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The intrinsic optical properties and peculiarities of the energy structure of hafnium dioxide largely determine the prospects for applying the latter in new generation devices of optoelectronics and nanoelectronics. In this work, we have studied the diffuse reflectance spectra at room temperature for a nominally pure nanostructured $HfO_2$ powder with a monoclinic crystal structure and, as well its photoluminescence in the temperature range of 40 - 300 K. We have also estimated the bandgap $E_g$ under the assumption made for indirect (5.31 eV) and direct (5.61 eV) allowed transitions. We have detected emission with a 4.2 eV maximum at T < 200 K and conducted an analysis of the experimental dependencies to evaluate the activation energies of thermal quenching (140 meV) and enhancement (3 meV) processes. Accounting for both the temperature behavior of the spectral characteristics and the estimation of the Huang-Rhys factor S >> 1 has shown that radiative decay of self-trapped excitons forms the mechanism of the indicated emission. In this case, the localization is mainly due to the interaction of holes with active vibrational modes of oxygen atoms in non-equivalent ($O_{3f}$ and $O_{4f}$) crystal positions. Thorough study of the discussed excitonic effects can advance development of hafnia-based structures with a controlled optical response., Comment: 21 pages, 7 figures, 2 tables, 56 references. Keywords: hafnium dioxide, self-trapped exciton, F-center, thermal quenching of luminescence, luminescence enhacement, Huang-Rhys factor, effective phonon energy, bandgap width

Introduction. Neural network models of autoassociative, distributed memory allow storage and retrieval of many items (vectors) where the number of stored items can exceed the vector dimension (the number of neurons in the network). This opens the possibility of a sublinear time search (in the number of stored items) for approximate nearest neighbors among vectors of high dimension. The purpose of this paper is to review models of autoassociative, distributed memory that can be naturally implemented by neural networks (mainly with local learning rules and iterative dynamics based on information locally available to neurons). Scope. The survey is focused mainly on the networks of Hopfield, Willshaw and Potts, that have connections between pairs of neurons and operate on sparse binary vectors. We discuss not only autoassociative memory, but also the generalization properties of these networks. We also consider neural networks with higher-order connections and networks with a bipartite graph structure for non-binary data with linear constraints. Conclusions. In conclusion we discuss the relations to similarity search, advantages and drawbacks of these techniques, and topics for further research. An interesting and still not completely resolved question is whether neural autoassociative memories can search for approximate nearest neighbors faster than other index structures for similarity search, in particular for the case of very high dimensional vectors., Comment: 31 pages

In this study, we demonstrated experimentally and theoretically that the charge transport mechanism in amorphous Hf$_{0.5}$Zr$_{0.5}$O$_2$ is phonon-assisted tunneling between traps like in HfO$_2$ and ZrO$_2$. The thermal trap energy of 1.25 eV and optical trap energy of 2.5 eV in Hf$_{0.5}$Zr$_{0.5}$O$_2$ were determined based on comparison of experimental data on transport with different theories of charge transfer in dielectrics. A hypothesis that oxygen vacancies are responsible for the charge transport in Hf$_{0.5}$Zr$_{0.5}$O$_2$ was discussed., Comment: 4 pages, 3 figures, 1 table

In this study, we demonstrated experimentally that formation of chains and islands of oxygen vacancies in hafnium sub-oxides (HfO$_x$, $x<2$) leads to percolation charge transport in such dielectrics. Basing on the model of \'{E}fros-Shklovskii percolation theory good quantitative agreement between the experimental and theoretical data of current-voltage characteristics were achieved. Based on the percolation theory suggested model shows that hafnium sub-oxides consist of mixtures of metallic Hf nanoscale clusters of 1-2 nm distributed onto non-stoichiometric HfO$_x$. It was shown that reported approach might describe low resistance state current-voltage characteristics of resistive memory elements based on HfO$_x$., Comment: 3 pages, 2 figures

In this study, we demonstrated experimentally and theoretically that oxygen vacancies are responsible for the charge transport in HfO$_2$. Basing on the model of phonon-assisted tunneling between traps, and assuming that the electron traps are oxygen vacancies, good quantitative agreement between the experimental and theoretical data of current-voltage characteristics were achieved. The thermal trap energy of 1.25 eV in HfO$_2$ was determined based on the charge transport experiments., Comment: 5 pages, 5 figures

The name "K3 surfaces" was coined by A. Weil in 1957 when he formulated a research programme for these surfaces and their moduli. Since then, irreducible holomorphic symplectic manifolds have been introduced as a higher dimensional analogue of K3 surfaces. In this paper we present a review of this theory starting from the definition of K3 surfaces and going as far as the global Torelli theorem for irreducible holomorphic symplectic manifolds as recently proved by M. Verbitsky. For many years the last open question of Weil's programme was that of the geometric type of the moduli spaces of polarised K3 surfaces. We explain how this problem has been solved. Our method uses algebraic geometry, modular forms and Borcherds automorphic products. We collect and discuss the relevant facts from the theory of modular forms with respect to the orthogonal group O(2,n). We also give a detailed description of quasi pull-back of automorphic Borcherds products. This part contains previously unpublished results. We apply our geometric-automorphic method to study moduli spaces of both polarised K3 surfaces and irreducible symplectic varieties., Comment: 71 pages. Fairly minor revisions. To appear in "Handbook of Moduli"

We study moduli spaces of O'Grady's ten-dimensional irreducible symplectic manifolds. These moduli spaces are covers of modular varieties of dimension 21, namely quotients of hermitian symmetric domains by a suitable arithmetic group. The interesting and new aspect of this case is that the group in question is strictly bigger than the stable orthogonal group. This makes it different from both the K3 and the K3^[n] case, which are of dimension 19 and 20 respectively.

We study the commutator subgroup of integral orthogonal groups belonging to indefinite quadratic forms. We show that the index of this commutator is 2 for many groups that occur in the construction of moduli spaces in algebraic geometry, in particular the moduli of K3 surfaces. We give applications to modular forms and to computing the fundamental groups of some moduli spaces.

We study the moduli spaces of polarised irreducible symplectic manifolds. By a comparison with locally symmetric varieties of orthogonal type of dimension 20, we show that the moduli space of 2d polarised (split type) symplectic manifolds which are deformation equivalent to degree 2 Hilbert schemes of a K3 surface is of general type if d is at least 12., Comment: Exposition improved, Reference to work of Debarre and Voisin added, Corollary 1.6 removed

For many classical moduli spaces of orthogonal type there are results about the Kodaira dimension. But nothing is known in the case of dimension greater than 19. In this paper we obtain the first results in this direction. In particular the modular variety defined by the orthogonal group of the even unimodular lattice of signature (2, 8m+2) is of general type if m is at least 5., Comment: 19 pages

The moduli space of polarised K3 surfaces of degree 2d is a quasi-projective variety of dimension 19. For general d very little has been known about the Kodaira dimension of these varieties. In this paper we present an almost complete solution to this problem. Our main result says that this moduli space is of general type for d>61 and for d=46,50,54,58,60., Comment: 47 pages

The dominant dielectric used currently in silicon devices is silicon oxide. Its application for future devices will be impeded by several fundamental limitations which lead to low reliability of semiconductor devices and to the necessity of alternative dielectrics. Amorphous silicon nitride and oxynitride are considered now as alternative to silicon oxide in future devices. One of the unique property of amorphous silicon nitride is the electron and hole capture by the deep traps with extremely long life time (10 years) in the captured state (the memory effect). This property is employed in memory devices and microprocessors in computers. Despite numerous efforts the nature of traps responsible for the memory effect in this material is so far unclear. In this paper we discuss the nature of such traps using the quantum-chemical simulation. The calculations show that the defects responsible for the electron and hole capture in amorphous silicon nitride can be the Si-Si defects created by excess silicon atoms., Comment: 4 pages, LaTex

A failure of chips in a huge amount of modern electronic devices is connected as a rule with the undesirable capturing of charge (electrons and holes) by traps in a thin insulating film of silicon oxide in transistors. It leads to a breakdown of transistors or to a destructive change of their characteristics. It is suggested that silicon oxide will be replaced in the next generation of nanoscale devices by silicon oxynitride. Therefore, it is very important to understand the nature of traps in this material. We discuss this nature using the quantum-chemical simulation., Comment: 4 pages, LaTex, 1 gif file with 2 figures

In the paper we study two types of relations: a one is between the elliptic genus of Calabi-Yau manifolds and Jacobi modular forms, another one is between the second quantized elliptic genus, Siegel modular forms and Lorentzian Kac-Moody Lie algebras. We also determine the structure of the graded ring of the weak Jacobi forms with integral Fourier coefficients. It gives us a number of applications to the theory of elliptic genus and of the second quantized elliptic genus., Comment: To appear in Algebra i Analiz (St. Petersburg Math. Journal) 11:5 (1999); AMS-TeX, 25 pages

The elliptic genus (EG) of a compact complex manifold was introduced as a holomorphic Euler characteristic of some formal power series with vector bundle coefficients. EG is an automorphic form in two variables only if the manifold is a Calabi--Yau manifold. In physics such a function appears as the partition function of N=2 superconformal field theories. In these notes we define the modified Witten genus or the automorphic correction of elliptic genus. It is an automorphic function in two variables for an arbitrary holomorphic vector bundle over a compact complex manifold. This paper is an exposition of the talks given by the author at Symposium "Automorphic forms and L-functions" at RIMS, Kyoto (January, 27, 1999) and at Arbeitstagung in Bonn (June, 20, 1999)., Comment: AMS-TeX, 21 pages

Barth and Nieto have found a remarkable quintic threefold which parametrizes Heisenberg invariant Kummer surfaces which belong to abelian surfaces with a (1,3)-polarization and a lecel 2 structure. A double cover of this quintic, which is also a Calabi-Yau variety, is birationally equivalent to the moduli space {\cal A}_3(2) of abelian surfaces with a (1,3)-polarization and a level 2 structure. As a consequence the corresponding paramodular group \Gamma_3(2) has a unique cusp form of weight 3. In this paper we find this cusp form which is \Delta_1^3. The form \Delta_1 is a remarkable weight 1 cusp form with a character with respect to the paramodular group \Gamma_3. It has several interesting properties. One is that it admits an infinite product representation, the other is that it vanishes of order 1 along the diagonal in Siegel space. In fact \Delta_1 is an element of a short series of modular forms with this last property. Using the fact that \Delta_1 is a weight 3 cusp form with respect to the group \Gamma_3(2) we give an independent construction of a smooth projective Calabi-Yau model of the moduli space {\cal A}_3(2)., Comment: 20 pages, Latex2e RIMS Preprint 1203

We investigate the existence and non-existence of modular forms of low weight with a character with respect to the paramodular group $\Gamma_t$ and discuss the resulting geometric consequences. Using an advanced version of Maa\ss\ lifting one can construct many examples of such modular forms and in particular examples of weight 3 cusp forms. Consequently we find many abelian coverings of low degree of the moduli space ${\Cal A}_t$ of (1,t)-polarized abelian surfaces which are not unirational. We also determine the commutator subgroups of the paramodular group $\Gamma_t$ and its degree 2 extension $\Gamma^+_t$. This has applications for the Picard group of the moduli stack ${\underline{\Cal A}}_t$. Finally we prove non-existence theorems for low weight modular forms. As one of our main results we obtain the theorem that the maximal abelian cover ${\Cal A}_t^{com}$ of ${\Cal A}_t$ has geometric genus 0 if and only if t=1, 2, 4 or 5. We also prove that ${\Cal A}_t^{com}$ has geometric genus 1 for t=3 and 7., Comment: 30 pages, AMS-TeX, 2 diagrams