We calculated the optical excitation and thermal ionization energies of oxygen vacancies in mHfO2 using atomic basis sets, a non-local density functional and periodic supercell. The thermal ionization energies of negatively charged V − and V 2− centres are consistent with values obtained by the electrical measurements. The results suggest that negative oxygen vacancies are the likely candidates for intrinsic electron traps in the hafnum-based gate stack devices.Hafnium based oxides are currently considered as a practical solution satisfying stringent criteria for integration of high-k materials in the devices in future technology nodes. However, high-k transistor performance is often affected by high and unstable threshold potential 1 , V t , and low carrier mobility 2 . These effects are usually attributed to a high concentration of charge traps and scattering centers in the bulk of the dielectric and/or at its interface with the silicon channel. Although the reported trap densities vary greatly with fabrication techniques, the majority of data point to existence of a specific intrinsic shallow electron centre common to all HfO 2 based stacks while some extrinsic defects, such as Zr substitution in HfO 2 , have also been considered 3 .Oxygen vacancies are dominating intrinsic defects in the bulk of many transition metal oxides including HfO 2 and ZrO 2 , and are thought to be also present in high concentrations in thin films. However, in spite of numerous experimental studies, evidence relating oxygen vacancies to measured characteristics of interface traps in high-k stacks is still mostly circumstantial. Therefore, accurate theoretical characterization of these defects is highly desirable.Previous theoretical calculations of oxygen vacancy in HfO 2 and ZrO 2 reported the ground state properties obtained within local or semilocal approximations to density functional theory (DFT) methods (see 4,5 for a review). This approach, however, significantly underestimates band gaps, which hampers determining energies of defect levels with respect to the band edges and precludes identifying shallow defect states 5,6,7 . As a result, most of the early local DFT calculations (except, perhaps, ref. 8 ) failed to predict unambiguosly negative charge states of oxygen vacancy in HfO 2 . Significant improvement was achieved by Robertson et al. 4,9,10 who used screened exchange approximation to predict vacancy energy levels including V − charge state. However, these calculations were performed using a small periodic supercell and therefore corresponded to extremely high vacancy concentrations. The quality of the functional used is also largely unknown and needs independent verification.In this work we used much bigger supercells and a nonlocal functional to calculate optical excitation and thermal ionization energies of oxygen vacancies in five charge states. To relate these energies to experimental data we distinguish optical absorption/reflection type measurements involving Frank-Condon type (vertical) excitations, and electric...

We have calculated the ionization energies, electron affinities, optical excitation energies, and relaxed electron and hole states at corners, kinks, and steps of the MgO (001) surface. The calculations are performed using an embedded cluster model and density functional theory and take into account the long-range surface polarization. The extent of localization of electronic states associated with specific structural defects at the surface is studied by the participation function method. The positions of energy levels of the surface sites with respect to the top of the surface valence band and the vacuum level are determined. The results demonstrate the existence of deep and shallow electron traps at steps, corners, and kinks of the MgO (001) surface, and establish direct correlation between common surface features and their spectroscopic and other electronic properties.

The earliest ideas of the polaron recognized that the coupling of an electron to ionic vibrations would affect its apparent mass and could effectively immobilize the carrier (self-trapping). We discuss how these basic ideas have been generalized to recognize new materials and new phenomena. First, there is an interplay between self-trapping and trapping associated with defects or with fluctuations in an amorphous solid. In high dielectric constant oxides, like HfO 2 , this leads to oxygen vacancies having as many as five charge states. In colossal magnetoresistance manganites, this interplay makes possible the scanning tunnelling microscopy (STM) observation of polarons. Second, excitons can self-trap and, by doing so, localize energy in ways that can modify the material properties. Third, new materials introduce new features, with polaron-related ideas emerging for uranium dioxide, gate dielectric oxides, Jahn-Teller systems, semiconducting polymers and biological systems. The phonon modes that initiate self-trapping can be quite different from the longitudinal optic modes usually assumed to dominate. Fourth, there are new phenomena, like possible magnetism in simple oxides, or with the evolution of short-lived polarons, like muons or excitons. The central idea remains that of a particle whose properties are modified by polarizing or deforming its host solid, sometimes profoundly. However, some of the simpler standard assumptions can give a limited, indeed misleading, description of real systems, with qualitative inconsistencies. We discuss representative cases for which theory and experiment can be compared in detail.

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Using ab initio density functional total energy and molecular dynamics simulations, we study the effects of various forms of nitrogen post deposition anneal (PDA) on the electric properties of hafnia in the context of its application as a gate dielectric in field effect transistors (FET). We consider the atomic structure and energetics of nitrogen containing defects which can be formed during the PDA in various N-based ambients: N2, N + 2 , N, NH3, NO, N2O. We analyse the role of such defects in fixed charge accumulation, electron trapping and in the growth of the interface SiO2 layer. We find that nitrogen anneal of the oxides leads to an effective immobilization of native defects such as oxygen vacancies and interstitial oxygen ions, which may inhibit growth of silica layer. Nitrogen in any form effectively incorporates into the pre-existing oxygen vacancies and, therefore may decrease the concentration of shallow electron traps. However, nitrogen in any form is unlikely to significantly reduce the fixed charge in the dielectric.

We present the results of a plane wave based density functional study of the structure and properties of tetragonal zirconia in the range of pressures from 0 to 50 GPa. We predict a transition to a fluorite-type cubic structure at 37 GPa which is likely to be of a soft mode origin and is accompanied by a power law decrease of the frequency of the Raman-active A(1g) mode. A detailed study of the pressure effect on phonon modes is given, including theoretical Raman spectra and their pressure dependence. Our results provide a consistent picture of the pressure-induced phase transition in tetragonal zirconia.

We discuss the adiabatic self-trapping of small polarons within the density functional theory (DFT). In particular, we carried out plane-wave pseudo-potential calculations of the triplet exciton in NaCl and found no energy minimum corresponding to the self-trapped exciton (STE) contrary to the experimental evidence and previous calculations. To explore the origin of this problem we modelled the self-trapped hole in NaCl using hybrid density functionals and an embedded cluster method. Calculations show that the stability of the self-trapped state of the hole drastically depends on the amount of the exact exchange in the density functional: at less than 30% of the Hartree-Fock exchange, only delocalized hole is stable, at 50% -both delocalized and self-trapped states are stable, while further increase of exact exchange results in only the self-trapped state being stable. We argue that the main contributions to the self-trapping energy such as the kinetic energy of the localizing charge, the chemical bond formation of the di-halogen quasi molecule, and the lattice polarization, are represented incorrectly within the Kohn-Sham (KS) based approaches.

Numerous reports claim that quantum advantage, which should emerge as a direct consequence of the advent of quantum computers, will herald a new era of chemical research because it will enable scientists to perform the kinds of quantum chemical simulations that have not been possible before. Such simulations on quantum computers, promising a significantly greater accuracy and speed, are projected to exert a great impact on the way we can probe reality, predict the outcomes of chemical experiments, and even drive design of drugs, catalysts, and materials. In this work we review the current status of quantum hardware and algorithm theory and examine whether such popular claims about quantum advantage are really going to be transformative. We go over subtle complications of quantum chemical research that tend to be overlooked in discussions involving quantum computers. We estimate quantum computer resources that will be required for performing calculations on quantum computers with chemical accuracy for several types of molecules. In particular, we directly compare the resources and timings associated with classical and quantum computers for the molecules H2 for increasing basis set sizes, and Cr2 for a variety of complete active spaces (CAS) within the scope of the CASCI and CASSCF methods. The results obtained for the chromium dimer enable us to estimate the size of the active space at which computations of non-dynamic correlation on a quantum computer should take less time than analogous computations on a classical computer. The transition point should occur at around 19 ≤ N ≤ 34, for CAS of the type (N, N ), under the assumption of the much-researched surface code. This is significantly smaller than the active spaces discussed in the context of quantum advantage in prior publications. Using this result, we speculate on the types of chemical applications for which the use of quantum computers would be both beneficial and relevant to industrial applications in the short term.