Jiří Vackář

Electronic structure of silicon nitride

Abstract The electronic structure of valence and conduction bands of silicon nitride SiNx layer deposited on a silicon substrate was studied using X-ray photoelectron spectroscopy (XPS) and X-ray bremsstrahlung isochromat spectroscopy (BIS), respectively, and compared with the density of states (DOS) taken from the literature. In the isochromat spectrum measured at photon energy 5415 eV, a strong maximum at 9.7 eV and a weak extended structure in the energy range up to 200 eV above the BIS edge were observed. A theoretical calculation of extended X-ray bremsstrahlung isochromat fine structure (EXBIFS) for silicon nitride has been performed using a multiple scattering method and partial probabilities of X-ray bremsstrahlung transitions calculated for continuum states in a dipole approximation. The results have shown that the X-ray bremsstrahlung isochromat fine structure for silicon nitride appears mainly due to electron transitions to the s states localized near Si ions.

Integration of free-free radiative-transition matrix elements

Abstract The calculation of radiative-transition matrix elements between continuum states of an electron moving in the finite-range spherical potential is concerned in this paper. We introduce a numerically safe and fast procedure which has been developed for this purpose. The numerical integration is employed within a certain finite region and the analytical integration outside. Both are performed by the computer program and the algorithm is presented here. Special care was given to the numerical stability so that the rapidly oscilating wave functions describing high-energy incident electrons (∽5 keV) may be integrated. The higher-order terms of the multipole expansion can be evaluated by this method, too.

Effect of atomic vibrations in XANES: polarization-dependent damping of the fine structure at the Cu K-edge of (creat)2CuCl4

Polarization-dependent damping of the fine structure in the Cu K-edge spectrum of creatinium tetrachlorocuprate [(creat)2CuCl4] in the X-ray absorption near-edge structure (XANES) region is shown to be due to atomic vibrations. These vibrations can be separated into two groups, depending on whether the respective atoms belong to the same molecular block; individual molecular blocks can be treated as semi-rigid entities while the mutual positions of these blocks are subject to large mean relative displacements. The effect of vibrations can be efficiently included in XANES calculations by using the same formula as for static systems but with a modified free-electron propagator which accounts for fluctuations in interatomic distances.

Finite Element Method in Density Functional Theory Electronic Structure Calculations

We summarize an ab-initio real-space approach to electronic structure calculations based on the finite-element method. This approach brings a new quality to solving Kohn Sham equations, calculating electronic states, total energy, Hellmann–Feynman forces and material properties particularly for non-crystalline, non-periodic structures. Precise, fully non-local, environment-reflecting real-space ab-initio pseudopotentials increase the efficiency by treating the core-electrons separately, without imposing any kind of frozen-core approximation. Contrary to the variety of well established k-space methods that are based on Bloch’s theorem and applicable to periodic structures, we don’t assume periodicity in any respect. The main asset of the present approach is the efficient combination of an excellent convergence control of standard, universal basis of industrially proved finite-element method and high precision of ab-initio pseudopotentials with applicability not restricted to periodic environment.

Convergence study of isogeometric analysis based on Bézier extraction in electronic structure calculations

Behavior of various, even hypothetical, materials can be predicted via ab-initio electronic structure calculations providing all the necessary information: the total energy of the system and its derivatives. In case of non-periodic structures, the existing well-established methods for electronic structure calculations either use special bases, predetermining and limiting the shapes of wave functions, or require artificial computationally expensive arrangements, like large supercells. We developed a new method for non-periodic electronic structures based on the density functional theory, environment-reflecting pseudopotentials and the isogeometric analysis with Bezier extraction, ensuring continuity for all quantities up to the second derivative. The approach is especially suitable for calculating the total energy derivatives and for molecular-dynamics simulations. Its main assets are the universal basis with the excellent convergence control and the capability to calculate precisely the non-periodic structures even lacking in charge neutrality. Within the present paper, convergence study for isogeometric analysis vs. standard finite-element approach is carried out and illustrated on sub-problems that appear in our electronic structure calculations method: the Poisson problem, the generalized eigenvalue problem and the density functional theory Kohn–Sham equations applied to a benchmark problem.

Python-based finite element code used as a universal and modular tool for electronic structure calculation

Ab-initio calculations of electronic states within the density-functional framework has been performed by means of the open source finite element package SfePy (Simple Finite Elements in Python, http://sfepy.org). We describe a new robust ab-initio real-space code based on (i) density functional theory, (ii) finite element method and (iii) environment-reflecting pseudopotentials. This approach brings a new quality to solving Kohn-Sham equations, calculating electronic states, total energy, Hellmann-Feynman forces and material properties particularly for non-crystalline, non-periodic structures. The main asset of the above approach is an efficient combination of excellent convergence control of standard, universal basis used in industrially proved finite-element method, high precision of ab-initio environment-reflecting pseudopotentials, and applicability not restricted to electrically neutral periodic environment. We present also numerical examples illustrating the outputs of the method.