Investigation of numerical atomic orbitals for first-principles calculations of the electronic and transport properties of silicon nanowire structures

This thesis is focused on the application of numerical atomic basis sets in studies of the structural, electronic and transport properties of silicon nanowire structures from first-principles within the framework of Density Functional Theory. First we critically examine the applied methodology and then offer predictions regarding the transport properties and realisation of silicon nanowire devices. The performance of numerical atomic orbitals is benchmarked against calculations performed with plane waves basis sets. After establishing the convergence of total energy and electronic structure calculations with increasing basis size we have shown that their quality greatly improves with the optimisation of the contraction for a fixed basis size. The double zeta polarised basis offers a reasonable approximation to study structural and electronic properties and transferability exists between various nanowire structures. This is most important to reduce the computational cost. The impact of basis sets on transport properties in silicon nanowires with oxygen and dopant impurities have also been studied. It is found that whilst transmission features quantitatively converge with increasing contraction there is a weaker dependence on basis set for the mean free path; the double zeta polarised basis offers a good compromise whereas the single zeta basis set yields qualitatively reasonable results. Studying the transport properties of nanowire-based transistor setups with p+-n-p+ and p+-i-p+ doping profiles it is shown that charge self-consistency affects the I-V characteristics more significantly than the basis set choice. It is predicted that such ultrascaled (3 nm length) transistors would show degraded performance due to relatively high source-drain tunnelling currents. Finally, it is shown the hole mobility of Si nanowires nominally doped with boron decreases monotonically with decreasing width at fixed doping density and increasing dopant concentration. Significant mobility variations are identified which can explain experimental observations.

Effective atomic orbitals for fuzzy atoms

The method of extracting effective atomic orbitals and effective minimal basis sets from molecular wave function characterizing the state of an atom in a molecule is developed in the framework of the "fuzzy" atoms. In all cases studied, there were as many effective orbitals that have considerable occupation numbers as orbitals in the classical minimal basis. That is considered to be of high conceptual importance

MO visualization of Pi Orbitals

In the spirit of trying to convert people to understanding atomic orbitals centered elsewhere than the origin, we continue the discussion of visualizing molecular orbitals, so called LCAO-MO, using various plotting tricks in Maple.

Triatomic Molecular Orbitals

If elementary Quantum Chemistry stops at diatomic molecules, some students may be left with false impressions concerning how one builds polyatomic molecule's LCAO-MOs. This reading discusses building such molecular orbitals from atomic orbitals centered at different spatial coordinates.

Slater integrals for screened hydrogenic orbitals /

Prepared for Air Force Weapons Laboratory.

Part I. Approximate Hartree-Fock wavefunctions one-electron properties and electronic structure of the water molecule. Part II. Perturbation-variational calculation of the nuclear spin-spin isotope coupling constant in HD

Part I

Several approximate Hartree-Fock SCF wavefunctions for the ground electronic state of the water molecule have been obtained using an increasing number of multicenter s, p, and d Slater-type atomic orbitals as basis sets. The predicted charge distribution has been extensively tested at each stage by calculating the electric dipole moment, molecular quadrupole moment, diamagnetic shielding, Hellmann-Feynman forces, and electric field gradients at both the hydrogen and the oxygen nuclei. It was found that a carefully optimized minimal basis set suffices to describe the electronic charge distribution adequately except in the vicinity of the oxygen nucleus. Our calculations indicate, for example, that the correct prediction of the field gradient at this nucleus requires a more flexible linear combination of p-orbitals centered on this nucleus than that in the minimal basis set. Theoretical values for the molecular octopole moment components are also reported.

Part II

The perturbation-variational theory of R. M. Pitzer for nuclear spin-spin coupling constants is applied to the HD molecule. The zero-order molecular orbital is described in terms of a single 1s Slater-type basis function centered on each nucleus. The first-order molecular orbital is expressed in terms of these two functions plus one singular basis function each of the types e^-r/r and e^-r ln r centered on one of the nuclei. The new kinds of molecular integrals were evaluated to high accuracy using numerical and analytical means. The value of the HD spin-spin coupling constant calculated with this near-minimal set of basis functions is J_HD = +96.6 cps. This represents an improvement over the previous calculated value of +120 cps obtained without using the logarithmic basis function but is still considerably off in magnitude compared with the experimental measurement of J_HD = +43 0 ± 0.5 cps.

Mechanical and chemical bonding properties of ground state BeH2

The crystal structure, mechanical properties and electronic structure of ground state BeH2 are calculated employing the first-principles methods based on the density functional theory. Our calculated structural parameters at equilibrium volume are well consistent with experimental results. Elastic constants, which well obey the mechanical stability criteria, are firstly theoretically acquired. The bulk modulus B, Shear modulus G, Young's modulus E, and Poisson's ratio upsilon are deduced from the elastic constants. The bonding nature in BeH2 is fully interpreted by combining characteristics in band structure, density of states, and charge distribution. The ionicity in the Be-H bond is mainly featured by charge transfer from Be 2s to H 1s atomic orbitals while its covalency is dominated by the hybridization of H 1s and Be 2p states. The Bader analysis of BeH2 and MgH2 are performed to describe the ionic/covalent character quantitatively and we find that about 1.61 (1.6) electrons transfer from each Be (Mg) atom to H atoms.

ELECTRON-STATES OF A STACKING-FAULT RIBBON IN SILICON

The electronic structure of a bounded intrinsic stacking fault in silicon is calculated. The method used is an LCAO-scheme (Linear Combinations of Atomic Orbitals) taking ten atomic orbitals of s-, p-, and d-type into account. The levels in the band gap are extracted using Lanczos' algorithm and a continued fraction representation of the local density of states. We find occupied states located up to 0.3 eV above the valence band maximum (E(v)). This significantly differs from the result obtained for the ideal infinite fault for which the interface state is located at E(v)+ 0.1 eV.

INFLUENCE OF THE 90-DEGREES PARTIAL DISLOCATION CORE STRUCTURE IN SILICON ON ENERGY-LEVELS

An LCAO-scheme taking into account 10 atomic orbitals (s-, p-, and d-type) is used to calculate the electronic structure of the reconstructed 90-degrees partial dislocation in Si. Two different valence force fields producing deviating results are used for modelling the core structure. Geometrical data published by another group is also used. The aim is to explore the influence of geometry on energy levels. We find that the band structure depends sensitively on bond angles. Using data determined by the Tersoff potential we obtain two bands of which the upper one penetrates deeply into the indirect band gap while the geometry minimizing the simple Keating potential leaves the gap completely clear of dislocation states. Thus, from a theoretical point of view, the chief difficulty in calculating the electronic structure of the reconstructed 90-degrees partial is the lack of accurate structural information.

ELECTRONIC AND MAGNETIC-STRUCTURE OF THE TERNARY COMPOUND ND2FE17N

The electronic and the magnetic structure of the Nd2Fe17N1 phase in the family of Nd-Fe-N ternary compounds have been calculated using the first-principles, spin-polarized orthogonalized linear-combination-of-atomic-orbitals method. Results are presented in the form of site-decomposed and spin-projected partial density of states. The occupation sites of the three N atoms are determined by an average radial distribution of all possible N site configurations. Both cases of N occupying the 3b and the 18g sites are studied. The results indicate that the 6c Fe sites have the maximum and the 18h Fe sites have the minimum local moments. This is in good agreement with experiment. It is concluded that the influence on the local moment due to lattice expansion is less important compared to that due to interatomic interaction between the N atom and its neighbors. The results also show the important role of N atoms in raising the Curie temperature of this compound.

ENERGY-LEVEL CALCULATIONS OF THE RECONSTRUCTED 90-DEGREES PARTIAL DISLOCATION IN SILICON

An LCAO scheme taking into account 10 atomic orbitals (s-, p-, and d-type) applied to a supercell containing 256 atoms is used to calculate the bound states of the reconstructed 90-degrees partial dislocation in Si. The results differ significantly from our earlier calculations on the unreconstructed 90-degrees partial using the same method. We find two bands separate from each other in the entire Brillouin zone and the upper band penetrates deep into the indirect band gap which is in contradiction with the general opinion that core reconstruction clears the band gap of dislocation states.

CALCULATED ELECTRONIC AND MAGNETIC-STRUCTURES OF THE NEW TERNARY RARE-EARTH IRON NITRIDE ND2FE17N3

The electronic and magnetic structures of Nd2Fe17 and Nd2Fe17N3 have been calculated using the first-principle, spin-polarized orthogonalized linear combination of atomic orbitals method. Comparative studies of the two materials reveal important effects of the nitrogen atoms (at 9e site) on the electronic and magnetic structures. Results are presented for the total density of states, site-projected partial density of states and the spin magnetic moments on four nonequivalent Fe sites. The highest magnetic moments are found to be located on the 6c site for Nd2Fe17 and on the 9d site for Nd2Fe17N3, in agreement with the neutron and Mossbauer experiments. The variation trends of the magnetic moments on different Fe sites are discussed in terms of the separation between Fe and N atoms. Compared with Nd2Fe17, an increase in the exchange splitting of the Fe d band is found in Nd2Fe17N3, which accounts for its higher Curie temperature as observed in experiments. The calculated results show that the nitrogen atoms are charge acceptors in these compounds.

ELECTRON-STATES OF A VACANCY IN THE CORE OF THE 90-DEGREES PARTIAL DISLOCATION IN SILICON

An LCAO scheme (linear combination of atomic orbitals) taking into account ten atomic orbitals (s-, p-, and d-type) is used to calculate the electronic structure of a vacancy present in the core of the reconstructed 90 degrees partial dislocation in silicon. The levels in the band gap are extracted using Lanczos' algorithm and a continued fraction representation of the local density of states. The three-fold degenerate stale of the ideal vacancy is split into three levels with energies 0.26, 1.1, and 1.9 eV measured from the valence band edge.

Photoionization of 1s electron and corresponding shake-up process in ground and excited lithium atoms

The cross sections of the 18 electron photoionization and corresponding shake-up processes for Li atoms in the ground state 1s(2)2s and excited states 1s(2)2p, 1s(2)3p, 1s(2)3p and 1s(2)3d are calculated using the multi-configuration Dirac-Fock method. The latest experimental photoelectron spectrum at hv = 100 eV [Cubaynes D et al. Phys. Rev. Lett. 99 (2007) 213004] has been reproduced by the present theoretical investigation excellently. The relative intensity of the shake-up satellites shows that the effects of correlation and relaxation become more important for the higher excited states of the lithium atom, which are explained very well by the spatial overlap of the initial and final state wavefunctions. In addition, strong dependence of the cross section on the atomic orbitals of the valence electrons are found, especially near the threshold.