One-Shot Approach for Enforcing Piecewise Linearity on Hybrid Functionals: Application to Band Gap Predictions

We present an efficient procedure for constructing nonempirical hybrid functionals to accurately predict band gaps of extended systems. We determine mixing parameters by enforcing the generalized Koopmans’ condition on localized electron states, which are achieved by inserting an optimized potential probe. Application of this scheme to a large set of materials yields band gaps with a mean error of 0.30 eV with respect to experiment. Next, we consider a perturbative one-shot approach in which the single-particle eigenvalues are calculated with the wave functions obtained at the semilocal level. In this way, the computational cost is reduced by ∼85% without loss of accuracy. The scheme is found to be robust upon consideration of different defect species and functional forms.

Interface Investigations on Titanium Nitride Bilayer Systems

Dominik Anwar Jaeger

Nanocomposite coatings composed of two phases with atomically sharp phase boundaries, show interesting mechanical properties. These properties are often originating from their high interface to volume ratio. Composites of nanocrystalline titanium nitride (TiN) grains surrounded by a one to two monolayer thick interlayer of silicon nitride (Si3N4) show an enhanced nanohardness. The central theme of this thesis is concernedwith the interfacial properties of two-dimensional bilayer systems, which are used as model systems to describe the interfaces occurring in nanocomposite coatings. The systems under investigation are TiN interfaces in contact with silicon (Si), silicon nitride (Si3N4) and aluminum nitride (AlN). The primary tool used to analyze the interfaces of bilayer systems is X-ray Photoelectron Spectroscopy (XPS) with emphasis put on the shake-up feature of the Ti 2p photoelectron line. Shake-ups in TiN are observed as an additional peak on the lower binding energy side of the energy lines of the Ti 2p orbitals. Shake-ups are strongly influenced by valence electrons and electron density distributions. This makes them a powerful tool to probe the chemical and electronic structure of TiN interfaces. The aim of this study is to utilize the shake-up energy and its intensity to gain insight into interfacial structures and correlate their changes to interfacial polarization and macroscopic mechanical properties. Single crystalline (sc-) and oxygen-free TiN as well as oxygen-free bilayer systems were deposited by unbalanced magnetron sputtering and analyzed by Angle Resolved (AR-)XPS. Bilayer samples were deposited and their quality was controlled using X-ray diffraction (crystallinity), Rutherford back scattering (elemental composition), and atomic force microscopy (roughness). All XPS samples were fabricated, transfered and analyzed whilst maintaining ultra high vacuum. A precise and self-consistent XPS data processing method was developed to evaluate Ti 2p spectra. This method accounts for the correct photoelectron line shape, background subtraction and photoelectron peak area intensity. Binding energy, shake-up energy and intensity ratios of shake-ups taken frompristine TiN surfaces are precisely determined, and the influence of oxygen on the information content in peak positions and intensities was investigated. The shake-up energy and intensity of bulk sc-TiN and its origin of the shake-up are discussed. An analytical description for the XPS signal ratio of bilayer systems is derived to separate the interfacial signals from the bulk information. The results obtained by this analytical description are strongly influenced by the interface thickness that has been found to be proportional to the overlayer thickness. The revealed interface properties show a correlation between the shake-up intensity and the interface morphology, oxygen content, overlayer material and overlayer thickness. AR-XPS and X-ray Photoelectron Diffraction (XPD) results were used to interpret the crystalline structure of the different TiN/AlN and TiN/Si3N4 bilayer systems. AlN shows XPD patterns indicating a crystalline growth of AlN on sc-TiN. The electrically insulating AlN overlayer creates a charge accumulation at the TiN interface, which results in an enhanced shake-up intensity. XPD patterns of Si3N4 systems revealed a crystalline growth of Si3N4 in the first 0.6nm. The intensity of the diffraction patterns reduces with increasing Si3N4 overlayer thickness due to a change in the growth behavior from crystalline to amorphous structures. Si3N4 films show, in comparison to AlN, reduced interface charging and hence a lower shakeup intensity. The crystalline growth of Si3N4 in the initial stages is hindered in systems where a bias voltage is applied to the substrate during the deposition process. In contrast to the unbiased systems, which have crystalline interfacial structures, the biased systems no longer show XPD patterns due to a loss of crystallinity. Additionally the shake-up intensity of biased systems is thickness-independent, which is in contrast to unbiased systems. The difference in the shake-up intensity of biased and unbiased Si3N4 is explained by a different band gap of the Si3N4 structure in the first two monolayers. This thesis shows that the increase in the shake-up intensity is correlated to intrinsic and extrinsic interface charging. The obtained results, in combination with theoretical structure models from literature, show that in one to two monolayer thick interlayers a build-up of interface polarization is unlikely. The observed nanohardness enhancement in TiN/Si3N4 systems is explained with already known hardness effects.

EPFL2012

Minimum energy path and atomistic mechanism of the elementary step in oxygen diffusion in silicon: A density-functional study

Jan Felix Binder, Alfredo Pasquarello

Using a density-functional scheme, we study the migration of a single O atom in a (110) plane between two adjacent bond-center sites in bulk Si. The minimum energy migration path is found through the nudged elastic band method within a generalized gradient approximation for the electronic structure. The energy barrier is then also evaluated within a hybrid functional scheme. We achieve for the transition barrier a best estimate of 2.3 eV in the generalized gradient approximation and of 2.7 eV in the hybrid functional scheme, both in fair agreement with the commonly accepted experimental value of 2.53 eV. The transition is characterized by a saddle point which does not occur at the midpoint between the two bond-center sites and by a pattern of displacements extending up to the second nearest-neighbor Si atoms. The atomistic mechanism of oxygen migration is analyzed from three complementary viewpoints involving the evolution of the structure, the Wannier centers, and the single-particle energies and wave functions. The diffusion process can be separated into two distinct parts. In one part, the exchange of the Si atoms in the first-neighbor shell of the diffusing O atom occurs through the formation of a threefold coordinated O center and an overcoordinated Si atom. In the other part, the Si-Si bond flips its position through the creation of occupied and unoccupied Si dangling bonds which give rise to states in the band gap.

American Physical Society2014

Interface Investigations on Titanium Nitride Bilayer Systems

Dominik Anwar Jaeger

EPFL2012