviors. In this review paper, the responses of the main classes of silica-based optical fibers are presented: radiation tolerant pure-silica core or fluorine doped optical fibers, germanosilicate optical fibers and radiation sensitive phosphosilicate and aluminosilicate optical fibers. Our current knowledge about the nature and optical properties of the point defects related to silica and these main dopants is presented. The efficiency of the known defects to reproduce the transient and steady state radiation induced attenuation between 300 nm and 2 µm wavelength range is discussed. The main parameters, related to the fibers themselves or extrinsic - harsh environments, profile of use - affecting the concentration, growth and decay kinetics of those defects are also reviewed. Finally, the main remaining challenges are discussed, including the increasing needs for accurate and multi-physics modeling tools.
Understanding the atomic structure of amorphous solids is important in predicting and tuning their macroscopic behavior. Here, we use a combination of high-energy X-ray diffraction, neutron diffraction, and molecular dynamics simulations to benchmark the atomic interactions in the high temperature stable liquid and low-density amorphous solid states of hafnia. The diffraction results reveal an average Hf–O coordination number of ~7 exists in both the liquid and amorphous nanoparticle forms studied. The measured pair distribution functions are compared to those generated from several simulation models in the literature. We have also performed ab initio and classical molecular dynamics simulations that show density has a strong effect on the polyhedral connectivity. The liquid shows a broad distribution of Hf–Hf interactions, while the formation of low-density amorphous nanoclusters can reproduce the sharp split peak in the Hf–Hf partial pair distribution function observed in experiment. The agglomeration of amorphous nanoparticles condensed from the gas phase is associated with the formation of both edge-sharing and corner-sharing HfO6,7 polyhedra resembling that observed in the monoclinic phase.
The structure of high-temperature liquids is an important topic for understanding the fragility of liquids. Here we report the structure of a high-temperature non-glass-forming oxide liquid, ZrO2, at an atomistic and electronic level. The Bhatia–Thornton number–number structure factor of ZrO2 does not show a first sharp diffraction peak. The atomic structure comprises ZrO5, ZrO6 and ZrO7 polyhedra with a significant contribution of edge sharing of oxygen in addition to corner sharing. The variety of large oxygen coordination and polyhedral connections with short Zr–O bond lifetimes, induced by the relatively large ionic radius of zirconium, disturbs the evolution of intermediate-range ordering, which leads to a reduced electronic band gap and increased delocalization in the ionic Zr–O bonding. The details of the chemical bonding explain the extremely low viscosity of the liquid and the absence of a first sharp diffraction peak, and indicate that liquid ZrO2 is an extremely fragile liquid.
HfO2 is widely investigated as the favoured material for resistive RAM device implementation. The structural features of HfO2 play a fundamental role in the switching mechanisms governing resistive RAM operations, and a comprehensive understanding of the relation between the atomistic properties and final device behaviour is still missing. In addition, despite the fact that ultra-scaled 10 nm resistive RAM will probably be made of amorphous HfO2, a deeper investigation of the structure is necessary. In this paper, the classical molecular dynamics technique was used to investigate the disordered atomic configuration of amorphous HfO2. The influence of density on both the atomistic structure and the diffusion of O species was carefully analysed. The results achieved show that the atomistic structure of an amorphous HfO2 system is strongly affected by the density, and the amorphous system is rearranged in an atomic configuration similar to the crystalline configuration at similar densities. The diffusion of oxygen atoms increases with the decrease of the density, consistent with a less-packed atomic structure which allows for easier movement of this species.
The complete set of partial pair distribution functions for a rare earth oxide liquid are measured by combining aerodynamic levitation, neutron and x-ray diffraction on Y2O3, and Ho2O3 melts at 2870 K. The average Y-O (or Ho-O) coordination of these isomorphic melts is measured to be 5.5(2), which is significantly less than the octahedral coordination of crystalline Y2O3 (or Ho2O3). Investigation of La2O3, ZrO2, and Al2O3 melts by x-ray diffraction and molecular dynamics simulations also show lower-than-crystal cation-oxygen coordination. These measurements suggest a general trend towards lower coordination compared to their crystalline counterparts. It is found that the coordination drop is larger for lower field strength, larger radius cations and is negligible for high field strength (network forming) cations, such as SiO2. These findings have broad implications for predicting the local structure and related physical properties of metal-oxide melts and oxide glasses.
We present the results of first-principles molecular-dynamics
simulations of molten silicates, based on the density functional
formalism. In particular, the structural properties of a calcium
aluminosilicate [CaO-Al2O3-SiO2] melt
are compared to those of a silica melt. The local structures of the two
melts are in good agreement with the experimental understanding of these
systems. In the calcium aluminosilicate melt, the number of nonbridging
oxygens found is in excess of the number obtained from a simple
stoichiometric prediction. In addition, the aluminum avoidance
principle, which states that links between AlO4 tetrahedra
are absent or rare, is found to be violated. Defects such as two-fold
rings and five-fold coordinated silicon atoms are found in comparable
proportions in both liquids. However, in the calcium aluminosilicate
melt, a larger proportion of oxygen atoms are three-fold coordinated. In
addition, fivefold coordinated aluminum atoms are observed. Finally
evidence of creation and anihilation of nonbridging oxygens is observed,
with these oxygens being mostly connected to Si tetrahedra.
In the advancement of complementary metal-oxide-semiconductor device technology, SiO2 was used as an outstanding dielectric and has dominated the microelectronics industry for the last few decades. However, with the recent size downscaling, ultrathin SiO2 is no longer suitable. ZrO2 has been introduced as a high-k dielectric to replace SiO2. This paper reviews recent progress of ZrO2 thin films as dielectric layers for volatile dynamic random access memory (DRAM) applications and as a gate dielectric for CMOS devices. Materials and electrical properties of ZrO2 films obtained by different deposition methods are compared. The effects of different top and bottom electrodes, and different doping elements, on ZrO2 dielectric properties are described. Applications discussed include the use of ZrO2 in Ge and SiGe nanocrystal-embedded nonvolatile flash memory devices. ZrO2 films as charge trapping layers in SOZOS (poly-Si/SiO2/ZrO2/SiO2/Si) and TAZOS (TaN/Al2O3/ZrO2/SiO2/Si) based nonvolatile flash memory stacks, and bipolar, unipolar, and nonpolar ZrO2-based resistive switching memory devices are also briefly discussed. The impact of electrode materials, metal nanocrystals, metal implantation, metal doping, metal layers, and oxide ion conductor buffer layer on resistive switching properties and switching parameters of emerging ZrO2-based resistive switching memory devices for high speed, low power, nanoscale, nonvolatile memory devices are briefly reviewed. A roadmap of the applications of ZrO2 thin film in future low power, nanoscale microelectronic device applications is realized from this review.
As high-permittivity dielectrics approach use in metal-oxide-semiconductor field-effect transistor production, an atomic level understanding of their dielectric properties and the capacitance of structures made from them is being rigorously pursued. We and others have shown that crystal structure of ZrO2 films have considerable effects on permittivity as well as band gap. The as-deposited films reported here appear amorphous below a critical thickness (~5.4 nm) and transform to a predominantly tetragonal phase upon annealing. At much higher thickness the stable monoclinic phase will be favored. These phase changes may have a significant effect on channel mobility.
High-κ metal oxides are a class of materials playing an increasingly important role in modern device physics and technology. Here we report theoretical investigations of the properties of structural and lattice dielectric constants of bulk amorphous metal oxides by a combined approach of classical molecular dynamics (MD), for structure evolution, and quantum mechanical first-principles density function theory (DFT), for electronic structure analysis. Using classical MD based on the Born-Mayer-Buckingham potential function within a melt and quench scheme, amorphous structures of high-κ metal oxides Hf1−xZrxO2 with different values of the concentration x are generated. The coordination numbers and the radial distribution functions of the structures are in good agreement with the corresponding experimental data. We then calculate the lattice dielectric constants of the materials from quantum mechanical first principles, and the values averaged over an ensemble of samples agree well with the available experimental data and are very close to the dielectric constants of their cubic form.
The atomic structure of amorphous and crystalline hafnium oxide (HfO2) films was examined using x-ray diffractometry and Hf edge x-ray absorption spectroscopy. According to the x-ray photoelectron spectroscopy and band data calculated by the density functional method, we found that the valence band of HfO2 consists of three subbands separated by ionic gaps. The upper subband is formed by O 2p, Hf 4f, and Hf 5d states; the intermediate subband is formed by O 2s and Hf 4f states, whereas the lower narrow subband is mainly formed by Hf 5p states. The energy gap of amorphous HfO2 is 5.7 eV as determined by electron energy loss spectroscopy. The band calculation results indicate the existence of light (0.3m0) and heavy (8.3m0) holes in the HfO2 film and the effective mass of electron lies in the interval of 0.7m0–2.0m0.
Recent developments in and around the SIESTA method of first-principles simulation of condensed matter are described and reviewed, with emphasis on (i) the applicability of the method for large and varied systems, (ii) efficient basis sets for the standards of accuracy of density-functional methods, (iii) new implementations, and (iv) extensions beyond ground-state calculations.
This book provides a practical guide to molecular dynamics and Monte Carlo simulation techniques used in the modelling of simple and complex liquids. Computer simulation is an essential tool in studying the chemistry and physics of condensed matter, complementing and reinforcing both experiment and theory. Simulations provide detailed information about structure and dynamics, essential to understand the many fluid systems that play a key role in our daily lives: polymers, gels, colloidal suspensions, liquid crystals, biological membranes, and glasses. The second edition of this pioneering book aims to explain how simulation programs work, how to use them, and how to interpret the results, with examples of the latest research in this rapidly evolving field. Accompanying programs in Fortran and Python provide practical, hands-on, illustrations of the ideas in the text.
This work presents both the parametrization procedure of a self-consistent charge density functional based tight-binding scheme (SCC-DFTB) for hafnium oxide and the structural as well as the electronic results of the simulations of amorphous hafnium oxide a-HfO2 using the data resulting during the parametrization. While aiming at describing amorphous hafnium oxide, the created parameters could be successfully compared to ab initio DFT data for hafnium and hafnium oxide crystalline structures. Furthermore the atomic structure and electronic properties obtained in the DFTB simulations of a-HfO2 compare well to other theoretical studies using classical many-body as well as quantum-mechanical approaches.
The migration of ions in HfOx was investigated by means of large-scale, classical molecular-dynamics simulations over the temperature range 1000≤T/K≤2000. Amorphous HfOx was studied in both stoichiometric and oxygen-deficient forms (i.e., with x = 2 and x = 1.9875); oxygen-deficient cubic and monoclinic phases were also studied. The mean square displacement of oxygen ions was found to evolve linearly as a function of time for the crystalline phases, as expected, but displayed significant negative deviations from linear behavior for the amorphous phases, that is, the behavior was sub-diffusive. That oxygen-ion migration was observed for the stoichiometricamorphous phase argues strongly against applying the traditional model of vacancy-mediated migration in crystals to amorphous HfO2. In addition, cation migration, whilst not observed for the crystalline phases (as no cation defects were present), was observed for both amorphous phases. In order to obtain activation enthalpies of migration, the residence times of the migrating ions were analyzed. The analysis reveals four activation enthalpies for the two amorphous phases: 0.29 eV, 0.46 eV, and 0.66 eV (values very close to those obtained for the monoclinic structure) plus a higher enthalpy of at least 0.85 eV. In comparison, the cubic phase is characterized by a single value of 0.43 eV. Simple kinetic Monte Carlo simulations suggest that the sub-diffusive behavior arises from nanoscale confinement of the migrating ions.
The previously developed high-performance parallel method of the atomistic simulation of the ion beam sputtering deposition process is applied to the SiO2 thin films. Structural properties of deposited films such as density, concentration of point defects, ring statistics, as well as effects arising from the interaction of high energy sputtered Si atoms with the growing film are discussed.
Amorphous (a)-HfO2 is a prototype high dielectric constant insulator with wide technological applications. Using ab initio calculations we show that excess electrons and holes can trap in a-HfO2 in energetically much deeper polaron states than in the crystalline monoclinic phase. The electrons and holes localize at precursor sites, such as elongated Hf-O bonds or undercoordinated Hf and O atoms, and the polaronic relaxation is amplified by the local disorder of amorphous network. Single electron polarons produce states in the gap at ∼2 eV below the bottom of the conduction band with average trapping energies of 1.0 eV. Two electrons can form even deeper bipolaron states on the same site. Holes are typically localized on undercoordinated O ions with average trapping energies of 1.4 eV. These results advance our general understanding of charge trapping in amorphous oxides by demonstrating that deep polaron states are inherent and do not require any bond rupture to form precursor sites.
Optical phenomena occur at surfaces and in thin films. However, unlike in microelectronics and opto-electronics, surface and thin film science is often hardly of any help in describing the basic processes taking place on optical surfaces. Optical surfaces are never of a well-defined single-crystalline or amorphous type, and the growth of optical films takes place under rather unclean and consequently undefined conditions. Our final interest is always optical, and there may also be an interest in the mechanical, thermal and electrical properties. The dependence of optical properties on thin film growth conditions is a severe constraint. There is a significant conflict between models based on ideal- and such based on real-structure films. This will be explained in Sect. 2. What we need is models that relate real film structure to desired optical properties. Such knowledge would allow the design and manufacture of coatings to be based on more realistic production conditions. Section 3 deals with aspects of thin film growth of variable dimensions, from isolated nanoclusters to continuous macroscopic films. The focus is on dielectric (Sect. 4) and metallic films (Sect. 5) and their optical properties.
The most significant processes for optical coating manufacture are variants of vacuum deposition. Thermal evaporation is the traditional process and still of great importance but in the last two decades there has been a major shift to the energetic processes, primarily ion and plasmaassisted deposition and various forms of sputtering. Vacuum processes are very flexible and so dominate short-run production but various forms of pulsed chemical vapor deposition are just starting to appear in long runs of very specialized components. There is also a wide range of other viable and occasionally used techniques, with various degrees of promise, ranging from arc evaporation to liquid deposition.
A new approach to the construction of first-principles pseudopotentials is described. The method allows transferability to be improved systematically while holding the cutoff radius fixed, even for large cutoff radii. Novel features are that the pseudopotential itself becomes charge-state dependent, the usual norm-conservation constraint does not apply, and a generalized eigenproblem is introduced. The potentials have a separable form well suited for plane-wave solid-state calculations, and show promise for application to first-row and transition-metal systems.
Realistic amorphous samples of a-Al2O3 and a-ZrO2 were generated by a hybrid classical and density functional theory (DFT) "melt and quench" molecular dynamics approach. The generated samples demonstrated good correlation with reference experimental and simulated properties.
A new study of the structure of vitreous silica has been made under greatly improved conditions. Using Rh Kα radiation with the method of fluorescence excitation, reliable intensity values were measured to 4π sinθ/λ = 20. The interpretation was in terms of pair functions, thereby eliminating the approximations in earlier work. Each silicon is tetrahedrally surrounded by 4 oxygen atoms, with a Si–O distance which is closely 1.62 Å. Each oxygen atom is bonded to 2 silicon atoms. The Si–O–Si bond angle α shows a distribution V(α) extending all the way from 120° to 180°, with a maximum at α = 144°. This wide variation in α is an important distinction between the vitreous and the crystalline forms of silica, and it furnishes an important criterion for any proposed model of vitreous silica. Good agreement with the measured pair function distribution curve was obtained by assuming a random orientation about the Si–O bond directions. The interpretation leads to the familiar random network model, but with the new results the model is more precise.
VESTA
is a three-dimensional visualization system for crystallographic studies and electronic state calculations. It has been upgraded to the latest version,
VESTA 3
, implementing new features including drawing the external morphology of crystals; superimposing multiple structural models, volumetric data and crystal faces; calculation of electron and nuclear densities from structure parameters; calculation of Patterson functions from structure parameters or volumetric data; integration of electron and nuclear densities by Voronoi tessellation; visualization of isosurfaces with multiple levels; determination of the best plane for selected atoms; an extended bond-search algorithm to enable more sophisticated searches in complex molecules and cage-like structures; undo and redo in graphical user interface operations; and significant performance improvements in rendering isosurfaces and calculating slices.
Optical transmission and photoconductivity spectra (7-14 eV) and the
field dependence of photoconductivity are presented for thermally grown
(amorphous) SiO2 films. It is argued that the clearest
experimental determination of the band gap in SiO2 can be
obtained from the field dependence of photoconductivity and its
similarity to internal photoemission; a band gap of 9.3 eV for amorphous
SiO2 is deduced from the data. In view of this result some
recent experimental band-gap determinations are criticized and the
literature on this subject is examined. The transmission experiments
were performed on thin thermally grown (amorphous) SiO2 films
(450-5000 Å) produced by etching off the silicon substrate and
using a fabrication method which is described in detail. The
photoconductivity measurements were performed on Al-SiO2-Si
structures (SiO2: 600-3500 Å). Diode experiments for
detecting photoluminescence and possibly excitons are also described.
The upper limit on photoluminescence yield was determined as
~10-4.
The threefold coordinated oxygen atom in solid silicon dioxide is studied in a cluster model using the MNDO method. Atomic configuration, electronic structure, optical and vibrational properties of three charge states of the defect are calculated. The positively-charged threefold coordinated oxygen atom is found to be the only stable charge state of the defect. UV optical absorption with energy greater than or equal to 7.5 eV and IR optical absorption near 410 cm(-1), 460 cm(-1) and 990 cm(-1) and depolarized Raman scattering in two latter bands are typical for this charge state. A model of photobleaching of oxygen-deficient centers in silica glass is suggested. (C) 1997 Elsevier Science B.V.
We propose that the structure of amorphous metal oxides can be regarded as a dual-dense-random-packing structure, which is a superposition of the dense random packing of metal atoms and that of oxygen atoms. Our ab initio molecular dynamics simulations show that the medium-range order of amorphous HfO_{2}, ZrO_{2}, TiO_{2}, In_{2}O_{3}, Ga_{2}O_{3}, Al_{2}O_{3,}, and Cu_{2}O is characterized by the pentagonal-bipyramid arrangement of metal atoms and that of oxygen atoms, and prove the validity of our dual-random-sphere-packing model. In other words, we find that the pentagonal medium-range order is universal independent of type of metal oxide.
The oxygen vacancy in silica has been studied with an ab-initio Hartree-Fock embedded cluster, and a semi-empirical MNDO isolated cluster method. The two approaches give similar results: the silicon atoms near the vacancy approach each other considerably; the defect formation energies differ by about 1 eV; two localized defect states appear in the fundamental gap, one fully occupied, one empty. A simplified configuration-interaction treatment performed with the semi-empirical technique gives an estimated value of 5 eV for the lowest electron excitation energy.
Realistic models of amorphous ZrO2 are generated in a ``melt-and-quench'' fashion using ab-initio molecular dynamics with ultrasoft pseudopotentials and a plane-wave basis set in the local-density approximation. First, the structural properties of the amorphous models are analyzed. Then, the vibrational and dielectric properties are analyzed in detail for one of the models using first-principles linear-response methods. The Born effective charges are found to be smaller than in the crystalline phases, while the electronic dielectric tensor is very similar to expectations based on the crystalline phases. The lattice dielectric constant turns out to be disappointingly small. A spectral analysis indicates only that the dominant contribution arises from low-frequency phonon peaks. A spatial decomposition of the lattice dielectric tensor is more revealing, indicating that the strongest contributors are four-coordinated O atoms. This work is motivated by current efforts to search for next-generation gate dielectrics to replace SiO2 in sub-0.1 mum CMOS technology.
Recent experiments at strain rates reaching 0.1 GHz suggest a power-law dependence of solid-phase shear stress on strain rate. Novel nonequilibrium molecular dynamics simulations of plastic flow have been carried out. These steady-state isothermal calculations appear to be consistent with the present-day experimental data and suggest that the flows of metals can be described by a single physical mechanism over a range of strain rates from 10 kHz to 1 THz.
This paper reviews half a century of research on radiation-induced point defects in pure and doped glassy silica and its crystalline polymorph α quartz, placing emphasis on trapped-electron centers because the vast majority of all presently known point defects in various forms of SiO2 are of the trapped-hole variety. The experimental technique most discussed here is electron spin resonance (ESR) because it provides the best means of identifying the point defects responsible for the otherwise difficult-to-attribute optical bands. It is emphasized that defects in α quartz have been unambiguously identified by exacting analyses of the angular dependencies of their ESR spectra in terms of the g matrix of the unpaired electron spin and the matrices of this spin's hyperfine interactions with non-zero-nuclear-spin 29Si and 17O nuclides in pure α quartz and/or with substitutional 27Al, 31P, or 73Ge in quartz crystals respectively doped with Al, P, or Ge. Many defects in pure and doped glassy silica can be unambiguously identified by noting the virtual identities of their spin Hamiltonian parameters with those of their far better characterized doppelgangers in α quartz. In fact, the Ge(1) trapped-electron center in irradiated Ge-doped silica glass is shown here to have a crystal-like nature(!), being virtually indistinguishable from the Ge(II) center in Ge-doped α quartz [R.J. McEachern, J.A. Weil, Phys. Rev. B 49 (1994) 6698]. Still, there are other defects occurring in glassy silica that are not found in quartz, and vice versa. Nevertheless, those defects in glasses without quartz analogues can be identified by analogies with chemically similar defects found in one or both polymorphs and/or by comparison with the vast literature of ESR of paramagnetic atoms and small molecules. Oxygen “pseudo vacancies” comprising trigonally coordinated borons paired with trigonally coordinated silicons were proposed to exist in unirradiated B2O3–3SiO2 glasses in order to account for observations of γ-ray-induced trapped-electron-type B- and Si-E′ centers [D.L. Griscom et al., J. Appl. Phys. 47 (1976) 960]. Analogous Al-E′ trapped-electron centers have been elucidated in silica glasses with Al impurities [K.L. Brower, Phys. Rev. B 20 (1979) 1799]). And it has been proposed [D.L. Griscom et al., J. Appl. Phys. 47 (1976) 960] that trapping of a second electron on such oxygen pseudo vacancies accounts for the predominant ESR-silent trapped-electron centers in irradiated silica glasses containing B or Al. The present paper additionally attempts to divine the identities of some of the ESR-silent radiation-induced trapped-electron centers in silica glasses free of foreign network-forming cations. This quest led to the doorstep of the most famous ESR-silent defect of all, the twofold-coordinated silicon, which is found only in silica glasses (not in quartz) and is responsible for the UV/visible optical properties of the oxygen-deficiency center known as ODC(II). The oxygen-deficiency center called ODC(I) is associated with an absorption band at 7.6eV and, though commonly believed to be a simple oxygen mono-vacancy, is clearly more complicated than that [e.g., A.N. Trukhin, J. Non-Cryst. Solids 352 (2006) 3002]. Certain well documented but persistently enigmatic ODC(I)↔ODC(II) “interconversions” [reviewed by L. Skuja, J. Non-Cryst. Solids 239 (1998) 16] have never been explained to universal satisfaction. An innovative combined ESR/thermo-stimulated-luminescence (TSL) study of a series of pure low-OH silica glasses with oxygen deficiencies of 0.000, ~0.015, and ~0.030vol.% [A.N. Trukhin et al., J. Non-Cryst. Solids, 353 (2007) 1560] places new constraints on all future models for ODC(II). Taking this history into account, specific redefinitions of both ODC(I) and ODC(II) are proposed here. The present review also revisits a study of X-ray-induced point defects in an ultra-low-OH, high-chlorine but otherwise ultra-high-purity silica glass [D.L. Griscom, E.J. Friebele, Phys. Rev. B34 (1986) 7524], arguing that (1) most of the reported E′γ and E′δ centers were created via the mechanism of dissociative electron capture at chlorine-decorated oxygen vacancies, (2) the concomitantly created interstitial chloride ions serve as ESR-silent trapped-electron traps, (3) the ESR-detected “Cl0” centers arise from hole trapping on O3≡Si–Cl units without detachment of the resulting Cl atom, and (4) those chlorine atoms that are detached by homolytic bond fission are ESR-silent. Finally, in chlorine-free, low-OH, high-purity silica glasses, up to 100% of the trapped-electron centers appear to be ESR silent and are tentatively ascribed to electron trapping in pairs below the mobility edge of the conduction band. In such cases, the sum of all trapped-hole centers has been found to decay exponentially with increasing isochronal annealing temperature in the range 100 to ~300K [D.L. Griscom, Nucl. Inst. & Methods B46 (1990) 12]. Overall, this review consolidates a large amount of long-existing but often underappreciated knowledge bearing on the natures of trapped-electron centers in pure and doped glassy silica, proposes new models for some of these, and raises a number of questions that cannot be fully answered without future performance of new experiments and/or ab initio calculations.
Formation energies and electronic properties of oxygen defects in amorphous HfO2 gate dielectrics are investigated by employing the first-principles method based on the density functional theory. We have found that the formation energy of neutral oxygen vacancy in amorphous HfO2 distributes from 4.7 to 6.1 eV, most of which is lower than the value for cubic HfO2, 6.0 eV. The decrease of the formation energy is due to the small coordination number of oxygen atom in the amorphous structure. It is also found that the atomic oxygen incorporation is more favorable in amorphous HfO2 than in crystal HfO2.
Atomistic simulation calculations based on energy minimization techniques have been used to study the energetics associated with M2O3 solution in ZrO2. Results predict that the binding energy of an oxygen vacancy to one or two substitutional cations is a strong function of dopant cation radius. Oxygen vacancies occupy sites that are first neighbour with respect to small dopants whereas oxygen vacancies are located in second neighbour sites with respect to large dopants. The crossover occurs at approximately Sc3+, which also exhibits the smallest binding energy. This behaviour is a consequence of long-range relaxation of the oxygen sublattice. The model is validated by comparing predicted lattice parameters of M2O3:ZrO2 solid solutions with experimental data.
Nonequilibrium computer simulations reveal that the equation of state of fluids undergoing shear flow, varies with strain rate. This observation prompted the development of a nonlinear generalization of irreversible thermodynamics to describe steady planar Couette flow, very far from equilibrium. In this paper we use computer simulation to perform a quantitative test of a prediction of this thermodynamics. The prediction tested is: fluids which exhibit positive shear dilatancy for isothermal shear flow should also cool as the strain rate is increased while keeping the internal energy constant. To perform calculations of this effect a new nonequilibrium molecular dynamics algorithm was developed to simulate Couette flow at constant internal energy.
We have investigated the peroxy-radical defect in glassy SiO2 by means of MOPN, a semiempirical molecular-orbital program, applied to a cluster of atoms chosen to simulate the defect. Our calculations are consistent with important features of Griscom's model of the defect as a perturbed O2- ion substituted for a single-bridging O2- ion in SiO2 and attached to a single silicon, and they place geometrical constraints on the defect structure for this model to be valid. We predict the existence of a related defect (the small peroxy radical, or SPR) wherein the peroxy radical is strongly bonded to two silicons. We have also investigated the formation of the peroxy radical. Griscom and co-workers envision peroxy linkages substituting for single-bridging oxygens during the growth process. They suggest that upon annealing these linkages readily give up an electron to form the observed radical. Our calculations lead us to argue against this process; rather, capture of a free hole seems more likely. We suggest that the SPR could form via a process in which neutral oxygen molecules diffuse through the solid and combine with E1′ centers to form peroxy radicals.
The energies of strained two-member and three-member rings of SiO4 tetrahedra are calculated using models based on continuous SiO2 networks. These rings are considered to form highly reactive ``defect'' centers in vitreous SiO2 and at its surface. The calculations are based on a generalized gradient approximation to density-functional theory, and give strain energies of 1.23 and 0.25 eV for two- and three-member rings, considerably smaller than those previously estimated from Hartree-Fock calculations applied to small hydrogen-terminated molecular models. Structural results are compared with experiment for solids and molecules containing such rings. Changes in bond charge densities due to ring strain are illustrated, and modifications of the electronic states of relaxed SiO2 networks caused by strained ring defects are discussed.
The local structural order of amorphous HfO2 films (a-HfO2) was examined using Hf L3-edge x-ray absorption spectroscopy and fine structure analyses. The fine structure simulation successfully reproduced the spectral evolution of the crystalline-to-amorphous phase transition by reducing the characteristic radius for atomic ordering to ∼3.5 Å. Detailed path-by-path analyses further showed that the vibrational displacement of oxygen atoms in a-HfO2 films is highly anisotropic showing mainly lateral dispersion perpendicular to a Hf-O bond. This anisotropic structural disorder is responsible for enhancing the dielectric constant accompanying phonon mode softening in the a-HfO2 film.
Models for defects in SiO2 fall into the two basic categories of "vacancy-bridge" and valence-alternation models. We have calculated the local electronic structure of the main defects in each model, using the tight-binding and recursion methods. The localization of each level is found and compared to that measured by ESR for the paramagnetic centers. The silicon dangling bond, the neutral oxygen vacancy, and the positively charged oxygen vacancy (E′ center) all give deep states near mid-gap. The Si—Si bond gives a bonding state in the lower gap and an antibonding state near the conduction-band minimum. The positive, threefold-coordinated oxygen site O3+(Si3) gives a state bound only by its Coulombic field. In general, all positively charged centers possess a "shallow" bound state 1-2 eV below the conduction-band minimum. Such shallow states account for the prevalence of optical absorption around 7.6 eV in SiO2. The nonbridging oxygen introduces states just above the valence-band maximum. The peroxyl bridge and radical give states both at mid-gap and in the lower part of the gap. A broad absorption band around 5-6 eV is associated with the peroxyl radical, for the first time. It is suggested that valence-alternation defects must still be present in v-SiO2, but at a much lower concentration, of order 1015 cm-3, than previously supposed, due to a higher valence-alternation creation energy in SiO2 than in a-Se or a-As2Se3.
The neutral oxygen vacancy in SiO2 is important both through its role in controlled refractive index changes and as an archetypal intrinsic defect. We have studied the very significant effects of lattice relaxation on the structure and properties of this defect in both pure and Ge-doped α-quartz using a hybrid classical–ab initio embedded-cluster method. The neutral vacancy induces very strong and anisotropic lattice distortion. At the vacancy site, the Si-Si distance in α-quartz relaxes to the same spacing as in elemental Si. The long-range distortion components extend further than 13 Å from the vacant site. The displacements of surrounding atoms are strongly asymmetric with respect to the vacancy, contrary to previous theoretical results. We predict a strong relaxation in the lowest triplet excited state of the vacancy and small (less than 1 eV) triplet luminescence energy. The strong dependence of the defect properties on the radius of the relaxed region is demonstrated and the applicability of small molecular cluster models is discussed.
We have performed ab initio molecular dynamics simulations to generate an atomic structure model of amorphous hafnium oxide (a-HfO2) via a melt-and-quench scheme. This structure is analyzed via bond-angle and partial pair distribution functions. These results give a Hf-O average nearest-neighbor distance of 2.2 Å, which should be compared to the bulk value, which ranges from 1.96 to 2.54 Å. We have also investigated the neutral O vacancy and a substitutional Si impurity for various sites, as well as the amorphous phase of Hf1−xSixO2 for x=0.25, 0.375, and 0.5.
We investigate the phase transformation of HfO2 under hydrostatic pressure through first-principles pseudopotential calculations within the local-density-functional approximation (LDA) and the generalized gradient approximation (GGA). We find that with increasing of pressure, HfO2 undergoes a series of structural transformations from monoclinic to orthorhombic I and then to orthorhombic II, consistent with experiments. The calculated transition pressures within the GGA are in good agreement with the measured values, while they are severely underestimated by the LDA. Analyzing the distribution of electron densities for the high-pressure phases, we find that the electron densities of the orthorhombic-II phase are more homogeneous than for the orthorhombic-I phase. Due to this distinct difference in the homogeneity of electron densities, the energy difference between the orthorhombic-I and orthorhombic-II phases is enhanced in the GGA; thus, the transition pressure between the two phases increases significantly.
Electronic band gaps and dielectric constants are obtained for amorphous hafnium silicates using first-principles methods. Models of amorphous (HfO2)x(SiO2)1−x for varying x are generated by ab initio molecular dynamics. The calculations show that the presence of Hf gives rise to low-lying conduction states which explain the experimentally observed nonlinear dependence of the band gap on hafnium content. Static dielectric constants are found to depend linearly on x, supporting recent experimental data.
Using first-principles density-functional theory calculations, we have investigated the structural, electronic, and dielectric properties, as well as the O vacancy formation in amorphous HfO2. The structural properties of the generated amorphous models were analyzed via the pair correlation functions and the distribution of the atomic coordination number. The PBE0 hybrid density functional was employed for the analysis of the electronic properties and the charge transition levels of the O vacancy in amorphous HfO2. The dielectric and vibrational properties of the generated models were analyzed using the linear response method based on the density functional perturbation theory. According to the generated structural models, the density of a-HfO2 was 8.63 g/cm3, and the average coordination numbers of O and Hf atom were 3.06 and 6.10, respectively. The electronic band gap of a-HfO2 was predicted to be 5.94 eV, and the static dielectric constants were calculated to be ∼ 22, both in good agreements with the experimental measurements. The computed formation energy of a neutral O vacancy in a-HfO2 was 6.50 eV on average, which is lower than that in m-HfO2 by 0.2–0.3 eV but remains higher than that in a-SiO2. Unlike in m-HfO2, the highest occupied defect levels of the negatively charged O vacancies in a-HfO2 may lie within the band-gap region of silicon. In addition, O vacancies in the charge state q =− 2 may appear as a stable state as the electron chemical potential lies within the electronic band gap, and thus, some of the O vacancies can possess the negative-U property in a-HfO2.
We present a statistical study of silicon and oxygen neutral defects in a silica glass model. This work is
performed following two complementary approaches: first-principles calculations and empirical potential molecular
dynamics. We show that the defect formation energies and structures are distributed and that the energy
distributions are correlated with the local stress before the defect formation. Combining defect energies calculated
from first principles and local stresses from empirical potential calculations in undefected silica, we are
able to predict the formation energy distributions in larger systems, the size of which precludes the use of ab
initio methods. Using the resulting prediction we will show that the cell size used in our modeling contains all
the formation energy fluctuations needed to describe a real glass.
We provide the first experimental evidence that edge-shared tetrahedra ( > Si < o/o > Si < ) can exist on the surface of silicon oxide thin films. These sites are characterized by infrared active Si-O-Si bending modes at 888 and 908 cm-1 and by their high reactivity toward both water and triethylsilanol. They are formed by annealing at high temperature (greater-than-or-equal-to 1400 K) and not by the recombination of surface silanol groups. Our observations confirm recent theoretical predictions.
The oxygen vacancy in silica is characterized theoretically using an ab initio unrestricted Hartree-Fock, embedded-cluster approach. Two models are adopted for the host crystal, α-quartz and β-cristobalite. The defect formation energy, the transition energies from the ground to the first excited singlet and triplet states and the corresponding luminescence are considered. The electronic structure of the defect in the different states is analysed, and it is shown that the excitation corresponds to a transition between a bonding and an anti-bonding combination of the dangling orbitals of the two silicon atoms adjacent to the vacancy. The influence of the size of the cluster and of the basis set adopted are discussed; the latter proves to be more important. Difficulties in the convergence procedure were encountered, especially in the case of the vacancy in quartz, which prevented us from obtaining a complete set of results. However, from a comparison of the two crystal systems and an analysis of the data obtained, it is concluded that the excitation and luminescence energies (≈5.5 and ≈3.5 eV to the triplet, and ≈8.5 and ≈7 eV to the singlet excited states) are compatible with the hypothesis that the oxygen vacancy is a model of the oxygen-deficient centre SiODC(I) in silica. The formation energy of the vacancy is estimated at about 7 eV.
The authors present a systematic approach to the derivation of empirical potential parameters for binary oxides; they also consider their modification for use in mixed oxide systems. Shell-model potentials are used but, unlike the case of the alkali halides within which polarisability and short-range interaction parameters can be transferred, modifications must be introduced when transferring potential parameters between different oxides. The anion polarisability varies with structure and with the nature of the host cation, and changes in cation coordination are reflected in the short-range repulsive cation-anion interaction. Parameters are derived for a range of oxides, and trends in these parameters are discussed. They discuss successful applications of the potentials to the calculation of perfect lattice properties. Equal success is enjoyed when defect and surface properties are considered; in particular the models correctly predict the activation energies for dopant diffusion in NiO, and to a large extent model the surface rumpling of MgO.
Density functional approximations for the exchange‐correlation energy EDFAxc of an electronic system are often improved by admixing some exact exchange Ex: Exc≊EDFAxc+(1/n)(Ex−EDFAx). This procedure is justified when the error in EDFAxc arises from the λ=0 or exchange end of the coupling‐constant integral ∫10 dλ EDFAxc,λ. We argue that the optimum integer n is approximately the lowest order of Görling–Levy perturbation theory which provides a realistic description of the coupling‐constant dependence Exc,λ in the range 0≤λ≤1, whence n≊4 for atomization energies of typical molecules. We also propose a continuous generalization of n as an index of correlation strength, and a possible mixing of second‐order perturbation theory with the generalized gradient approximation.