Gaussian Approximation Potential: an interatomic potential derived from first principles Quantum Mechanics

Simulation of materials at the atomistic level is an important tool in studying microscopic structure and processes. The atomic interactions necessary for the simulation are correctly described by Quantum Mechanics. However, the computational resources required to solve the quantum mechanical equations limits the use of Quantum Mechanics at most to a few hundreds of atoms and only to a small fraction of the available configurational space. This thesis presents the results of my research on the development of a new interatomic potential generation scheme, which we refer to as Gaussian Approximation Potentials. In our framework, the quantum mechanical potential energy surface is interpolated between a set of predetermined values at different points in atomic configurational space by a non-linear, non-parametric regression method, the Gaussian Process. To perform the fitting, we represent the atomic environments by the bispectrum, which is invariant to permutations of the atoms in the neighbourhood and to global rotations. The result is a general scheme, that allows one to generate interatomic potentials based on arbitrary quantum mechanical data. We built a series of Gaussian Approximation Potentials using data obtained from Density Functional Theory and tested the capabilities of the method. We showed that our models reproduce the quantum mechanical potential energy surface remarkably well for the group IV semiconductors, iron and gallium nitride. Our potentials, while maintaining quantum mechanical accuracy, are several orders of magnitude faster than Quantum Mechanical methods.

First principles interatomic potential for tungsten based on Gaussian process regression

An accurate description of atomic interactions, such as that provided by first principles quantum mechanics, is fundamental to realistic prediction of the properties that govern plasticity, fracture or crack propagation in metals. However, the computational complexity associated with modern schemes explicitly based on quantum mechanics limits their applications to systems of a few hundreds of atoms at most. This thesis investigates the application of the Gaussian Approximation Potential (GAP) scheme to atomistic modelling of tungsten - a bcc transition metal which exhibits a brittle-to-ductile transition and whose plasticity behaviour is controlled by the properties of $\frac{1}{2} \langle 111 \rangle$ screw dislocations. We apply Gaussian process regression to interpolate the quantum-mechanical (QM) potential energy surface from a set of points in atomic configuration space. Our training data is based on QM information that is computed directly using density functional theory (DFT). To perform the fitting, we represent atomic environments using a set of rotationally, permutationally and reflection invariant parameters which act as the independent variables in our equations of non-parametric, non-linear regression. We develop a protocol for generating GAP models capable of describing lattice defects in metals by building a series of interatomic potentials for tungsten. We then demonstrate that a GAP potential based on a Smooth Overlap of Atomic Positions (SOAP) covariance function provides a description of the $\frac{1}{2} \langle 111 \rangle$ screw dislocation that is in agreement with the DFT model. We use this potential to simulate the mobility of $\frac{1}{2} \langle 111 \rangle$ screw dislocations by computing the Peierls barrier and model dislocation-vacancy interactions to QM accuracy in a system containing more than 100,000 atoms.

Splitting the Fast and Slow Motions in Molecular Dynamics Simulations Based on the Change of Cold Potential Well Bottom

The atomic motion is coupled by the fast and slow components due to the high frequency vibration of atoms and the low frequency deformation of atomic lattice, respectively. A two-step approximate method was presented to determine the atomic slow motion. The first step is based on the change of the location of the cold potential well bottom and the second step is based on the average of the appropriate slow velocities of the surrounding atoms. The simple tensions of one-dimensional atoms and two-dimensional atoms were performed with the full molecular dynamics simulations. The conjugate gradient method was employed to determine the corresponding location of cold potential well bottom. Results show that our two-step approximate method is appropriate to determine the atomic slow motion under the low strain rate loading. This splitting method may be helpful to develop more efficient molecular modeling methods and simulations pertinent to realistic loading conditions of materials.

The coulomb potential energy effect on the intensity of the characteristic lines at highly charged ion incendence on Al surface

The Al atomic characteristic spectral lines were induced by the impact of Ar-40(q+) ions (8 <= q <= 16; kinetic energy 150 keV) on Al surface. The result shows that by Penning impinging and resonant capture, the ion energy is deposited on the Al surface to excite the target atom, which is different from light excitation. Not only are the transitions betweem electronic configurations of the atomic complex excited, but the enhancing tendency of the characteristic spectral line intensity is consistent with the enhancing tendency of the coulomb potential energy of the incident ions with increasing charged states.

Atomic Structures and Radiative Properties of He-like Ions in Debye Plasmas

A detailed investigation of plasma screening effects on atomic structure and transition properties are presented for He-like ions embedded in dense plasma environment. Multi-configuration Dirac-Fock calculations were carried out for these ions by considering a Debye-Huckel potential. A large-scale relativistic configuration-interaction method is adopted to calculate transition energies and transition probabilities and to allow for a systematic improvement of the calculations. Comparison of the presently calculated results with others, when available, is made.

Synthesis and evaluation of Gd-DTPA-labeled arabinogalactans as potential MRI contrast agents

Arabinogalactan derivatives conjugated with gad olinium-diethylenetriaminepentaacetic acid (Gd-DTPA) by ethylenediamine (Gd-DTPA-CMAG-A(2)) or hexylamine (Gd-DTPA-CMAG-A(6)) have been synthesized and characterized by means of Fourier transform infrared spectra (FTIR), C-13 nuclear magnetic resonance (C-13 NMR), size exclusion chromatography (SEC), and inductively coupled plasma atomic emission spectrometry (ICP-AES).

Atomic force microscopy imaging of molybdenum oxide film electrodeposited on a carbon electrode

Non-stoichiometric mixed-valent molybdenum(VI, V) oxide film was grown on carbon substrates by the electrodeposition method. Responses of the prepared molybdenum oxide thin films to potential and to different solution acidities were studied by cyclic voltammetry, and the corresponding morphological changes of the film were monitored by atomic force microscopy (AFM). AFM images of the molybdenum oxide film show that the characteristic domed structure on the film surface increased during the transition from the oxidized state to the reduced state without signification change in the KMS surface roughness value. Furthermore, AFM studies show that the solution acidity has great effect on the morphology of the films, and the films undergo a homogenizing process with increasing pH of the solutions. (C) 1999 Elsevier Science S.A. All rights reserved.

Discrimination between low atomic number materials from their characteristic scattering of X-ray radiation

C.R. Bull and R. Zwiggelaar, 'Discrimination between low atomic number materials from their characteristic scattering of X-ray radiation', Journal of Agricultural Engineering Research 68 (2), 77-87 (1997)

Review of inspection techniques based on the elastic and inelastic scattering of X-rays and their potential in the food and agricultural industry

C.R. Bull, R. Zwiggelaar and R.D. Speller, 'Review of inspection techniques based on the elastic and inelastic scattering of X-rays and their potential in the food and agricultural industry', Journal of Food Engineering 33 (1-2), 167-179 (1997)

Atomic layer deposition of copper for CMOS interconnects

This work concerns the atomic layer deposition (ALD) of copper. ALD is a technique that allows conformal coating of difficult topographies such as narrow trenches and holes or even shadowed regions. However, the deposition of pure metals has so far been less successful than the deposition of oxides except for a few exceptions. Challenges include difficulties associated with the reduction of the metal centre of the precursor at reasonable temperatures and the tendency of metals to agglomerate during the growth process. Cu is a metal of special technical interest as it is widely used for interconnects on CMOS devices. These interconnects are usually fabricated by electroplating, which requires the deposition of thin Cu seed layers onto the trenches and vias. Here, ALD is regarded as potential candidate for replacing the current PVD technique, which is expected to reach its limitations as the critical dimensions continue to shrink. This work is separated into two parts. In the first part, a laboratory-scale ALD reactor was constructed and used for the thermal ALD of Cu. In the second part, the potentials of the application of Cu ALD on industry scale fabrication were examined in a joint project with Applied Materials and Intel. Within this project precursors developed by industrial partners were evaluated on a 300 mm Applied Materials metal-ALD chamber modified with a direct RF-plasma source. A feature that makes ALD a popular technique among researchers is the possibility to produce high- level thin film coatings for micro-electronics and nano-technology with relatively simple laboratory- scale reactors. The advanced materials and surfaces group (AMSG) at Tyndall National Institute operates a range of home-built ALD reactors. In order to carry out Cu ALD experiments, modifications to the normal reactor design had to be made. For example a carrier gas mechanism was necessary to facilitate the transport of the low-volatile Cu precursors. Precursors evaluated included the readily available Cu(II)-diketonates Cu-bis(acetylacetonate), Cu-bis(2,2,6,6-tetramethyl-hepta-3,5-dionate) and Cu-bis(1,1,1,5,5,5-hexafluoacetylacetonate) as well as the Cu-ketoiminate Cu-bis(4N-ethylamino- pent-3-en-2-onate), which is also known under the trade name AbaCus (Air Liquide), and the Cu(I)- silylamide 1,3-diisopropyl-imidazolin-2-ylidene Cu(I) hexamethyldisilazide ([NHC]Cu(hmds)), which was developed at Carleton University Ottawa. Forming gas (10 % H2 in Ar) was used as reducing agent except in early experiments where formalin was used. With all precursors an extreme surface selectivity of the deposition process was observed and significant growth was only achieved on platinum-group metals. Improvements in the Cu deposition process were obtained with [NHC]Cu(hmds) compared with the Cu(II) complexes. A possible reason is the reduced oxidation state of the metal centre. Continuous Cu films were obtained on Pd and indications for saturated growth with a rate of about 0.4 Å/cycle were found for deposition at 220 °C. Deposits obtained on Ru consisted of separated islands. Although no continuous films could be obtained in this work the relatively high density of Cu islands obtained was a clear improvement as compared to the deposits grown with Cu(II) complexes. When ultra-thin Pd films were used as substrates, island growth was also observed. A likely reason for this extreme difference to the Cu films obtained on thicker Pd films is the lack of stress compensation within the thin films. The most likely source of stress compensation in the thicker Pd films is the formation of a graded interlayer between Pd and Cu by inter-diffusion. To obtain continuous Cu films on more materials, reduction of the growth temperature was required. This was achieved in the plasma assisted ALD experiments discussed in the second part of this work. The precursors evaluated included the AbaCus compound and CTA-1, an aliphatic Cu-bis(aminoalkoxide), which was supplied by Adeka Corp.. Depositions could be carried out at very low temperatures (60 °C Abacus, 30 °C CTA-1). Metallic Cu could be obtained on all substrate materials investigated, but the shape of the deposits varied significantly between the substrate materials. On most materials (Si, TaN, Al2O3, CDO) Cu grew in isolated nearly spherical islands even at temperatures as low as 30 °C. It was observed that the reason for the island formation is the coalescence of the initial islands to larger, spherical islands instead of forming a continuous film. On the other hand, the formation of nearly two-dimensional islands was observed on Ru. These islands grew together forming a conductive film after a reasonably small number of cycles. The resulting Cu films were of excellent crystal quality and had good electrical properties; e.g. a resistivity of 2.39 µΩ cm was measured for a 47 nm thick film. Moreover, conformal coating of narrow trenches (1 µm deep 100/1 aspect ratio) was demonstrated showing the feasibility of the ALD process.

Atomic layer deposition of interface control layers for the fabrication of III/V MOS devices

The continued advancement of metal oxide semiconductor field effect transistor (MOSFET) technology has shifted the focus from Si/SiO2 transistors towards high-κ/III-V transistors for high performance, faster devices. This has been necessary due to the limitations associated with the scaling of the SiO2 thickness below ~1 nm and the associated increased leakage current due to direct electron tunnelling through the gate oxide. The use of these materials exhibiting lower effective charge carrier mass in conjunction with the use of a high-κ gate oxide allows for the continuation of device scaling and increases in the associated MOSFET device performance. The high-κ/III-V interface is a critical challenge to the integration of high-κ dielectrics on III-V channels. The interfacial chemistry of the high-κ/III-V system is more complex than Si, due to the nature of the multitude of potential native oxide chemistries at the surface with the resultant interfacial layer showing poor electrical insulating properties when high-κ dielectrics are deposited directly on these oxides. It is necessary to ensure that a good quality interface is formed in order to reduce leakage and interface state defect density to maximise channel mobility and reduce variability and power dissipation. In this work, the ALD growth of aluminium oxide (Al2O3) and hafnium oxide (HfO2) after various surface pre-treatments was carried out, with the aim of improving the high-κ/III-V interface by reducing the Dit – the density of interface defects caused by imperfections such as dangling bonds, dimers and other unsatisfied bonds at the interfaces of materials. A brief investigation was performed into the structural and electrical properties of Al2O3 films deposited on In0.53Ga0.47As at 200 and 300oC via a novel amidinate precursor. Samples were determined to experience a severe nucleation delay when deposited directly on native oxides, leading to diminished functionality as a gate insulator due to largely reduced growth per cycle. Aluminium oxide MOS capacitors were prepared by ALD and the electrical characteristics of GaAs, In0.53Ga0.47As and InP capacitors which had been exposed to pre-pulse treatments from triethyl gallium and trimethyl indium were examined, to determine if self-cleaning reactions similar to those of trimethyl aluminium occur for other alkyl precursors. An improved C-V characteristic was observed for GaAs devices indicating an improved interface possibly indicating an improvement of the surface upon pre-pulsing with TEG, conversely degraded electrical characteristics observed for In0.53Ga0.47As and InP MOS devices after pre-treatment with triethyl gallium and trimethyl indium respectively. The electrical characteristics of Al2O3/In0.53Ga0.47As MOS capacitors after in-situ H2/Ar plasma treatment or in-situ ammonium sulphide passivation were investigated and estimates of interface Dit calculated. The use of plasma reduced the amount of interface defects as evidenced in the improved C-V characteristics. Samples treated with ammonium sulphide in the ALD chamber were found to display no significant improvement of the high-κ/III-V interface. HfO2 MOS capacitors were fabricated using two different precursors comparing the industry standard hafnium chloride process with deposition from amide precursors incorporating a ~1nm interface control layer of aluminium oxide and the structural and electrical properties investigated. Capacitors furnished from the chloride process exhibited lower hysteresis and improved C-V characteristics as compared to that of hafnium dioxide grown from an amide precursor, an indication that no etching of the film takes place using the chloride precursor in conjunction with a 1nm interlayer. Optimisation of the amide process was carried out and scaled samples electrically characterised in order to determine if reduced bilayer structures display improved electrical characteristics. Samples were determined to exhibit good electrical characteristics with a low midgap Dit indicative of an unpinned Fermi level

Molecular dynamics simulation of fractures using an N-body potential

Molecular dynamics has been employed to model the fracture of a twodimensional triangular atomic lattice. The N-body Sutton-Chen potential developed for fcc metals and its extended version (Rafii-Tabar and Sutton) for fcc random binary alloys were used for the interatomic interactions. It is shown that at low temperatures cleavage fractures can occur in both an elemental metal and an alloy. At elevated temperatures the nucleation of dislocations is shown to cause a brittle-to-ductile transition. For the brittle crack propagation in the elemental metal, crack propagation speeds have been computed for different stress rates, and a crack instability found to exist as the speed reaches a critical value of about 32% of the Rayleigh wave speed. For the random alloy, we find that the dislocation movement can be affected by the distorted lattice.

Molecular dynamics simulation of fractures using an N-body potential

Molecular dynamics has been employed to model the fracture of a two dimensional triangular atomic lattice. The N-body Sutton-Chen potential developed for fcc metals and its extended version (Rafii-Tabar and Sutton) for fcc random binary alloys were used for the interatomic interactions. It is shown that at low temperatures cleavage fractures can occur in both an elemental metal and an alloy. At elevated temperatures the nucleation of dislocations is shown to cause a brittle-to-ductile transition. For the brittle crack propagation in the elemental metal, crack propagation speeds have been computed for different stress rates, and a crack instability found to exist as the speed reaches a critical value of about 32% of the Rayleigh wave speed. For the random alloy, we find that the dislocation movement can be affected by the distorted lattice.

SrTiO3(001)(2x1) reconstructions: First-principles calculations of surface energy and atomic structure compared with scanning tunneling microscopy images

(1x1) and (2x1) reconstructions of the (001) SrTiO3 surface were studied using the first-principles full-potential linear muffin-tin orbital method. Surface energies were calculated as a function of TiO2 chemical potential, oxygen partial pressure and temperature. The (1x1) unreconstructed surfaces were found to be energetically stable for many of the conditions considered. Under conditions of very low oxygen partial pressure the (2x1) Ti2O3 reconstruction [Martin R. Castell, Surf. Sci. 505, 1 (2002)] is stable. The question as to why STM images of the (1x1) surfaces have not been obtained was addressed by calculating charge densities for each surface. These suggest that the (2x1) reconstructions would be easier to image than the (1x1) surfaces. The possibility that the presence of oxygen vacancies would destabilise the (1x1) surfaces was also investigated. If the (1x1) surfaces are unstable then there exists the further possibility that the (2x1) DL-TiO2 reconstruction [Natasha Erdman Nature (London) 419, 55 (2002)] is stable in a TiO2-rich environment and for p(O2)>10(-18) atm.

Atomic excitation during recollision-free ultrafast multi-electron tunnel ionization

Modern intense ultrafast pulsed lasers generate an electric field of sufficient strength to permit tunnel ionization of the valence electrons in atoms(1). This process is usually treated as a rapid succession of isolated events, in which the states of the remaining electrons are neglected(2). Such electronic interactions are predicted to be weak, the exception being recollision excitation and ionization caused by linearly polarized radiation(3). In contrast, it has recently been suggested that intense field ionization may be accompanied by a two-stage 'shake-up' reaction(4). Here we report a unique combination of experimental techniques(5-8) that allows us to accurately measure the tunnel ionization probability for argon exposed to 50-fs laser pulses. Most significantly for the current study, this measurement is independent of the optical focal geometry(7,8), equivalent to a homogenous electric field. Furthermore, circularly polarized radiation negates recollision. The present measurements indicate that tunnel ionization results in simultaneous excitation of one or more remaining electrons through shake-up(9). From an atomic physics standpoint, it may be possible to induce ionization from specific states, and will influence the development of coherent attosecond extreme-ultraviolet-radiation sources(10). Such pulses have vital scientific and economic potential in areas such as high-resolution imaging of in vivo cells and nanoscale extreme-ultraviolet lithography.